Skip to main content
Log in

Promoting-mode free formalism for excited state radiationless decay process with Duschinsky rotation effect

  • Published:
Science in China Series B: Chemistry Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. DiBartolo B, Goldberg V, eds. Radiationless Processes. New York: Plenum Press, 1980

    Google Scholar 

  2. Lin S H. Rate of Interconversion of electronic and vibrational energy. J Chem Phys, 1966, 44: 3759–3767

    Article  Google Scholar 

  3. Engleman R, Jortner J. The energy gap law for radiationless transitions in large molecules. Mol Phys, 1970, 18: 145–164

    Article  Google Scholar 

  4. Freed K F, Jortner J. Multiphonon processes in the nonradiative decay of large molecules. J Chem Phys, 1970, 52: 6272–6291

    Article  CAS  Google Scholar 

  5. Nitzan A, Jortner J. Optical selection studies of radiationless decay in an isolated large molecule. J Chem Phys, 1971, 55: 1355–1368

    Article  CAS  Google Scholar 

  6. 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

    Article  CAS  Google Scholar 

  7. Fischer S F. Anharmonicities in the theory of non-radiative transitions for polyatomic molecules. Chem Phys Lett, 1971, 11: 577–582

    Article  CAS  Google Scholar 

  8. 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

    Article  CAS  Google Scholar 

  9. 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

    Article  CAS  Google Scholar 

  10. Yan Y J, Mukamel S. Eigenstate-free, Green function, calculation of molecular absorption and fluorescence line shapes. J Chem Phys, 1986, 85: 5908–5923

    Article  CAS  Google Scholar 

  11. 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

    Article  CAS  Google Scholar 

  12. Small G J. Herzberg-Teller vibronic coupling and the Duschinsky effect. J Chem Phys, 1971, 54: 3300–3306

    Article  CAS  Google Scholar 

  13. 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

    Article  CAS  Google Scholar 

  14. Mochizuchi Y, Kaya K, Ito M. SVL fluorescence and duschinskii effect in the S1 state of pyridine. Chem Phys Lett, 1981, 54: 375–382

    Google Scholar 

  15. 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

    Article  CAS  Google Scholar 

  16. Small G J, Burke F B. Mixed crystal spectroscopy of 1,3-diazaazulene. J Chem Phys, 1977, 66: 1767–1778

    Article  CAS  Google Scholar 

  17. 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

    Article  CAS  Google Scholar 

  18. 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

    Article  CAS  Google Scholar 

  19. 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

    Article  CAS  Google Scholar 

  20. 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

    Article  CAS  Google Scholar 

  21. 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

    Article  CAS  Google Scholar 

  22. 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

    Article  CAS  Google Scholar 

  23. 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

    Article  Google Scholar 

  24. 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

    Article  CAS  Google Scholar 

  25. Lax M. The Franck-Condon principle and its application to crystals. J Chem Phys, 1952, 20: 1752

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to ZhiGang Shuai.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 10425420, 20433070 and 90503013)

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11426-008-0130-4

Keywords

Navigation