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cmcerning the theoretical estimation of internal energy a m t r i i by the to16onal motion between biphenyl and biphenyl anion radical, direct calculation of self-exchange electroo trader d o n was investigated. With the introduction of a proper average bond length and angle parameters cboodBp>, a multiple step reladion Nelson method wsp developed to deal with the torsional reorganhtion energy. Basedon the above model, an estimation of plre t o m reachieved. The results of 0.140 and 0.125 eV of t o r s i d reorganization energy for a c m s d o n at the levels d4-31G and of0.U eV obtained by Miller et d . piom the rate meaaue-eStimatethe reoqgdzationenergyamtriibypue t o m motion of Bp. organidon energy At,p with an appImimation d AtJ wsp m m , rrspectively, are in good agN!m€ ¶t W i t h the value ments. This implies the efficiency and validity ofour method to Keywordr multiple step relaxation Nelson method, internal reorganbation energy, torsional motion, biphenyl molecule, electron bander * Project supported by the Chinese Research Endowment of Hui-Chun Chin and Tsung-Dao Lee.31G and HP/DZP, mpectively.p*25 As defied above, the value of A1,2 is the sum of these two torsional potential h e r s , and it is 53.75 and 47.02 kJ-mol-' at the levels of 4-31G and HP/DZE' , respectively. In the case of A 1, 1, in fact, the difference between AE( #+-+ anion) and AE(bond Bp-+co-plane) is small, which is also true between AE (co-plane+ +neutral) and AE (bond Bp-f +#I. As a result, Al,l can be simply regded aa 0, and thedore torsional reorganization energy of selfexchange reaction of h ,, is about 27 Id * mol -' at the 4-31G level and 24 kJmol-' at the HP/DZP level. According to Eq. ( 3 ) , the i n t e d reorganization energy contributed by torsional motion of Bp is about 13.5 kJ * mol-' (or about0.140 eV) and 12 kJ*mol-' (or about Vol. 20 No. 10 2002 Chinese Journal of Chemistry 967 B: Chem. 1999, 42, 441. Keltemr, A. M.; Landgraf, S.; Grampp, G . Spectrachim. A d a , P m A 2001, 57, 1959. L i , X . Y.; Tang, X. S.; Xiao, S. Q . ; He, F. C. J. Md. strud. 1995, 342, 181. Li, X. Y.; He, F. C. J . Camp. C h . 1999, 20,597. Z h a n g , X . D . ; W a n g , . Y . N . ; C u o , J . X . ; m , Q . Y . Z i m m t , M . B . J . Phys. b. Am, 102, 5529. Min, W.; Sun, L. h P h y s . -C h i m . Sin. 2001, 17, 924 (in Chinese). Davis, W. B . ; b, M. A . ; Wmielewski, M. R. J.
cmcerning the theoretical estimation of internal energy a m t r i i by the to16onal motion between biphenyl and biphenyl anion radical, direct calculation of self-exchange electroo trader d o n was investigated. With the introduction of a proper average bond length and angle parameters cboodBp>, a multiple step reladion Nelson method wsp developed to deal with the torsional reorganhtion energy. Basedon the above model, an estimation of plre t o m reachieved. The results of 0.140 and 0.125 eV of t o r s i d reorganization energy for a c m s d o n at the levels d4-31G and of0.U eV obtained by Miller et d . piom the rate meaaue-eStimatethe reoqgdzationenergyamtriibypue t o m motion of Bp. organidon energy At,p with an appImimation d AtJ wsp m m , rrspectively, are in good agN!m€ ¶t W i t h the value ments. This implies the efficiency and validity ofour method to Keywordr multiple step relaxation Nelson method, internal reorganbation energy, torsional motion, biphenyl molecule, electron bander * Project supported by the Chinese Research Endowment of Hui-Chun Chin and Tsung-Dao Lee.31G and HP/DZP, mpectively.p*25 As defied above, the value of A1,2 is the sum of these two torsional potential h e r s , and it is 53.75 and 47.02 kJ-mol-' at the levels of 4-31G and HP/DZE' , respectively. In the case of A 1, 1, in fact, the difference between AE( #+-+ anion) and AE(bond Bp-+co-plane) is small, which is also true between AE (co-plane+ +neutral) and AE (bond Bp-f +#I. As a result, Al,l can be simply regded aa 0, and thedore torsional reorganization energy of selfexchange reaction of h ,, is about 27 Id * mol -' at the 4-31G level and 24 kJmol-' at the HP/DZP level. According to Eq. ( 3 ) , the i n t e d reorganization energy contributed by torsional motion of Bp is about 13.5 kJ * mol-' (or about0.140 eV) and 12 kJ*mol-' (or about Vol. 20 No. 10 2002 Chinese Journal of Chemistry 967 B: Chem. 1999, 42, 441. Keltemr, A. M.; Landgraf, S.; Grampp, G . Spectrachim. A d a , P m A 2001, 57, 1959. L i , X . Y.; Tang, X. S.; Xiao, S. Q . ; He, F. C. J. Md. strud. 1995, 342, 181. Li, X. Y.; He, F. C. J . Camp. C h . 1999, 20,597. Z h a n g , X . D . ; W a n g , . Y . N . ; C u o , J . X . ; m , Q . Y . Z i m m t , M . B . J . Phys. b. Am, 102, 5529. Min, W.; Sun, L. h P h y s . -C h i m . Sin. 2001, 17, 924 (in Chinese). Davis, W. B . ; b, M. A . ; Wmielewski, M. R. J.
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