Design Strategies

Molecules with Baird-aromatic T₁ states in general have a low E(T₁), as the aromatic character leads to a stabilization of that state relative to the S₀ state, which is Hückel anti- or nonaromatic.(35,39,41) Cyclobutadiene (CBD), which is T₁-state Baird-aromatic, fulfills the first criterion as E(S₁)/E(T₁)=2.84.(42) The opposite applies to benzene (T₁-state Baird-antiaromatic) because E(S₁)/E(T₁)=1.35.(43) Thus, one should search for (moderately) Baird-aromatic compounds with E(T₁) that are approximately double the E(T₁) of CBD (0.59 eV)(42) to achieve an E(T₁) similar to the band gap of silicon (1.11 eV). If one can identify compound classes influenced by Baird-aromaticity and throughout which the S₁ and T₁ states are described by the same HOMO → LUMO singly excited electron configuration (except for a spin-flip), it should be possible to find specific compounds that fit the requirements. In such compound classes, the absolute changes in E(T₁) and E(S₁) should be similarly large because the two states will be influenced in the same manner by, for example, electronic or steric effects caused by substituents. Throughout the compound class, the energy difference between the two states will then equal twice the exchange integral, i.e., ΔE(S₁ – T₁)=2K_ij=2K_H,L (i and j=orbitals involved in excitation, H=HOMO and L=LUMO).

Now, if the E(T₁) and E(S₁) of the various specific compounds in the compound class are plotted against an (anti)aromaticity index (∼coordinate), one can tentatively determine a threshold degree of (anti)aromaticity between the compounds that satisfy the singlet fission criterion and those that do not (Figure 1). At that threshold, E(S₁) will equal twice E(T₁), and potential singlet fission chromophores will be found on the right side of the threshold (orange region in Figure 1). However, the hypothesis summarized in Figure 1 assumes that 2K_H,L is constant over the interval, but even if HOMO and LUMO keep their respective symmetries throughout a compound class, their spatial localization may shift; as a result, 2K_H,L will change in size. The importance of colocalization of the HOMO and LUMO to the same atoms for a large 2K_H,L becomes clear through a comparison of naphthalene with azulene: naphthalene with a HOMO and LUMO colocalized to the same atoms has an ΔE(S₁ – T₁) of 1.7 eV, while azulene, where the HOMO and LUMO are not fully colocalized and somewhat polarized toward different ends of the molecule, has an ΔE(S₁ – T₁) of 0.5 eV.(44) Similarly, the ΔE(S₁ – T₁) of individual compounds within a compound class will vary if there is a change in the spatial distribution of HOMO and/or LUMO throughout the class.

Figure 1

Figure 1. Desired arrangement of the lowest electronic states within a particular compound class that encompasses both S₀ aromatic (T₁/S₁ antiaromatic) compounds and S₀ antiaromatic (T₁/S₁ aromatic) compounds. Compounds within the orange region have 2E(T₁) E(S₁).

We first test our design strategy on substituted fulvenes (pentafulvenes) being a compound class with E(T₁) and E(S₁) that span a large part of the region between the corresponding excited-state energies of benzene and CBD.(45−49) This feature is a result of the “aromatic chameleon” character of fulvenes, meaning that they can adapt to the different aromaticity rules in different electronic states: Baird’s rule in T₁ and S₁ and Hückel’s rule in S₀.(50) π-Electron withdrawing groups (EWGs) at the exocyclic position lead to low-lying T₁ and S₁ states, as they enhance the Baird-aromatic character of these states (Figure 2A). Computations have shown that fulvenes and related compounds with triplet ground (T₀) states are possible,(50,51) explained by the fact that the cyclopentadienyl cation (Cp⁺) has a triplet ground state.(52−54) Assuming that the T₁ and S₁ states are described by the same electron configuration, except for the multiplicity difference, this means that a particular EWG at the exocyclic position of a fulvene will have the same stabilizing effect in S₁ as in T₁ when compared to the parent fulvene as a reference.

Figure 2

Figure 2. (A) Postulated (idealized) variation in excitation energies of fulvenes as one goes from electron donating groups (EDGs) to electron withdrawing groups (EWGs). The figure displays the ideally constant energy difference between E(T₁) and E(S₁) (ΔE(S₁ – T₁)=2K_ij), upon which our hypothesis is based. (B) E(S₁)/E(T₁) ratio for four experimentally investigated fulvene derivatives, i.e., TClDCF, TClDMF, DMF, and TClDPF (see refs (46) and (47)).

Indeed, the tunability of E(T₁) and E(S₁) was earlier observed experimentally for four fulvene derivatives: 1,2,3,4-tetrachloro-6,6-dipyrrolidinofulvene (TClDPF), 1,2,3,4-tetrachloro-6,6-dimethylfulvene (TClDMF), 1,2,3,4-tetrachloro-6,6-dicyanofulvene (TClDCF), and 6,6-dimethylfulvene (DMF) (Figure 2B).(45,46) For singlet fission, it is rewarding that the experimental E(S₁)/E(T₁) ratio increases when going from TClDPF to TClDCF (Figure 2B) so that E(S₁) in TClDCF is (at least) nearly twice larger than E(T₁). With TClDCF being a stable organic compound, together with the recently reported INDT derivatives,(37) it is revealed that a large number of chromophores, which to various extents are influenced by aromaticity in their T₁ states, are awaiting to be discovered and used in singlet fission photovoltaics. In fact, the experimental ΔE(S₁ – T₁) values for the four fulvenes displayed in Figure 2B are similar for three compounds (TClDPF, TClDMF, and DMF) yet are possibly higher for TClDCF, as only an upper limit of E(T₁) was assessed for the latter compound (1.45, 1.50, 1.52, and E(S₁)/E(T₁) ratio of TClDCF, which is 1.95 or higher, suggests that this compound may indeed function as a singlet fission chromophore.

The design strategy outlined for fulvenes in Figure 2A utilizes electronic substituent effects, but altered steric congestion can also change E(T₁) and E(S₁). Again, this effect can be exemplified on fulvenes by altering the CC bond lengths in silico. This modulates the energies of the HOMO and LUMO (Figure 3A) by changing the strength of either the bonding or the antibonding character of an orbital at a particular bond. If the T₁ and S₁ states are HOMO → LUMO single excitations, this allows for tuning of the E(T₁) and E(S₁). As seen for the parent fulvene (Figure 3B), the relevant states change in energy as a function of CC bond lengths, and the absolute energy changes for the T₁ and S₁ states in each of the two types of distortions. Specifically, the energies of the two states decrease by 0.81 and 0.68 eV when the r_2,3 bond is shortened from 1.54 to 1.38 Å, and they decrease in energy by 0.98 and 0.86 eV when the r_1,2=r_3,4 distances are elongated from 1.35 to 1.45 Å. Thus, ΔE(S₁ – T₁) remains rather constant if there is no gradual shift in the location of the HOMO relative to the LUMO along the distortion coordinate. The T₂ state in the distorted parent fulvene, on the other hand, displays smaller changes (0.19 and 0.48 eV, respectively). Indeed, molecular contortion (bending and twisting) has recently been shown to be one means for altering E(T₁) and E(S₁) so as to improve singlet fission performance of an existing chromophore.(55)

Figure 3

Figure 3. (A) Plots of HOMO and LUMO of the parent fulvene, and (B) two plots showing how E(T₁)_v, E(S₁)_v, and E(T₂)_v vary as functions of the CC bond lengths marked in red. Calculations at TD-M06-2X/6-311+G(d,p) level.

A further design approach is to combine Baird’s rule with Clar’s rule,(56−58) as that particular isomer among a series of isomeric polycyclic antiaromatic hydrocarbons (PAAHs) that maximizes the total number of aromatic monocycles in the T₁ state (one Baird π-quartet or π-octet plus Clar π-sextets) has the lowest E(T₁) value.(59) By selecting the proper isomer, it should be possible to identify the T₁-state Baird-aromatic compounds with E(T₁)=1.1–1.2 eV, which fulfill the singlet fission criteria. However, it is important to note that the isomer, which is ideal for singlet fission, is not necessarily the one that is the most strongly Baird-aromatic in its T₁ state, as also concluded by Ryerson et al.(40) Another more established approach for the design of singlet fission chromophores is the diradical character-based design.(6,20,24,26,60−62) It has been found that molecules with the proper amount of open-shell singlet diradical character often satisfy the singlet fission criteria,(26,63) and a connection between the diradical character and aromaticity has been described for heteroacenes.(24) A link to our approach based on Baird-aromaticity can likely be formulated, yet the extent of diradical character in the S₀ state may not necessarily reflect Baird-aromaticity in the T₁ state (vide infra).

Finally, it should be noted that our design strategies are approaches for identification of candidate chromophores for singlet fission. The strategies do not take into consideration, for example, nonradiative decay processes from the S₁ state to the S₀ state. Indeed, it has earlier been observed that some 4nπ-electron compounds can have very short excited-state lifetimes (less than 1 ns),(64) a feature that could limit the applicability of Baird-aromatic chromophores in singlet fission photovoltaics. We calculated spin–orbit coupling (SOC) elements as a means to determine the probability for intersystem crossings; however, photophysical processes that are limiting for singlet fission performance are likely best probed experimentally. Thus, further careful design is needed, for example, to constrain the molecules into rigid frameworks, hampering the geometric distortions that open pathways for nonradiative decay.

Design Strategy Tested on Substituted Model Fulvenes

As pointed out by Zeng et al.,(25) the parent fulvene cannot be used for singlet fission applications since it has a low-lying T₂ state, and it also undergoes efficient S₁/S₀ radiationless decay via two possible conical intersections (one planar and one twisted).(75,76) As seen below, the first of the two drawbacks is overcome by utilizing electronic substituent effects. The second drawback can likely be alleviated by benzannelation, leading to a rigidification of the molecular structure. We explored fulvenes substituted at the exocyclic 6-position (substituents X, Figure 4) and/or at the endocyclic 2- and 5-positions (substituents Y). The substituents X and Y were selected as electron neutral, electron donating, and electron withdrawing. With the chosen substituents, we span fulvenes with calculated E(T₁)_a in the range 0.10–2.81 eV. We did not consider fulvenes substituted at the 3- and 4-positions because substituents at these positions have only weak electronic impact due to steric hindrance, which twists the substituents out of conjugation with the 5-membered ring.(49) It should also be emphasized that the fulvenes of Figure 4 are model compounds (many are experimentally unrealistic) that allow us to explore the design hypothesis of Figures 1 and 2A. The initial set included 225 fulvenes, but 2 had triplet ground states (T₀), 15 rearranged to an isomeric compound in the S₀ and/or T₁ state, and 49 had a HOMO and/or LUMO not analogous to those of the parent fulvene. These 66 were not further analyzed, whereby the set included 159 fulvenes (Table S2), i.e., 71% of the initial set.

Figure 4

Figure 4. Di- and tetrasubstituted fulvene derivatives included in this work.

Throughout the fulvenes with the T₁ and S₁ states described as singly excited HOMO → LUMO excitations, there are still complications. This is exemplified through two fulvenes that represent limiting cases with, respectively, high and low E(T₁) and E(S₁) values (Figure S1). The first fulvene with X=NH₂ and Y=CN has E(T₁)_v=2.92 eV, E(T₁)_a=2.49 eV, and E(S₁)_v=4.19 eV, while the second fulvene with X=CN and Y=NH₂ has a triplet ground (T₀) state −0.17 eV below the lowest singlet state and E(S₁)_v=1.45 eV. Although the HOMO and LUMO each are analogous in the two compounds, there is a marked difference in the spatial distribution of LUMO that impact K_H,L (Figure S1). As a consequence, ΔE(S₁ – T₁)_v,v equals 1.66 eV for the first of these fulvenes while 0.66 eV for the second. The ΔE(S₁ – T₁)_v,a of the two fulvenes are fortuitously very similar (1.70 and 1.62 eV, respectively), while the ΔE(S₁ – T₁)_a,a could not be computed as it was not possible to locate the relaxed S₁-state geometries of the fulvenes with neither TD-DFT or CASSCF.

The two fulvenes above further represent limiting cases with regard to singlet and triplet aromaticity because the first one is strongly 6π-electron Hückel-aromatic in its S₀ state (Baird-antiaromatic in T₁ and S₁), while the second one is 4π-electron Baird-aromatic in its T₀ state (Hückel-antiaromatic in the lowest singlet state). For the fulvene with X=NH₂ and Y=CN, NICS(1)_zz,S0=−24.8 ppm and NICS(1)_zz,T1=23.8 ppm, while for the fulvene with X=CN and Y=NH₂, NICS(1)_zz,S0=27.4 ppm and NICS(1)_zz,T0=−11.9 ppm. Noteworthy, the strongly Baird-aromatic cyclopentadienyl cation in its T₀ state,(77,78) representing the limiting Baird-aromatic resonance structure of a fulvene in its triplet state,(49) has a NICS(1)_zz,T0 value of −26.3 ppm. In its lowest singlet state, the cyclopentadienyl cation is also strongly diradical, as evidenced by a y₀ value of 0.96. However, the fulvene with X=CN and Y=NH₂, having a T₀ state, is not extensively diradical in its lowest singlet state (y₀=0.09), and other fulvenes with low E(T₁) have even lower diradical character (Table S10). This should be compared with the reported diradical characters of tetracene and pentacene (y₀=0.28 and 0.42, respectively).(63) Thus, although increased Baird-aromatic character of the T₁ state lowers the E(T₁) of fulvenes, it is not followed by increased diradical character of the S₀ states until one has reached fulvenes with inverted order between the lowest singlet and triplet states.

For the fulvenes in Figure 4, the changes in (anti)aromaticity when going from S₀ to T₁, as given by ΔNICS(1)_zz,T1–S0, correlate to a reasonable extent with E(T₁) (R²=0.82, Figure S3), similar to what we found earlier.(49) However, when regarding E(T₁) in dependence of Baird (anti)aromaticity in the T₁ state (NICS(1)_zz,T1) the correlation is lower (R²=0.68, Figure S4). It is noteworthy that fulvenes with E(T₁)_a in the range of 1.1–1.2 eV have NICS(1)_zz,T1 values in the range of −4 to −2 ppm, i.e., they are nonaromatic in their T₁ states. In the S₁ state, we did not run NICS calculations due to computational complications, yet calculations using the MCI in the S₁ and T₁ states for selected fulvenes reveal that the two states for each of the investigated fulvenes are similarly (anti)aromatic (see Table S6).

In Figure 5A and B, we plot E(T₁)_v, E(T₁)_a, and E(S₁)_v against NICS(1)_zz,S0, thereby revealing that the computed S₀-state aromaticity, which is the easiest to calculate, led to good correlations. Similar correlations were also found when plotting these energies against the difference between the NICS in T₁ and S₀, ΔNICS(1)_zz,T1–S0 (Figure S3), which should be the NICS index that best matches E(T₁). Importantly, and in support of our hypothesis outlined above (Figures 1 and 2A), it is clear in Figure 5A that E(T₁)_v, E(T₁)_a, and E(S₁) vary with NICS(1)_zz,S0 in essentially identical ways. However, when plotting ΔE(S₁ – T₁) against NICS(1)_zz,S0, it is revealed that only when both E(S₁) and E(T₁) are vertically excited energies is there a reasonable fit with the mean average deviation (MAD) from the least-squares fitted trendline of 0.10 eV (Figure 5C). Here, it is also notable that ΔE(S₁ – T₁) is gradually lowered as one goes to fulvenes that are S₀ antiaromatic/T₁ aromatic, a feature explained by the shift in the spatial distribution of the HOMO and LUMO, leading to small K_H,L.

Figure 5

Figure 5. Plots of excited-state energies and energy differences against degree of (anti)aromaticity in S₀. (A) E(T₁)_v and E(S₁)_v versus NICS(1)_zz,S0, (B) E(T₁)_a and E(S₁)_v versus NICS(1)_zz,S0. (C) The energy difference between the S₁ and T₁ states versus NICS(1)_zz,S0 (D) E(T₂)_v and E(S₁)_v versus NICS(1)_zz,S0 for tetrasubstituted fulvenes. R² is the squared correlation coefficient. NICS(1)_zz,S0 computed at GIAO/(U)M06-2X/6-311+G(d,p) level. In (A), the parent fulvene is indicated by red marks.

Now, how do these plots agree with the hypothesis presented in Figure 2? Clearly, when based on the ZHA scheme, the 2E(T₁)_a=E(S₁)_v threshold is reached at fulvenes with NICS(1)_zz,S0=−13.5 ppm (dashed line in Figure 5B), while when based on the approach with E(T₁)_v, the threshold appears at the extrapolated value of 45.2 ppm. As the ZHA scheme exaggerates E(S₁)/E(T₁) while the approach with vertically excited E(T₁) underestimates the ratio, it can be concluded that the 2E(T₁)=E(S₁) threshold is placed along the aromaticity coordinate represented by NICS(1)_zz,S0. If the threshold is placed in the middle between the two limiting values then it is placed at NICS(1)_zz,S0=15.8 ppm, i.e., at fulvenes that are rather strongly Hückel-antiaromatic in S₀ and Baird-aromatic in T₁.

With regard to the second threshold, E(S₁) E(T₂), it is clear in Figure 5D that E(T₂) shows no correlation with NICS(1)_zz,S0 (R²=0.00). Because most substituted fulvenes have E(T₂) in the range 2.2–3.5 eV, it is gradually more probable that the criterion E(S₁) E(T₂) is met for fulvenes with NICS(1)_zz,S0 above 2.5 ppm, as the trendlines for E(T₂) and E(S₁) cross at this value. Obviously, the fulvenes with NICS(1)_zz,S0 values at ∼15 ppm will also satisfy the second criterion, but their E(T₁) will likely be far below 1 eV.

As found above, by changing the bonding or antibonding character of the HOMO and LUMO through geometric distortions (Figure 3), one can tune E(S₁) and E(T₁) of the parent fulvene simultaneously and similarly since the S₁ and T₁ excitations are described by the same singly excited configuration except for the spin flip. Thus, ΔE(S₁ – T₁) is constant along the distortion coordinate. However, ΔE(S₁ – T₁) does not have the same value if one goes between differently substituted fulvenes as the spatial (de)localization of the HOMO and LUMO vary between the fulvenes. Hence, we analyzed how the E(T₁) and E(S₁) values change upon distortion in four substituted fulvenes in which the ΔE(S₁ – T₁) values at the minimum geometry vary from 0.84 to 1.41 eV (Figure 6). Upon distorting the C2–C3 bond length, the E(T₁) and E(S₁) values change simultaneously and similarly in three of the four fulvenes. The exception is 6,6-diaminofulvene (Figure 6B) in which the S₁ state at several of the geometries is described by a different configuration than the T₁ state, revealing the importance of having the S₁ and T₁ states described by the same configuration.

Figure 6

Figure 6. Variations in E(T)_v, E(S₁)_v, and E(T₂)_v dependence on the C2–C3 bond length (red) in four fulvenes. Data points marked correspond to other excitations than that of the singly excited HOMO–LUMO configuration of the parent fulvene.

The calculations show that the hypothesis on the rational tuning of E(T₁) and E(S₁) utilizing excited-state Baird- and ground-state Hückel-aromaticity is valid with TD-DFT. However, is that also the case at the CASPT2 level? The latter calculations disclose potential multireference character and whether the fulvenes exhibit double excitation character in certain excited states or not. Table S7 lists the excitations at CASPT2 and TD-M06-2X levels for a few fulvenes for which the two criteria are met (or nearly met). In short, the E(T₁) at the CASPT2 level are similar or slightly higher (0.2 eV) than those calculated with M06-2X. With regard to the E(S₁), the CASPT2 energies are higher in all cases except one and sometimes 0.4 eV higher than those at M06-2X level. For the lowest S₀ and T₁ states, the CASSCF calculations reveal one predominant configuration with a weight between 0.80 and 0.93, revealing good agreement with %TAE_e([T]) (Table S9) for the first of these states. We observe that almost all of the compounds preserve the energy order of the different states and fulfill the singlet fission criteria (Table S7). The exceptions are the two model fulvenes with X=BF₂, Y=F and with X=CN and Y=SiH₃. For these fulvenes, E(S₁) and E(T₂) are very close in energy, a feature that can lead to an S₁/T₂ intersystem crossing. However, one still cannot discard the possibility for singlet exciton fission because the calculated SOC for S₁/T₂ is merely 1.7 cm^–1, i.e., –1, which indicates a very weak coupling,(79) despite some cases with similarly small SOCs are large enough for ISC.(80) Further results on SOC elements, which generally are small, and T₁/S₀ intersystem crossing are given in the Supporting Information, yet ISC also depends on the Franck–Condon weighted density of states according to the Fermi Golden Rule,(81) which is not considered in the present work.

Earlier Experimentally Investigated Fulvenes

We next considered the dicyanofulvenes (DCFs) that earlier have been synthesized by Finke et al.(82) We chose to explore six of these DCFs using our strategy. The TD-M06-2X calculations using the ZHA scheme point out that these compounds could serve as singlet fission chromophores (Figure 7); however, the S₁ and T₂ states are close in energy for DClDPDCF. Importantly, the adiabatic E(T₁) are rather close to 1 eV, despite with M06-2X all are below. Similarly as seen for the model fulvenes, CASPT2 gives E(T₁)_a, which are higher than those of M06-2X, with 0.2–0.4 eV. In their S₀ states, DClDPDCF and TClDCF are influenced by Hückel-antiaromaticity, evident by NICS(1)_zz,S0 values of 10.1 and 23.1 ppm, respectively. On the other hand, they are nonaromatic in the T₁ states, as the NICS(1)_zz,T1 values are −0.2 and 1.3 ppm, respectively. Substituted fulvenes and fulvenoid species, which are clearly Baird-aromatic in their T₁ states, have been designed computationally, but these have E(T₁) which are far below 1 eV.(50)

Figure 7

Figure 7. T₁, S₁, and T₂ energies (in eV) of six previously synthesized fulvenes computed at TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) (normal print) and CASPT2(14in14)/ANO-RCC-VDZP//M06-2X/6-311+G(d,p) (italics) levels.

Interestingly, the calculated E(S₁)_v/E(T₁)_a ratios of DClDPDCF and TClDCF are well above 2, despite that they are nonaromatic in T₁. The other four DCFs in Figure 7 fulfill the E(S₁)/E(T₁)> 2 criterion, yet only three of them fulfill the E(S₁) E(T₂) criterion. The three DCFs that were also calculated at the CASPT2 level have E(S₁)/E(T₁) ratios that are similar to those at the M06-2X level.

A potential caveat for fulvenes is their nonrigidity, as they can relax geometrically in the S₁ and T₁ state, making it difficult to predict their usefulness as singlet fission chromophores. Pentacene, tetracene, and DPB relax less in energy in their T₁ states compared to fulvenes (Table S8). Interestingly, from the two ratios of E(S₁)_v/E(T₁)_v and E(S₁)_v/E(T₁)_a (Table S8), one can conclude that the relative degree of energy relaxation is smaller in the established singlet fission chromophores than in the fulvenes investigated here.

Application to Other Compound Classes

Numerous additional compound classes, which to various extents are influenced by Baird-aromaticity in their T₁ and S₁ states and have the potential to be suitable for singlet fission photovoltaics, can be listed. For that reason we explored if a similar design strategy for fulvenes can be used to identify and tailor CBDs, pentalenes, and their benzannelated derivatives as suitable singlet fission chromophores. We showed earlier that E(T₁) of isomeric PAAHs vary with the number of aromatic monocycles in the T₁ state.(59) In short, the isomer with the lowest E(T₁) has the maximum number of disjoint aromatic monocycles (one triplet diradical Baird-aromatic π-quartet/π-octet plus closed-shell Hückel-aromatic π-sextets). In other words, it is described by Clar’s rule(56−58) in an extended version that incorporates Baird’s 4n rule.(59) Provided the S₁ state is influenced similarly as the T₁ state, we argue that the benzannelation approach can be used to identify new singlet fission chromophores since E(T₁) and E(S₁) will be changed in energy by comparable amounts (cf. Figure 1).

The parent CBD has the correct arrangement of its T₁, S₁, and T₂ states for singlet fission (E(T₁)=0.51, E(S₁)=2.70 and E(T₂)=4.69 eV with M06-2X, Figure 8). However, it is exceedingly unstable, and E(T₁) is too low. Instead, three substituted CBDs (SCBD1–SCBD3), which are persistent at room temperature,(83,84) were explored. Additionally, we probed an experimentally unexplored silyl-substituted CBD (SCBD4) with a more suitable energy level arrangement than the three persistent CBDs. All four substituted CBDs fulfill the fundamental singlet fission criteria, except the E(T₁) of each one is too low.

Figure 8

Figure 8. Parent and substituted cyclobutadienes and their excitation energies (in eV) computed at TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) level.

For the three tetrasilyl-substituted CBDs (SCBD2–SCBD4), there is a correlation (R²=0.97) between E(T₁)_a and the difference in aromaticity between S₀ and T₁, as measured by ΔNICS(1)_zz,T1-S0 (Figure S7). However, the CBD with tBu substituents (SCBD1) does not correlate with them, revealing that both electronic and geometric factors contribute to the E(T₁)_a of substituted CBDs. Moreover, in the silyl-substituted CBDs, the T₁ and S₁ states follow similar trends (Figure S7) because the E(T₁)_a of SCBD3 and SCBD4 increases by 0.21 and 0.42 eV when compared to the E(T₁)_a of SCBD2, while E(S₁)_v increases by 0.32 and 0.52 eV, respectively. In contrast, the E(T₂)_v of SCBD3 and SCBD4, within the ZHA scheme, is lower in energy by 0.34 and 0.71 eV, respectively, when compared to that of SCBD2.

Pentalenes as 8π-electron compounds were examined next, and in the Supporting Information, we also discuss results for indacenes being 12π-electron compounds. In particular, we looked at substituents that induce geometry changes to see if they alter the E(T₁)_a, E(S₁)_v, and E(T₂)_v to any significant extents (Figure 9). Pentalenes are strongly T₁-state Baird-aromatic,(59) but according to our calculations, the parent compound only satisfies the 2E(T₁)_a E(S₁)_v criterion. Two further drawbacks are the calculated E(T₁)_a of ∼0.6 eV and the exceptionally low stability of the parent pentalene; however, persistent substituted pentalenes have been reported.(85,86) One could argue that substituents can tune E(T₁) because the HOMO and LUMO have opposing nodal features at the formal C–C single bonds. However, substituents at the 1,2- and 4,5-positions change E(T₁)_a minutely, even when they are bulky. Rewardingly, the singlet fission criteria according to the ZHA scheme are satisfied for all three substituted pentalenes.

Figure 9

Figure 9. Parent and substituted pentalenes and their excitation energies (in eV) computed at the TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) level.

Because CBD has the correct state ordering while benzene does not (Figure 1), it should be possible to tailor compounds with the proper ordering of E(T₁), E(S₁), and E(T₂) through fusion of benzene and CBD rings in certain proportions and with certain connectivities. That said, how should CBD optimally be benzannelated to arrive at suitable singlet fission chromophores? Also, can sterically congestive substituents alter the excited-state energy levels of the larger benzannelated CBD compounds? A selection of benzannelated CBDs were examined (Figure 10). The same reasoning and questions were applied to pentalenes (vide infra).

Figure 10

Figure 10. Benzannelated cyclobutadiene compounds and their excitation energies (in eV) computed at TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) and CASPT2/ANO-RCC-VDZP//CASSCF(n,m)/ANO-RCC-VDZP (italics, n=m=8 for BENZCBD1 and n=m=12, for BENZCBD2) levels. The compounds for which both singlet fission criteria are satisfied are marked in green. For full compound names, see Figure S20.

Indeed, fusion of one CBD and one benzene ring into benzocyclobutadiene (BENZCBD1) yields a compound that, according to computations, has the correct state ordering for singlet fission. The calculated E(T₁)_a is slightly higher than ideal, yet BENZCBD1 is still a highly reactive species and may also, as a result of the small CBD ring, decay nonradiatively to the S₀ state. Among the three isomers with one CBD and two benzene rings, only one isomer satisfies the two singlet fission criteria: BENZCBD2. Using the extended version of Clar’s rule,(59) it becomes clear that this isomer is the only isomer among the three that can be described by two aromatic monocycles in its T₁ state: one triplet diradical Baird-aromatic π-quartet and one closed-shell Hückel-aromatic π-sextet (see Figure S19 for ACID plots).(59) In the S₀ state, it is notable that the diradical character increases somewhat when going from BENZCBD1 (y₀=0.11, Table S10) to BENZCBD2 (y₀=0.23).

An interesting aspect of the E(T₁)_a, E(S₁)_v, and E(T₂)_v of the two naphtoCBDs is the fact that when going from BENZCBD2 to BENZCBD3 the T₁ and S₁ states increase in energy by near-identical amounts (0.86 and 0.84 eV, respectively), while the T₂ state goes up by much less (0.18 eV). This suggests that the T₁ and S₁ states in the two compounds are described by the same electron configuration (except for the multiplicity), following Figure 1. Indeed, according to TD-DFT computations, the S₁ states of both compounds are singly excited HOMO → LUMO excitations (see Table S18). Here, it can be noted that when increasing the molecular size from BENZCBD1 to the dibenzannelated BENZCBD2–BENZCBD4, the energy differences between the vertical and adiabatic excited-state energies decrease, both in T₁ and S₁ (Table S26).

One can tune E(T₁) and E(S₁) in two ways: through benzannelation and through C–C bond length distortions (or generally, geometric contortions).(55) As seen below, the first provides for larger tunings of the excited-state energies of PAAHs because C–C bond length distortions in BENZCBD2, a small PAAH, lead to variations in E(T₁) and E(S₁) in the range of 0.1–0.2 eV (see Figure S15). In larger benzannelated PAAHs, where HOMO and LUMO are delocalized over further atoms, the energy tunings will be even smaller. Tuning through benzannelation should therefore be the preferred means to broadly identify PAAHs that satisfy the singlet fission criteria, while bond length changes provide fine-tuning of E(T₁) and E(S₁). When fusing a benzene ring onto BENZCBD2, leading to BENZCBD5, the T₁ and S₁ states are lowered in energy by 0.24 and 0.22 eV, respectively, while the T₂ state increases by 0.10 eV. Thus, E(S₁)_v follows the pattern of E(T₁)_a when going from BENZCBD2 to BENZCBD5, in line with the hypothesis outlined in Figure 1 providing a general means for singlet fission chromophore design. Indeed, with BENZCBD5, we identify a PAAH that satisfies the two singlet fission criteria; however, it is a truly unstable compound(87) with some diradical character in S₀ (y₀=0.28).

Several interesting patterns emerge when going to more extensively benzannelated CBDs. Benzobiphenylene (BENZCBD6), when compared to biphenylene (BENZCBD4), has E(T₁) and E(S₁), which are lower by 0.52 and 0.56 eV, respectively, while E(T₂) is lower by 0.30 eV. Hence, the E(S₁)_v/E(T₁)_a ratio upon fusion of one benzene ring onto biphenylene in an angular manner increases from 1.57 to 1.73, while extending in a linear way to BENZPENT7 lowers it to 1.32. Further angular benzannelation to trans-dinaphthoCBD (BENZCBD9) brings E(T₁)_a well below E(S₁)_v, but the E(S₁)_v/E(T₁)_a ratio is still smaller than 2. Here, it should be noted that the connectivity is crucial because BENZCBD9 has a higher E(S₁)_v/E(T₁)_a ratio than the isomeric BENZCBD8. Going to the penta- and hexabenzannelated CBDs, BENZCBD10 and BENZCBD11, both singlet fission criteria become satisfied within the ZHA scheme. According to M06-2X, the first of these compounds has E(T₁)_a in the ideal energy range. Another feature of importance is the oscillator strengths for transitions to S₁ in the benzannelated CBDs, which are suitable for singlet fission. Indeed, transitions to this state are weakly allowed in BENZCBD5, BENZCBD7, and BENZCBD8 (Table S19), and one of these compounds (BENZCBD5) is in theory interesting for singlet fission.

The Baird-aromatic character of a benzannelated 4nπ-electron compound in its T₁ state increases with the possibility to form local aromatic monocycles (one Baird- and several Hückel-aromatic ones).(59) Still, the Hückel-antiaromatic character of these compounds in their S₀ states is significant, in line with an often observed low stability, and NICS-XY scans indicate that it is even accentuated in BENZCBD5 when compared to the other two (Figure 11). However, the T₁-state Baird-aromaticity in the CBD ring in this compound is more apparent according to NICS-XY; but a weak global diatropic circuit also exists, as indicated by the ACID plot (Figure S19). Interestingly, the CBD unit in BENZCBD5 in the T₁ state seems equally aromatic as in BENZCBD10 and BENZCBD11 but less aromatic to that of BENZCBD9 (Figure S17). However, the assessment of the aromaticity of the CBD ring based on NICS is not suitable, as the NICS value in a PAAH is a composite of ring currents in several 4nπ-electron circuits. HOMA, a geometry-based aromaticity index,(73,74) is more suited, and it indeed shows that the aromaticity of the CBD ring in BENZCBD5 (HOMA=0.41), which is close to that of the T₁-state CBD (HOMA=0.45), is higher than in BENZCBD9–BENZCBD11 (HOMA=0.13, 0.21, and 0.27, respectively). Here, it is notable that the HOMA of the T₁ state of CBD is low, as the C–C bond lengths (1.434 Å) are considerably longer than the reference value (R_opt=1.388 Å) that results in a HOMA of 1.0.

Figure 11

Figure 11. NICS-XY scans of (A) BENZCBD1, (B) BENZCBD2, (C) BENZCBD5, (D) BENZPENT1, (E) BENZPENT3, and (F) BENZPENT7 in their S₀ and T₁ states calculated at GIAO/M06-2X/6-311+G(d,p) level.

Similar patterns upon benzannelation to the CBDs are found for pentalenes. A drawback with pentalenes is their transitions to the S₁ state, which are forbidden or very weakly allowed (for calculated oscillator strengths, see Table S23); however, the excitation to the S₂ state in a 5,10-bis(styryl)-substituted dibenzo[a,e]pentalene has shown to provide an entry point to singlet fission.(88) The monobenzannelation in BENZPENT1 increases E(T₁) when compared to the parent pentalene (Figure 12), similar to what was found for CBD and BENZCBD1, but BENZPENT1 is less ideal for singlet fission as E(S₁) ≈ E(T₂). On the other hand, the energy relaxation in the S₁ state, calculated as E(S₁)_v – E(S₁)_a, is much smaller in BENZPENT1 than in BENZCBD1 (Figure S26), and E(S₁)_a/E(T₁)_a equals 2.06.

Figure 12

Figure 12. Benzannelated pentalenes and their excitation energies (in eV) computed at TD-M06-2X/def2-TZVPD//(U)M06-2X/6-311+G(d,p) (normal print) and CASPT2/ANO-RCC-VDZP//CASSCF(12,12)/ANO-RCC-VDZP (italics) levels. The compounds for which both singlet fission criteria are satisfied are marked in green. Additional benzannelated pentalenes are found in the Supporting Information. The at the E(S₁)_v of BENZPENT10 indicates the two-configurational character of the S₁ state.

With a more isolated T₁-state Baird-aromatic pentalene unit, BENZPENT3 satisfies the singlet fission criteria according to the ZHA scheme but with a slightly low E(T₁). Interestingly, dibenzo[a,e]pentalene (BENZPENT5), which corresponds to the core of the compound that experimentally undergoes singlet fission when excited to S₂, satisfies none of the singlet fission criteria, yet the bis(styryl)-substitution brings down E(T₁) whereby the experimentally explored compound fulfills the criteria (see Figure S22 for a comparison of dibenzo[a,e]pentalene with 5,10-bis(styryl)dibenzo[a,e]pentalene). Noteworthy, the 5,10-bis(styryl) substitution introduces a new conjugation path, 1,8-diphenyl-octa-1,3,5,7-tetraene (see Figure S22), and the diradical spin density of the T₁ state is concentrated to this segment. The S₁ state, in contrast, is not lowered as much as the T₁ state, yet this state is potentially unsuitable for TD-DFT, as it is known that the S₁ state in 1,8-diphenyloctatetraene has double-excitation character.(89−91) Opposing dibenzo[a,e]pentalene (BENZPENT5), dibenzo[a,f]pentalene (BENZPENT6), the much less stable dibenzopentalene isomer,(92) satisfies both criteria, but its E(T₁) is very low.

The T₁ and S₁ states of all benzannelated pentalenes except one are described by singly excited HOMO–LUMO excitations (the exception being BENZPENT10 with an S₁ state described as HOMO–2 → LUMO (63%) plus HOMO → LUMO (37%)). Thus, several trends can be observed when expanding to larger benzannelated pentalenes. However, an important feature to note in the four panels of Figure 13 is the fact that E(T₁) and E(S₁) follow each other closely when the benzannelation is changed. For that reason, one should compare ΔE(S₁ – T₁) in a selection of compounds that follow one type of benzannelation. For example, in Figure 13A, the ΔE(S₁ – T₁)_v,a spans from 0.94 to 1.11 eV, while ΔE(S₁ – T₁)_v,v spans from 0.39 to 0.63 eV, indicating a similar 2K_H,L within the specific selection of the compound. The first trend to note is a gradual and similar lowering of E(T₁) and E(S₁) found when going successively from BENZPENT5 to the hexabenzannelated BENZPENT19 (Figure 13A), following the angular connectivity that maximizes the number of aromatic monocycles in T₁.(59) With BENZPENT19, a compound that has been synthesized and further investigated experimentally,(93) one has reached a point where 2E(T₁) E(S₁), i.e., one is within the orange region of Figure 1. Interestingly, BENZPENT19 has very similar E(T₁)_a, E(S₁)_v and E(T₂)_v values to those of BENZPENT3, and it contains four angular segments (∼BENZPENT3).

Figure 13

Figure 13. Variation in E(T₁)_a, E(S₁)_v, and E(T₂)_v calculated using the ZHA approach as a function of benzannelation in selected benzannelated pentalenes. Compounds that satisfy the singlet fission criteria are represented by yellow bars. Computations at TD-M06-2X/def2-TZVPD//(U)M06-2X/6-311+G(d,p) level. The at E(S₁)_v of BENZPENT10 indicates the two-configurational character of the S₁ state. Further comparisons are given in Figure S23. Results of T₁-aromaticity assessments are found in Figures S25–S28.

When instead going from the parent pentalene to the linear dinaphtho[a,e]pentalene (BENZPENT16), both E(T₁)_a and E(S₁)_v increase, the E(S₁)_v/E(T₁)_a ratio becomes successively smaller, and E(T₂)_v is placed gradually further below E(S₁)_v (Figure 13B). Interestingly, the ΔE(S₁ – T₁)_v,a of BENZPENT10, having a two-configurational S₁ state (vide supra), is smaller than that of the other four compounds in Figure 13B (1.12 vs 1.26–1.34 eV). The linear connectivity, which is undesirable for singlet fission chromophores, is further evidenced from the isomeric tetrabenzopentalenes BENZPENT12–BENZPENT16 (Figure S23). Also, on the basis of NICS as well as HOMA, the T₁-state aromatic character of the pentalene unit decreases when going from BENZPENT13 and BENZPENT14 to BENZPENT15 and BENZPENT16, i.e., from angular-benzannelated to linear-benzannelated compounds. In the case of BENZPENT15, we have an intermediate situation as the molecule is a combination of linear and angular connectivities. Again, the inclusion of angular-benzannelated segments leads to tuning of E(S₁)/E(T₁) toward higher values while linear ones do the opposite.

However, there is also another route to benzannelated pentalenes that satisfy the singlet fission criteria. Further benzannelation of dibenzo[a,f]pentalene BENZPENT6 yields BENZPENT11 and BENZPENT17, which both recently were synthesized.(94) The first two satisfy the singlet fission criteria (Figures 12 and 13C) but with low E(T₁)_a values and high diradical characters (y₀=0.48 and 0.60, respectively). Finally, BENZPENT3 and BENZPENT7, similar to BENZCBD2 and BENZCBD5, respectively, satisfy the singlet fission criteria. Now, starting at BENZPENT3 and fusing a benzene ring or a naphthalene unit to the opposite side of the pentalene unit, one obtains benzonaphthopentalene (BENZPENT8) and trans-dinaphthopentalene (BENZPENT14), respectively, for which E(T₁)_a and E(S₁)_v increase by significant amounts and the E(S₁)_v/E(T₁)_a ratio drops well below 2 (Figure 13D). The same is found when going from BENZPENT7 to BENZPENT12, revealing that a singlet fission chromophore can be ruined by overbenzannelation. It is only when at the hexabenzannelated pentalene BENZPENT19 with four angular segments that the singlet fission criteria again are satisfied, a compound in which the T₁ state can be described with a markedly Baird-aromatic central 8π-electron pentalene moiety (HOMA=0.75) and four Hückel-aromatic 6π-electron units.(59) Interestingly, when gradually building up the four angular segments going from BENZPENT8 (HOMA=0.47), BENZPENT14 (HOMA=0.67), and BENZPENT18 (HOMA=0.70) to BENZPENT19, the Baird-aromatic character of the pentalene unit increases. Thus, benzannelation together with an attention to connectivity can be used to simultaneously tune E(T₁) and E(S₁) to similar extents such that one reaches a situation where 2E(T₁) E(S₁) E(T₂).

The General Design Approach and Its Limitations

As the design approach applies to compound classes in which the extent of excited-state Baird-(anti)aromatic character varies among the individual compounds, E(T₁) and E(S₁) will change similarly along the aromaticity tuning coordinate, while E(T₂) should remain more constant or change differently. The model further assumes that throughout an investigated compound class, (i) HOMO and LUMO each keep the same character (∼symmetry), (ii) the T₁ and S₁ states are described by singly excited HOMO → LUMO excitations, and (iii) the spatial distributions of HOMO and LUMO are similar. The model is not applicable to compound classes in which these requirements do not hold (for example, triafulvenes, vida infra), or it is only applicable to a part of the compound class.

Information on the E(T₁) and ΔE(S₁ – T₁)=2K_H,L of the parent compound is needed for the most simple back-of-an-envelope design using the model. A third parameter to consider is the slope, i.e., the extent by which E(T₁) and E(S₁) change in response to altered (anti)aromaticity, but a few different compounds within the compound class must be computed for this information. At the singlet fission threshold, E(T₁)=ΔE(S₁ – T₁)=2K_H,L. Thus, if the parent compounds in two compound classes have the same E(T₁) but different 2K_H,L then the compound class with the larger 2K_H,L will have the threshold placed at a less T₁ aromatic compound than what is the case in the compound class with a smaller 2K_H,L (Figure 14A and B). A series of further situations are exemplified in Figure S37. Here it should be noted that the additional fulfilment of the E(S₁) E(T₂) criterion may restrict the useful region, pushing it toward increased Baird-aromaticity.

Figure 14

Figure 14. (A and B) Schematic drawings of the changes in E(T₁) and E(S₁) as functions of increased T₁ and S₁ aromatic character for a compound class with (A) large K_H,L and (B) small K_H,L. Slopes of E(T₁) and E(S₁) as well as the position and E(T₁) of the parent compound (marked as 0 on the x-axis) are kept constant in the two plots. (C) 1,1-Disubstituted siloles with X and Y=H, Me, CF₃, F, SiH₃, and SiMe₃ as high-E(T₁) singlet fission chromophores (for explicit energies, see Figure S33). (D) Benzannelated pentalenes where the terminal benzo rings have been exchanged for thiopheno rings (for explicit energies, see Figure S36). A comparison against the completely benzannelated pentalenes is given in the Supporting Information.

The E(T₁) of the parent compound depends on its extent of T₁ aromaticity; if the parent compound is strongly (weakly) influenced by Baird-aromaticity it will have a low (high) E(T₁). The K_H,L depends on the extent of colocalization of HOMO and LUMO, as exemplified by naphthalene and azulene with 2K_H,L values of 1.7 and 0.5 eV, respectively.(44) Extrapolating from this observation, by strict localization of HOMO and LUMO to different atoms, one can, together with spin-polarization, design a molecule (heptazine) that has its S₁ state at a lower energy than its T₁ state,(95) i.e., a negative ΔE(S₁ – T₁). To instead achieve a large positive 2K_H,L, the HOMO and LUMO should be localized to the same atoms, ideally a small number (see siloles below).

However, as noted above, ΔE(S₁ – T₁) is not constant for fulvenes (Figure 5A), as it decreased for fulvenes with EWGs as exocyclic substituents, which lead to a polarization of LUMO toward the substituents, and consequently, a lowered 2K_H,L and ΔE(S₁ – T₁). On the other hand, the model applies well to 1,1-disubstituted siloles, i.e., 1-silacyclopenta-2,4-dienes, which are cross-hyperconjugated “aromatic chameleons”.(47) For the latter compounds, ΔE(S₁ – T₁) varies within the narrow interval of 2.14–2.34 eV (Figure 14C). Rewardingly, siloles may provide access to singlet fission chromophores with high E(T₁) (∼2 eV) according to our computations, and the 2K_H,L is high due to colocalizations of HOMO and LUMO to mainly the four C atoms of the diene unit (Figure S35). As siloles are already extensively explored in experiments,(96,97) they may provide interesting targets as singlet fission chromophores.

Although the design approach had complications with pentafulvenes, the tria- and heptafulvenes are even more complex. The parent tria- and heptafulvenes have E(T₁) at 2.71 and 1.41 eV, respectively, and 2K_H,L at 1.87 and 1.54 eV, respectively. Thus, the parent heptafulvene, but not the triafulvene, fulfils the 2E(T₁) E(S₁) criterion. To lower E(T₁), exocyclic electron donating substituents X are needed in both compound classes,(45) but several substituted triafulvenes in their T₁ and S₁ states are described by other electron configurations than the singly excited HOMO → LUMO configuration that corresponds to the T₁ and S₁ states in the parent compound (see Figure S31). In heptafulvene, the 2E(T₁) E(S₁) criterion is satisfied, but one needs to step toward increased T₁ aromaticity in order to achieve heptafulvenes that also satisfy the E(S₁) E(T₂) criterion. However, the E(T₁) and ΔE(S₁ – T₁) values vary extensively among substituted heptafulvenes (see Figure S32 and Table S28), and their nonplanar structures in S₀ and/or T₁ are dilemma. Thus, the model also fails when large conformational changes occur within a compound class, either along the (anti)aromaticity coordinate in the S₀ and/or T₁ states or upon excitation.

Our design approach also applies to the benzannelated pentalenes (Figure 13). The parent pentalene is strongly Baird-aromatic in T₁, and it has an E(T₁)_a of 0.63 eV and 2K_H,L of 1.26 eV. Thus, the singlet fission threshold should be placed at benzannelated pentalenes that are less T₁ Baird-aromatic than the parent pentalene (BENZPENT3 or BENZPENT4 are computed to be close to the threshold, Figure 12). Now, as the NICS values of BENZPENT3 and BENZPENT4 are composites of 8π-, 12π- and 16π-electron circuits, NICS is not a suitable method for the assessment of the T₁ aromaticity of a pentalene subunit within a benzannelated pentalene. HOMA is a better aromaticity index, and we indeed find the pentalene units in BENZPENT3 and BENZPENT4 to be less aromatic (HOMA=0.72 and 0.73, respectively) than the parent pentalene (HOMA=0.86). The design approach also applies to thieno-annelated benzopentalenes (see Figure S36). In regard to these, they have E(T₁) that are slightly higher than the purely benzannelated pentalenes (Figures 14D and S36), revealing the impact of the incorporation of heterocycles as a means for fine-tuning E(T₁). Thieno-annelated benzopentalenes could be synthetically feasible, and also, these could be interesting targets for research on singlet fission photovoltaics.

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.9b12435.

• Tables with absolute relative energies, excitation energies, aromaticity data (MCI, HOMA, NICS(1)_zz), and diradical character. Plots of excitation energies versus HOMA and NICS(1)_zz, molecular orbitals, and NICS-XY scans. List of compounds include the following: substituted fulvenes, substituted CBDs, substituted pentalenes, substituted indacenes, benzannelated CBDs, benzannelated pentalenes, triafulvenes, heptafulvenes, siloles, and thieno-benzannelated pentalenes (PDF)

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We are grateful to M. Abrahamsson and G. London for interesting discussions on the manuscript and to L. Karas, N. Proos Vedin, and J. Toldo for technical assistance. We acknowledge the Wenner–Gren Foundation for a postdoctoral fellowship of O.E.B., the Swedish Research Council (grant 2015-04538) for financial support, and the Swedish National Infrastructure for Computing via the National Supercomputer Center in Linköping, Sweden for generous allotment of computer time. J.R.S. would like to thank the Swedish Fulbright Commission, the American Scandinavian Foundation, and the HSU College of Natural Resources and Science for supporting his time at UU.

• Abstract

  

  Figure 1

  

  Figure 1. Desired arrangement of the lowest electronic states within a particular compound class that encompasses both S₀ aromatic (T₁/S₁ antiaromatic) compounds and S₀ antiaromatic (T₁/S₁ aromatic) compounds. Compounds within the orange region have 2E(T₁) E(S₁).

  Figure 2

  

  Figure 2. (A) Postulated (idealized) variation in excitation energies of fulvenes as one goes from electron donating groups (EDGs) to electron withdrawing groups (EWGs). The figure displays the ideally constant energy difference between E(T₁) and E(S₁) (ΔE(S₁ – T₁)=2K_ij), upon which our hypothesis is based. (B) E(S₁)/E(T₁) ratio for four experimentally investigated fulvene derivatives, i.e., TClDCF, TClDMF, DMF, and TClDPF (see refs (46) and (47)).

  Figure 3

  

  Figure 3. (A) Plots of HOMO and LUMO of the parent fulvene, and (B) two plots showing how E(T₁)_v, E(S₁)_v, and E(T₂)_v vary as functions of the CC bond lengths marked in red. Calculations at TD-M06-2X/6-311+G(d,p) level.

  Figure 4

  

  Figure 4. Di- and tetrasubstituted fulvene derivatives included in this work.

  Figure 5

  

  Figure 5. Plots of excited-state energies and energy differences against degree of (anti)aromaticity in S₀. (A) E(T₁)_v and E(S₁)_v versus NICS(1)_zz,S0, (B) E(T₁)_a and E(S₁)_v versus NICS(1)_zz,S0. (C) The energy difference between the S₁ and T₁ states versus NICS(1)_zz,S0 (D) E(T₂)_v and E(S₁)_v versus NICS(1)_zz,S0 for tetrasubstituted fulvenes. R² is the squared correlation coefficient. NICS(1)_zz,S0 computed at GIAO/(U)M06-2X/6-311+G(d,p) level. In (A), the parent fulvene is indicated by red marks.

  Figure 6

  

  Figure 6. Variations in E(T)_v, E(S₁)_v, and E(T₂)_v dependence on the C2–C3 bond length (red) in four fulvenes. Data points marked correspond to other excitations than that of the singly excited HOMO–LUMO configuration of the parent fulvene.

  Figure 7

  

  Figure 7. T₁, S₁, and T₂ energies (in eV) of six previously synthesized fulvenes computed at TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) (normal print) and CASPT2(14in14)/ANO-RCC-VDZP//M06-2X/6-311+G(d,p) (italics) levels.

  Figure 8

  

  Figure 8. Parent and substituted cyclobutadienes and their excitation energies (in eV) computed at TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) level.

  Figure 9

  

  Figure 9. Parent and substituted pentalenes and their excitation energies (in eV) computed at the TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) level.

  Figure 10

  

  Figure 10. Benzannelated cyclobutadiene compounds and their excitation energies (in eV) computed at TD-M06-2X/def2-TZVPD//M06-2X/6-311+G(d,p) and CASPT2/ANO-RCC-VDZP//CASSCF(n,m)/ANO-RCC-VDZP (italics, n=m=8 for BENZCBD1 and n=m=12, for BENZCBD2) levels. The compounds for which both singlet fission criteria are satisfied are marked in green. For full compound names, see Figure S20.

  Figure 11

  

  Figure 11. NICS-XY scans of (A) BENZCBD1, (B) BENZCBD2, (C) BENZCBD5, (D) BENZPENT1, (E) BENZPENT3, and (F) BENZPENT7 in their S₀ and T₁ states calculated at GIAO/M06-2X/6-311+G(d,p) level.

  Figure 12

  

  Figure 12. Benzannelated pentalenes and their excitation energies (in eV) computed at TD-M06-2X/def2-TZVPD//(U)M06-2X/6-311+G(d,p) (normal print) and CASPT2/ANO-RCC-VDZP//CASSCF(12,12)/ANO-RCC-VDZP (italics) levels. The compounds for which both singlet fission criteria are satisfied are marked in green. Additional benzannelated pentalenes are found in the Supporting Information. The at the E(S₁)_v of BENZPENT10 indicates the two-configurational character of the S₁ state.

  Figure 13

  

  Figure 13. Variation in E(T₁)_a, E(S₁)_v, and E(T₂)_v calculated using the ZHA approach as a function of benzannelation in selected benzannelated pentalenes. Compounds that satisfy the singlet fission criteria are represented by yellow bars. Computations at TD-M06-2X/def2-TZVPD//(U)M06-2X/6-311+G(d,p) level. The at E(S₁)_v of BENZPENT10 indicates the two-configurational character of the S₁ state. Further comparisons are given in Figure S23. Results of T₁-aromaticity assessments are found in Figures S25–S28.

  Figure 14

  

  Figure 14. (A and B) Schematic drawings of the changes in E(T₁) and E(S₁) as functions of increased T₁ and S₁ aromatic character for a compound class with (A) large K_H,L and (B) small K_H,L. Slopes of E(T₁) and E(S₁) as well as the position and E(T₁) of the parent compound (marked as 0 on the x-axis) are kept constant in the two plots. (C) 1,1-Disubstituted siloles with X and Y=H, Me, CF₃, F, SiH₃, and SiMe₃ as high-E(T₁) singlet fission chromophores (for explicit energies, see Figure S33). (D) Benzannelated pentalenes where the terminal benzo rings have been exchanged for thiopheno rings (for explicit energies, see Figure S36). A comparison against the completely benzannelated pentalenes is given in the Supporting Information.

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      Molecular design for efficient singlet fission

      Ito, Soichi; Nagami, Takanori; Nakano, Masayoshi

      Journal of Photochemistry and Photobiology, C: Photochemistry Reviews
      (2018),
      34
      (),
      85-120CODEN:
      JPPCAF;
      ISSN: 1389-5567.

      (Elsevier B.V.)

      A review. Singlet fission is a photophys. process in mols. and mol. aggregates, in which a singlet exciton generated by irradn. splits into two triplet excitons. Recently, singlet fission has attracted a great deal of attention from the viewpoint of applications in org. photovoltaic cells, where singlet fission has a possibility of improving the photoelec. conversion efficiency. Although singlet fission was first obsd. about 50 years ago in anthracene crystals, and the mechanism has been investigated in detail for a small no. of mol. systems such as tetracene and pentacene crystals, the relationships between mol. or crystal structures and singlet fission efficiency are yet to be precisely clarified. Thus, mol. structure – singlet fission relationships and mol. or crystal design guidelines for efficient singlet fission are intensely desired for realizing efficient photovoltaic energy conversion, and exptl. and theor. investigations advance rapidly. We introduce three investigation steps, which are based on bottom-up theor. modeling from a mol. to a mol. aggregate or crystal. The modeling involves energy level matching at the mol. level, electronic coupling at the aggregate level, and singlet fission dynamics including exciton-phonon (vibronic) coupling, by emphasizing the importance of interplay between each step. From the modeling, we present several design guidelines for efficient singlet fission, which is together with practical mol. structures, chem. modifications and mol. configurations.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXivFCku74%253D&md5=4f57ac0f40a9bc49a0b6f79ad9533fb9

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      Minami, T.; Ito, S.; Nakano, M. Fundamental of Diradical-Character-Based Molecular Design for Singlet Fission. J. Phys. Chem. Lett. 2013, 4, 2133– 2137, DOI: 10.1021/jz400931b

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      20

      Fundamental of Diradical-Character-Based Molecular Design for Singlet Fission

      Minami, Takuya; Ito, Soichi; Nakano, Masayoshi

      Journal of Physical Chemistry Letters
      (2013),
      4
      (13),
      2133-2137CODEN:
      JPCLCD;
      ISSN: 1948-7185.

      (American Chemical Society)

      The fundamental of diradical-character-based mol. design for singlet fission is clarified through the correlation between the diradical character, the first singlet (S1) and triplet (T1) excitation energies, the frontier orbital energy gap, and the energy level matching condition (2E(T1) – E(S1) ≈ 0 or

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXptlCgsr4%253D&md5=4395e6adc01babfe1515a66d311512d7

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      Zeng, T.; Goel, P. Design of Small Intramolecular Singlet Fission Chromophores: An Azaborine Candidate and General Small Size Effects. J. Phys. Chem. Lett. 2016, 7, 1351– 1358, DOI: 10.1021/acs.jpclett.6b00356

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      21

      Design of Small Intramolecular Singlet Fission Chromophores: An Azaborine Candidate and General Small Size Effects

      Zeng, Tao; Goel, Prateek

      Journal of Physical Chemistry Letters
      (2016),
      7
      (7),
      1351-1358CODEN:
      JPCLCD;
      ISSN: 1948-7185.

      (American Chemical Society)

      We report the first attempt to design small intramol. singlet fission chromophores, with the aid of quantum chem. and explicitly simulating the time evolution of state populations using quantum dynamics method. We start with three previously proposed azaborine-substituted intermol. singlet fission chromophores. Through analyzing their frontier orbital amplitudes, we select a BN-substituted azulene as the building block. Covalently connecting two such monomers and tuning their relative configuration, we examine three dimers. One dimer is found to be an eminent candidate: the triplet-pair state is quickly formed within 1 silicon::polycryst.,, and the two triplets are ready to be disentangled. We elucidate the general small size effects in intramol. singlet fission and focus on specific aspects which should be taken care of when manipulating the fission rate through steric hindrance.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XkslGqt70%253D&md5=bdb0554f3fc3eb17b45c7664b3d8ebb1

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      Match, C.; Perkins, J.; Schreckenbach, G. Simple Computational Screening of Potential Singlet Fission Molecules. Theor. Chem. Acc. 2018, 137, 109, DOI: 10.1007/s00214-018-2290-4

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      Nakano, M. Open-Shell-Character-Based Molecular Design Principles: Applications to Nonlinear Optics and Singlet Fission. Chem. Rec. 2017, 17, 27– 62, DOI: 10.1002/tcr.201600094

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      Open-Shell-Character-Based Molecular Design Principles: Applications to Nonlinear Optics and Singlet Fission

      Nakano, Masayoshi

      Chemical Record
      (2017),
      17
      (1),
      27-62CODEN:
      CRHEAK;
      ISSN: 1528-0691.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      Open-shell character, e.g., diradical character, is a quantum chem. well-defined quantity in ground-state mol. systems, which is not an observable but can quantify the degree of effective bond weakness in the chem. sense or electron correlation strength in the phys. sense. Because this quantity also correlates to specific excited states, physicochem. properties concerned with those states are expected to strongly correlate to the open-shell character. This feature enables us to open a new path to revealing the mechanism of these properties as well as to realizing new design principles for efficient functional mol. systems. This account explains the open-shell-character-based mol. design principles and introduces their applications to the rational design of highly efficient nonlinear optical and singlet fission mol. systems.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhtlShurfE&md5=1b07f1a1af532cc83425079f045d2cdc

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      Ito, S.; Nakano, M. Theoretical Molecular Design of Heteroacenes for Singlet Fission: Tuning the Diradical Character by Modifying π-Conjugation Length and Aromaticity. J. Phys. Chem. C 2015, 119, 148– 157, DOI: 10.1021/jp5103737

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      Theoretical Molecular Design of Heteroacenes for Singlet Fission: Tuning the Diradical Character by Modifying π-Conjugation Length and Aromaticity

      Ito, Soichi; Nakano, Masayoshi

      Journal of Physical Chemistry C
      (2015),
      119
      (1),
      148-157CODEN:
      JPCCCK;
      ISSN: 1932-7447.

      (American Chemical Society)

      A theor. mol. design for efficient singlet fission (SF) is performed for several heteroacene models involving nitrogen (N) atoms based on the diradical character criterion of the energy level matching conditions. This criterion is found to be closely related to the relative contributions of diradical and zwitterionic resonance structures of the heteroacenes, i.e., the aromaticity of the central ring(s). From the anal. of the diradical characters of these heteroacene models, the increase in the aromaticity of the central ring(s) is found to prefer the diradical form to the zwitterionic form. From the comparison of the excitation energies evaluated by multireference second-order perturbation theory calcns., two promising candidates, chosen based on the diradical character criterion, are found to satisfy the energy level matching conditions and to possess high triplet energies of ∼1.1 eV, which are suitable for an application in org. photovoltaic cells. The proposed two candidates are shown to have mutually different types of the first excited singlet states, which are distinguished by the primary excitation configurations. These results suggest that the proposed two candidates exhibit different singlet fission dynamics due to the different amplitude of the electronic coupling.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitV2ju7fE&md5=ae8b1b61f3c332de221cecaede8c7113

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      Zeng, T.; Ananth, N.; Hoffmann, R. Seeking Small Molecules for Singlet Fission: A Heteroatom Substitution Strategy. J. Am. Chem. Soc. 2014, 136, 12638– 12647, DOI: 10.1021/ja505275m

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      Seeking Small Molecules for Singlet Fission: A Heteroatom Substitution Strategy

      Zeng, Tao; Ananth, Nandini; Hoffmann, Roald

      Journal of the American Chemical Society
      (2014),
      136
      (36),
      12638-12647CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      We design theor. small mol. candidates for singlet fission chromophores, aiming to achieve a balance between sufficient diradical character and kinetic persistence. We develop a perturbation strategy based on the captodative effect to introduce diradical character into small π-systems. Specifically, this can be accomplished by replacing pairs of not necessarily adjacent C atoms with isoelectronic and isosteric pairs of B and N atoms. Three rules of thumb emerge from our studies to aid further design: (i) Lewis structures provide insight into likely diradical character; (ii) formal radical centers of the diradical must be well-sepd.; (iii) stabilization of radical centers by a donor (N) and an acceptor (B) is essential. Following the rules, we propose candidate mols. Employing reliable multireference calcns. for excited states, we identify three likely candidate mols. for SF chromophores. These include a benzene, a naphthalene, and an azulene, where four C atoms are replaced by a pair of B and a pair of N atoms.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsVSnsrfP&md5=252ab72cf2c676144b0f4e7d0d05f51f

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      Ito, S.; Minami, T.; Nakano, M. Diradical Character Based Design for Singlet Fission of Condensed-Ring Systems with 4nπ Electrons. J. Phys. Chem. C 2012, 116, 19729– 19736, DOI: 10.1021/jp3072684

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      Diradical Character Based Design for Singlet Fission of Condensed-Ring Systems with 4nπ Electrons

      Ito, Soichi; Minami, Takuya; Nakano, Masayoshi

      Journal of Physical Chemistry C
      (2012),
      116
      (37),
      19729-19736CODEN:
      JPCCCK;
      ISSN: 1932-7447.

      (American Chemical Society)

      By applying the diradical character based mol. design guideline for singlet fission (SF), we investigate the feasibility of efficient SF in condensed-ring π-conjugated mols. with 4nπ electrons (n=4, 5, …), i.e., antiarom. polycyclic hydrocarbons composed of five- and six-membered rings. The multiple diradical character (yi), which takes a value between 0 (closed shell) and 1 (pure open shell), is defined as the occupation no. of the lowest unoccupied natural orbital (LUNO) + i (i=0, 1, …) calcd. using the approx. spin-projected spin-UHF method. The excitation energies are also evaluated using the tuned long-range cor. time-dependent d. functional theory method with the Tamm-Dancoff approxn. to examine the energy level matching conditions for SF: (i) 2E(T1) – E(S1) ∼ 0 or ≤ 0 and (ii) 2E(T1) – E(T2)

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xht1KmsL7E&md5=71e724b13bea11298ec80ba071215c44

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      Chen, Y.; Shen, L.; Li, X. Effects of Heteroatoms of Tetracene and Pentacene Derivatives on Their Stability and Singlet Fission. J. Phys. Chem. A 2014, 118, 5700– 5708, DOI: 10.1021/jp503114b

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      Effects of Heteroatoms of Tetracene and Pentacene Derivatives on Their Stability and Singlet Fission

      Chen, Yuhan; Shen, Li; Li, Xiyou

      Journal of Physical Chemistry A
      (2014),
      118
      (30),
      5700-5708CODEN:
      JPCAFH;
      ISSN: 1089-5639.

      (American Chemical Society)

      The effects of the introduction of an sp2-hybridized nitrogen atom (=N-) and thiophene ring on the structure geometries, frontier MO energies, and excited state energies related to singlet fission (SF) for some tetracene and pentacene derivs. were theor. investigated by quantum chem. methods. The introduction of a nitrogen atom significantly decreases the energies of frontier MOs and hence improves their stabilities in air and light illumination. More importantly, it is helpful for reducing the energy loss of the exothermic singlet fission of pentacene derivs. For fused benzene-thiophene structures, the (α, β) connection pattern could stabilize the frontier MOs, while the (β, β) connection pattern can promote the thermodn. driving force of singlet fission. These facts provide a theor. ground for rational design of SF materials.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtFens7bN&md5=2e6ee780697588cecb98355257bf03d9

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      Singh, S.; Jones, W. J.; Siebrand, W.; Stoicheff, B. P.; Schneider, W. G. Laser Generation of Excitons and Fluorescence in Anthracene Crystals. J. Chem. Phys. 1965, 42, 330– 342, DOI: 10.1063/1.1695695

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      Laser generation of excitons and fluorescence in anthracene crystals

      Singh, S.; Jones, W. J.; Siebrand, W.; Stoicheff, B. P.; Schneider, W. G.

      Journal of Chemical Physics
      (1965),
      42
      (1),
      330-42CODEN:
      JCPSA6;
      ISSN: 0021-9606.

      Exptl. and theoretical studies are reported of the short-lived and delayed fluorescence of anthracene single crystals, excited by single- and double-proton absorption. A giant-pulse ruby laser provides the primary source of radiation of 14,400 cm.-1 (up to 1027 photons/cm.2 sec.) and is also used to generate 2nd-harmonic radiation from adenosine 5′-diphosphate, as well as stimulated Raman radiation of 12,800 and 17,500 cm.-1 from liquid O. The time dependence of the fluorescence intensity is studied as a function of laser intensity, crystal temp., and excitation wavelength. The very intense fast fluorescence with a half-life of 30 nsec. at 300°K., characteristic of singlet exciton decay, and the relatively weak delayed fluorescence which involves intermediate triplet states, are sepd. by using sectored disks. The triplet state at 14,750 cm.-1 can be populated (1) by direct absorption of laser photons, involving an activation energy of 350 cm.-1; (2) via 2-photon absorption, presumably leading to a vibrationally excited state of the 1B2u exciton, followed by intersystem crossing; (3) via 1-photon (2nd-harmonic) excitation from levels ≥700 cm.-1 into the singlet absorption band, followed by conversion of the singlet exciton into a triplet pair. The latter process is suggested by the observed activation energy of 700 cm.-1 In agreement with these interpretations, the delayed fluorescence intensity varies with the 2nd to 4th power of the laser intensity, depending on the exptl. conditions. Also, light of 17,500 cm.-1 leads exclusively to process (1), light of 12,800 cm.-1 exclusively to (2). Triplet lifetimes from 2-17 msec. are obtained, depending on crystal purity, which indicates that unimol. triplet decay is an extrinsic, radiationless process. A singlet-triplet intersystem crossing rate const. of ∼3 × 10-5 sec.-1 is estd. The triplet-triplet annihilation rate const. is ∼5 × 10-11 cm.3 sec.-1 This value, considered together with the triplet-pair creation process, suggests a triplet exchange rate ⪆1013 sec.-1 and a triplet diffusion const. ⪆5 × 10-4 cm.2/sec.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF2MXhvFyjtQ%253D%253D&md5=7a939ac766c41d53bcc49f62422007a6

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      Groff, R. P.; Avakian, P.; Merrifield, R. E. Coexistence of Exciton Fission and Fusion in Tetracene Crystals. Phys. Rev. B 1970, 1, 815– 817, DOI: 10.1103/PhysRevB.1.815

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      Burgos, J.; Pope, M.; Swenberg, Ch. E.; Alfano, R. R. Heterofission in Pentacene-Doped Tetracene Single Crystals. Phys. Status Solidi B 1977, 83, 249– 256, DOI: 10.1002/pssb.2220830127

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      Heterofission in pentacene-doped tetracene single crystals

      Burgos, J.; Pope, M.; Swenberg, C. E.; Alfano, R. R.

      Physica Status Solidi B: Basic Research
      (1977),
      83
      (1),
      249-56CODEN:
      PSSBBD;
      ISSN: 0370-1972.

      The magnetic field and the temp. dependence of both guest and host fluorescence in pentacene-doped tetracene single crystals was studied. From an anal. of the exptl. results pentacene enters substitutionally into the host lattice sites and thermally activated heterofission is site-dependent with activation energies ≈ (0.13 ± 0.01) eV and .ltorsim.0.06 eV. From a kinetic fit to the temp. dependence of the green and red fluorescence, a thermally activated host singlet exciton diffusion coeff. of ≈ 2 × 10-2 cm2/s is inferred; its activation energy is (0.018 ± 0.001) eV. The heterofission rate of ≈ (4.7 ± 0.5) × 10-10 cm3 s-1 was detd. and location of the pentacene triplet level is found at (0.86 ± 0.03) eV.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2sXlslGjtL0%253D&md5=934556b5642fb2fe13cd77706d3b48c9

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      Johnson, J. C.; Nozik, A. J.; Michl, J. High Triplet Yield from Singlet Fission in a Thin Film of 1,3-Diphenylisobenzofuran. J. Am. Chem. Soc. 2010, 132, 16302– 16303, DOI: 10.1021/ja104123r

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      High Triplet Yield from Singlet Fission in a Thin Film of 1,3-Diphenylisobenzofuran

      Johnson, Justin C.; Nozik, Arthur J.; Michl, Josef

      Journal of the American Chemical Society
      (2010),
      132
      (46),
      16302-16303CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      Direct observation of triplet absorption and ground-state depletion upon pulsed excitation of a polycryst. thin solid film of 1,3-diphenylisobenzofuran at 77 K revealed a 200 ± 30% triplet yield, which was attributed to singlet fission.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtlOnsLvM&md5=e715b469a3c20c180c8fa1819457801e

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      Schrauben, J. N.; Ryerson, J. L.; Michl, J.; Johnson, J. C. Mechanism of Singlet Fission in Thin Films of 1,3-Diphenylisobenzofuran. J. Am. Chem. Soc. 2014, 136, 7363– 7373, DOI: 10.1021/ja501337b

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      Mechanism of Singlet Fission in Thin Films of 1,3-Diphenylisobenzofuran

      Schrauben, Joel N.; Ryerson, Joseph L.; Michl, Josef; Johnson, Justin C.

      Journal of the American Chemical Society
      (2014),
      136
      (20),
      7363-7373CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      In order to elucidate the mechanism of singlet fission in thin films of 1,3-diphenylisobenzofuran (1) the authors have performed ultrafast transient absorption spectroscopy as a function of sample temp. and excitation fluence on polycryst. thin films composed of two polymorphs. The authors earlier investigations revealed that films enriched in a particular polymorph of 1 displayed near 200% efficiency for triplet formation at 77 K, while films composed primarily of a second polymorph had a very low triplet quantum yield. Present data confirm the triplet yield disparities in the two polymorphs and demonstrate the distinct fates of the initially prepd. singlets in films of different structure. Singlet fission is inhibited in the more stable polymorph due to rapid excimer formation and trapping. The less stable polymorph undergoes highly efficient singlet fission with a dominant time const. of 10-30 ps and without strong thermal activation. Transient absorption measurements with varying excitation fluence indicate that singlet-singlet annihilation is a primary competitor of singlet fission at higher fluence and that fission from higher-lying states can also contribute to the triplet formation process. Measurements employing different excitation energies and sample temps. reveal the role that trapping processes play in attenuating the triplet quantum yield to produce the complex temp. dependence of the singlet fission yield. The rate consts. for singlet fission itself are essentially temp. independent.

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      Baird, N. C. Quantum organic photochemistry. II. Resonance and Aromaticity in the Lowest ³ ππState of Cyclic Hydrocarbons. J. Am. Chem. Soc. 1972, 94, 4941– 4948, DOI: 10.1021/ja00769a025

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      Quantum organic photochemistry. II. Resonance and aromaticity in the lowest 3ππstate of cyclic hydrocarbons

      Baird, N. Colin

      Journal of the American Chemical Society
      (1972),
      94
      (14),
      4941-8CODEN:
      JACSAT;
      ISSN: 0002-7863.

      The concepts of aromaticity, antiaromaticity, and Dewar resonance energy are extended to the lowest ππtriplet state of conjugated hydrocarbons by comparing the bonding energy of triplets to the most stable biradical ref. structure. Arguments based upon simple perturbation theory indicate that the rules for ground state aromaticity are reversed in the 3ππstate (4n rings display “aromatic” character whereas 4n + 2 systems display “antiaromaticity”). Semiempirical SCF-LCAO-MO calcns. by the neglect-of-nonbonded-differential-overlap method confirm these predictions, and predict transition, bonding, and stabilization energies for a wide range of triplets including those for cyclobutadiene and derivs., cyclooctatetraene and derivs., nonclassical polyenes, 3-7-membered rings contg. exocyclic C atoms, benzenoid hydrocarbons, butalene, azulene, and cyclodecapentaene. The preference of certain hydrocarbon triplets for a completely planar rather than 90° twisted structure (such as methylenecyclo-propene, fulvene, and heptafulvene) is analyzed by perturbation theory. The consequences of aromatic and antiaromatic character to the exothermicity of ortho addn. are explored for several hydrocarbon triplets.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE38XkslCksb0%253D&md5=fd74d4499d8dfcca1fe6d296285623a6

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      Ottosson, H. Organic photochemistry: Exciting Excited-State Aromaticity. Nat. Chem. 2012, 4, 969– 971, DOI: 10.1038/nchem.1518

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      Organic photochemistry Exciting excited-state aromaticity

      Ottosson, Henrik

      Nature Chemistry
      (2012),
      4
      (12),
      969-971CODEN:
      NCAHBB;
      ISSN: 1755-4330.

      (Nature Publishing Group)

      In 1972, Baird published rules describing aromaticity and antiaromaticity in the lowest triplet excited states of annulenes. The fortieth anniversary of Baird’s rules – which are the reverse of Hueckel’s rules for aromaticity and antiaromaticity in the ground state – ought to be celebrated before 2012 comes to an end.

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      Rosenberg, M.; Dahlstrand, C.; Kilså, K.; Ottosson, H. Excited State Aromaticity and Antiaromaticity: Opportunities for Photophysical and Photochemical Rationalizations. Chem. Rev. 2014, 114, 5379– 5425, DOI: 10.1021/cr300471v

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      Excited State Aromaticity and Antiaromaticity: Opportunities for Photophysical and Photochemical Rationalizations

      Rosenberg, Martin; Dahlstrand, Christian; Kilsaa, Kristine; Ottosson, Henrik

      Chemical Reviews (Washington, DC, United States)
      (2014),
      114
      (10),
      5379-5425CODEN:
      CHREAY;
      ISSN: 0009-2665.

      (American Chemical Society)

      In this review the authors described the development of the excited state aromaticity concept over time, a development which has progressed slowly over several decades and in different branches of chem. As a result, the concept has not been as visible to the chem. community as desirable. This review provides accumulative collection of studies that strongly support the existence of aromaticity and antiaromaticity effects in the lowest excited states of cyclic π-conjugated mols. The excited state (anti)aromaticity effects could be equally useful for understanding of excited state properties and processes as ground state aromaticity is useful for rationalization of ground state properties and processes.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXlsl2ks7s%253D&md5=4f1023c0fa4c093032d1bc71d30885db

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      Oh, J.; Sung, Y. M.; Hong, Y.; Kim, D. Spectroscopic Diagnosis of Excited-State Aromaticity: Capturing Electronic Structures and Conformations upon Aromaticity Reversal. Acc. Chem. Res. 2018, 51, 1349– 1358, DOI: 10.1021/acs.accounts.7b00629

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      Spectroscopic Diagnosis of Excited-State Aromaticity: Capturing Electronic Structures and Conformations upon Aromaticity Reversal

      Oh, Juwon; Sung, Young Mo; Hong, Yongseok; Kim, Dongho

      Accounts of Chemical Research
      (2018),
      51
      (6),
      1349-1358CODEN:
      ACHRE4;
      ISSN: 0001-4842.

      (American Chemical Society)

      A review. Aromaticity, the special energetic stability derived from cyclic [4n + 2]π-conjugated electronic structures, has been the topic of intense interest in chem. because it plays a crit. role in rationalizing mol. stability, reactivity, and phys./chem. properties. Recently, the pioneering work by Colin Baird on aromaticity reversal, postulating that arom. (antiarom.) character in the ground state reverses to antiarom. (arom.) character in the lowest excited triplet state, has attracted much scientific attention. The completely reversed aromaticity in the excited state provides direct insight into understanding the photophys./chem. properties of photoactive materials. In turn, the application of arom. mols. to photoactive materials has led to numerous studies revealing this aromaticity reversal. However, most studies of excited-state aromaticity have been based on the theor. point of view. The exptl. evaluation of aromaticity in the excited state is still challenging and strenuous because the assessment of (anti)aromaticity with conventional magnetic, energetic, and geometric indexes is difficult in the excited state, which practically restricts the extension and application of the concept of excited-state aromaticity. Time-resolved optical spectroscopies can provide a new and alternative avenue to evaluate excited-state aromaticity exptl. while observing changes in the mol. features in the excited states. Time-resolved optical spectroscopies take advantage of ultrafast laser pulses to achieve high time resoln., making them suitable for monitoring ultrafast changes in the excited states of mol. systems. This can provide valuable information for understanding the aromaticity reversal.This Account presents recent breakthroughs in the exptl. assessment of excited-state aromaticity and the verification of aromaticity reversal with time-resolved optical spectroscopic measurements. To scrutinize this intriguing and challenging scientific issue, expanded porphyrins have been utilized as the ideal testing platform for investigating aromaticity because they show distinct arom. and antiarom. characters with aromaticity-specific spectroscopic features. Expanded porphyrins exhibit perfect arom. and antiarom. congener pairs having the same mol. framework but different nos. of π electrons, which facilitates the study of the pure effect of aromaticity by comparative analyses. On the basis of the characteristics of expanded porphyrins, time-resolved electronic and vibrational absorption spectroscopies capture the changes in electronic structure and mol. conformations driven by the change in aromaticity and provide clear evidence for aromaticity reversal in the excited states. The approaches described in this Account pave the way for the development of new and alternative exptl. indexes for the evaluation of excited-state aromaticity, which will enable overarching and fundamental comprehension of the role of (anti)aromaticity in the stability, dynamics, and reactivity in the excited states with possible implications for practical applications.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjvVSksLc%253D&md5=8e24d0c31644703531f08b314da63df7

  37. 37

      Fallon, K. J.; Budden, P.; Salvadori, E.; Ganose, A. M.; Savory, C. N.; Eyre, L.; Dowland, S.; Ai, Q.; Goodlett, S.; Risko, C.; Scanlon, D. O.; Kay, C. W. M.; Rao, A.; Friend, R. H.; Musser, A. J.; Bronstein, H. Exploiting Excited-State Aromaticity to Design Highly Stable Singlet Fission Materials. J. Am. Chem. Soc. 2019, 141, 13867– 13876, DOI: 10.1021/jacs.9b06346

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      37

      Exploiting excited-state aromaticity to design highly stable singlet fission materials

      Fallon, Kealan J.; Budden, Peter; Salvadori, Enrico; Ganose, Alex M.; Savory, Christopher N.; Eyre, Lissa; Dowland, Simon; Ai, Qianxiang; Goodlett, Stephen; Risko, Chad; Scanlon, David O.; Kay, Christopher W. M.; Rao, Akshay; Friend, Richard H.; Musser, Andrew J.; Bronstein, Hugo

      Journal of the American Chemical Society
      (2019),
      141
      (35),
      13867-13876CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      Singlet fission, the process of forming two triplet excitons from one singlet exciton, is a characteristic reserved for only a handful of org. mols. due to the atypical energetic requirement for low energy excited triplet states. The predominant strategy for achieving such a trait is by increasing ground state diradical character; however, this greatly reduces ambient stability. Herein, we exploit Baird’s rule of excited state aromaticity to manipulate the singlet-triplet energy gap and create novel singlet fission candidates. We achieve this through the inclusion of a [4n] 5-membered heterocycle, whose electronic resonance promotes aromaticity in the triplet state, stabilizing its energy relative to the singlet excited state. Using this theory, we design a family of derivs. of indolonaphthyridine thiophene (INDT) with highly tunable excited state energies. Not only do we access novel singlet fission materials, they also exhibit excellent ambient stability, imparted due to the delocalized nature of the triplet excited state. Spin-coated films retained up to 85% activity after several weeks of exposure to oxygen and light, while analogous films of TIPS-pentacene showed full degrdn. after 4 days, showcasing the excellent stability of this class of singlet fission scaffold. Extension of our theor. anal. to almost ten thousand candidates reveals an unprecedented degree of tunability and several thousand potential fission-capable candidates, while clearly demonstrating the relationship between triplet aromaticity and singlet-triplet energy gap, confirming this novel strategy for manipulating the exchange energy in org. materials.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhsFSku73L&md5=0a0a7bc43984992df2b7883fde556f2f

  38. 38

      Shukla, D.; Wan, P. Evidence for a Planar Cyclically Conjugated 8π System in the Excited State: Large Stokes Shift Observed for Dibenz[b,f]oxepin Fluorescence. J. Am. Chem. Soc. 1993, 115, 2990– 2991, DOI: 10.1021/ja00060a063

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      38

      Evidence for a planar cyclically conjugated 8π system in the excited state: large Stokes shift observed for dibenz[b,f]oxepin fluorescence

      Shukla, Deepak; Wan, Peter

      Journal of the American Chemical Society
      (1993),
      115
      (7),
      2990-1CODEN:
      JACSAT;
      ISSN: 0002-7863.

      The fluorescence emissions of dibenz[b,f]oxepin (I, X=O) and dibenzo[b,f]thiepin (I, X=S) exhibit unexpectedly large Stokes shifts (≈4720 cm-1). The equil. geometries of I on the excited-state surface are planar and are the fluorescent states. The driving force for torsional twisting to a planar geometry is believed to be the attainment of a conjugated 8π cyclic array in the central ring, which would be highly unfavorable (antiarom.) in the ground state. The vibrational fine structure (progression of ≈1500 cm-1) and relatively long lifetime of the emission band obsd. for I (X=O), along with corroborating reactivity data, indicate that these compds. exhibit the characteristics of a planar and arom. mol. in S1.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3sXitlegt78%253D&md5=dacbf0e58476739b6f9ba604f61a1482

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      Toldo, J.; El Bakouri, O.; Solà, M.; Norrby, P.-O.; Ottosson, H. Is Excited-State Aromaticity a Driving Force for Planarization of Dibenzannelated 8π-Electron Heterocycles?. ChemPlusChem 2019, 84, 712– 721, DOI: 10.1002/cplu.201900066

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      39

      Is Excited-State Aromaticity a Driving Force for Planarization of Dibenzannelated 8π-Electron Heterocycles?

      Toldo, Josene; El Bakouri, Ouissam; Sola, Miquel; Norrby, Per-Ola; Ottosson, Henrik

      ChemPlusChem
      (2019),
      84
      (6),
      712-721CODEN:
      CHEMM5;
      ISSN: 2192-6506.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      Compds. with dibenzannelated heterocycles with eight π-electrons are found in a range of applications. These mols. often adopt a bent structure in the ground state (S0) but can become planar in the first excited states (S1 and T1) because of the cyclically conjugated 4nπ central ring, which fulfils the requirements for excited state aromaticity. We report on a quantum chem. investigation of the arom. character in the S1 and T1 states of dibenzannelated seven- and six-membered heterocycles with one, two, or three heteroatoms in the 8π-electron ring. These states could have ππor nπcharacter. We find that compds. with one or two heteroatoms in the central ring have ππstates as their S1 and T1 states. They are to a significant degree influenced by excited state aromaticity, and their optimal structures are planar or nearly planar. Among the heteroatoms, nitrogen provides for the strongest excited state aromaticity whereas oxygen provides for the weakest, following the established trend of the S0 state. Yet, dibenzannelated seven-membered-ring compds. with N=N bonds have non-arom. nπstates with strongly puckered structures as their S1 and T1 states.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXotl2rsbw%253D&md5=1e0da0b30c73875f80df7c775be455ab

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      Ryerson, J. L.; Zaykov, A.; Aguilar
      Suarez, L. E.; Havenith, R. W. A.; Stepp, B. R.; Dron, P. I.; Kaleta, J.; Akdag, A.; Teat, S. J.; Magnera, T. F.; Miller, J. R.; Havlas, Z.; Broer, R.; Faraji, S.; Michl, J.; Johnson, J. C. Structure and Photophysics of Indigoids for Singlet Fission: Cibalackrot. J. Chem. Phys. 2019, 151, 184903, DOI: 10.1063/1.5121863

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      Structure and photophysics of indigoids for singlet fission: Cibalackrot

      Ryerson, Joseph L.; Zaykov, Alexandr; Aguilar Suarez, Luis E.; Havenith, Remco W. A.; Stepp, Brian R.; Dron, Paul I.; Kaleta, Jiri; Akdag, Akin; Teat, Simon J.; Magnera, Thomas F.; Miller, John R.; Havlas, Zdenek; Broer, Ria; Faraji, Shirin; Michl, Josef; Johnson, Justin C.

      Journal of Chemical Physics
      (2019),
      151
      (18),
      184903/1-184903/16CODEN:
      JCPSA6;
      ISSN: 0021-9606.

      (American Institute of Physics)

      We report an investigation of structure and photophysics of thin layers of cibalackrot, a sturdy dye derived from indigo by double annulation at the central double bond. Evapd. layers contain up to three phases, two cryst. and one amorphous. Relative amts. of all three have been detd. by a combination of X-ray diffraction and FT-IR reflectance spectroscopy. Initially, excited singlet state rapidly produces a high yield of a transient intermediate whose spectral properties are compatible with charge-transfer nature. This intermediate more slowly converts to a significant yield of triplet, which, however, does not exceed 100% and may well be produced by intersystem crossing rather than singlet fission. The yields were detd. by transient absorption spectroscopy and cor. for effects of partial sample alignment by a simple generally applicable procedure. Formation of excimers was also obsd. In order to obtain guidance for improving mol. packing by a minor structural modification, calcns. by a simplified frontier orbital method were used to find all local maxima of singlet fission rate as a function of geometry of a mol. pair. The method was tested at 48 maxima by comparison with the ab initio Frenkel-Davydov exciton model. (c) 2019 American Institute of Physics.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitFOls77L&md5=baac68449b6fc5222a85530d568fd2cc

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      Ueda, M.; Jorner, K.; Sung, Y. M.; Mori, T.; Xiao, Q.; Kim, D.; Ottosson, H.; Aida, T.; Itoh, Y. Energetics of Baird Aromaticity Supported by Inversion of Photoexcited of Chiral [4n]Annulene Derivatives. Nat. Commun. 2017, 8, 346, DOI: 10.1038/s41467-017-00382-1

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      Energetics of Baird aromaticity supported by inversion of photoexcited chiral [4n]annulene derivatives

      Ueda Michihisa; Xiao Qi; Aida Takuzo; Itoh Yoshimitsu; Jorner Kjell; Ottosson Henrik; Sung Young Mo; Kim Dongho; Mori Tadashi; Aida Takuzo

      Nature communications
      (2017),
      8
      (1),
      346
      ISSN: .

      For the concept of aromaticity, energetic quantification is crucial. However, this has been elusive for excited-state (Baird) aromaticity. Here we report our serendipitous discovery of two nonplanar thiophene-fused chiral [4n]annulenes (Th4) COT Saddle and (Th6) CDH Screw , which by computational analysis turned out to be a pair of molecules suitable for energetic quantification of Baird aromaticity. Their enantiomers were separable chromatographically but racemized thermally, enabling investigation of the ring inversion kinetics. In contrast to (Th6) CDH Screw , which inverts through a nonplanar transition state, the inversion of (Th4) COT Saddle , progressing through a planar transition state, was remarkably accelerated upon photoexcitation. As predicted by Baird’s theory, the planar conformation of (Th4) COT Saddle is stabilized in the photoexcited state, thereby enabling lower activation enthalpy than that in the ground state. The lowering of the activation enthalpy, i.e., the energetic impact of excited-state aromaticity, was quantified experimentally to be as high as 21-22 kcal mol(-1).Baird’s rule applies to cyclic π-conjugated molecules in their excited state, yet a quantification of the involved energetics is elusive. Here, the authors show the ring inversion kinetics of two nonplanar and chiral [4n]annulenes to support Baird’s rule from an energetic point of view.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1cbhsVKgtQ%253D%253D&md5=825b23cf4008a0a4fb10e38653618bb3

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      Eckert-Maksić, M.; Vazdar, M.; Barbatti, M.; Lischka, H.; Maksić, Z. B. Automerization Reaction of Cyclobutadiene and Its Barrier Height: An Ab Initio Benchmark Multi-reference Average-Quadratic Coupled Cluster Study. J. Chem. Phys. 2006, 125, 064310, DOI: 10.1063/1.2222366

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      Automerization reaction of cyclobutadiene and its barrier height: An ab initio benchmark multireference average-quadratic coupled cluster study

      Eckert-Maksic, Mirjana; Vazdar, Mario; Barbatti, Mario; Lischka, Hans; Maksic, Zvonimir B.

      Journal of Chemical Physics
      (2006),
      125
      (6),
      064310/1-064310/9CODEN:
      JCPSA6;
      ISSN: 0021-9606.

      (American Institute of Physics)

      The problem of the double bond flipping interconversion of the two equiv. ground state structures of cyclobutadiene (CBD) is addressed at the multireference av.-quadratic coupled cluster level of theory, which is capable of optimizing the structural parameters of the ground, transition, and excited states on an equal footing. The barrier height involving both the electronic and zero-point vibrational energy contributions is 6.3 kcal mol-1, which is higher than the best earlier theor. est. of 4.0 kcal mol-1. This result is confirmed by including into the ref. space the orbitals of the CC σ bonds beyond the std. π orbital space. It places the present value into the middle of the range of the measured data (1.6-10 kcal mol-1). An adiabatic singlet-triplet energy gap of 7.4 kcal mol-1 between the transition state 1Btg and the first triplet 3A2g state is obtained. A low barrier height for the CBD automerization and a small ΔE(3A2g,1B1g) gap bear some relevance on the highly pronounced reactivity of CBD, which is briefly discussed.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xotl2itbw%253D&md5=7bd50762674678b87933cda1da6505e3

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      Bryce-Smith, D.; Gilbert, A. The Organic Photochemistry of Benzene – I. Tetrahedron 1976, 32, 1309– 1326, DOI: 10.1016/0040-4020(76)85002-8

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      Tetrahedron
      (1976),
      32
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      1309-26CODEN:
      TETRAB;
      ISSN: 0040-4020.

      A review with 113 refs.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2sXltVej&md5=4f5b65d8510cec636484fa2f5bb63355

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      Michl, J.; Thulstrup, E. W. Why is Azulene Blue and Anthracene White? A Simple MO Picture. Tetrahedron 1976, 32, 205– 209, DOI: 10.1016/0040-4020(76)87002-0

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      Why is azulene blue and anthracene white? A simple MO picture

      Michl, J.; Thulstrup, E. W.

      Tetrahedron
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      32
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      205-9CODEN:
      TETRAB;
      ISSN: 0040-4020.

      The longest wavelength singlet-singlet absorption band which dets. the color of the title compds. (I and II, resp.) is due to HOMO→LUMO excitation. The large difference between the lowest singlet-singlet excitation energies of I and II, which have almost identical ionization potentials and electron affinities, was interpreted by the explicit introduction of an electron repulsion term into the simple Hueckel picture in which excitation energies are expressed as orbital energy differences. The differences in the magnitude of the singlet-triplet splitting and the structural features responsible for differences between I and II are discussed.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE28XhsFSjtLk%253D&md5=50db8207db1eed4acb0ee141c2795230

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      Ottosson, H.; Kilså, K.; Chajara, K.; Piqueras, M. C.; Crespo, R.; Kato, H.; Muthas, D. Scope and Limitations of Baird’s Theory on Triplet State Aromaticity: Application to the Tuning of Singlet-Triplet Energy Gaps in Fulvenes. Chem. – Eur. J. 2007, 13, 6998– 7005, DOI: 10.1002/chem.200700362

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      Scope and limitations of Baird’s theory on triplet state aromaticity: application to the tuning of singlet-triplet energy gaps in fulvenes

      Ottosson, Henrik; Kilsa, Kristine; Chajara, Khalil; Carmen Piqueras, Mari; Crespo, Rauel; Kato, Haruhisa; Muthas, Daniel

      Chemistry – A European Journal
      (2007),
      13
      (24),
      6998-7005, S6998/1-S6998/23CODEN:
      CEUJED;
      ISSN: 0947-6539.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      Utilizing Baird’s theory on triplet state aromaticity, we show that the singlet-triplet energy gaps (ΔEST) of pentafulvenes are easily varied through substitution by as much as 36 kcal mol-1. This exploits the fact that fulvenes act as arom. chameleons in which the dipoles reverse on going from the singlet ground state (S0) to the lowest ππtriplet state (T1); thus, their electron distributions are adapted so as to achieve some aromaticity in both states. The results are based on quantum chem. calcns. with the OLYP d. functional theory method and the CASPT2 ab initio method, as well as spectroscopic detn. of ΔEST by triplet sensitization. The findings can also be generalized to fulvenes other than the pentafulvenes, even though the effect is attenuated as the size of the fulvene increases. Our studies thus reveal that triplet-state aromaticity can greatly influence the properties of conjugated compds. in the T1 state.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXhtVWhu7nE&md5=f6aae8f28ca97d01bda50455b2e3056f

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      Rosenberg, M.; Ottosson, H.; Kilså, K. Influence of Excited State Aromaticity in the Lowest Excited Singlet States of Fulvene Derivatives. Phys. Chem. Chem. Phys. 2011, 13, 12912– 12919, DOI: 10.1039/c0cp02821e

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      Influence of excited state aromaticity in the lowest excited singlet states of fulvene derivatives

      Rosenberg, Martin; Ottosson, Henrik; Kilsa, Kristine

      Physical Chemistry Chemical Physics
      (2011),
      13
      (28),
      12912-12919CODEN:
      PPCPFQ;
      ISSN: 1463-9076.

      (Royal Society of Chemistry)

      The absorption spectra and excited state dipole moments of four differently substituted fulvenes have been investigated both exptl. and computationally. The results reveal that the excited state dipole moment of fulvenes reverses in the first excited singlet state when compared to the ground state. The oppositely polarized electron d. distributions, which dominate the ground state and the first excited singlet state of fulvenes, resp., reflect the reversed π-electron counting rules for aromaticity in the two states (4n + 2 vs. 4n, resp.). The results show that substituents indeed influence the polarity of fulvenes in the two states, however, cooperative interactions between the substituents and the fulvene moiety are most pronounced in the ground state.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXosVWju7w%253D&md5=a98bb2bea600d477e5aa074422c890ad

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      Jorner, K.; Emanuelsson, R.; Dahlstrand, C.; Tong, H.; Denisova, A. V.; Ottosson, H. Impact of Ground and Excited State Aromaticity on Silole and Cyclopentadiene Excitation Energies and Excited State Polarities. Chem. – Eur. J. 2014, 20, 9295– 9303, DOI: 10.1002/chem.201402577

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      Impact of Ground- and Excited-State Aromaticity on Cyclopentadiene and Silole Excitation Energies and Excited-State Polarities

      Jorner, Kjell; Emanuelsson, Rikard; Dahlstrand, Christian; Tong, Hui; Denisova, Aleksandra V.; Ottosson, Henrik

      Chemistry – A European Journal
      (2014),
      20
      (30),
      9295-9303CODEN:
      CEUJED;
      ISSN: 0947-6539.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      A new qual. model for estg. the properties of substituted cyclopentadienes and siloles in their lowest ππexcited states is introduced and confirmed through quantum chem. calcns., and then applied to explain earlier reported exptl. excitation energies. According to model, which is based on excited-state aromaticity and antiaromaticity, siloles and cyclopentadienes are cross-hyperconjugated arom. chameleons that adapt their electronic structures to conform to the various aromaticity rules in different electronic states (Hueckel’s rule in the π2 electronic ground state (S0) and Baird’s rule in the lowest ππexcited singlet and triplet states (S1 and T1)). By using pen-and-paper arguments, one can explain polarity changes upon excitation of substituted cyclopentadienes and siloles, and one can tune their lowest excitation energies by combined considerations of ground- and excited-state aromaticity/antiaromaticity effects. Finally, the arom. chameleon model can be extended to other monocyclic compd. classes of potential use in org. electronics, thereby providing a unified view of the S0, T1, and S1 states of a range of different cyclic cross-π-conjugated and cross-hyperconjugated compd. classes.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtFWns7%252FP&md5=dbf6a578035ae514213747fe5e5745fb

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      Yu, D.; Rong, C.; Lu, T.; De Proft, F.; Liu, S. Baird’s Rule in Substituted Fulvene Derivatives: An Information-Theoretic Study on Triplet-State Aromaticity and Antiaromaticity. ACS Omega 2018, 3, 18370– 18379, DOI: 10.1021/acsomega.8b02881

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      Baird’s Rule in Substituted Fulvene Derivatives: An Information-Theoretic Study on Triplet-State Aromaticity and Antiaromaticity

      Yu, Donghai; Rong, Chunying; Lu, Tian; De Proft, Frank; Liu, Shubin

      ACS Omega
      (2018),
      3
      (12),
      18370-18379CODEN:
      ACSODF;
      ISSN: 2470-1343.

      (American Chemical Society)

      Originated from the cyclic delocalization of electrons resulting in extra stability and instability, aromaticity and antiaromaticity are important chem. concepts whose appreciation and quantification are still much of recent interest in the literature. Employing information-theoretic quantities can provide us with more insights and better understanding about them, as we have previously demonstrated. In this work, we examine the triplet-state aromaticity and antiaromaticity, which are governed by Baird’s 4n rule, instead of H.ovrddot.uckel’s 4n + 2 rule for the singlet state. To this end, we have made use of 4 different aromaticity indexes and 8 information-theoretic quantities, examd. a total of 22 substituted fulvene derivs., and compared the results both in singlet and triplet states. It is found that cross-correlations of these two categories of mol. property descriptors enable us to better understand the nature and propensity of aromaticity and antiaromaticity for the triplet state. Our results have not only demonstrated the existence and validity of Baird’s rule but also shown that H.ovrddot.uckel’s rule and Baird’s rule indeed share the same theor. foundation because with these cross-correlation patterns we are able to distinguish them from each other simultaneously in both singlet and triplet states. Our results should provide new insights into the nature of aromaticity and antiaromaticity in the triplet state and pave the road toward new ways to quantify this pair of important chem. concepts.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisF2gurfP&md5=513803bf6d3f6f51b1197bd2eeabe5dc

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      Yadav, S.; El Bakouri, O.; Jorner, K.; Tong, H.; Dahlstrand, C.; Solà, M.; Ottosson, H. Exploiting the Aromatic Chameleon Character of Fulvenes for Computational Design of Baird-Aromatic Triplet Ground State Compounds. Chem. – Asian J. 2019, 14, 1870– 1878, DOI: 10.1002/asia.201801821

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      Exploiting the Aromatic Chameleon Character of Fulvenes for Computational Design of Baird-Aromatic Triplet Ground State Compounds

      Yadav, Sangeeta; El Bakouri, Ouissam; Jorner, Kjell; Tong, Hui; Dahlstrand, Christian; Sola, Miquel; Ottosson, Henrik

      Chemistry – An Asian Journal
      (2019),
      14
      (10),
      1870-1878CODEN:
      CAAJBI;
      ISSN: 1861-4728.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      Due to the reversal in electron counts for aromaticity and antiaromaticity in the closed-shell singlet state (normally ground state, S0) and lowest ππtriplet state (T1 or T0), as given by Hueckel’s and Baird’s rules, resp., fulvenes are influenced by their substituents in the opposite manner in the T1 and S0 states. This effect is caused by a reversal in the dipole moment when going from S0 to T1 as fulvenes adapt to the difference in electron counts for aromaticity in various states; they are arom. chameleons. Thus, a substituent pattern that enhances (reduces) fulvene aromaticity in S0 reduces (enhances) aromaticity in T1, allowing for rationalizations of the triplet state energies (ET) of substituted fulvenes. Through quantum chem. calcns., we now assess which substituents and which positions on the pentafulvene core are the most powerful for designing compds. with low or inverted ET. As a means to increase the π-electron withdrawing capacity of cyano groups, we found that protonation at the cyano N atoms of 6,6-dicyanopentafulvenes can be a route to on-demand formation of a fulvenium dication with a triplet ground state (T0). The five-membered ring of this species is markedly Baird-arom., although less than the cyclopentadienyl cation known to have a Baird-arom. T0 state.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXislCitLg%253D&md5=56b200076c5a89ac4cb327de5d0f6fc7

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      Möllerstedt, H.; Crespo, R.; Piqueras, M. C.; Ottosson, H. Fulvenes, Fulvalenes, and Azulene: Are They Aromatic Chameleons?. J. Am. Chem. Soc. 2004, 126, 13938– 13939, DOI: 10.1021/ja045729c

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      50

      Fulvenes, fulvalenes, and azulene: are they aromatic chameleons?

      Mollerstedt Helene; Piqueras Mari Carmen; Crespo Raul; Ottosson Henrik

      Journal of the American Chemical Society
      (2004),
      126
      (43),
      13938-9
      ISSN: 0002-7863.

      On the basis of the theory of Baird on reversal of Huckel’s rule for aromaticity and antiaromaticity of annulenes when going from the electronic ground state (S0) to the lowest pipitriplet state (T1) (J. Am. Chem. Soc. 1972, 94, 4941), we argue that fulvenes, fulvalenes, and azulene are “aromatic chameleons”. The dipole moments of fulvenes in T1 should be of comparable magnitude to those of S0, but due to the reversal of Huckel’s aromaticity rule in T1, their dipole should be in the opposite direction. Thereby, they are capable of adopting some aromaticity in both the T1 and S0 states as they adapt their dipolar resonance structures. The same applies to fulvalenes and azulene in their lowest quintet states (Q1) when compared to S0. Our hypothesis on chameleon behavior is supported by quantum chemical OLYP, CASSCF, and CASPT2 calculations of dipole moments, pi-orbital populations, and energies.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BD2crmtlSnsw%253D%253D&md5=6ada97f5aed47cd51272b76fd46cec4f

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      Solel, E.; Kozuch, S. Tuning the Spin, Aromaticity, and Quantum Tunneling in Computationally Designed Fulvalenes. J. Org. Chem. 2018, 83, 10826– 10834, DOI: 10.1021/acs.joc.8b01541

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      51

      Tuning the Spin, Aromaticity, and Quantum Tunneling in Computationally Designed Fulvalenes

      Solel, Ephrath; Kozuch, Sebastian

      Journal of Organic Chemistry
      (2018),
      83
      (18),
      10826-10834CODEN:
      JOCEAH;
      ISSN: 0022-3263.

      (American Chemical Society)

      Pentafulvalene is a sym. unsatd. hydrocarbon built from two five-membered rings connected by an exocyclic double bond, where each ring is one electron short of being a 6π-electron arom. system. Here, we show computationally that by selectively introducing electron withdrawing and donating substituents, we can design pentafulvalene derivs. that exhibit tunable aromaticity properties. Pentafulvalene can be shaped into a species with connected arom.-antiarom. rings, which can also achieve π-bond shifting by carbon tunneling. We propose an NMR technique that can exptl. prove such tunneling mechanism. In addn., we devised a doubly arom. fulvalene involving both H.ovrddot.uckel and Baird aromaticities. These results can open possibilities to create novel mols. in terms of spin state, aromaticity, and reactivity by quantum tunneling.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhsFejsL3L&md5=befaf110854ae53c7119a7a3d89f16b3

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      Breslow, R.; Chang, H. W.; Hill, R.; Wasserman, E. Stable Triplet States of Some Cyclopentadienyl Cations. J. Am. Chem. Soc. 1967, 89, 1112– 1119, DOI: 10.1021/ja00981a015

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      Stable triplet states of some cyclopentadienyl cations

      Breslow, Ronald; Chang, Hai Won; Hill, Roger; Wasserman, Edel

      Journal of the American Chemical Society
      (1967),
      89
      (5),
      1112-19CODEN:
      JACSAT;
      ISSN: 0002-7863.

      A no. of cyclopentadienyl cations have been prepd. in soln., and for all of them a triplet state has been detected. This is the ground state for the pentachloro cation (I), a low-lying excited state for the pentaphenyl cation (II, R=Ph), and a somewhat higher state for less sym. cations (II, R=p-MeOC6H4, p-ClC6H4 Me, β-naphthyl, p-MeC6H4). The methods used for detection include E.S.R. spectra of frozen solns., magnetic susceptibility detns., and an N.M.R. method. 20 references.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF2sXmsV2ltQ%253D%253D&md5=50f42b99fe9594c840b83d3e1b010a1e

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      Antiaromaticity

      Breslow, Ronald

      Accounts of Chemical Research
      (1973),
      6
      (12),
      393CODEN:
      ACHRE4;
      ISSN: 0001-4842.

      A review with 38 refs.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2cXis1eqsQ%253D%253D&md5=090a552d977463ce6175e9c2823840b1

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      Wörner, H. J.; Merkt, F. Photoelectron Spectroscopic Study of the First Singlet and Triplet States of the Cyclopentadienyl Cation. Angew. Chem., Int. Ed. 2006, 45, 293– 296, DOI: 10.1002/anie.200503032

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      Photoelectron spectroscopic study of the first singlet and triplet states of the cyclopentadienyl cation

      Worner, Hans Jakob; Merkt, Frederic

      Angewandte Chemie, International Edition
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      45
      (2),
      293-296CODEN:
      ACIEF5;
      ISSN: 1433-7851.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      The pulsed-field ionization zero-kinetic-energy photoelectron spectrum of the C5H5 radical is recorded after direct excitation from the ~X 2E”1 ground state and two-photon excitation via the ~A 2A”2 electronically excited state. The intensity distributions of the spectra enables the characterization of the energetics, symmetry, and structure of the lowest two electronic states of the cation.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xlslyksg%253D%253D&md5=ab491b0b14470afb559019afeae7b4ef

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      Conrad-Burton, F. S.; Liu, T.; Geyer, F.; Costantini, R.; Schlaus, A. P.; Spencer, M. S.; Wang, J.; Sanchez, R. H.; Zhang, B.; Xu, Q.; Steigerwald, M. L.; Xiao, S.; Li, H.; Nuckolls, C. P.; Zhu, X. Controlling Singlet Fission by Molecular Contortion. J. Am. Chem. Soc. 2019, 141, 13143– 13147, DOI: 10.1021/jacs.9b05357

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      Controlling singlet fission by molecular contortion

      Conrad-Burton, Felisa S.; Liu, Taifeng; Geyer, Florian; Costantini, Roberto; Schlaus, Andrew P.; Spencer, Michael S.; Wang, Jue; Sanchez, Raul Hernandez; Zhang, Boyuan; Xu, Qizhi; Steigerwald, Michael L.; Xiao, Shengxiong; Li, Hexing; Nuckolls, Colin P.; Zhu, Xiaoyang

      Journal of the American Chemical Society
      (2019),
      141
      (33),
      13143-13147CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      Singlet fission, the generation of two triplet excited states from the absorption of a single photon, may potentially increase solar energy conversion efficiency. A major roadblock in realizing this potential is the limited no. of mols. available with high singlet fission yields and sufficient chem. stability. Here, we demonstrate a strategy for developing singlet fission materials in which we start with a stable mol. platform and use strain to tune the singlet and triplet energies. Using perylene diimide as a model system, we tune the singlet fission energetics from endoergic to exoergic or iso-energetic by straining the mol. backbone. The result is an increase in the singlet fission rate by 2 orders of magnitude. This demonstration opens a door to greatly expanding the mol. toolbox for singlet fission.

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      Solà, M. Forty Years of Clar’s Aromatic π-Sextet Rule. Front. Chem. 2013, 1, 22, DOI: 10.3389/fchem.2013.00022

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      Forty years of Clar’s aromatic π-sextet rule

      Sola Miquel

      Frontiers in chemistry
      (2013),
      1
      (),
      22
      ISSN: 2296-2646.

      In 1972 Erich Clar formulated his aromatic π-sextet rule that allows discussing qualitatively the aromatic character of benzenoid species. Now, 40 years later, Clar’s aromatic π-sextet rule is still a source of inspiration for many chemists. This simple rule has been validated both experimentally and theoretically. In this review, we select some particular examples to highlight the achievement of Clar’s aromatic π-sextet rule in many situations and we discuss two recent successful cases of its application.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC2cflvVGmuw%253D%253D&md5=9fe5e8101921ef264034c40046a70b9d

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      El
      Bakouri, O.; Poater, J.; Feixas, F.; Solà, M. Exploring the Validity of the Glidewell–Lloyd Extension of Clar’s π-Sextet Rule: Assessment from Polycyclic Conjugated Hydrocarbons. Theor. Chem. Acc. 2016, 135, 205, DOI: 10.1007/s00214-016-1970-1

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      Ayub, R.; Bakouri, O. E.; Jorner, K.; Solà, M.; Ottosson, H. Can Baird’s and Clar’s Rules Combined Explain Triplet State Energies of Polycyclic Conjugated Hydrocarbons with Fused 4nπ- and (4n+2)π-Rings?. J. Org. Chem. 2017, 82, 6327– 6340, DOI: 10.1021/acs.joc.7b00906

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      59

      Can Baird’s and Clar’s Rules Combined Explain Triplet State Energies of Polycyclic Conjugated Hydrocarbons with Fused 4nπ- and (4n + 2)π-Rings?

      Ayub, Rabia; El Bakouri, Ouissam; Jorner, Kjell; Sola, Miquel; Ottosson, Henrik

      Journal of Organic Chemistry
      (2017),
      82
      (12),
      6327-6340CODEN:
      JOCEAH;
      ISSN: 0022-3263.

      (American Chemical Society)

      Compds. that can be labeled as “arom. chameleons” are π-conjugated compds. that are able to adjust their π-electron distributions so as to comply with the different rules of aromaticity in different electronic states. We used quantum chem. calcns. to explore how the fusion of benzene rings onto arom. chameleonic units represented by biphenylene, dibenzocyclooctatetraene, and dibenzo[a,e]pentalene modifies the first triplet excited states (T1) of the compds. Decreases in T1 energies are obsd. when going from isomers with linear connectivity of the fused benzene rings to those with cis- or trans-bent connectivities. The T1 energies decreased down to those of the parent (isolated) 4nπ-electron units. Simultaneously, we observe an increased influence of triplet state aromaticity of the central 4n ring as given by Baird’s rule and evidenced by geometric, magnetic, and electron d. based aromaticity indexes (HOMA, NICS-XY, ACID, and FLU). Because of an influence of triplet state aromaticity in the central 4nπ-electron units, the most stabilized compds. retain the triplet excitation in Baird π-quartets or octets, enabling the outer benzene rings to adapt closed-shell singlet Clar π-sextet character. Interestingly, the T1 energies go down as the total no. of arom. cycles within a mol. in the T1 state increases.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXot1yntr4%253D&md5=cb8d23972464cea417558c657e9332ae

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      Paci, I.; Johnson, J. C.; Chen, X.; Rana, G.; Popović, D.; David, D. E.; Nozik, A. J.; Ratner, M. A.; Michl, J. Singlet Fission for Dye-Sensitized Solar Cells: Can a Suitable Sensitizer Be Found?. J. Am. Chem. Soc. 2006, 128, 16546– 16553, DOI: 10.1021/ja063980h

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      60

      Singlet Fission for Dye-Sensitized Solar Cells: Can a Suitable Sensitizer Be Found?

      Paci, Irina; Johnson, Justin C.; Chen, Xudong; Rana, Geeta; Popovic, Duska; David, Donald E.; Nozik, Arthur J.; Ratner, Mark A.; Michl, Josef

      Journal of the American Chemical Society
      (2006),
      128
      (51),
      16546-16553CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      Improvements in the efficiency of dye-sensitized photovoltaic cells are possible by using dyes capable of singlet fission into 2 triplets, thus producing 2 electron-hole pairs from a single photon. In addn. to derivs. of large alternant hydrocarbons, those of biradicals are also candidates for a favorable ordering of excited-state energy levels, E(T2), E(S1)> 2E(T1). A large no. of favorable structures was examd. by the semiempirical PPP method and some also by the time-dependent DFT method. Several candidates were identified for exptl. examn.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XhtlWmur3E&md5=1209f57bd46e51e21e69c84b2c350bfb

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      Akdag, A.; Havlas, Z.; Michl, J. Search for a Small Chromophore with Efficient Singlet Fission: Biradicaloid Heterocycles. J. Am. Chem. Soc. 2012, 134, 14624– 14631, DOI: 10.1021/ja3063327

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      Search for a Small Chromophore with Efficient Singlet Fission: Biradicaloid Heterocycles

      Akdag, Akin; Havlas, Zdenek; Michl, Josef

      Journal of the American Chemical Society
      (2012),
      134
      (35),
      14624-14631CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      Of the five small biradicaloid heterocycles whose S1, S2, T1, and T2 adiabatic excitation energies were examd. by the CASPT2/ANO-L-VTZP method, two have been found to meet the state energy criterion for efficient singlet fission and are recommended to the attention of synthetic chemists and photophysicists.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtFOisr7L&md5=41828188421bf220751c941b25e216bf

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      Minami, T.; Nakano, M. Diradical Character View of Singlet Fission. J. Phys. Chem. Lett. 2012, 3, 145– 150, DOI: 10.1021/jz2015346

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      Diradical Character View of Singlet Fission

      Minami, Takuya; Nakano, Masayoshi

      Journal of Physical Chemistry Letters
      (2012),
      3
      (2),
      145-150CODEN:
      JPCLCD;
      ISSN: 1948-7185.

      (American Chemical Society)

      The feasibility conditions of singlet fission on the excitation energy differences are revealed as functions of the multiple diradical characters yi [defined by the occupation nos. of the LUNO (=Lowest Unoccupied Natural Orbital) + i (i=0, 1, …), where 0 ≤ yi ≤ 1 and yi ≥ yj (i> j)] using the linear H4 full CI model. The diradical characters suited for singlet fission are found to lie in the region with y0> 0.10 except for y0 ∼ y1, though its energy efficiency is better in case of smaller y0, to which diradical and multiradical compds. with low/intermediate diradical characters such as open-shell singlet polycyclic arom. hydrocarbons belong. These findings indicate that the multiple diradical character is an effective indicator for exploring mol. systems for efficient singlet fission.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhs1Ojur3L&md5=76b624a9c479e109deb646a65856640e

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      Ito, S.; Nagami, T.; Nakano, M. Diradical Character-Based Design for Singlet Fission of Bisanthene Derivatives: Aromatic-Ring Attachment and π-Plane Twisting. J. Phys. Chem. Lett. 2016, 7, 3925– 390, DOI: 10.1021/acs.jpclett.6b01885

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      Diradical Character-Based Design for Singlet Fission of Bisanthene Derivatives: Aromatic-Ring Attachment and π-Plane Twisting

      Ito, Soichi; Nagami, Takanori; Nakano, Masayoshi

      Journal of Physical Chemistry Letters
      (2016),
      7
      (19),
      3925-3930CODEN:
      JPCLCD;
      ISSN: 1948-7185.

      (American Chemical Society)

      We demonstrate a diradical character-based mol. design for singlet fission using polycyclic arom. hydrocarbons, bisanthene derivs. Two types of chem. modifications-arom.-ring attachment and π-plane twisting-are examd. in order to satisfy the energy level matching condition for singlet fission. Detailed anal. of the electronic structures of the model mols. using nucleus-independent chem. shift, MOs, and their energies has demonstrated the usefulness of the relationship between the resonance structure and aromaticity and that between nonplanarity of π-conjugated systems and redn. of orbital overlap for tuning the diradical character. This result provides a novel design guideline for polycyclic arom. hydrocarbons toward efficient singlet fission.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFWqtrbK&md5=4d4096d1b63c0045d5517449a4ee6136

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      Wirz, J. Electronic Structure and Photophysical Properties of Planar Conjugated Hydrocarbons with a 4n-Membered Ring, Part II. Jerusalem Symposia on Quantum Chemistry and Biochemistry 1977, 10, 283– 294, DOI: 10.1007/978-94-010-1273-7_24

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      Electronic structure and photophysical properties of planar conjugated hydrocarbons with a 4n-membered ring

      Wirz, Jakob

      Jerusalem Symposia on Quantum Chemistry and Biochemistry
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      10
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      283-94CODEN:
      JSQCA7;
      ISSN: 0075-3696.

      The UV of I through VI, which exhibit systematic features which differ radically from the pattern obsd. with benzenoid hydrocarbons, are assigned using a PDP-SCF-CI calcn. The assignments are corroborated by polarization measurements on III through V. The triplet rate absorption spectra and energies of III, V, and VI are detd. by flash photolysis and energy transfer expts. The fluorescence and triplet yield trends are an example of the photophys. consequences of an avoided hypersurface crossing.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE1cXhsFWrsbo%253D&md5=b3c9bf58088a0af108b358c4c37c31d4

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      Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-class Functionals and 12 Other Function. Theor. Chem. Acc. 2008, 120, 215– 241, DOI: 10.1007/s00214-007-0310-x

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      The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

      Zhao, Yan; Truhlar, Donald G.

      Theoretical Chemistry Accounts
      (2008),
      120
      (1-3),
      215-241CODEN:
      TCACFW;
      ISSN: 1432-881X.

      (Springer GmbH)

      We present two new hybrid meta exchange-correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amt. of nonlocal exchange (2X), and it is parametrized only for nonmetals. The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree-Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree-Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochem., four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for mol. excitation energies. We also illustrate the performance of these 17 methods for three databases contg. 40 bond lengths and for databases contg. 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochem., kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chem. and for noncovalent interactions.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXltFyltbY%253D&md5=c31d6f319d7c7a45aa9b716220e4a422

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      Andersson, K.; Malmqvist, P.-Å.; Roos, B. O. Second-Order Perturbation Theory with a Complete Active Space Self-Consistent Field Reference Function. J. Chem. Phys. 1992, 96, 1218– 1226, DOI: 10.1063/1.462209

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      Second-order perturbation theory with a complete active space self-consistent field reference function

      Andersson, Kerstin; Malmqvist, Per Aake; Roos, Bjoern O.

      Journal of Chemical Physics
      (1992),
      96
      (2),
      1218-26CODEN:
      JCPSA6;
      ISSN: 0021-9606.

      The recently implemented second-order perturbation theory based on a complete active space SCF ref. function has been extended by allowing the Fock-type one-electron operator, which defines the zeroth-order Hamiltonian to have nonzero elements also in nondiagonal matrix blocks. The computer implementation is now less straightforward and more computer time will be needed in obtaining the second-order energy. The method is illustrated in a series of calcns. on N2, NO, O2, CH3, CH2, and F-.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK38XptFKhsw%253D%253D&md5=9b11f4ec21a64ab3f5cfd44355156b1a

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      Zeng, T.; Hoffmann, R.; Ananth, N. The Low-Lying Electronic States of Pentacene and Their Roles in Singlet Fission. J. Am. Chem. Soc. 2014, 136, 5755– 5764, DOI: 10.1021/ja500887a

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      The Low-Lying Electronic States of Pentacene and Their Roles in Singlet Fission

      Zeng, Tao; Hoffmann, Roald; Ananth, Nandini

      Journal of the American Chemical Society
      (2014),
      136
      (15),
      5755-5764CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      We present a detailed study of pentacene monomer and dimer that serves to reconcile extant views of its singlet fission. We obtain the correct ordering of singlet excited-state energy levels in a pentacene mol. (E (S1)

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXktlens7o%253D&md5=f7a7f04cad176c35966c447e4ae956c9

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      Grotjahn, R.; Maier, T. M.; Michl, J.; Kaupp, M. Development of a TDDFT-Based Protocol with Local Hybrid Functionals for the Screening of Potential Singlet Fission Chromophores. J. Chem. Theory Comput. 2017, 13, 4984– 4996, DOI: 10.1021/acs.jctc.7b00699

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      Development of a TDDFT-Based Protocol with Local Hybrid Functionals for the Screening of Potential Singlet Fission Chromophores

      Grotjahn, Robin; Maier, Toni M.; Michl, Josef; Kaupp, Martin

      Journal of Chemical Theory and Computation
      (2017),
      13
      (10),
      4984-4996CODEN:
      JCTCCE;
      ISSN: 1549-9618.

      (American Chemical Society)

      Chromophores suitable for singlet fission need to meet specific requirements regarding the relative energies of their S0, S1, and T1 (and T2) electronic states. Accurate quantum-chem. computations of the corresponding energy differences are highly desirable for materials design. Methods based on d. functional theory (DFT) have the advantage of being applicable to larger, often more relevant systems compared to more sophisticated post-Hartree-Fock methods. However, most exchange-correlation functionals do not provide the needed accuracy, in particular, due to an insufficient description of the T1 state. Here the authors use a recent singlet fission chromophore test set to evaluate a wide range of DFT-based methods, with an emphasis on local hybrid functionals with a position-dependent exact-exchange admixt. New ref. vertical CC2/CBS benchmark excitation energies for the test set were generated, which exhibit somewhat more uniform accuracy than the previous CASPT2-based data. These CC2 ref. data were used to evaluate a wide range of functionals, comparing full linear-response TDDFT, the Tamm-Dancoff approxn. (TDA), and ΔSCF calcns. Two simple 2-parameter local hybrid functionals and the more empirical M06-2X global meta-GGA hybrid provide the overall best accuracy. Due to its lower empiricism and wide applicability, the Lh12ct-SsifPW92 local hybrid is suggested as the main ingredient of an efficient computational protocol for prediction of the relevant excitation energies in singlet fission chromophores. Full TDDFT for the S1, S2, and T2 excitations is combined with ΔSCF for the T1 excitations. Making use also of some error compensation with suitable DFT-optimized structures, even the most crit. T1 excitations can be brought close to the target accuracy of 0.20 eV, while the other excitation energies are obtained even more accurately. This fully DFT-based protocol should become a useful tool in the field of singlet fission.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhsVelu7vJ&md5=6c0e0f9703d2e210438c1029ea0900c7

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      Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; van Eikema
      Hommes, N. J. R. Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe. J. Am. Chem. Soc. 1996, 118, 6317– 6318, DOI: 10.1021/ja960582d

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      Nucleus-independent chemical shifts: a simple and efficient aromaticity probe

      Schleyer, Paul v.R.; Maerker, Christoph; Dransfeld, Alk; Jiao, Haijun; van Eikema Hommes, Nicolaas J. R.

      Journal of the American Chemical Society
      (1996),
      118
      (26),
      6317-6318CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      Nucleus-independent chem. shifts (NICS), the neg. of the abs. magnetic shieldings (in ppm) computed at the ab initio GIAO-HF/6-31 + Glevel at ring centers (non-weighted means of the heavy atom coordinates), are proposed as a simple and efficient magnetic probe for characterizing aromaticity and antiaromaticity. For a series of five membered heterocycles, NICS correlate with arom. stabilization energies, magnetic susceptibility exaltations, and geometric criteria of aromaticity. Arom. compds. have neg. NICS (e.g., -9.7 for benzene and -15.1 for pyrrole), whereas antiarom. systems, in contrast, exhibit pos. NICS values (18.1 for pentalene and 27.6 for cyclobutadiene). In addn., NICS can characterize the individual rings in polycyclic arom. (e.g., -19.7 and -7.0 for the five- and seven-membered rings in azulene) and antiarom. (e.g., -2.5 and 22.5 for the six- and four-membered rings in benzocyclobutadiene) systems as well as the spherical aromaticity of cage compds., e.g., closo-B12H122- (-34.4) and the 1,3-dehydro-5,7-adamantanediyl dication (-50.1). The C60 NICS confirm that the 5-rings are paramagnetic and the 6-rings are diamagnetic, but the magnitudes are not large.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XjsFCis7Y%253D&md5=fd205be78733a8f593307d4863afb340

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      Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Which NICS Aromaticity Index for Planar π Rings Is Best?. Org. Lett. 2006, 8, 863– 866, DOI: 10.1021/ol0529546

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      Which NICS Aromaticity Index for Planar π Rings Is Best?

      Fallah-Bagher-Shaidaei, Hossein; Wannere, Chaitanya S.; Corminboeuf, Clemence; Puchta, Ralph; Schleyer, Paul v. R.

      Organic Letters
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      8
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      863-866CODEN:
      ORLEF7;
      ISSN: 1523-7060.

      (American Chemical Society)

      Five increasingly sophisticated aromaticity indexes, based on nucleus-independent chem. shifts (NICS), were evaluated against a uniform set of arom. stabilization energies (ASE) for 75 mono- and polyheterocyclic five-membered rings. While acceptable statistical correlations were given by all of the NICS methods, the most fundamentally grounded index, NICS(0)πzz (based on the π contribution to the out-of-plane zz tensor component), performed best statistically (cc=0.980) and in practice. The easily computable NICS(1)zz index is a useful alternative (cc=0.968).

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XpsVKgtQ%253D%253D&md5=c83cb9ff9c976543f65e5c7f05ec92d6

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      Wolinski, Krzysztof; Hinton, James F.; Pulay, Peter

      Journal of the American Chemical Society
      (1990),
      112
      (23),
      8251-60CODEN:
      JACSAT;
      ISSN: 0002-7863.

      An implementation of the gauge independent at. orbital (GIAO) method for the ab initio SCF calcn. of NMR chem. shifts is described. By using modern techniques borrowed from anal. deriv. methods, the efficiency of the GIAO method was significantly improved. Results with several basis sets, some of them large, are presented for methane, Me fluoride, cyclopropene, cyclopropane, oxirane, benzene, carbon disulfide, the sulfate and thiosulfate anions, di-Me sulfide, DMSO, and di-Me sulfone. Computer timings for energy and chem. shielding calcns. are given for a few large org. mols. Comparisons are made with the individual gauge for localized orbitals method of Schindler and Kutzelnigg, and with the localized orbital/local origin method of Hansen and Bouman. The GIAO method appears to converge faster than the localized techniques, i.e., it provides the same accuracy with a smaller basis, particularly for the individual tensor components. The computational effort for the ab initio calcn. of the NMR chem. shifts is only ∼2.5 times that of the energy calcn.

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      Bultinck, P.; Rafat, M.; Ponec, R.; Van Gheluwe, B.; Carbó-Dorca, R.; Popelier, P. Electron Delocalization and Aromaticity in Linear Polyacenes: Atoms in Molecules Multicenter Delocalization Index. J. Phys. Chem. A 2006, 110, 7642– 7648, DOI: 10.1021/jp0609176

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      Electron Delocalization and Aromaticity in Linear Polyacenes: Atoms in Molecules Multicenter Delocalization Index

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      Journal of Physical Chemistry A
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      7642-7648CODEN:
      JPCAFH;
      ISSN: 1089-5639.

      (American Chemical Society)

      Mol. aromaticity in the linear polyacenes is studied using an atoms in mols. based six center index (SCI-AIM) which measures the electron delocalization. SCI-AIM values for the linear polyacenes indicate decreasing aromaticity going from outer to inner rings in the polyacene series. The SCI-AIM approach is compared to a Mulliken-like approach, and a crit. comparison to the PDI index is made.

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      Krygowski, T. M. Crystallographic Studies of Inter- and Intramolecular Interactions Reflected in Aromatic Character of π-Electron Systems. J. Chem. Inf. Model. 1993, 33, 70– 78, DOI: 10.1021/ci00011a011

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      Krygowski, T. M.; Cyranski, M. K. Structural Aspects of Aromaticity. Chem. Rev. 2001, 101, 1385– 1419, DOI: 10.1021/cr990326u

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      Krygowski, Tadeusz Marek; Cyranski, Michal Ksawery

      Chemical Reviews (Washington, D. C.)
      (2001),
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      1385-1419CODEN:
      CHREAY;
      ISSN: 0009-2665.

      (American Chemical Society)

      A review, with 240 refs. in which the importance of a notion in the chem. vocabulary and an outline of the criteria of aromaticity is discussed.

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      Bearpark, M. J.; Bernardi, F.; Olivucci, M.; Robb, M. A.; Smith, B. R. Can Fulvene S₁ Decay Be Controlled? A CASSCF Study with MMVB Dynamics. J. Am. Chem. Soc. 1996, 118, 5254– 5260, DOI: 10.1021/ja9542799

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      Can Fulvene S1 Decay Be Controlled? A CASSCF Study with MMVB Dynamics

      Bearpark, Michael J.; Bernardi, Fernando; Olivucci, Massimo; Robb, Michael A.; Smith, Barry R.

      Journal of the American Chemical Society
      (1996),
      118
      (22),
      5254-5260CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      CASSCF and CASMP2 calcns. show that the min. on the fulvene S1 potential energy surface is an S0/S1 conical intersection with a 90° twisted methylene group. We have also located a distinct planar azulene-like crossing point at higher energy, where the methylene is free to twist. The fulvene intersection – which exists for all twist angles – leads to efficient, irreversible radiationless decay and explains the lack of obsd. S1 fluorescence. We have modeled the femtosecond excited state motion leading to ultrafast decay that would be initiated by exciting the 0-0 and higher vibrational levels using semiclassical mol. dynamics with a hybrid quantum-mech./force-field potential (MMVB). Our simulation suggests that, with increased vibrational energy, decay occurs in the planar crossing region before relaxation by twisting can take place, and that isomerization might only be seen by pumping the 0-0 transition in laser studies.

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      Mendive-Tapia, D.; Lasorne, B.; Worth, G. A.; Bearpark, M. J.; Robb, M. A. Controlling the Mechanism of Fulvene S₁/S₀ Decay: Switching Off the Stepwise Population Transfer. Phys. Chem. Chem. Phys. 2010, 12, 15725– 15733, DOI: 10.1039/c0cp01757d

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      Controlling the mechanism of fulvene S1/S0 decay: switching off the stepwise population transfer

      Mendive-Tapia, David; Lasorne, Benjamin; Worth, Graham A.; Bearpark, Michael J.; Robb, Michael A.

      Physical Chemistry Chemical Physics
      (2010),
      12
      (48),
      15725-15733CODEN:
      PPCPFQ;
      ISSN: 1463-9076.

      (Royal Society of Chemistry)

      Direct quantum dynamics simulations were performed to model the radiationless decay of the first excited state S1 of fulvene. The full space of thirty normal mode nuclear coordinates was explicitly considered. By default, ultrafast internal conversion takes place centered on the higher-energy planar region of the S1/S0 conical intersection seam, giving the stepwise population transfer characteristic of a sloped surface crossing, and leading back to the ground state reactant. Two possible schemes for controlling whether stepwise population transfer occurs or not-either altering the initial geometry distribution or the initial momentum compn. of the photo-excited wavepacket-were explored. In both cases, decay was successfully induced to occur in the lower-energy twisted/peaked region of the crossing seam, switching off the stepwise population transfer. This absence of re-crossing is a direct consequence of the change in the position on the intersection at which decay occurs (our target for control), and its consequences should provide an exptl. observable fingerprint of this system.

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      Gogonea, V.; Schleyer, P. v. R.; Schreiner, P. R. Consequences of Triplet Aromaticity in 4nπ-Electron Annulenes: Calculation of Magnetic Shieldings for Open-Shell Species. Angew. Chem., Int. Ed. 1998, 37, 1945– 1948, DOI: 10.1002/(SICI)1521-3773(19980803)37: 13/143.0.CO;2-E

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      Consequences of triplet aromaticity in 4nπ-electron annulenes: calculation of magnetic shieldings for open-shell species

      Gogonea, Valentin; Schleyer, Paul von Rague; Schreiner, Peter R.

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      (1998),
      37
      (13/14),
      1945-1948CODEN:
      ACIEF5;
      ISSN: 1433-7851.

      (Wiley-VCH Verlag GmbH)

      This paper presents evidence that triplet states of 4nπ-electron annulenes are arom. The first comprehensive ab initio [B3LYP and CCSD(T) levels] calcns. of adiabatic singlet-triplet sepns., arom. stabilization energies, and the magnetic properties of six neutral or charged 4nπ-electron annulenes are reported. Chem. shifts, magnetic susceptibilities, and magnetic susceptibility exaltations for singlet and triplet species were calcd. at the GIAO-SCF level.

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      Villaume, S.; Fogarty, H. A.; Ottosson, H. Triplet-State Aromaticity of 4n -Electron Monocycles: Analysis of Bifurcation in the π Contribution to the Electron Localization Function. ChemPhysChem 2008, 9, 257– 264, DOI: 10.1002/cphc.200700540

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      Triplet-state aromaticity of 4nπ-electron monocycles: analysis of bifurcation in the π contribution to the electron localization function

      Villaume, Sebastien; Fogarty, Heather A.; Ottosson, Henrik

      ChemPhysChem
      (2008),
      9
      (2),
      257-264CODEN:
      CPCHFT;
      ISSN: 1439-4235.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      The π contribution to the electron localization function (ELF) is used to compare 4nπ- and (4n + 2)π-electron annulenes, with particular focus on the aromaticity of 4nπ-electron annulenes in their lowest triplet state. The anal. is performed on the electron d. obtained at the level of OLYP d. functional theory, as well as at the CCSD and CASSCF ab initio levels. Two criteria for aromaticity of all-carbon annulenes are set up: the span in the bifurcation values ΔBV(ELFπ) should be small, ideally zero, and the bifurcation value for ring closure of the π basin RCBV(ELFπ) should be high (≥ 0.7). From these criteria, nearly all 4nπ-electron annulenes are arom. in their lowest triplet states, similar to (4n + 2)π-electron annulenes in their singlet ground states. For singlet biradical cyclobutadiene and cyclooctatetraene constrained to D4h and D8h symmetry, resp., the RCBV(ELFπ) at the CASSCF level is lower (0.531 and 0.745) than for benzene (0.853), even though they have equal proportions of α- and β-electrons.

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      Gao, X.; Bai, S.; Fazzi, D.; Niehaus, T.; Barbatti, M.; Thiel, W. Evaluation of Spin-Orbit Couplings with Linear-Response Time-Dependent Density Functional Methods. J. Chem. Theory Comput. 2017, 13, 515– 524, DOI: 10.1021/acs.jctc.6b00915

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      Evaluation of Spin-Orbit Couplings with Linear-Response Time-Dependent Density Functional Methods

      Gao, Xing; Bai, Shuming; Fazzi, Daniele; Niehaus, Thomas; Barbatti, Mario; Thiel, Walter

      Journal of Chemical Theory and Computation
      (2017),
      13
      (2),
      515-524CODEN:
      JCTCCE;
      ISSN: 1549-9618.

      (American Chemical Society)

      A new versatile code based on Python scripts was developed to calc. spin-orbit coupling (SOC) elements between singlet and triplet states. The code, named PySOC, is interfaced to third-party quantum chem. packages, such as Gaussian 09 and DFTB+. SOCs are evaluated using linear-response (LR) methods based on time-dependent d. functional theory (TDDFT), the Tamm-Dancoff approxn. (TDA), and time-dependent d. functional tight binding (TD-DFTB). The evaluation employs Casida-type wave functions and the Breit-Pauli (BP) spin-orbit Hamiltonian with an effective charge approxn. For validation purposes, SOCs calcd. with PySOC are benchmarked for several org. mols., with SOC values spanning several orders of magnitudes. The computed SOCs show little variation with the basis set, but are sensitive to the chosen d. functional. The benchmark results are in good agreement with ref. data obtained using higher-level spin-orbit Hamiltonians and electronic structure methods, such as CASPT2 and DFT/MRCI. PySOC can be easily interfaced to other third-party codes and other methods yielding CI-type wave functions.

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      Samanta, P. K.; Kim, D.; Coropceanu, V.; Brédas, J. L. Up-Conversion Intersystem Crossing Rates in Organic Emitters for Thermally Activated Delayed Fluorescence: Impact of the Nature of Singlet vs Triplet Excited States. J. Am. Chem. Soc. 2017, 139, 4042– 4051, DOI: 10.1021/jacs.6b12124

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      Up-Conversion Intersystem Crossing Rates in Organic Emitters for Thermally Activated Delayed Fluorescence: Impact of the Nature of Singlet vs. Triplet Excited States

      Samanta, Pralok K.; Kim, Dongwook; Coropceanu, Veaceslav; Bredas, Jean-Luc

      Journal of the American Chemical Society
      (2017),
      139
      (11),
      4042-4051CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      The rates for up-conversion intersystem crossing (UISC) from the T1 state to the S1 state are calcd. for a series of org. emitters with an emphasis on thermally activated delayed fluorescence (TADF) materials. Both the spin-orbit coupling and the energy difference between the S1 and T1 states (ΔEST) are evaluated, at the d. functional theory (DFT) and time-dependent DFT levels. The calcd. UISC rates and ΔEST values are in good agreement with available exptl. data. The authors’ results underline that small ΔEST values and sizable spin-orbit coupling matrix elements have to be simultaneously realized to facilitate UISC and ultimately TADF. Importantly, the spatial sepn. of the highest occupied and lowest unoccupied MOs of the emitter, a widely accepted strategy for the design of TADF mols., does not necessarily lead to a sufficient redn. in ΔEST; in fact, either a significant charge-transfer (CT) contribution to the T1 state or a minimal energy difference between the local-excitation and charge-transfer triplet states is required to achieve a small ΔEST. Also, having S1 and T1 states of a different nature is found to strongly enhance spin-orbit coupling, which is consistent with the El-Sayed rule for ISC rates. Overall, the authors’ results indicate that having either similar energies for the local-excitation and charge-transfer triplet states or the right balance between a substantial CT contribution to T1 and somewhat different natures of the S1 and T1 states, paves the way toward UISC enhancement and thus TADF efficiency improvement.

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      Marian, C. M. Spin-Orbit Coupling and Intersystem Crossing in Molecules. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012, 2, 187– 203, DOI: 10.1002/wcms.83

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      Spin-orbit coupling and intersystem crossing in molecules

      Marian, Christel M.

      Wiley Interdisciplinary Reviews: Computational Molecular Science
      (2012),
      2
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      187-203CODEN:
      WIRCAH;
      ISSN: 1759-0884.

      (Wiley-Blackwell)

      A review. Many light-induced mol. processes involve a change in spin state and are formally forbidden in non-relativistic quantum theory. To make them happen, spin-orbit coupling (SOC) has to be invoked. Intersystem crossing (ISC), the nonradiative transition between two electronic states of different multiplicity, plays a key role in photochem. and photophysics with a broad range of applications including mol. photonics, biol. photosensors, photodynamic therapy, and materials science. Quantum chem. has become a valuable tool for gaining detailed insight into the mechanisms of ISC. After a short introduction highlighting the importance of ISC and a brief description of the relativistic origins of SOC, this article focusses on approx. SOC operators for practical use in mol. applications and reviews state-of-the-art theor. methods for evaluating ISC rates. Finally, a few sample applications are discussed that underline the necessity of studying the mechanisms of ISC processes beyond qual. rules such as the El-Sayed rules and the energy gap law.

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      Finke, A. D.; Jahn, B. O.; Saithalavi, A.; Dahlstrand, C.; Nauroozi, D.; Haberland, S.; Gisselbrecht, J.-P.; Boudon, C.; Mijangos, E.; Schweizer, W. B.; Ott, S.; Ottosson, H.; Diederich, F. The 6,6-Dicyanopentafulvene Core: A Template for the Design of Electron-Acceptor Compounds. Chem. – Eur. J. 2015, 21, 8168– 8176, DOI: 10.1002/chem.201500379

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      The 6,6-Dicyanopentafulvene Core: A Template for the Design of Electron-Acceptor Compounds

      Finke, Aaron D.; Jahn, Burkhard O.; Saithalavi, Anas; Dahlstrand, Christian; Nauroozi, Djawed; Haberland, Sophie; Gisselbrecht, Jean-Paul; Boudon, Corinne; Mijangos, Edgar; Schweizer, W. Bernd; Ott, Sascha; Ottosson, Henrik; Diederich, Francois

      Chemistry – A European Journal
      (2015),
      21
      (22),
      8168-8176CODEN:
      CEUJED;
      ISSN: 0947-6539.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      The electron-accepting ability of 6,6-dicyanopentafulvenes (DCFs) can be varied extensively through substitution on the five-membered ring. The redn. potentials for a set of 2,3,4,5-tetraphenyl-substituted DCFs, with varying substituents at the para-position of the Ph rings, strongly correlate with their Hammett σp-parameters. By combining cyclic voltammetry with DFT calcns. ((U)B3LYP/6-311+G(d)), using the conductor-like polarizable continuum model (CPCM) for implicit solvation, the abs. redn. potentials of a set of twenty DCFs were reproduced with a mean abs. deviation of 0.10 eV and a max. deviation of 0.19 eV. The exptl. studied DCFs have redn. potentials within 3.67-4.41 eV, however, the computations reveal that DCFs with exptl. redn. potentials ≤5.3 eV could be achieved, higher than that of F4-TCNQ (5.02 eV). Thus, the DCF core is a template that allows variation in the redn. potentials by ∼1.6 eV.

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      Sekiguchi, A.; Tanaka, M.; Matsuo, T.; Watanabe, H. From a Cyclobutadiene Dianion to a Cyclobutadiene: Synthesis and Structural Characterization of Tetrasilyl-Substituted Cyclobutadiene. Angew. Chem., Int. Ed. 2001, 40, 1675– 1677, DOI: 10.1002/1521-3773(20010504)40:93.0.CO;2-G

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      From a cyclobutadiene dianion to a cyclobutadiene: synthesis and structural characterization of tetrasilyl-substituted cyclobutadiene

      Sekiguchi, Akira; Tanaka, Masanobu; Matsuo, Tsukasa; Watanabe, Hidetoshi

      Angewandte Chemie, International Edition
      (2001),
      40
      (9),
      1675-1677CODEN:
      ACIEF5;
      ISSN: 1433-7851.

      (Wiley-VCH Verlag GmbH)

      Lithiation of tetrasilyl cyclobutadiene cobalt complex I with lithium in THF followed by reaction with BrCH2CH2Br gave cyclobutadiene deriv. II which on photolysis gave cyclododecadiyne III. The crystal structure of II was detd.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXjslChurY%253D&md5=135e594aa9c206992860456c9e19a014

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      Maier, G.; Neudert, J.; Wolf, O. Tetrakis(Trimethylsilyl)Cyclobutadiene and Tetrakis(Trimethylsilyl)Tetrahedrane. Angew. Chem., Int. Ed. 2001, 40, 1674– 1675, DOI: 10.1002/1521-3773(20010504)40:93.0.CO;2-I

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      Tetrakis(trimethylsilyl)cyclobutadiene and tetrakis(trimethylsilyl)tetrahedrane

      Maier, Gunther; Neudert, Jorg; Wolf, Oliver

      Angewandte Chemie, International Edition
      (2001),
      40
      (9),
      1674-1675CODEN:
      ACIEF5;
      ISSN: 1433-7851.

      (Wiley-VCH Verlag GmbH)

      Coupling reaction of tris(trimethylsilyl)cyclopropenylium hexachloroantimonate with lithiated (trimethylsilyl)diazomethane gave 11% trimethylsilyl[1,2,3-tris(trimethylsilyl)-2-cyclopropen-1-yl]diazomethane which on thermolysis at 50° gave tetrakis(trimethylsilyl)cyclobutadiene (8) along-with Me3SiN:C:C(SiMe3)C(SiMe3):C:NSiMe3. Irradn. of a mixt. of 8 gave title tetrakis(trimethylsilyl)tetrahedrane.

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      Hafner, K.; Süss, H. U. 1,3,5-Tri- Tert-Butylpentalene. A Stabilized Planar 8π-Electron System. Angew. Chem., Int. Ed. Engl. 1973, 12, 575– 577, DOI: 10.1002/anie.197305751

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      Levi, Z. U.; Tilley, T. D. Versatile Synthesis of Pentalene Derivatives via the Pd-Catalyzed Homocoupling of Haloenynes. J. Am. Chem. Soc. 2009, 131, 2796– 2797, DOI: 10.1021/ja809930f

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      Versatile Synthesis of Pentalene Derivatives via the Pd-Catalyzed Homocoupling of Haloenynes

      Levi, Zerubba U.; Tilley, T. Don

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      131
      (8),
      2796-2797CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      A palladium-catalyzed, reductive homocoupling of haloenynes, e.g. ArC≡CPh (Ar=2-BrC6H4, 2-Br-3-thienyl), yields a diverse range of polysubstituted pentalene derivs., including annulated dibenzopentalenes, e.g. I, and dithienylpentalenes, e.g. II.

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      Miyamoto, T.; Odaira, Y. The Reaction of Phenanthro[ζ]cyclobutadiene. Tetrahedron Lett. 1973, 14, 43– 46, DOI: 10.1016/S0040-4039(01)95572-8

  88. 88

      Wu, Y.; Wang, Y.; Chen, J.; Zhang, G.; Yao, J.; Zhang, D.; Fu, H. Intramolecular Singlet Fission in an Antiaromatic Polycyclic Hydrocarbon. Angew. Chem., Int. Ed. 2017, 56, 9400– 9404, DOI: 10.1002/anie.201704668

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      Intramolecular singlet fission in an antiaromatic polycyclic hydrocarbon

      Wu, Yishi; Wang, Yuancheng; Chen, Jianwei; Zhang, Guanxin; Yao, Jiannian; Zhang, Deqing; Fu, Hongbing

      Angewandte Chemie, International Edition
      (2017),
      56
      (32),
      9400-9404CODEN:
      ACIEF5;
      ISSN: 1433-7851.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      Singlet fission (SF), in which one singlet exciton (S1) splits into two triplets (T1) on adjacent mols. through a correlated triplet-pair 1(TT) state, requires precise but difficult tuning of exciton energetics and intermol. electronic couplings in the solid state. Antiarom. 4nπ dibenzopentalenes (DPs) are demonstrated as a new class of single-chromophore-based intramol. SF materials that exhibit an optically allowed S2 state with E(S2)> 2 × E(T1) and an optically forbidden S1 state. Ultrafast population transfer from a high-lying S2 state to a 1(TT) state was obsd. in monomeric soln. of styryl-substituted DP (SDP) on a sub-picosecond timescale. There is evidence of exciton diffusion (ED) of the 1(TT) state to yield two individual long-lived triplets in SDP thin film. The overall triplet yield via intramol. SF and subsequent triplet-pair diffusion can be as high as 142 ± 10 % in thin film.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhtFensr3J&md5=eadbf6ec7c2d393250af8570cee6fb44

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      Hudson, B. S.; Kohler, B. E. Polyene Spectroscopy: The Lowest Energy Excited Singlet State of Diphenyloctatetraene and Other Linear Polyenes. J. Chem. Phys. 1973, 59, 4984– 5002, DOI: 10.1063/1.1680717

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      Polyene spectroscopy. Lowest energy excited singlet state of diphenyloctatetraene and other linear polyenes

      Hudson, Bruce S.; Kohler, Bryan E.

      Journal of Chemical Physics
      (1973),
      59
      (9),
      4984-5002CODEN:
      JCPSA6;
      ISSN: 0021-9606.

      Optical absorption and emission spectra at liq. He temps. of solns. of all-trans-1,8-diphenyloctatetraene in single crystals of bibenzyl and polycryst. n-paraffin matrixes are presented which show an excited singlet state at a lower energy than the 1Bu state responsible for the strong absorption of all linear polyenes. The transition from the ground state to this level has an oscillator strength of ∼0.05. The location of this low-energy weak transition removes a no. of discrepancies between the expected and obsd. fluorescence properties of diphenyloctatetraene. The obsd. vibronic pattern is consistent with the Raman spectrum which is also reported. Substantial indirect evidence is presented which indicates that many, and perhaps all, linear polyenes have a similar ordering of excited states. A review of the available information on diphenylpolyenes is presented.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2cXhtFCntbo%253D&md5=0bff3b4e7d5e93be75e968d5fb5cb65f

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      Holtom, G. R.; McClain, W. M. Two-photon excitation spectra of the low energy excited states of diphenylhexatriene and diphenyloctatetraene. Chem. Phys. Lett. 1976, 44, 436– 439, DOI: 10.1016/0009-2614(76)80699-9

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      Two-photon excitation spectra of the low energy excited states of diphenylhexatriene and diphenyloctatetraene

      Holtom, G. R.; McClain, W. M.

      Chemical Physics Letters
      (1976),
      44
      (3),
      436-9CODEN:
      CHPLBC;
      ISSN: 0009-2614.

      All-trans-diphenylhexatriene and diphenyloctatetraene in soln. show a very strong 2-photon absorption beginning at about the same energy as the one-photon spectrum. This supports the postulated presence of a low-lying 1Ag electronic state.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE2sXmtlSisg%253D%253D&md5=d4c0ade0dc5e7a0a6955f4e9f4047d33

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      Fiedor, L.; Dudkowiak, A.; Pilch, M. The Origin of the Dark S₁ State in Carotenoids: A Comprehensive Model. J. R. Soc., Interface 2019, 16, 20190191, DOI: 10.1098/rsif.2019.0191

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      The origin of the dark S1 state in carotenoids: a comprehensive model

      Fiedor, Leszek; Dudkowiak, Alina; Pilch, Mariusz

      Journal of the Royal Society, Interface
      (2019),
      16
      (158),
      20190191/1-20190191/11CODEN:
      JRSICU;
      ISSN: 1742-5662.

      (Royal Society)

      A review. In carotenoids, by analogy to polyenes, the symmetry of the π-electron system is often invoked to explain their peculiar electronic features, in particular the inactivity of the S0 → S1 transition in one-photon excitation. In this review, we verify whether the mol. symmetry of carotenoids and symmetry of their π-electron system are supported in exptl. and computational studies. We focus on spectroscopic techniques which are sensitive to the electron d. distribution, including the X-ray crystallog., electronic absorption, two-photon techniques, CD, NMR, Stark and vibrational spectroscopies, and on this basis we seek for the origin of inactivity of the S1 state. We come across no exptl. and computational evidence for the symmetry effects and the existence of symmetry restrictions on the electronic states of carotenoids. They do not possess an inversion center and the C2h symmetry approxn. of carotenoid structure is by no means justified. In effect, the application of symmetry rules (and notification) to the electronic states of carotenoids in this symmetry group may lead to a wrong interpretation of exptl. data. This conclusion together with the results summarized in the review allows us to advance a consistent model that explains the inactivity of the S0 → S1 transition. Within this model, S1 is never accessible from S0 due to the neg. synergy of (i) the contributions of double excitations of very low probability, which elevate S1 energy, and (ii) a non-verticality of the S0 → S1 transition, due to the breaking of Born-Oppenheimer approxn. Certainly, our simple model requires a further exptl. and theor. verification.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXms1yjtQ%253D%253D&md5=9b6ee2db80fe0577ed2d5282481f95bc

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      Baker, W.; McOmie, J. F. W.; Parfitt, S. D.; Watkins, D. A. M. 799. Attempts to Prepare New Aromatic Systems. Part VI. 1:2–5:6-Dibenzopentalene and Derivatives. J. Chem. Soc. 1957, 0, 4026– 4037, DOI: 10.1039/JR9570004026

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      Attempts to prepare new aromatic systems. VI. 1,2,5,6-Dibenzopentalene and derivatives

      Baker, Wilson; McOmie, J. F. W.; Parfitt, S. D.; Watkins, D. A. M.

      Journal of the Chemical Society
      (1957),
      
      (),
      4026-37CODEN:
      JCSOA9;
      ISSN: 0368-1769.

      2-Benzylideneindan-1,3-dione was added to PhMgBr (from 8.3 g. PhBr) in Et2O, boiled 1 hr., poured into dil. HCl, and on elution from Al2O3 with alc. gave 2-diphenylmethyl-3-phenylinden-1-one (I), m. 154° [differs from Kohler’s (C.A. 1, 1849) conclusion that 3,4-dihydro-3-oxo-4-phenyl-1,2,5,6-dibenzopentalene (II) was formed]; 2,4-dinitrophenylhydrazone, m. 249°; oxime, m. 159-62°. 2-(Diphenylmethyl)indan-1,3-dione (III), m. 128-9°, was similarly prepd. by using increased amts. of reagents. III and PhMgBr gave I. I with Cr2O3 in HOAc gave Ph2CO and 2-PhCOC6H4CO2H while III gave Ph2CO, Ph2CHCO2H, and phthalic acid. Ph2CHCH(CO2H)2 (2 g.) was heated with 20 g. polyphosphoric acid at 120° 1 hr., poured into H2O, and crystd. from C6H6 to give 3,4,7,8-tetrahydro-3,4-dioxo-1,2,5,6-dibenzopentalene (IV), m. 259°, sol. in hot but not cold aq. NaOH, gives a CHCl3 sol. green Cu deriv., gives no color with alc. FeCl3, and remains unchanged by Na in hot ethylene glycol; mono-2,4-dinitrophenylhydrazone, m. 297° (decompn.); mono-4-toluenesulfonylhydrazone, m. 116°. 3-Phenylindan-1-one (V) (2,4-dinitrophenylhydrazone, m. 209-10°) and Ph2CHCH2CO2H were prepd. from cinnamic acid and AlCl3. V (21 g.) in 50 cc. (EtO)2CO (VI) was added slowly to 150 cc. VI in which 2.3 g. Na was dissolved and heated at 150° to give trans-Et 1-oxo-3-phenylindan-2-carboxylate (VII), m. 103-4°; 2,4-dinitrophenylhydrazone, m. 179°. The ester prepd. by Yost (C.A. 45, 2928i) was probably the cis isomer. VII (2 g.) was heated at 160° 3 min. with excess polyphosphoric acid and poured into H2O to give IV. V (10 g.), 9 g. (CO2Et)2, and 40 cc. EtOH was added with stirring to 100 cc. warm EtOH contg. 10 g. Na and poured into dil. HCl giving 1-oxo-3-phenyl-2-indanylglyoxylic acid (VIII), m. 213°, and probably 3-phenyl-2-(3-phenyl-1-indenylidene)indan-1-one, m. 185°; Me ester of VIII, m. 148°. Cyclization of VIII with polyphosphoric acid gave IV. IV (1.0 g.), 6 g. Zn-Hg, 20 cc. H2O, 50 cc. concd. HCl, 1 cc. HOAc, and 5 cc. MePh was refluxed 40 hrs. giving 3,4,7,8-tetrahydro-1,2,5,6-dibenzopentalene (IX), m. 95°. IX (0.2 g. and 0.3 g. chloranil was boiled in 10 cc. C6H6 14 hrs., poured into dil. NaOH, and extd. with Et2O to give 3(or 7)-(2,3,5,6-tetrachloro-4-hydroxyphenoxy)-1,2,5,6-dibenzopentalene (X), m. 210°. Sublimation of X at 230°/12 mm. gave IX. IV (0.5 g.) and 5 g. PCl5 was heated at 100° 5 min. to give 3,3,4,4,7,8-hexachloro-3,4,7,8-tetrahydro-1,2,5,6-dibenzopentalene, m. 207°, and 8(or 7)-chloro-3,4,7,8-tetrahydro-3,4-dioxo-1,2,5,6-dibenzopentalene, m. 172°. IV with LiAlH4 gave 2 stereoisomers of 3,4,7,8-tetrahydro-3,4-dihydroxy-1,2,5,6-dibenzopentalene: isomer A, m. 262° (di-Ac deriv., m. 109-10°; Bz deriv., m. 169°); isomer B, m. 200° (di-Ac deriv., m. 158°). IV (1 g.) in Et2O was boiled with MeMgI and 3,4,7,8-tetrahydro-3-methylene-4-oxo-1,2,5,6-dibenzopentalene (XI), m. 156°; sepd. XI gives a red soln. with concd. H2SO4. 2-Benzylidene-3-phenylindan-1-one (XIa) (5 g.), 200 cc. C6H6, and 50 g. AlCl3 was refluxed 6 hrs. and poured into H2O giving 3,4,7,8-tetrahydro-3-oxo-4-phenyl-1,2,5,6-dibenzopentalene (XII), m. 132°; 2,4-dinitrophenylhydrazone, m. 271°. To 2.5 g. XII in a warm soln. of 1 g. Na in 50 cc. ethylene glycol was added pure N2H4, the mixt. refluxed 20 hrs., poured into H2O, and extd. with Et2O to give 3,4,7,8-tetrahydro-3-phenyl-1,2,5,6-dibenzopentalene (XIII), m. 112°. XII (10 g.) and 10 g. PCl5 in 100 cc. C6H6 was boiled 10 hrs., distd. to dryness in vacuo, and crystd. from light petr. giving 3,3-dichloro-3,4,7,8-tetrahydro-4-phenyl-1,2,5,6-dibenzopentalene (XIV), m. 151°, which hydrolyzes in damp air or alc. KOH or reacts with Ag2O in anhyd. C6H6 to give XII. XIV with Zn-HCl gave XIII. When XIV is melted under reduced pressure or boiled in pyridine 45 min., 3,3,4(or 7)-trichloro-3,4,7,8-tetrahydro-4-phenyl-1,2,5,6-dibenzopentalene, m. 214° (decompn.), is obtained. The 4-toluenesulfonylhydrazone of XII, m. 204°, reacts with Na in ethylene glycol to give 3,4,7,8-tetrahydro-3-(2-hydroxyethoxy)-4-phenyl-1,2,5,6-dibenzopentalene, m. 147°, and similarly replacing glycol with cyclohexanol as solvent XII gave 3-cyclohexyloxy-3,4,7,8-tetrahydro-4-phenyl-1,2,5,6-dibenzopentalene, m. 133°. XII with LiAlH4 gave 3,4,7,8-tetrahydro-3-hydroxy-4-phenyl-1,2,5,6-dibenzopentalene (XV), m. 176-8° (Ac deriv., m. 151°), while reduction with Al(OCHMe2)3 gave a 2nd isomer (XVI) of XV, m. 148°; Ac deriv., m. 145°. The Ac derivs. of XV and XVI do not decomp. on heating alone or with anhyd. K2CO3. XV (1 g.) and 1 g. anhyd. CuSO4 was boiled 4 hrs. in 30 cc. xylene, then filtered, and the residue washed with Et2O. Evapn. of the filtrate and washings gave 4,7(?)-dihydro-4-phenyl-1,2,5,6-dibenzopentalene (XVII), m. 178-80°, and an unknown compd. (XVIII), m. 158-9°. XVII and XVIII were also prepd. by heating XV with anhyd. CuSO4 7 hrs., but after 10 hrs. only XVIII was isolated. A similar dehydration of XVI gave XVII after 1.5 hrs. and XVIII after 3 hrs. boiling. When either XV or XVI was heated with P2O5 in C6H6 a substance was formed which melted at about 60°, solidified at about 80°, and then m. 154°, ν 745 and 702 cm.-1 Dry air contg. Br and CHCl3 passed through a CHCl3 soln. of XII yielded 3,4-dihydro-3-oxo-4-phenyl-1,2,5,6-dibenzopentalene (XIX), m. 266-9° (decompn.). IV and PhMgBr refluxed 1 hr. gave 3,4,7,8-tetrahydro-3-hydroxy-4-oxo-3-phenyl-1,2,5,6-dibenzopentalene (XX), m. 120°. Similarly, IV and excess PhMgBr or PhLi gave XIX and XX. The epoxide of XIa (XXI), m. 164°, was prepd. by the reaction of H2O2 with XIa in the presence of NaOH. 1,3-Dihydroxy-2,4-diphenylnaphthalene, n. 163-5°, was prepd. by the reaction of XXI with polyphosphoric acid at 160° and 192°, by heating with excess concd. HCl 3 hrs., or by reaction with BF3. XII and PhMgBr in Et2O boiled 5 hrs. gave 3,4,7,8-tetrahydro-3-hydroxy-3,4-diphenyl-1,2,5,6-dibenzopentalene (XXII), m. 160°. Dehydration of XXII with anhyd. CuSO4 gave 4,7-dihydro-3,4-diphenyl-1,2,5,6-dibenzopentalene (XXIII), m. 202-4°. XXIII in CCl4 with oxides of N prepd. from fuming HNO3, H2SO4, and As2O3 gave a cryst. addn. compd., C28H20N2O4, m. 242°.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaG1cXisFCnuw%253D%253D&md5=4d4659ba869a3fbe16dfcf2bd812856d

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      Oshima, H.; Fukazawa, A.; Yamaguchi, S. Facile Synthesis of Polycyclic Pentalenes with Enhanced Hückel Antiaromaticity. Angew. Chem., Int. Ed. 2017, 56, 3270– 3274, DOI: 10.1002/anie.201611344

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      Facile Synthesis of Polycyclic Pentalenes with Enhanced Hueckel Antiaromaticity

      Oshima, Hiroya; Fukazawa, Aiko; Yamaguchi, Shigehiro

      Angewandte Chemie, International Edition
      (2017),
      56
      (12),
      3270-3274CODEN:
      ACIEF5;
      ISSN: 1433-7851.

      (Wiley-VCH Verlag GmbH & Co. KGaA)

      Pentalenes represent highly reactive Hueckel antiaroms. with 8π electrons. Usually, pentalenes are stabilized by incorporation of two benzene rings in a fused fashion. In dibenzo[a,e]pentalenes, however, the high aromaticity of the fused benzene rings compromises the inherent antiaromaticity of the pentalene core. Herein, the authors disclose that this forfeited antiaromaticity can be restored by fusing four addnl. arom. rings onto the peripheral positions of dibenzo[a,e]pentalenes. Such polycyclic pentalenes were prepd. by successive transannular cyclizations via in situ-generated tetrakisdehydro[16]annulenes. The thus obtained compds. showed intriguing properties, for example, characteristic absorptions in the visible-to-near-IR (NIR) region and low redn. potentials. These results hence afford a design principle to produce highly antiarom. yet stable pentalenes. The antiaromaticity of the pentalene core can be widely tuned via the degree of aromaticity of the peripherally fused rings.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXlsVyltg%253D%253D&md5=896814635a6672ca1309b0416ded7118

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      Konishi, A.; Okada, Y.; Kishi, R.; Nakano, M.; Yasuda, M. Enhancement of Antiaromatic Character via Additional Benzoannulation into Dibenzo[a,f]Pentalene: Syntheses and Properties of Benzo[a]Naphtho[2,1-f]Pentalene and Dinaphtho[2,1-a,f]Pentalene. J. Am. Chem. Soc. 2019, 141, 560– 571, DOI: 10.1021/jacs.8b11530

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      Enhancement of Antiaromatic Character via Additional Benzoannulation into Dibenzo[a,f]pentalene: Syntheses and Properties of Benzo[a]naphtho[2,1-f]pentalene and Dinaphtho[2,1-a,f]pentalene

      Konishi, Akihito; Okada, Yui; Kishi, Ryohei; Nakano, Masayoshi; Yasuda, Makoto

      Journal of the American Chemical Society
      (2019),
      141
      (1),
      560-571CODEN:
      JACSAT;
      ISSN: 0002-7863.

      (American Chemical Society)

      Understanding the structure-property relationships in antiarom. mols. is crucial for controlling their electronic properties and designing new org. optoelectronic materials. Dibenzo[a,f]pentalene, a structural isomer of dibenzopentalene, displays open-shell and antiarom. character harmonization, which is not shared by the well-known isomer, dibenzo[a,e]pentalene. The next questions of interest concern the topol. effects of the π-extension on the harmonization of the open-shell and antiarom. character in the dibenzo[a,f]pentalene π-system. Herein, we describe the synthesis and characterization of the π-extended (bis)annulated analogs, benzo[a]naphtho[2,1-f]pentalene 4 and dinaphtho[2,1-a,f]pentalene 5. The solid-state structures and the magnetic and optoelectronic properties characterized these π-extended analogs as closed-shell antiarom. mols., in sharp contrast with dibenzo[a,f]pentalene 2. In these π-extended analogs, the open-shell character was annihilated whereas the antiarom. character was retained. The fusion of addnl. hexagons into 2 shifted the main 4nπ-conjugated circuit from a global to a local system. Further investigations into magnetic ring currents using gauge-including magnetically induced current (GIMIC) calcns. suggested that an enhanced local paratropic ring current appeared in the pentalene core of 5. The preservation of the benzenoid character in the addnl. fused hexagons confined the paratropicity to the pentalene subunit, and the inherent presence of an o-quinoidal structure highlighted the 4nπ-electron delocalization on the pentalene unit. The antiaromaticity of 4 and 5 was characterized by their small HOMO-LUMO energy gap. Both exptl. and computational results demonstrated that the [a,f]-type ring fusion of the pentalene core effectively enhanced the antiarom. character compared with the [a,e]-type ring fusion in the reported bisannulated[a,e]pentalenes. The findings of this study could potentially be used for the rational design of optoelectronic devices based on novel antiarom. mols.

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      Ehrmaier, J.; Rabe, E. J.; Pristash, S. R.; Corp, K. L.; Schlenker, C. W.; Sobolewski, A. L.; Domcke, W. Singlet-Triplet Inversion in Heptazine and in Polymeric Carbon Nitrides. J. Phys. Chem. A 2019, 123, 8099– 8108, DOI: 10.1021/acs.jpca.9b06215

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      Singlet-Triplet Inversion in Heptazine and in Polymeric Carbon Nitrides

      Ehrmaier, Johannes; Rabe, Emily J.; Pristash, Sarah R.; Corp, Kathryn L.; Schlenker, Cody W.; Sobolewski, Andrzej L.; Domcke, Wolfgang

      Journal of Physical Chemistry A
      (2019),
      123
      (38),
      8099-8108CODEN:
      JPCAFH;
      ISSN: 1089-5639.

      (American Chemical Society)

      According to Hund’s rule, the lowest triplet state (T1) is lower in energy than the lowest excited singlet state (S1) in closed-shell mols. The exchange integral lowers the energy of the triplet state and raises the energy of the singlet state of the same orbital character, leading to a pos. singlet-triplet energy gap (ΔST). Exceptions are known for biradicals and charge-transfer excited states of large mols. in which the HOMO and the LUMO are spatially sepd., resulting in a small exchange integral. In the present work, we discovered with ADC(2), CC2, EOM-CCSD, and CASPT2 calcns. that heptazine (1,3,4,6,7,9,9b-heptaazaphenalene or tri-s-triazine) exhibits an inverted S1/T1 energy gap (ΔST ≈ -0.25 eV). This appears to be the first example of a stable closed-shell org. mol. exhibiting S1/T1 inversion at its equil. geometry. The origins of this phenomenon are the nearly pure HOMO-LUMO excitation character of the S1 and T1 states and the lack of spatial overlap of HOMO and LUMO due to a unique structure of these orbitals of heptazine. The S1/T1 inversion is found to be extremely robust, being affected neither by substitution of heptazine nor by oligomerization of heptazine units. Using time-resolved photoluminescence and transient absorption spectroscopy, we investigated the excited-state dynamics of 2,5,8-tris(4-methoxyphenyl)-1,3,4,6,7,9,9b-heptaazaphenalene (TAHz), a chem. stable heptazine deriv., in the presence of external heavy atom sources as well as triplet-quenching oxygen. These spectroscopic data are consistent with TAHz singlet excited state decay in the absence of a low-energy triplet loss channel. The absence of intersystem crossing and an exceptionally low radiative rate result in unusually long S1 lifetimes (of the order of hundreds of nanoseconds in nonaq. solvents). These features of the heptazine chromophore have profound implications for org. optoelectronics as well as for water-splitting photocatalysis with heptazine-based polymers (e.g., graphitic carbon nitride) which have yet to be systematically explored and exploited.

      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhs12jsbbK&md5=09a33ee027b0f9ba2631e3cc0df26355

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      Corey, J. Y. Siloles. Part 1: Synthesis, Characterization, and Applications. Adv. Organomet. Chem. 2011, 59, 1– 180, DOI: 10.1016/B978-0-12-378649-4.00001-0

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      Siloles: part 1: synthesis, characterization, and applications

      Corey, Joyce Y.

      Advances in Organometallic Chemistry
      (2011),
      59
      (),
      1-180CODEN:
      AOMCAU;
      ISSN: 0065-3055.

      (Academic Press)

      A review. This review focuses on the synthesis, characterization, and uses of siloles.

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      Corey, J. Y. Siloles. Part 2: Silaindenes (Benzosiloles) and Silafluorenes Dibenzosiloles): Synthesis, Characterization, and Applications. Adv. Organomet. Chem. 2011, 59, 1– 180, DOI: 10.1016/B978-0-12-378649-4.00001-0

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      Siloles: part 1: synthesis, characterization, and applications

      Corey, Joyce Y.

      Advances in Organometallic Chemistry
      (2011),
      59
      (),
      1-180CODEN:
      AOMCAU;
      ISSN: 0065-3055.

      (Academic Press)

      A review. This review focuses on the synthesis, characterization, and uses of siloles.

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      Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Self-Consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72, 650– 654, DOI: 10.1063/1.438955

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      Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions

      Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A.

      Journal of Chemical Physics
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      72
      (1),
      650-4CODEN:
      JCPSA6;
      ISSN: 0021-9606.

      A contracted Gaussian basis set (6-311G is developed by optimizing exponents and coeffs. at the Moller-Plesset (MP) second-order level for the ground states of first-row atoms. This has a triple split in the valence s and p shells together with a single set of uncontracted polarization functions on each atom. The basis is tested by computing structures and energies for some simple mols. at various levels of MP theory and comparing with expt.

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       ISSN: 0192-8651.

       (John Wiley & Sons, Inc.)

       In this report, we summarize and describe the recent unique updates and addns. to the MOLCAS quantum chem. program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with d. functional theory in the MC-PDFT method, addnl. methods for computation of magnetic properties, methods for diabatization, anal. gradients of state av. complete active space SCF in assocn. with d. fitting, methods for constrained fragment optimization, large-scale parallel multireference CI including analytic gradients via the interface to the COLUMBUS package, and approxns. of the CASPT2 method to be used for computations of large systems. In addn., the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package COBRAMM. Further, a module to run mol. dynamics simulations is added and two surface hopping algorithms are included to enable nonadiabatic calcns. Finally, we report on the subject of improvements with respects to alternative file options and parallelization. © 2015 Wiley Periodicals, Inc.

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       ISSN: 0009-2614.

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       We show that the purely first-principles Weizmann-4 (W4) computational thermochem. method developed in our group can reproduce available Active Thermochem. Tables atomization energies for 35 mols. with a 3σ uncertainty of under 1 kJ/mol. We then employ this method to generate the W4-11 dataset of 140 total atomization energies of small first-and second-row mols. and radicals. These cover a broad spectrum of bonding situations and multireference character, and as such are an excellent, quasi-automated benchmark (available electronically as Supporting Information) for parametrization and validation of more approx. methods (such as DFT functionals and composite methods). Secondary contributions such as relativity can be included or omitted at will, unlike with exptl. data. A broad variety of more approx. methods is assessed against the W4-11 benchmark and recommendations are made.

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       ISSN: 1089-5639.

       (American Chemical Society)

       We report a general method for the investigation and quantification of delocalization in mols. The method is based on the anisotropy of the current-induced d. (ACID). Compared to the c.d., which has been frequently used to investigate delocalization, the ACID approach has several advantages: it is a scalar field which is invariant with respect to the relative orientation of the magnetic field and the mol., it is not a simple function of the overall electron d., it has the same symmetry as the wave function, and it can be plotted as an isosurface. Several selected examples demonstrate the predictive power and the general applicability of this method.

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       A review. The ACID method is an intuitive and generally applicable method for the investigation and visualization of electron delocalization and bond conjugation in ground, excited and transition states. In the prototype examples for different types of delocalization presented in this review, the ACID anal. is in agreement with previous alternative theor. studies.

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       CEUJED;
       ISSN: 0947-6539.

       (Wiley-VCH Verlag GmbH & Co. KGaA)

       Nucleus-independent chem. shift (NICS)-based methods are very popular for the detn. of the induced magnetic field under an external magnetic field. These methods are used mostly (but not only) for the detn. of the aromaticity and antiaromaticity of mols. and ions, both qual. and quant. The ghost atom that serves as the NICS probe senses the induced magnetic field and reports it in the form of an NMR chem. shift. However, the source of the field cannot be detd. by NICS. Thus, in a multi-ring system that may contain more than one induced current circuit (and therefore more than one source of the induced magnetic field) the NICS value may represent the sum of many induced magnetic fields. This may lead to wrong assignments of the aromaticity (and antiaromaticity) of the systems under study. In this paper, we present a NICS-based method for the detn. of local and global ring currents in conjugated multi-ring systems. The method involves placing the NICS probes along the X axis, and if needed, along the Y axis, at a const. height above the system under study. Following the change in the induced field along these axes allows the identification of global and local induced currents. The best NICS type to use for these scans is NICSπZZ, but it is shown that at a height of 1.7 Å above the mol. plane, NICSZZ provides the same qual. picture. This method, namely the NICS-XY-scan, gives information equiv. to that obtained through c.d. anal. methods, and in some cases, provides even more details.

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• Supporting Information

  ---

  The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.9b12435.

  • Tables with absolute relative energies, excitation energies, aromaticity data (MCI, HOMA, NICS(1)_zz), and diradical character. Plots of excitation energies versus HOMA and NICS(1)_zz, molecular orbitals, and NICS-XY scans. List of compounds include the following: substituted fulvenes, substituted CBDs, substituted pentalenes, substituted indacenes, benzannelated CBDs, benzannelated pentalenes, triafulvenes, heptafulvenes, siloles, and thieno-benzannelated pentalenes (PDF)

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