Methods for calculating vibrational energy levels

Canadian Journal of Chemistry

Volumn 82, Issue 6, 2004, Pages 900-914

  Carrington Jr , Tucker ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Contracted basis functions; Kinetic energy operators; Lanczos algorithm; Preconditioning; Vibrational energy levels

Indexed keywords

ALGORITHMS; HAMILTONIANS; ITERATIVE METHODS; MATRIX ALGEBRA; VECTORS;

HAMILTONIAN MATRIX; VIBRATIONAL ENERGY LEVELS;

ELECTRON ENERGY LEVELS;

ALGORITHM; CALCULATION; ENERGY; KINETICS; REVIEW; VIBRATION;

EID: 9944236731     PISSN: 00084042     EISSN: None     Source Type: Journal    
DOI: 10.1139/v04-014     Document Type: Review

References (94)

1. G.H. Herzberg. Infrared and Raman spectra. Van Nostrand Reihnold, Toronto. 1945.
2. G.H. Herzberg. Electronic spectra of polyatomic molecules. Van Nostrand Reinhold, Toronto. 1966.
3. M.R. Aliev and J.K.G. Watson. In Molecular spectroscopy: Modern research. Vol. III. Edited by K.N. Rao. Academic Press, Orlando. 1985. pp. 1-67.
4. D. Papousek and M.R. Aliev. Molecular vibrational-rotational spectra. Elsevier, Amsterdam. 1982.
5. S. Carter and N.C. Handy. Comput. Phys. Rep. 5, 115 (1986).
6. E.L. Sibert. Int. Rev. Phys. Chem. 9, 1 (1990).
7. J. Tennyson. Comp. Phys. Rep. 4, 1 (1986).
8. Z. Bačič and J.C. Light. Annu. Rev. Phys. Chem. 40, 469 (1989).
9. T. Carrington, Jr. Encyclopedia of computational chemistry. Edited by Paul von Ragué Schleyer. Vol. 5. John Wiley and Sons, Bern, Switzerland. 1998.
10. A.G. Császár (Editor). Spectrochim. Acta Part A 58 (2002). A special issue on first principles rovibrational spectroscopy.
11. W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling. Numerical recipes. Cambridge University Press, Cambridge, UK. 1989.
12. B. Podolsky. Phys. Rev. 32, 812 (1928).
13. A. Nauts and X. Chapuisat. Mol. Phys. 55, 1287 (1985).
14. X. Chapuisat, A. Nauts, and J.-P. Brunet. Mol. Phys. 72, 1 (1991).
15. X. Chapuisat, A. Belfhal, and A. Nauts. J. Mol. Spectrosc. 149, 274 (1991).
16. X. Chapuisat and C. Iung. Phys. Rev. A, 45, 6217 (1992).
17. F. Gatti, C. Iung, M. Menou, Y. Justum, A. Nauts, and X. Chapuisat. J. Chem. Phys. 108, 8804 (1998).
18. C. Iung, F. Gatti, A. Viel, and X. Chapuisat. Phys. Chem. Chem. Phys. 1, 3377 (1999).
19. B.T. Sutcliffe. In Current aspects of quantum chemistry, Studies in theoretical and physical chemistry. Vol. 21. Edited by R. Carbo. Elsevier, Amsterdam. 1982. pp. 99-125.
20. B.T. Sutcliffe and J. Tennyson. Int. J. Quantum Chem. 39, 183 (1991).
21. J. Tennyson and B.T. Sutcliffe. J. Chem. Phys. 77, 4061 (1982).
22. G. Brocks, A. Van Der Avoird, B.T. Sutcliffe, and J. Tennyson. Mol. Phys. 50, 1025 (1983).
23. S.S. Xantheas and B.T. Sutcliffe. J. Chem. Phys. 103, 8022 (1995).
24. N.C. Handy. Mol. Phys. 61, 207 (1987).
25. M. Mladenoví, J. Chem. Phys. 112, 1070 (2000).
26. M. Mladenović. J. Chem. Phys. 112, 1082 (2000).
27. T.J. Lukka, J. Chem. Phys. 102, 3945 (1995).
28. M.J. Bramley and T. Carrington, Jr. J. Chem. Phys. 99, 8519 (1993).
29. X.-G. Wang and T. Carrington, Jr. J. Chem. Phys. 113, 7097 (2000).
30. R.J. Whitehead and N.C. Handy. J. Mol. Spectrosc. 55, 356 (1975).
31. J.C. Light and T. Carrington, Jr. Adv. Chem. Phys. 114, 263 (2000).
32. Z. Bačić and J.C. Light. Annu. Rev. Phys. Chem. 40, 469 (1989).
33. H. Wei and T. Carrington, Jr. J. Chem. Phys. 97, 3029 (1992).
34. J. Echave and D.C. Clary. Chem. Phys. Lett. 190, 225 (1992).
35. S. Carter and N.C. Handy. Comput. Phys. Commun. 51, 49 (1988).
36. J.R. Henderson and J. Tennyson. Chem. Phys. Lett. 173, 133 (1990).
37. X.T. Wu, A.B. McCoy, and E.E Hayes. J. Chem. Phys. 110, 2354 (1999).
38. Y. Qiu, J.Z.H. Zhang, and Z. Bačić. J. Chem. Phys. 108, 4804 (1998).
39. A. Bahel and Z. Bačić. J. Chem. Phys. 111, 11164 (1999).
40. M. Mladenović. Spectrochim. Acta Part A, 58, 809 (2002).
41. M. Mladenović. Spectrochim. Acta Part A, 58, 795 (2002).
42. D. Luckhaus. J. Chem. Phys. 113, 1329 (2000).
43. M.J. Bramley and N.C. Handy. J. Chem. Phys. 98, 1378 (1993).
44. J.M. Bowman and B. Gazdy. J. Chem. Phys. 94,454 (1991).
45. S. Carter and N.C. Handy. Mol. Phys. 100, 681 (2002).
46. J. Koput, S. Carter, and N. Handy. J. Chem. Phys. 115, 8345 (2001).
47. N.C. Handy, S. Carter, and S.M. Colwell. Mol. Phys. 96, 477 (1999).
48. R.E. Wyatt. Adv. Chem. Phys. 73, 231 (1989).
49. H. Koeppel, W. Domcke, and L.S. Cederbaum. Adv. Chem. Phys. 57, 59 (1984).
50. C. Iung and C. Leforestier. J. Chem. Phys. 90, 3198 (1989).
51. J.A. Bentley, J.-P. Brunet, R.E. Wyatt, R.A. Friesner, and C. Leforestier. Chem. Phys. Lett. 161, 393 (1989).
52. M.J. Bramley and T. Carrington, Jr. J. Chem. Phys. 101, 8494 (1994).
53. D. Neuhauser. J. Chem. Phys. 93, 2611 (1990).
54. R.B. Lehoucq, S.K. Gray, D.-H. Zhang, and J.C. Light. Comput. Phys. Commun. 109, 15 (1998).
55. H.Y. Mussa and J. Tennyson. J. Chem. Phys. 109, 10 885 (1998).
56. N.R. Wall and D. Neuhauser. J. Chem. Phys. 102, 8011 (1995).
57. V.A. Mandelshtam and H.S. Taylor. J. Chem. Phys. 102, 7390 (1995).
58. V.A. Mandelshtam and H.S. Taylor. J. Chem. Phys. 106, 5085 (1997).
59. H.-G. Yu and S.C. Smith. Ber. Bunsenges. Phys. Chem. 101, 400 (1997).
60. R. Chen and H. Guo. J. Chem. Phys. 108, 6068 (1998).
61. G.H. Golub and C.F. Van Loan. Matrix computations. Johns Hopkins University Press, Baltimore, Md. 1989.
62. R.A. Friesner, R.E. Wyatt, C. Hempel, and B. Criner. J. Comput. Phys. 64, 220 (1986).
63. U. Manthe and H. Koeppel. J. Chem. Phys. 93, 345 (1990).
64. J.K. Cullum and R.A. Willoughby. Lanczos algorithms for large symmetric eigenvalue computations. Birkhäuser, Boston, Mass. 1985.
65. D.C. Sorensen. SIAM J. Math. Anal. Appl. 13, 357 (1992).
66. R.B. Lehoucq, D.C. Sorensen, and C. Yang. ARPACK users guide: Solution of large scale eigenvalue problems by implicitly restarted Arnoldi methods. SIAM, Philadelphia, Pa. 1998.
67. J. Baglama, D. Calvetti, and L. Reichel. BIT, 36, 400 (1996).
68. S. Huang and T. Carrington, Jr. Chem. Phys. Lett. 312, 311 (1999).
69. P.-N. Roy and T. Carrington, Jr. J. Chem. Phys. 103, 5600 (1995).
70. P.-N. Roy and T. Carrington, Jr. Chem. Phys. Lett. 257, 98 (1996).
71. M.J. Bramley, J.W. Tromp, T. Carrington, Jr., and G.C. Corey. J. Chem. Phys. 100, 6175 (1994).
72. C. Leforestier. J. Chem. Phys. 101, 7357 (1994).
73. G.C. Corey and D.J. Lemoine. Chem. Phys. 1992, 97, 4115.
74. C. Leforestier, L.B. Braly, K. Liu, M.J. Elrod, and R.J. Saykally. J. Chem. Phys. 106, 8527 (1997).
75. X.-G. Wang and T. Carrington, Jr. J. Chem. Phys. 115, 9781 (2001).
76. R. Chen, G. Ma, and H. Guo. J. Chem. Phys. 114, 4764 (2001).
77. P.R. Bunker and Per Jensen. Molecular symmetry and spectroscopy. 2nd ed. NRC Research Press, Ottawa, Ont., Canada. 1998.
78. X.-G. Wang and T. Carrington, Jr. J. Chem. Phys. 114, 1473 (2001).
79. R. Chen and H. Guo. J. Chem. Phys. 114, 1467 (2001).
80. N.M. Poulin, M.J. Bramley, T. Carrington, H.G. Kjaergaard, and B.R. Henry. J. Chem. Phys. 104, 7807 (1996).
81. X.-G. Wang and T. Carrington, Jr. J. Chem. Phys. 118, 6946 (2003).
82. S.-W. Huang and T. Carrington, Jr. J. Chem. Phys. 112, 8765 (2000).
83. B. Poirier and T. Carrington, Jr. J. Chem. Phys. 114, 9254 (2001).
84. T. Ericsson and A. Ruhe. Math. Comp. 63, 494 (1991).
85. F. Webster, P.J. Rosky, and R.A. Friesner. Comput. Phys. Commun. 63, 494 (1991).
86. H. Kono. Chem. Phys. Lett. 214, 137 (1993).
87. R. E. Wyatt. Phys. Rev. E, 51, 3643 (1995).
88. J.J. Dongarra, I.S. Duff, D.C. Sorensen, and H.A. van der Vorst. Numerical linear algebra for high-performance computers. SIAM, Philadelphia, Pa. 1998.
89. B. Poirier. Numer. Linear Algebra Appl. 7, 715 (2000).
90. R.A. Friesner, J.A. Bentley, M. Menou, and C. Leforestier. J. Chem. Phys. 99, 324 (1993).
91. M.J. Bramley and T. Carrington, Jr. J. Chem. Phys. 101, 8494 (1994).
92. X.T. Wu and E.F. Hayes. J. Chem. Phys. 107, 2705 (1997).
93. A. Viel and C. Leforestier. J. Chem. Phys. 112, 1212 (2000).
94. X.-G. Wang and T. Carrington, Jr. J. Chem. Phys. 117, 6923 (2002).