Unified time‐path approach to the effect of anharmonicity on the molecular vibrational spectroscopy in solution (original) (raw)

Abstract

We obtain a closed expression for the response function for damped anharmonic vibrational modes using the Feynman rule obtained through the nonequilibrium generating functional derived in our previous paper ͓Phys. Rev. E 53, 214 ͑1996͔͒. The linear absorption spectra are explicitly calculated through the Feynman diagrams for molecules with anharmonic potential in solution. The dependence of the spectra both on the temperature and on the solvent nature can be taken into account in our theory. The result is examined numerically for various dampings, anharmonicities, and temperatures.

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References (53)

  1. D. Zimdars, A. Tokmakoff, S. Chen, S. R. Greenfield, and F. Fayer, Phys. Rev. Lett. 70, 2718 ͑1993͒.
  2. A. Tokmakoff, D. Zimdars, B. Sauter, R. S. Francis, A. S. Kwok, and M. D. Fayer, J. Chem. Phys. 101, 1741 ͑1994͒.
  3. A. Tokmakoff and F. D. Fayer, J. Chem. Phys. 103, 2810 ͑1995͒.
  4. R. F. Loring and S. Mukamel, J. Chem. Phys. 83, 2116 ͑1985͒.
  5. D. Vanden Bout, L. J. Muller, and M. Berg, Phys. Rev. Lett. 67, 3700 ͑1991͒.
  6. L. J. Muller, D. Vanden Bout, and M. Berg, J. Chem. Phys. 99, 810 ͑1993͒.
  7. R. Inaba, K. Tominaga, M. Tasumi, K. A. Nelson, and K. Yoshihara, Chem. Phys. Lett. 211, 183 ͑1993͒.
  8. Y. Tanimura and S. Mukamel, J. Chem. Phys. 99, 9496 ͑1993͒.
  9. K. Tominaga, and K. Yoshihara, Phys. Rev. Lett. 74, 3061 ͑1995͒.
  10. K. Tominaga, G. P. Keogh, Y. Naitoh, and K. Yoshihara, J. Raman Spec- trosc. 26, 495 ͑1995͒.
  11. S. P. Palese, J. T. Buontempo, L. Schilling, W. T. Lotshaw, Y. Tanimura, S. Mukamel, and R. J. D. Miller, J. Phys. Chem. 98, 12466 ͑1994͒.
  12. T. Steffen and K. Duppen, Phys. Rev. Lett. 76, 1224 ͑1996͒.
  13. E. P. Ippen and C. V. Shank, Appl. Phys. Lett. 26, 92 ͑1975͒.
  14. C. Kalpouzos, W. T. Lotshaw, D. McMorrow, and G. A. Kenney-Wallace, J. Phys. Chem. 91, 2028 ͑1987͒.
  15. T. Hattori and T. Kobayashi, J. Chem. Phys. 94, 3332 ͑1991͒.
  16. M. Cho, M. Du, N. F. Scherer, G. R. Fleming, and S. Mukamel, J. Phys. Chem. 99, 2410 ͑1993͒.
  17. S. Palese, L. Schilling, R. J. Dwayne Miller, P. R. Staver, and W. T. Lotshaw, J. Phys. Chem. 98, 6308 ͑1994͒.
  18. K. A. Nelson and E. P. Ippen, Adv. Chem. Phys. 75, 1 ͑1989͒.
  19. Y. J. Yan and S. Mukamel, J. Chem. Phys. 94, 997 ͑1991͒.
  20. R. W. Hallwarth, Prog. Quantum. Electron. 5, 1 ͑1977͒.
  21. J. T. Fourkas, H. Kawashima, and K. A. Nelson, J. Chem. Phys. 103, 4393 ͑1995͒.
  22. I. Ohmine and H. Tanaka, Chem. Rev. 93, 2545 ͑1993͒.
  23. M. Cho, G. R. Fleming, S. Saito, and I. Ohmine, J. Chem. Phys. 100, 6672 ͑1994͒.
  24. S. Sastry, H. E. Stanley, and F. Sciortino, J. Chem. Phys. 100, 5361 ͑1994͒.
  25. B. M. Garraway and K.-A. Suominen, Rep. Prog. Phys. 58, 365 ͑1995͒.
  26. S. Nakajima, Prog. Theor. Phys. 20, 948 ͑1960͒; R. Zwanzig, J. Chem. Phys. 33, 1338 ͑1960͒; H. Mori, Prog. Theor. Phys. 33, 423 ͑1965͒.
  27. R. P. Feynman and F. L. Vernon, Ann. Phys. ͑N.Y.͒ 24, 118 ͑1963͒.
  28. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics, 2nd ed. ͑Springer, Berlin, 1995͒, Vol 2.
  29. F. Neugebauer, D. Malzahn, and V. May, Chem. Phys. 201, 151 ͑1995͒.
  30. A. O. Caldeira and A. J. Leggett, Phys. Status Solidi A 121, 587 ͑1983͒.
  31. W. R. Frensley, Rev. Mod. Phys. 62, 745 ͑1990͒. 32 One further applies the rotating wave approximation ͑RWA͒ to simplify the bilinear system-bath interaction. The equation of motion with RWA does not have temperature restriction, however, one should bare in mind that the exact equation of motion can be applied only at the high tempera- ture. Therefore, an applicability of the equation of motion must be checked carefully.
  32. Y. Tanimura and R. Kubo, J. Phys. Soc. Jpn. 58, 101 ͑1989͒.
  33. Y. Tanimura and P. G. Wolynes, Phys. Rev. A 43, 4131 ͑1991͒
  34. Y. Tanimura and P. G. Wolynes, J. Chem. Phys. 96, 8485 ͑1992͒.
  35. Y. Tanimura and S. Mukamel, Phys. Rev. E 47, 118 ͑1993͒; J. Opt. Soc. Am. B 10, 2263͑1993͒; Ultrafast Spectroscopy in Chemical System, edited by J. D. Simon ͑Kluwer, Dordrecht, 1994͒, p. 327.
  36. K. Okumura and Y. Tanimura, Phys. Rev. E 53, 214 ͑1996͒.
  37. R. Fukuda, M. Sumino, and K. Nomoto, Phys. Rev. A 45, 3559 ͑1992͒; R. Fukuda and M. Sumino, ibid. 44, 6252 ͑1991͒.
  38. The general bilinear molecular-solvent coupling considered in Ref. 37 is the form Ϫ ͚ iϭ0 N c i j q i q j , where q 0 ϵQ instead of Ϫ ͚ iϭ1 N c i q i Q.
  39. S. Mukamel, Principles of Nonlinear Optical Spectroscopy ͑Oxford Uni- versity Press, New York, 1995͒.
  40. A. O. Caldeira and A. J. Leggett, Physica A 121, 587 ͑1983͒; 130, 374͑E͒ ͑1985͒; Ann. Phys. ͑USA͒ 149, 374 ͑1983͒; 153, 445͑E͒ ͑1984͒.
  41. H. Grabert, P. Schramm, and G.-L. Ingold, Phys. Rep. 168, 115 ͑1988͒.
  42. The bilinearly corrected propagators are derived for the general coupling constant c i j ͑see Ref. 39͒ in Ref. 37, In our special case the bilinear coupling constants c i j is set to c i j ϭ␦ i0 (1Ϫ␦ j0 )c j ϩ␦ j0 (1Ϫ␦ i0 )c i .
  43. H. Haken and H. C. Wolf, Molecular Physics and Elements of Quantum Chemistry ͑Springer, Berlin, 1995͒.
  44. R. Fukuda, M. Komachiya, S. Yokojima, Y. Suzuki, K. Okumura, and T. Inagaki, Prog. Theor. Phys. Suppl. No. 121 ͑1995͒.
  45. R. Fukuda, Phys. Rev. Lett. 61, 1549 ͑1988͒.
  46. R. Fukuda, Prog. Theor. Phys. 78 1487 ͑1987͒; R. Fukuda, M. Ko- machiya, and M. Ukita, Phys. Rev. D 38, 3747 ͑1988͒; M. Komachiya, M. Ukita, and R. Fukuda, ibid. 42, 2792 ͑1990͒.
  47. M. Ukita, M. Komachiya, and R. Fukuda, Int. J. Mod. Phys. A 5, 1789 ͑1990͒.
  48. K. Okumura, Prog. Theor. Phys. 87, 703 ͑1992͒; Y. Yokojima, Nucl. Phys. B 390, 319 ͑1993͒.
  49. M. Ukita, Doctoral thesis, Keio University, 1991.
  50. T. Inagaki and R. Fukuda, Phys. Rev. B 46, 10931 ͑1992͒; T. Inagaki, ibid. 52, 1219 ͑1995͒.
  51. K. Okumura, J. Magn. Magn. Mater. 140-144, 191 ͑1995͒; Phys. Rev. B 52, 13358 ͑1995͒.
  52. K. Okumura, Int. J. Mod. Phys. A 11, 65 ͑1996͒; S. Yokojima, Phys. Rev. D 51, 2996 ͑1995͒.
  53. At the time of proofreading of this paper, we have finished the following papers. K. Okumura and Y. Tanimira, ''Femtosecond two-dimensional spectroscopy from anharmonic vibrational modes of molecules in con- densed phase'' ͑IMS preprint, 1996͒; ''The ͑2nϩ1͒th-order off-resonant spectroscopy from the ͑nϩ1͒th-order anharmonicities of molecular vibra- tional modes in condensed phase'' ͑IMS preprint, 1996͒.