Computationally efficient recurrence relations for one-dimensional Franck-Condon overlap integrals

Molecular Physics

Volumn 108, Issue 11, 2010, Pages 1513-1529

  Schmidt, P P ^a,b  

^a DALHOUSIE UNIVERSITY   (Canada)

^b Department of Physics ^*  (United States)

Author keywords

Franck Condon factors; harmonic oscillator overlap; Morse oscillator overlap; non Condon factors; recurrence relations

Indexed keywords

ANALYTICAL EXPRESSIONS; BASIS SETS; COMPUTATIONALLY EFFICIENT; DIRECT USE; DISSOCIATION LIMIT; EIGENVALUES; EIGENVECTORS; FRANCK-CONDON; FRANCK-CONDON FACTORS; GAMMA FUNCTION; HARMONIC OSCILLATOR FUNCTIONS; HARMONIC OSCILLATOR MODEL; HARMONIC OSCILLATORS; MACHINE PRECISION; MATRIX ELEMENTS; MORSE OSCILLATOR; MORSE POTENTIALS; OVERLAP INTEGRALS; QUANTUM NUMBERS; RECURRENCE RELATIONS;

BAND STRUCTURE; CHEMICAL BONDS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON TRANSITIONS; HARMONIC ANALYSIS; HARMONIC FUNCTIONS; MOLECULAR ORBITALS; OSCILLATORS (MECHANICAL); SCHRODINGER EQUATION; WAVE FUNCTIONS;

OSCILLATORS (ELECTRONIC);

EID: 77954043826     PISSN: 00268976     EISSN: 13623028     Source Type: Journal    
DOI: 10.1080/00268971003762142     Document Type: Article

References (66)

1. J. Franck, Trans. Faraday Soc. 21, 536 (1925).
2. E.U. Condon, Phys. Rev. 28, 1182 (1926).
3. E. Hutchisson, Phys. Rev. 36, 410 (1930).
4. D.R. Bates, Proc. Roy. Soc. A 196, 217 (1949).
5. C. Manneback, Physica 17, 1001 (1951).
6. P.A. Fraser and W.R. Jarmain, Proc. Phys. Soc. (London) A 66, 76 (1953).
7. W.R. Jarmain and P.A. Fraser, Proc. Phys. Soc. (London) A 66, 1153 (1953).
8. M. Wagner, Z. Natursorsch. 14a, 81 (1959).
9. F. Ansbacher, Z. Naturforsch. 14a, 889 (1959).
10. N.R. Tawde and N.S. Murthy, Physica 25, 610 (1959).
11. R.N. Zare, E.O. Larsson and R.A. Berg, J. Mol. Spect. 15, 117 (1965).
12. J. Katriel and G. Adam, J. Phys. B. Mol. Phys. 3, 13 (1970).
13. K. Nishikawa, Int. J. Quant. Chem. 12, 859 (1977).
14. T.E. Sharp and H.M. Rosenstock, J. Chem. Phys. 41, 3453 (1964).
15. T.R. Faulkner and F.S. Richardson, J. Chem. Phys. 70, 1201 (1979).
16. F. Iachello, Chem. Phys. Lett. 78, 581 (1981).
17. R.W. Nicholis, J. Chem. Phys. 74, 6980 (1981).
18. S. Waldenstrøm and K.R. Naqvi, Chem. Phys. Lett. 85, 581 (1982).
19. S. Waldenstrøm and K.R. Naqvi, J. Chem. Phys. 77, 1613 (1982).
20. R.W. Nicholis, J. Chem. Phys. 77, 1614 (1981).
21. F.H. Tipping and F.J. Ogilvie, J. Chem. Phys. 79, 2537 (1983).
22. A. Palma and J. Morales, Int. J. Quant. Chem. (QuantSymp.) 17, 393 (1983).
23. A. Palma, L. Sandoval and J. Morales, Int. J. Quant. Chem. (Quant. Chem. Symp.) 21, 729 (1987).
24. J. Morales, Phys. Rev. A 36, 4101 (1987).
25. M. Berrondo, A. Palma and J.L. López-Bonilla, Int. J. Quant. Chem. 31, 243 (1987).
26. F. Karlsson and C. Jedrzejek, J. Chem. Phys. 86, 3532 (1987).
27. S. Waldenstrøm and K. Razi Naqvi, J. Chem. Phys. 87, 3563 (1987).
28. N. Rajamanickam, Acta Phys. Hung. 63, 51 (1988).
29. D. Secrest, J. Phys. Chem. 95, 1058 (1991).
30. A. Matsumoto and K. Iwamoto, J. Quant. Spect. 50, 103 (1993).
31. K. Iwamoto and A. Matsumoto, J. Quant. Spect. 52, 901 (1994).
32. E. Ley-Koo, S. Mateos-Cortés and G. Villa-Torres, Int. J. Quant. Chem. 56, 175 (1995).
33. N.M. Avram and Gh.E. Drǎgǎnescu, Int. J. Quant. Chem. 64, 655 (1997).
34. A. Palma, Int. J. Quant. Chem. 63, 229 (1997).
35. M. Carvajal, J.M. Arias and J. Gómez-Camacho, Phys. Rev. A 59, 3462 (1998).
36. F. Iachello and M. Ibrahim, J. Phys. Chem. A 102, 9427 (1998).
37. R. Islampour, M. Dehestani and S.H. Lin, J. Mol. Spectros. 194, 179 (1999).
38. A. Palma, V.M. León and L. Sandoval, Int. J. Quant. Chem. 75, 11 (1999).
39. A. Frank, R. Lemus and F. Pérez-Bernal, J. Math. Chem. 25, 383 (1999).
40. A. Frank, A.L. Rivera and K.B. Wolf, Phys. Rev. A 61, 054102 (2000).
41. F.J. Mélendez, L. Sandoval and A. Palma, J. Mol. Struct. (Theochem.) 580, 91 (2002).
42. J.C. López V., A.L. Rivera, Yu.F. Smirnov and A. Frank, Int. J. Quant. Chem. 88, 280 (2002).
43. K.B. Kumar, N. Rajamanickam, S.P. Bagare, F.F. Gomez and J.J.L. Gonzalez, Astroparticle Phys. 20, 67 (2003).
44. M. Lee and M. Kim, J. Chem. Phys. 119, 5085 (2003).
45. J. Liang, H. Zheng, X. Zhang, R. Li and Z. Chu, Mol. Phys. 105, 1903 (2007).
46. P. Siders and R.A. Marcus, J. Am. Chem. Soc. 103, 741 (1981).
47. B.W. Spath and W.H. Miller, Chem. Phys. Lett. 262, 486 (1996).
48. Yu.F. Smirnov, Nuc. Phys. 39, 346 (1962).
49. M. Moshinsky, The Harmonic Oscillator in Modern Physics: From Atoms to Quarks (Gordon and Breach, New York, 1969).
50. M. Moshinsky and Yu.F. Smirnov, The Harmonic Oscillator in Modern Physics (Harwood Academic, Amsterdam, 1996).
51. P.P. Schmidt, Int. J. Quant. Chem. 90, 202 (2002).
52. H. Margenau and G. Murphy, The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1955).
53. W.H. Press, S.A. Teuklosky, W.T. Vettering and B.P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, UK, 1992).
54. P.M. Morse, Phys. Rev. 34, 57 (1929).
55. S. Flügge, Practical Quantum Mechanics (Springer-Verlag, Berlin, 1994).
56. J.N. Murrell, S. Carter, S.C. Farantos, P. Huxley and A.J.C. Varandas, Molecular Potential Energy Functions (Wiley, Chichester, UK, 1984).
57. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic Press, New York, 1980).
58. National Institutes of Standards and Technology, Physical Reference Base, http://physics.nist.gov/cuu/ Constants/index.html
59. A. Szabo and N.S. Ostlund, Modern Quantum Chemistry, Introduction to Advanced Electronic Structure Theory (Dover, New York, 1996); (previously published by McGraw-Hill, New York, 1989).
60. E.A. Power, Introductory Quantum Electrodynamics (Longmans, London, 1964).
61. W.P. Healy, Non-relativistic Quantum Electrodynamics (Academic Press, New York, 1982).
62. J.M. Turlet, Ph. Kottis and M.R. Philpott, Adv. Chem. Phys. 54, 303 (1983).
63. M.R. Philpott, J. Phys. C. Solid State Phys. 1, 42 (1968).
64. S. Carter and N.C. Handy, Comp. Phys. Rep. 5, 115 (1986).
65. S. Carter, N.C. Handy and I.M. Mills, Phil. Trans. R. Soc. A 332, 309 (1990).
66. P.P. Schmidt, Mol. Phys. 105, 1217 (2007).