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Volumn 102, Issue 7, 1980, Pages 2152-2163

Vertical and Nonvertical” Energy Transfer Processes. A General Classical Treatment “

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EID: 0001106707     PISSN: 00027863     EISSN: 15205126     Source Type: Journal    
DOI: 10.1021/ja00527a002     Document Type: Article
Times cited : (224)

References (99)
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    • 15, 155 (1964); Discuss. Faraday Soc.
    • R. A. Marcus, Annu. Rev. Phys. Chem., 15, 155 (1964); Discuss. Faraday Soc., 29, 21 (1960).
    • (1960) Annu. Rev. Phys. Chem. , vol.29 , pp. 21
    • Marcus, R.A.1
  • 39
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    • G. L. Eichhorn, Ed., Elsevier, Amsterdam
    • N. Sutin in “Inorganic Biochemistry”, Vol. 2, G. L. Eichhorn, Ed., Elsevier, Amsterdam, 1973, p 611.
    • (1973) “Inorganic Biochemistry” , vol.2 , pp. 611
    • Sutin, N.1
  • 43
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    • Faraday Trans. 2
    • N. Agmon, J. Chem. Soc., Faraday Trans. 2, 74, 388 (1978).
    • (1978) J. Chem. Soc. , vol.74 , pp. 388
    • Agmon, N.1
  • 55
    • 85023006763 scopus 로고    scopus 로고
    • These conditions are generally satisfied for most of the systems studied so far. For highly polar transitions in polar solvents, however, this contribution can amount to some kcal/mol.30a As far as contribution (2) is concerned, it can be shown that even a substantial change in a highly contributing low-frequency mode corresponds to a negligible energy contribution. For example, in the extreme case of a change in vibrational frequency from 50 to 10 cm-1 (figures which are probably appropriate for the torsional mode of ground-and excited-state stilbene’2), the corresponding energy contribution is less than 1 kcal/mol.
    • Contribution (1) can be neglected in nonpolar, solvents or when the change in dipole moment between ground and excited state is small. These conditions are generally satisfied for most of the systems studied so far. For highly polar transitions in polar solvents, however, this contribution can amount to some kcal/mol.30a As far as contribution (2) is concerned, it can be shown that even a substantial change in a highly contributing low-frequency mode corresponds to a negligible energy contribution. For example, in the extreme case of a change in vibrational frequency from 50 to 10 cm-1 (figures which are probably appropriate for the torsional mode of ground-and excited-state stilbene’2), the corresponding energy contribution is less than 1 kcal/mol.
    • Contribution (1) can be neglected in nonpolar, solvents or when the change in dipole moment between ground and excited state is small.
  • 59
    • 85012669286 scopus 로고
    • C. H. Bamford and C. F. H. Tipper, Eds., Elsevier, Amsterdam
    • See, for example, R. P. Wayne in “Comprehensive Chemical Kinetics”, Vol. 2, C. H. Bamford and C. F. H. Tipper, Eds., Elsevier, Amsterdam, 1969, p 189.
    • (1969) “Comprehensive Chemical Kinetics” , vol.2 , pp. 189
    • Wayne, R.P.1
  • 61
    • 85023084657 scopus 로고
    • (eq 31) modes results in a quadratic free energy relationship identical with the Marcus equation (eq 10) (see, for example, V. G. Levich in “Physical Chemistry: an Advanced Treatise”, H. Eyring, D. Henderson, and W. Jost, Eds., Academic Press, New York, 1970, p 896; R. R. Dogonadze in “Reactions of Molecules at Electrodes”, N. S. Hush, Ed., Wiley, New York,. In such a case, eq 10 rather than eq 12 should be inserted into eq 22. As we will see later, the use of eq 12 in our classical treatment (leading to eq 29) formally corresponds to a situation in which high-energy distorted modes are also present.
    • A quantum-mechanical treatment of a situation where the transfer probability is determined only by the classical (eq 31) modes results in a quadratic free energy relationship identical with the Marcus equation (eq 10) (see, for example, V. G. Levich in “Physical Chemistry: an Advanced Treatise”, Vol. IXB, H. Eyring, D. Henderson, and W. Jost, Eds., Academic Press, New York, 1970, p 896; R. R. Dogonadze in “Reactions of Molecules at Electrodes”, N. S. Hush, Ed., Wiley, New York, 1971. In such a case, eq 10 rather than eq 12 should be inserted into eq 22. As we will see later, the use of eq 12 in our classical treatment (leading to eq 29) formally corresponds to a situation in which high-energy distorted modes are also present.
    • (1971) A quantum-mechanical treatment of a situation where the transfer probability is determined only by the classical , vol.IXB
  • 64
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    • 25, 34 (1974); S. Efrima and M. Bixon, J. Chem. Phys., 64, 3639 (1976); S. Efrima and M. Bixon, Chem. Phys.
    • S. Efrima and M. Bixon, Chem. Phys. Lett., 25, 34 (1974); S. Efrima and M. Bixon, J. Chem. Phys., 64, 3639 (1976); S. Efrima and M. Bixon, Chem. Phys., 13, 447 (1976).
    • (1976) Chem. Phys. Lett. , vol.13 , pp. 447
    • Efrima, S.1    Bixon, M.2
  • 70
    • 85023101166 scopus 로고    scopus 로고
    • If a single broad minimum is assumed for the triplet excited state, the scheme should be modified so as to consider two back-energy transfer paths leading to ground cis and trans isomers. However, owing to the small free-energy difference between the two isomers (see later), the free-energy change of the two back processes is approximately the same. Thus the use of eq 18 is acceptable. A more detailed, though still incomplete, kinetic scheme is given in ref 19. See also ref
    • It should be noted that eq 29 is based on the kinetic scheme of eq 18, which is certainly too simple for treating the stilbene case. If a single broad minimum is assumed for the triplet excited state, the scheme should be modified so as to consider two back-energy transfer paths leading to ground cis and trans isomers. However, owing to the small free-energy difference between the two isomers (see later), the free-energy change of the two back processes is approximately the same. Thus the use of eq 18 is acceptable. A more detailed, though still incomplete, kinetic scheme is given in ref 19. See also ref 61.
    • It should be noted that eq 29 is based on the kinetic scheme of eq 18, which is certainly too simple for treating the stilbene case. , pp. 61
  • 85
    • 84864745069 scopus 로고
    • iw (S0 ’ S.) ~27 X 10* cm”1;4 jw (Ti ’ S0) ~18 X 103 cm”1;83 Si-T 1 splitting ~2 X 103 cm 1 80 Benzil4'8”’81'84 and p-anisil84 have similar Stokes shift values.
    • D. J. Morantz and A. J. C. Wright, J. Chem. Phys., 54, 692 (1971). iw (S0 ’ S.) ~27 X 10* cm”1;4 jw (Ti ’ S0) ~18 X 103 cm”1;83 Si-T 1 splitting ~2 X 103 cm 1 80 Benzil4'8”’81'84 and p-anisil84 have similar Stokes shift values.
    • (1971) J. Chem. Phys. , vol.54 , pp. 692
    • Morantz, D.J.1    Wright, A.J.C.2
  • 92
    • 85023117574 scopus 로고    scopus 로고
    • As mentioned in ref 39, the two equations are equivalent on practical grounds. The small differences between the present values and those given in ref 41 depend on an improvement in the graphical fitting procedure.
    • In ref 41, eq 11 instead of eq 12 was used to correlate AG* with AG. As mentioned in ref 39, the two equations are equivalent on practical grounds. The small differences between the present values and those given in ref 41 depend on an improvement in the graphical fitting procedure.
    • ref 41, eq 11 instead of eq 12 was used to correlate AG* with AG.


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