Vibrational energy levels via finite-basis calculations using a quasi-analytic form of the kinetic energy

Journal of Chemical Theory and Computation

Volumn 7, Issue 5, 2011, Pages 1428-1442

  Vázquez, Juana ^a,b   Harding, Michael E ^a,b   Stanton, John F ^a   Gauss, Jürgen ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79955911372     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct100711u     Document Type: Article

References (174)

1. Nielsen, H. H. In Handbuch der Physik, Part. 1; Flügge, S., Ed.; Spring-Verlag: Berlin, 1959; Vol. 37, p 171.
2. Papoušek, D. and Aliev, M. R. Molecular Vibrational-Rotational Spectra, 1st ed.; Elsevier Scientifics: New York, 1982.
3. Konen, I. M.; Li, E. X. J.; Lester, M. I.; Vázquez, J.; Stanton, J. F. J. Chem. Phys. 2006, 125, 074310
4. Matthews, D. A.; Vázquez, J.; Stanton, J. F. Mol. Phys. 2007, 105, 2659
5. Vázquez, J.; Stanton, J. F. Mol. Phys. 2007, 105, 101
6. McCoy, A. B.; Sibert, E. L., III J. Chem. Phys. 1991, 95, 3476
7. McCoy, A. B.; Sibert, E. L., III In Dynamics of Molecules and Chemical Reactions; Wyatt, R. E.; Zhang, J. Z. H., Eds.; Marcel Dekker: New York, 1996; p 151.
8. Norris, L. S.; Ratner, M. A.; Roitberg, A. E.; Gerber, R. B. J. Chem. Phys. 1996, 105, 11261
9. Bucknell, M. G.; Handy, N. C.; Boys, S. F. Mol. Phys. 1974, 28, 759
10. Whitehead, R. J.; Handy, N. C. J. Mol. Spectrosc. 1975, 55, 356
11. Carney, G. D.; Kern, C. W. Int. J. Quant. Chem. Suppl. 1975, Y-9, 317
12. Carney, G. D.; Langhoff, S. R.; Curtiss, L. A. J. Chem. Phys. 1977, 66, 3724
13. Carney, G. D.; Sprandel, L. L.; Kern, C. W. Adv. Chem. Phys. 1978, 37, 305
14. Dunn, K. M.; Boggs, J. E.; Pulay, P. J. Chem. Phys. 1986, 85, 5838
15. Dunn, K. M.; Boggs, J. E.; Pulay, P. J. Chem. Phys. 1987, 86, 5088
16. Bowman, J. M. J. Chem. Phys. 1978, 68, 608
17. Bowman, J. M.; Christoffel, K. M; Tobin, F. J. Phys. Chem. 1979, 83, 905
18. Tobin, F.; Bowman, J. M. Chem. Phys. 1980, 47, 151
19. Christoffel, K. M.; Bowman, J. M. Chem. Phys. Lett. 1982, 85, 220
20. Carter, S.; Bowman, J. M.; Harding, L. B. Spectrochim. Acta 1997, 53A, 1179
21. Carter, S.; Bowman, J. M. J. Chem. Phys. 1998, 108, 4397
22. Bégué, D.; Gohaud, N.; Pouchan, C.; Cassan-Chenaï, P.; Liévin, J. J. Chem. Phys. 2007, 127, 164115
23. Harris, D. O.; Engerholm, G. G.; Gwinn, W. D. J. Chem. Phys. 1965, 43, 1515
24. Endres, P. F. J. Chem. Phys. 1967, 47, 798
25. Dickinson, A. S.; Certain, P. R. J. Chem. Phys. 1968, 49, 4209
26. Lill, J. V.; Parker, G. A.; Light, J. C. Chem. Phys. Lett. 1982, 89, 483
27. Heather, R. W.; Light, J. C. J. Chem. Phys. 1983, 79, 147
28. Light, J. C.; Hamilton, I. P.; Lill, J. V. J. Chem. Phys. 1985, 82, 1400
29. Bowman, J. M.; Carrington, T., Jr.; Meyer, H. D. Mol. Phys. 2008, 106, 2145
30. Stanton, J. F.; Gauss, J. Int. Rev. Phys. Chem. 2000, 19, 61
31. Ruden, T. A.; Taylor, P. R.; Helgaker, T. J. Chem. Phys. 2003, 119, 1951
32. Park, S. C.; Braams, B. J.; Bowman, J. M. J. Theor. Comput. Chem. 2005, 4, 163
33. Huang, X.; Braams, B. J.; Bowman, J. M. J. Chem. Phys. 2005, 122, 044308
34. Xie, Z.; Braams, B. J.; Bowman, J. M. J. Chem. Phys. 2005, 122, 224307
35. Sharma, A. R.; Braams, B. J.; Carter, S.; Shepler, B. C.; Bowman, J. M. J. Chem. Phys. 2009, 130, 174301
36. Li, G. Y.; Wang, S.-W.; Rosenthal, C.; Rabitz, H. J. Math. Chem. 2001, 30, 1
37. Carter, S.; Culik, S. J.; Bowman, J. M. J. Chem. Phys. 1997, 107, 10458
38. Jung, J. O.; Gerber, R. B. J. Chem. Phys. 1996, 105, 10332
39. Beck, M. H.; Jäckle, A.; Worth, G. A.; Meyer, H. D. Phys. Rep. 2000, 324, 1
40. Mátyus, E.; Czakó, G.; Sutcliffe, B. T.; Császár, A. G. J. Chem. Phys. 2007, 127, 084102
41. Meyer, R.; Günthard, H. H. J. Chem. Phys. 1968, 49, 1510
42. Pickett, H. M. J. Chem. Phys. 1972, 56, 1715
43. Lukka, T. J. J. Chem. Phys. 1995, 102, 3945
44. Schwenke, D. W. J. Chem. Phys. 2003, 118, 10431
45. Watson, J. K. G. J. Mol. Spectrosc. 2004, 228, 645
46. Fehrensen, B.; Luckhaus, D.; Quack, M. Chem. Phys. Lett. 1999, 300, 312
47. Luckhaus, D. J. Chem. Phys. 2000, 113, 1329
48. Luckhaus, D. J. Chem. Phys. 2003, 118, 8797
49. Lauvergnat, D.; Nauts, A. J. Chem. Phys. 2002, 116, 8560
50. Lauvergnat, D.; Baloïtcha, E.; Dive, G.; Desouter-Lecomte, M. Chem. Phys. 2006, 326, 500
51. Yurchenko, S. N.; Thiel, W.; Jensen, P. J. Mol. Spectrosc. 2007, 245, 126
52. Makarewicz, J. In Computational Molecular Spectroscopy; Jensen, P.; Bunker, P. R., Eds.; Wiley: Chichester, U.K., 2000; p 391.
53. Mátyus, E.; Czakó, G.; Császár, A. G. J. Chem. Phys. 2009, 130, 134112
54. Nauts, A.; Chapuisat, X. Mol. Phys. 1985, 55, 1287
55. Chapuisat, X.; Belafhal, A.; Nauts, A. J. Mol. Spectrosc. 1991, 149, 274
56. Gatti, F.; Iung, C.; Leforestier, C.; Chapuisat, X. J. Chem. Phys. 1999, 111, 7236
57. Gatti, F. J. Chem. Phys. 1999, 111, 7225
58. Gatti, F.; Muñoz, C.; Iung, C. J. Chem. Phys. 2001, 114, 8275
59. Mladenović, M. J. Chem. Phys. 2000, 112, 1070
60. Mladenović, M. J. Chem. Phys. 2000, 112, 1082
61. Wang, X.-G.; Carrington, T., Jr. J. Chem. Phys. 2004, 121, 2937
62. Sutcliffe, B. T. In Conceptual Trends in Quantum Chemistry; Kryachko, S.; Calais, J. L., Eds.; Kluwer: Dordrecht The Netherlands, 1994; p 53; and references therein.
63. Sutcliffe, B. T.; Tennyson, J. Int. J. Quantum Chem. 1991, 39, 183
64. Tennyson, J.; Sutcliffe, B. T. J. Chem. Phys. 1982, 77, 4061
65. Brocks, G.; Avoird, A. v. D.; Sutcliffe, B. T. Mol. Phys. 1983, 50, 1025
66. Handy, N. C. Mol. Phys. 1987, 61, 207
67. Császár, A. G.; Handy, N. C. J. Chem. Phys. 1995, 102, 3962
68. Vendrell, O.; Gatti, F.; Meyer, H.-D. J. Chem. Phys. 2007, 127, 184303
69. Gatti, F.; Iung, C. Phys. Rep. 2009, 484, 1
70. Watson, J. K. G. Mol. Phys. 1968, 15, 479
71. Watson, J. K. G. Mol. Phys. 1970, 19, 465
72. Webster, F.; Huang, M.-J.; Wolfsberg, M. J. Chem. Phys. 1981, 75, 2306
73. Maessen, B.; Wolfsberg, M. J. Chem. Phys. 1984, 80, 4651
74. Maessen, B.; Wolfsberg, M. J. Phys. Chem. 1984, 88, 6420
75. Chen, C.-L.; Maessen, B.; Wolfsberg, M. J. Chem. Phys. 1985, 83, 1795
76. Searles, D. J.; von Nagy-Felsobuki, E. I. J. Chem. Phys. 1991, 95, 1107
77. Wang, F.; von Nagy-Felsobuki, E. I. Mol. Phys. 1992, 77, 1197
78. Searles, D.; von Nagy-Felsobuki, E. I. Ab Initio Variational Calculations of Molecular Vibration-Rotation Spectra. Lecture Notes in Chemistry, 1st ed.; Springer-Verlag: Berlin, Germany, 1993; No. 61.
79. Page, A. J.; von Nagy-Felsobuki, E. I. Mol. Phys. 2007, 105, 2527
80. Carter, S.; Bowman, J. M.; Handy, N. C. Theor. Chem. Acc. 1998, 100, 191
81. Carter, S.; Bowman, J. M. J. Phys. Chem. A 2000, 104, 2355
82. Bowman, J. M.; Huang, X. C.; Carter, S. Spectrochim. Acta 2002, 58A, 839
83. Aoyagi, M.; Gray, S. K. J. Chem. Phys. 1991, 94, 195
84. Seideman, T.; Miller, W. H. J. Chem. Phys. 1992, 97, 2499
85. Balint-Kurti, G. G.; Pulay, P. J. Mol. Struct. (THEOCHEM) 1995, 341, 1
86. Yonehara, T.; Yamamoto, T.; Kato, S. Chem. Phys. Lett. 2004, 393, 98
87. Wang, F.; McCourt, F. R. W.; von Nagy-Felsobuki, E. I. J. Mol. Struct. (THEOCHEM) 2000, 497, 227
88. Mátyus, E.; Šimunek, J.; Császár, A. G. J. Chem. Phys. 2009, 131, 074106
89. Rauhut, G. J. Chem. Phys. 2004, 121, 9313
90. Rauhut, G.; Hrenar, T. Chem. Phys. 2008, 346, 160
91. Heislbetz, S.; Rauhut, G. J. Chem. Phys. 2010, 132, 124102
92. Louck, J. D. J. Mol. Spectrosc. 1976, 61, 107
93. Makushkin, Y. S.; Ulenikov, O. N. J. Mol. Spectrosc. 1977, 68, 1
94. Harding, M. E.; Vázquez, J.; Ruscic, B.; Wilson, A. K.; Gauss, J.; Stanton, J. F. J. Chem. Phys. 2008, 128, 114111
95. Amat, G.; Henry, L. Cah. Phys. 1958, 12, 273
96. Amat, G.; Henry, L. Cah. Phys. 1961, 12, 472
97. Hougen, J. T. J. Chem. Phys. 1962, 36, 519
98. Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vibration. The Theory of Infrared and Raman Vibrational Spectra; Dover Publications: New York, 1955.
99. Handbook of Mathematical Functions; Abramowitz, M.; Stegun, I. A., Eds. Dover Publications: New York, 1972.
100. Aliev, M. R. Opt. Spectrosc. 1969, 26, 463
101. Mladenović, M. Spectrochim. Acta 2002, 58A, 795
102. Huber, D. Int. J. Quantum Chem. 1985, 28, 245
103. Aliev, M. R.; Watson, J. K. G. In Molecular Spectroscopy: Modern Research.; Rao, K. N., Ed.; Academic Press: Orlando, FL, 1985; Vol. III, p 1.
104. Wick, G. C. Phys. Rev. 1950, 80, 268
105. Mandl, F.; Shaw, G. Quantum Field Theory; Wiley: New York, 1984.
106. The ladder operator formalism used here does not correspond to a complete second quantization formalism for creation and annihilation operators. Concepts and premises, as for example, vacuum and creation/annihilation of normal modes are not defined.
107. The contributions from the potential (V ̂) and pseudopotential (U ̂) could be integrated jointly numerically or analytically, which would lead to a small reduction of the computational cost. However, the main purpose of this study is to analyze the magnitude of each contribution independently and to point out the advantages of the quasi-analytic calculation of KEO expressed as a Taylor expansion around the equilibrium configuration.
108. Nemes, L. In Vibrational Spectra and Structure; During, J. R., Ed.; Elsevier: Amsterdam, The Netherlands, 1981; Vol. 10, p 395.
109. Lanczos, C. J. Res. Natl. Bur. Stand. 1950, 45, 255
110. Cullum, J. K.; Willoughby, R. A. Lanczos Algorithms for Large Symmetry Eigenvalue Computations; Birkhäuser: Boston, MA, 1985; Vol. 1-2.
111. Simon, H. D. Math. Comput. 1984, 42, 115
112. Golub, G. H.; Van Loan, C. F. Matrix Computations; Johns Hopkins University Press: Baltimore, MD, 1996.
113. The most efficient way for the reorthogonalization of a Hermitian matrix was found to be a formulation of the modified Gram-Schmidt method, which heavily involves highly optimized BLAS and LAPACK routines (see http://www.netlib.org/ lapack/). A complete Cholesky decomposition of the overlap matrix of the complete set of Lanczos vectors is performed, and the Lanczos vectors are then multiplied in place with the inverse triangular matrix resulting from the Cholesky procedure.
114. Furtenbacher, T.; Császár, A. G.; Tennyson, J. J. Mol. Spectrosc. 2007, 245, 115
115. Polyansky, O. L.; Császár, A. G.; Shirin, S. V.; Zobov, N. F.; Barletta, P.; Tennyson, J.; Schwenkey, D. W.; Knowles, P. J. Science 2003, 299, 539
116. Barletta, P.; Shirin, S. V.; Zobov, N. F.; Polyansky, O. L.; Tennyson, J.; Valeev, E. F.; Császár, A. G. J. Chem. Phys. 2006, 125, 204307
117. DEWE stands for discrete variable representation (D) of the Eckart-Watson (EW) Hamiltonian with exact inclusion of an arbitrary potential energy function (E).
118. Schuurman, M. S.; Muir, S. R.; Allen, W. D.; Schaefer, H. F., III J. Chem. Phys. 2004, 120, 11586
119. Wheeler, S. E.; Robertson, K. A.; Allen, W. D.; Schaefer, H. F., III; Bomble, Y. J.; Stanton, J. F. J. Chem. Phys. A 2007, 111, 3819
120. α B e α, which contributes to the zero-point energy of nonlinear polyatomic molecules.
121. Bartholomae, R.; Martin, D.; Sutcliffe, B. T. J. Mol. Spectrosc. 1981, 87, 367
122. Carter, S.; Handy, N. C. J. Mol. Spectrosc. 1982, 95, 9
123. In the case of numerical approaches this problem is addressed in different ways, see for example ref 40 and also: Scivetti, I.; Kohanoff, J.; Gidopoulos, N. I. Int. J. Quantum Chem. 2011, 111, 307
124. Sarka, K.; Bunker, P. R. J. Mol. Spectrosc. 1987, 122, 259
125. Epa, V. C.; Bunker, P. R. J. Mol. Spectrosc. 1991, 150, 511
126. Fermi, E. Z. Physik 1931, 71, 250
127. Suzuki, I. J. Mol. Spectrosc. 1968, 25, 479
128. Cihla, Z.; Chédin, A. J. Mol. Spectrosc. 1971, 40, 337
129. Chédin, A.; Cihla, Z. J. Mol. Spectrosc. 1973, 47, 554
130. Jobard, I.; Chédin, A. J. Mol. Spectrosc. 1975, 57, 464.
131. Chédin, A. J. Mol. Spectrosc. 1979, 76, 430
132. Lacy, M. Mol. Phys. 1982, 45, 253
133. Steele, D.; Person, W. B.; Brown, K. G. J. Phys. Chem. 1981, 85, 2007
134. Allen, W. D.; Yamaguchi, Y.; Császár, A. G.; Clabo, D. A., Jr.; Remington, R. B.; Schaefer, H. F., III Chem. Phys. 1990, 145, 427
135. Maslen, P. E.; Jayatilaka, D.; Colwell, S. M.; Amos, R. D.; Handy, N. C. J. Chem. Phys. 1991, 95, 7409
136. Martins Filho, H. P. Spectroschim. Acta. 2002, 58A, 2621
137. Martin, J. M. L.; Taylor, P. R.; Lee, T. J. Chem. Phys. Lett. 1993, 205, 535
138. Császár, A. G. J. Phys. Chem. 1992, 96, 7898
139. Rodriguez-Garcia, V.; Hirata, S.; Yagi, K.; Hirao, K.; Taketsugu, T.; Schweigert, I.; Tasumi, M. J. Chem. Phys. 2007, 126, 124303
140. Czakó, G.; Furtenbacher, T.; Császár, A. G.; Szalay, V. Mol. Phys. 2004, 102, 2411
141. -1; (fc) stands for "frozen core", i.e., that only the valence electrons were correlated in the post Hartree-Fock treatment.
142. 2 and HFCO, respectively.
143. Morokuma, K.; Kato, S.; Hirao, K. J. Chem. Phys. 1980, 72, 6800
144. Morokuma, K.; Kato, S. In Potential energies surfaces and dynamics calculations for chemical reactions and molecular energy transfer; Truhlar, D. G., Ed.; Plenum: New York, 1981; p 243.
145. Goddard, J. D.; Schaefer, H. F., III J. Chem. Phys. 1990, 93, 4907
146. Kamiya, K.; Morokuma, K. J. Chem. Phys. 1991, 94, 7287
147. Francisco, J. S.; Zhao, Y. J. Chem. Phys. 1992, 96, 7587
148. Wei, T.-G.; Wyatt, R. E. J. Phys. Chem. 1993, 97, 13580
149. Yamamoto, T.; Kato, S. J. Chem. Phys. 1997, 107, 6114
150. Bartlett, R. J. Annu. Rev. Phys. Chem. 1981, 32, 359
151. Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618
152. Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007
153. Viel, A.; Leforestier, C. J. Chem. Phys. 2000, 112, 1212
154. Leforestier, C.; Viel, A.; Gatti, F.; Mũnoz, C.; Iung, C. J. Chem. Phys. 2001, 114, 2099
155. Iung, C.; Ribeiro, F. J. Chem. Phys. 2005, 123, 174105
156. Iung, C.; Ribeiro, F.; Sibert, E. L., III J Phys. Chem. A 2006, 110, 5420
157. Ribeiro, F.; Iung, C.; Leforestier, C. J. Chem. Phys. 2005, 123, 054106
158. Ribeiro, F.; Iung, C.; Leforestier, C. J. Theor. Comput. Chem. 2003, 2, 609
159. Pasin, G.; Gatti, F.; Iung, C.; Meyer, H. D. J. Chem. Phys. 2006, 124, 194304
160. Wang, X.-G.; Carrington, T., Jr. J. Chem. Phys. 2009, 130, 094101
161. Green, W. H.; Jayatilaka, D.; Willetts, A.; Amos, R. D.; Handy, N. C. J. Chem. Phys. 1990, 93, 4965
162. Vázquez, J.; Stanton, J. F. Mol. Phys. 2006, 104, 377
163. Mills, I. M. In Modern Spectroscopy: Modern Research; Rao, K. N.; Matthews, C. W., Eds.; Academic Press: New York, 1972; Vol. I, p 115.
164. Friesner, R. A.; Bentley, M.; Menou, M.; Leforestier, C. J. Chem. Phys. 1993, 99, 324
165. Choi, Y. S.; Moore, C. B. J. Chem. Phys. 1991, 94, 5414
166. Choi, Y. S.; Moore, C. B. J. Chem. Phys. 1992, 97, 1010
167. Choi, Y. S.; Moore, C. B. J. Chem. Phys. 1995, 103, 9981
168. Morgan, H. W.; Staats, P. A.; Goldstein, J. H. J. Chem. Phys. 1956, 25, 337
169. Stratton, R. F.; Nielsen, A. H. J. Mol. Spectrosc. 1960, 4, 373
170. Kattenberg, H. W.; Elst, R.; Oskam, A. J. Mol. Spectrosc. 1971, 39, 29
171. Mizuno, M.; Saëki, D. Spectrochim. Acta 1978, 34A, 407
172. Wong, M.; Johns, J. W. C.; Mckellar, A. R. W. J. Mol. Spectrosc. 1982, 94, 79
173. -1.
174. Herzberg, G. Molecular Spectra and Molecular Structure; van Nostrand: New York, 1950; Vol. I-III.