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Apeloig, Y.1
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36
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34249942975
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We use DFT Kohn-Sham (KS) orbitals. The energies of KS orbitals were discussed and compared to those calculated by HF and EH (extended Hückel) methods, and it was found that although the absolute energies of KS orbitals are very different from those calculated by HF and EH methods, a linear relationship exists between the DFT orbital energies and orbital energies calculated with other methods.21b Thus, for comparison purposes the KS orbital energies are valid
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21b Thus, for comparison purposes the KS orbital energies are valid.
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38
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33845269042
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Good agreement was found between HOMO-LUMO gaps calculated at B3LYP/6-31G(d) and experimental values for oligothiphenes; see: Zade, S. S.; Bendikov, M. Org. Lett. 2006, 8, 5243.
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(c) Good agreement was found between HOMO-LUMO gaps calculated at B3LYP/6-31G(d) and experimental values for oligothiphenes; see: Zade, S. S.; Bendikov, M. Org. Lett. 2006, 8, 5243.
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34249931561
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21c
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21c
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42
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34249951571
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A band-gap of 8.1 eV was previously calculated for a ladder polysilane (R = H) by a one dimensional tight-binding self-consistent-field crystal orbital (SCF-CO) method. However, the authors commented that this band-gap is highly over-estimated, by a factor of 3-4: Yamaguchi, Y.; Shioya, J. Synthetic Mat. 1993, 59, 29.
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(b) A band-gap of 8.1 eV was previously calculated for a ladder polysilane (R = H) by a one dimensional tight-binding self-consistent-field crystal orbital (SCF-CO) method. However, the authors commented that this band-gap is highly over-estimated, by a factor of 3-4: Yamaguchi, Y.; Shioya, J. Synthetic Mat. 1993, 59, 29.
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43
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24644480178
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For a recent highlight on the construction of molecules with a small HOMO-LUMO gap, see
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For a recent highlight on the construction of molecules with a small HOMO-LUMO gap, see: Perepichka, D. F.; Bryce, M. R. Angew. Chem., Int. Ed. 2005, 44, 5370.
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Kyushin, S.1
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45
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34249941380
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- (n = 1) was calculated also using a larger basis set, including diffuse functions, at the UB3LYP/6-31G+(d) level. At this level of theory, the three bridging Si-Si bond lengths are 2.381, 2.363, and 2.381 A, while the longitudinal Si-Si bonds are 2.385 and 2.376 Å. Increasing the basis set from 6-31G(d) to 6-31G+(d) shortens the bridging Si-Si bonds while lengthening the longitudinal Si-Si bonds.
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- (n = 1) was calculated also using a larger basis set, including diffuse functions, at the UB3LYP/6-31G+(d) level. At this level of theory, the three bridging Si-Si bond lengths are 2.381, 2.363, and 2.381 A, while the longitudinal Si-Si bonds are 2.385 and 2.376 Å. Increasing the basis set from 6-31G(d) to 6-31G+(d) shortens the bridging Si-Si bonds while lengthening the longitudinal Si-Si bonds.
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46
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34249930834
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2 = 0.999). For details see Figure 2S in the Supporting Information.
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2 = 0.999). For details see Figure 2S in the Supporting Information.
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47
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34249944054
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This work will be published elsewhere
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This work will be published elsewhere.
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48
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34249936817
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Transition states were not located
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(a) Transition states were not located.
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49
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34249938705
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The reliability of the UB3LYP energies for calculating singlet 1,4-biradicals was tested for the model biradical 1 (R, H, n, 1) by comparison with several high-level ab initio and DFT methods. Similar trends in the relative energies of bicyclic 1 (n, 1) and of biradical 1′ (R, H, n, 1) were calculated by DFT or ab initio methods. For example, the biradical 1′ (R, H, n, 1) lies 47.6, 45.8, and 31.9 kcal/mol above the bicyclic 1 (R, H, n, 1) at UB3LYP/ 6-31G(d)//UB3LYP/6-31G(d, UMP2/6-31G(d)//UMP2/6-31G(d) and CAS-(6,6)/6-31G(d)// CAS(6,6)/6-31G(d) levels of theory, respectively. We have also found that the UB3LYP/6-31G(d) and UB3LYP/6-311+G(3d) geometries and relative energies of all the species on the PES for the isomerization of syn-1 (R, H, n, 2) to anti-1 (R, H, n, 2, closed shell and biradicals) are very similar, justifying the use of the smaller basis set for 2 R, Me, n, 2
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(b) The reliability of the UB3LYP energies for calculating singlet 1,4-biradicals was tested for the model biradical 1 (R = H, n = 1) by comparison with several high-level ab initio and DFT methods. Similar trends in the relative energies of bicyclic 1 (n = 1) and of biradical 1′ (R = H, n = 1) were calculated by DFT or ab initio methods. For example, the biradical 1′ (R = H, n = 1) lies 47.6, 45.8, and 31.9 kcal/mol above the bicyclic 1 (R = H, n = 1) at UB3LYP/ 6-31G(d)//UB3LYP/6-31G(d), UMP2/6-31G(d)//UMP2/6-31G(d) and CAS-(6,6)/6-31G(d)// CAS(6,6)/6-31G(d) levels of theory, respectively. We have also found that the UB3LYP/6-31G(d) and UB3LYP/6-311+G(3d) geometries and relative energies of all the species on the PES for the isomerization of syn-1 (R = H, n = 2) to anti-1 (R = H, n = 2) (closed shell and biradicals) are very similar, justifying the use of the smaller basis set for 2 (R = Me, n = 2).
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50
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0038252597
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2〉 expectation value is 0.9 for both syn-2′ and anti-2′. Since the energies of triplet syn-2′ and anti-2′ are very close to those of the pure singlet state energies, the energies calculated for pure and contaminated wave functions are nearly the same (energy difference of ca. ±0.2 kcal/mol). For a formula of how to calculate the energy of a pure singlet state and a discussion see: Gräfenstein, J.; Hjerpe, A. M.; Kraka, E.; Cremer, D. J. Phys. Chem. A 2000, 104, 1748.
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2〉 expectation value is 0.9 for both syn-2′ and anti-2′. Since the energies of triplet syn-2′ and anti-2′ are very close to those of the pure singlet state energies, the energies calculated for pure and contaminated wave functions are nearly the same (energy difference of ca. ±0.2 kcal/mol). For a formula of how to calculate the energy of a pure singlet state and a discussion see: Gräfenstein, J.; Hjerpe, A. M.; Kraka, E.; Cremer, D. J. Phys. Chem. A 2000, 104, 1748.
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0001917369
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For calculated Si-Si bond energies see:, Rappoport, Z, Apeloig, Y, Eds, Wiley: Chichester, U.K, Chapter 1, p
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(a) For calculated Si-Si bond energies see: Karni, M.; Apeloig, Y.; Kapp, J.; Schleyer, P. v. R. In The Chemistry of Organic Silicon Compounds; Rappoport, Z., Apeloig, Y., Eds.; Wiley: Chichester, U.K., 2001; Vol. 3, Chapter 1, p 1.
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0001019927
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For experimental Si-Si bond energies see:, Patai, S, Rappoport, Z, Eds, Wiley: Chichester, U.K, Chapter 5, p
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(b) For experimental Si-Si bond energies see: Walsh, R. In The Chemistry of Organic Silicon Compounds; Patai, S., Rappoport, Z., Eds.; Wiley: Chichester, U.K., 1989; Chapter 5, p 371.
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Walsh, R.1
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