Abstract
In the present work, through the path integral of Gaussian type correlation function, a new formalism based on Fermi-Golden Rule for calculating the rate constant of nonradiative decay process with Duschinsky rotation effect in polyatomic molecules is developed. The advantage of the present path-integral formalism is promoting-mode free. In order to get the rate constant, a “transition rate matrix” needs to be calculated. The rate constant calculated previously is only an approximation of diagonal elements of our “transition rate matrix”. The total rate should be the summation over all the matrix elements.
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DiBartolo B, Goldberg V, eds. Radiationless Processes. New York: Plenum Press, 1980
Lin S H. Rate of Interconversion of electronic and vibrational energy. J Chem Phys, 1966, 44: 3759–3767
Engleman R, Jortner J. The energy gap law for radiationless transitions in large molecules. Mol Phys, 1970, 18: 145–164
Freed K F, Jortner J. Multiphonon processes in the nonradiative decay of large molecules. J Chem Phys, 1970, 52: 6272–6291
Nitzan A, Jortner J. Optical selection studies of radiationless decay in an isolated large molecule. J Chem Phys, 1971, 55: 1355–1368
Siebrand W. Calculation of Franck-Condon factors for radiationless transitions based on selective excitation of single vibronic levels. J Chem Phys, 1971, 54: 363–367
Fischer S F. Anharmonicities in the theory of non-radiative transitions for polyatomic molecules. Chem Phys Lett, 1971, 11: 577–582
Hayashi M, Mebel A M, Liang K K, Lin S H. Ab initio calculations of radiationless transitions between excited and ground singlet electron states of ethylene. J Chem Phys, 1998, 108: 2044–2055
Mebel A M, Hayashi M, Liang K K, Lin S H. Ab initio calculations of vibronic spectra and dynamics for small polyatomic molecules: Role of Duschinsky effect. J Phys Chem A, 1999, 103: 10674–10690
Yan Y J, Mukamel S. Eigenstate-free, Green function, calculation of molecular absorption and fluorescence line shapes. J Chem Phys, 1986, 85: 5908–5923
Wunsch L, Metz F, Neusser H J, Schlag E W. Two-photon spectroscopy in the gas phase: Assignments of molecular transitions in benzene. J Chem Phys, 1977, 66: 386–400
Small G J. Herzberg-Teller vibronic coupling and the Duschinsky effect. J Chem Phys, 1971, 54: 3300–3306
Warren J A, Hayes J M, Small G J. Symmetry reduction-vibronically induced mode mixing in the S1 state of β-methylnaphthalene. J Chem Phys, 1984, 80: 1786–1790
Mochizuchi Y, Kaya K, Ito M. SVL fluorescence and duschinskii effect in the S1 state of pyridine. Chem Phys Lett, 1981, 54: 375–382
Burke F B, Eslinger D R, Small G J. Medium independent Duschinsky rotation in the S1 state of the azaazulenes and azulene. J Chem Phys, 1975, 63: 1309–1310
Small G J, Burke F B. Mixed crystal spectroscopy of 1,3-diazaazulene. J Chem Phys, 1977, 66: 1767–1778
Hemley R J, Leopold D G, Vaida V, Karplus M. The singlet states of styrene. Theoretical vibrational analysis of the ultraviolet spectrum. J Chem Phys, 1985, 82: 5379–5397
Eiden G C, Weisshaar J C. Vibronic coupling mechanism in the à 2A2-\( \tilde B \) 2B2 excited states of benzyl radical. J Chem Phys, 1996, 104: 8896–8912
Lunardi G, Pecile C. N,N′-dicyanoquinonediimines as a molecular constituent of organic conductors: Vibrational behavior and electron-molecular vibration coupling. J Chem Phys, 1991, 95: 6911–6923
Falchi A, Gellini C, Salvi P R, Hafner K. Vibrational and electronic properties of antiaromatic systems: A spectroscopic study of 1,3,5-tri-tert-butylpentalene. J Phys Chem, 1995, 99: 14659–14666
Sinclair E, Yu H, Phillips D. The ground and first excited singlet state torsional potentials of 2-phenylindole from supersonic jet fluorescence spectra. J Chem Phys, 1997, 106: 5797–5804
Ianconescu R, Pollak E. Photoinduced cooling of polyatomic molecules in an electronically excited state in the presence of Dushinskii rotations. J Phys Chem A, 2004, 108: 7778–7784
Peng Q, Yi Y P, Shuai Z G, Shao J S. Excited state radiationless decay process with Duschinsky rotation effect: Formalism and implementation. J Chem Phys, 2007, 126: 114302
Peng Q, Yi Y P, Shuai Z G, Shao J S. Toward quantitative prediction of molecular fluorescence quantum efficiency: Role of Duschinsky rotation. J Am Chem Soc, 2007, 129, 9333–9339
Lax M. The Franck-Condon principle and its application to crystals. J Chem Phys, 1952, 20: 1752
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Supported by the National Natural Science Foundation of China (Grant Nos. 10425420, 20433070 and 90503013)
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Niu, Y., Peng, Q. & Shuai, Z. Promoting-mode free formalism for excited state radiationless decay process with Duschinsky rotation effect. Sci. China Ser. B-Chem. 51, 1153–1158 (2008). https://doi.org/10.1007/s11426-008-0130-4
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DOI: https://doi.org/10.1007/s11426-008-0130-4