Chapter 9 An Active Database Approach to Complete Rotational-Vibrational Spectra of Small Molecules

Annual Reports in Computational Chemistry

Volumn 3, Issue , 2007, Pages 155-176

  Császár, Attila G ^a   Czakó, Gábor ^a   Furtenbacher, Tibor ^a   Mátyus, Edit ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

ab initio; active database; carbon dioxide; computational molecular spectroscopy; DMS; internal coordinate Hamiltonians; MARVEL; PES; water; Watsonian

Indexed keywords

EID: 34548664125     PISSN: 15741400     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1574-1400(07)03009-5     Document Type: Review

References (172)

1. +. Astrophys. J. 454 (1995) L169-L173
2. 2. J. Mol. Struct. 780-81 (2006) 283-294
3. Harris F.E. Current methods for Coulomb few-body problems. Adv. Quant. Chem. 47 (2004) 129-155
4. Armour E.A.G., Richard J.-M., and Varga K. Stability of few-charge systems in quantum mechanics. Phys. Rep. 413 (2005) 1-90
5. Császár A.G., Tarczay G., Leininger M.L., Polyansky O.L., Tennyson J., and Allen W.D. Dream or reality: complete basis set full configuration interaction potential energy hypersurfaces. In: Demaison J., Sarka K., and Cohen E.A. (Eds). Spectroscopy from Space (2001), Kluwer, Dordrecht 317-339
6. Császár A.G., Allen W.D., Yamaguchi Y., and Schaefer III H.F. Ab initio determination of accurate ground electronic state potential energy hypersurfaces for small molecules. In: Jensen P., and Bunker P.R. (Eds). Computational Molecular Spectroscopy (2000), Wiley, New York 15-68
7. Tarczay G., Császár A.G., Klopper W., and Quiney H.M. Anatomy of relativistic energy corrections in light molecular systems. Mol. Phys. 99 (2001) 1769-1794
8. Balasubramanian K. Relativistic Effects in Chemistry. Part A. Theory and Techniques (1997), Wiley, New York
9. Born M., and Oppenheimer J.R. Zur Quantentheorie der Molekeln. Ann. Phys. 84 (1927) 457-484
10. Born M. Kopplung der Elektronen- und Kernbewegung in Molekeln und Kristallen. Göttinger Nachr. Acad. Wiss. Math. Nat. Kl. 6 (1951) 1-3
11. Born M., and Huang K. Dynamical Theory of Crystal Lattices (1956), Oxford University Press, London
12. Bunker P.R., and Jensen P. The Born-Oppenheimer approximation. In: Jensen P., and Bunker P.R. (Eds). Computational Molecular Spectroscopy (2000), Wiley, New York 1-12
13. Nielsen H.H. The vibration-rotation energies of molecules. Rev. Mod. Phys. 23 (1951) 90-136
14. Papoušek D., and Aliev M.R. Molecular Vibration-Rotation Spectra (1982), Elsevier, Amsterdam
15. Mills I.M. In: Rao K.N., and Mathews C.W. (Eds). Molecular Spectroscopy: Modern Research (1972), Academic Press, New York
16. Gaw J.F., Willetts A., Green W.H., and Handy N.C. Advances in Molecular Vibrations and Collision Dynamics (1990), JAI Press, Greenwich, CT
17. Clabo D.A., Allen W.D., Remington R.B., Yamaguchi Y., and Schaefer III H.F. A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent field higher derivative methods-asymmetric-top molecules. Chem. Phys. 123 (1988) 187-239
18. Allen W.D., Yamaguchi Y., Császár A.G., Clabo D.A., Remington R.B., and Schaefer III H.F. A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent field higher derivative methods-linear polyatomic molecules. Chem. Phys. 145 (1990) 427-466
19. Aliev M.R., and Watson J.K.G. In: Narahari Rao K. (Ed). Molecular Spectroscopy: Modern Research, vol. III (1985), Academic Press, San Diego, CA 1-67
20. Polyansky O.L., Császár A.G., Shirin S.V., Zobov N.F., Barletta P., Tennyson J., Schwenke D.W., and Knowles P.J. High accuracy ab initio rotation-vibration transitions for water. Science 299 (2003) 539-542
21. Furtenbacher, T., Császár, A.G., Tennyson, J. MARVEL: Measured active rotational-vibrational energy levels, J. Mol. Spectry., 2007, submitted
22. Császár A.G., Furtenbacher T., and Czakó G. The greenhouse effect on Earth and the complete spectroscopy of water. Magy. Kém. Foly. 112 (2006) 123-128 (in Hungarian)
23. +. J. Chem. Phys. 122 (2005) 041102
24. Kolos W., Szalewicz K., and Monkhorst H.J. New Born-Oppenheimer potential energy curve and vibrational energies for the electronic ground state of the hydrogen molecule. J. Chem. Phys. 84 (1986) 3278-3283
25. + molecular ions. Eur. Phys. J. D 12 (2000) 449-466
26. 2 +-like systems. J. Chem. Phys. 126 (2007) 024102
27. 2 + and its isotopomers. J. Phys. B 32 (1999) L89-L91
28. Cencek W., Komasa J., and Rychlewski J. Configuration interaction and Hylleraas configuration interaction methods in valence bond theory. Diatomic two-electron systems. J. Chem. Phys. 95 (1991) 2572-2576
29. Wolniewicz L. Nonadiabatic energies of the ground state of the hydrogen molecule. J. Chem. Phys. 103 (1995) 1792-1799
30. Frolov A.M., and Smith V.H. Scaled-time dynamics of ionization of Rydberg Stark states by half-cycle pulses. J. Phys. B 28 (1995) L449-L456
31. Bunker P.R., and Moss R.E. Breakdown of Born-Oppenheimer approximation-effective vibration-rotation Hamiltonian for a diatomic molecule. Mol. Phys. 33 (1977) 417-424
32. Bunker P.R., and Moss R.E. Effect of the breakdown of the Born-Oppenheimer approximation on the rotation-vibration Hamiltonian of a triatomic molecule. J. Mol. Spectry. 80 (1980) 217-228
33. Sellers H., and Pulay P. The adiabatic correction to molecular potential surfaces in the SCF approximation. Chem. Phys. Lett. 103 (1984) 463-465
34. 2 and other molecular effects. J. Chem. Phys. 84 (1986) 4481-4484
35. Kutzelnigg W. The adiabatic approximation I. The physical background of the Born-Handy ansatz. Mol. Phys. 90 (1997) 909-916
36. Valeev E.F., and Sherrill C.D. The adiabatic correction to molecular potential surfaces in the SCF approximation. J. Chem. Phys. 118 (2003) 3921-3927
37. Gauss J., Tajti A., Kállay M., Stanton J.F., and Szalay P.G. Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory. J. Chem. Phys. 125 (2006) 144111
38. 2O. J. Phys. Chem. A 105 (2001) 2352-2360
39. +. J. Chem. Phys. 114 (2001) 1693-1699
40. Ruscic B., Pinzon R.E., Morton M.L., Von Laszevski G., Bittner S.J., Nijsure S.G., Amin K.A., Minkoff M., and Wagner A.F. Introduction to active thermochemical tables: several "key" enthalpies of formation revisited. J. Phys. Chem. A 108 (2004) 9979-9997
41. Ruscic B., Boggs J.E., Burcat A., Császár A.G., Demaison J., Janoschek R., Martin J.M.L., Morton M., Rossi M.J., Stanton J.F., Szalay P.G., Westmoreland P.R., Zabel F., and Bérces T. IUPAC critical evaluation of thermochemical properties of selected radicals, Part I. J. Phys. Chem. Ref. Data 34 (2005) 573-656
42. Feeley R., Seiler P., Packard A., and Frenklach M. Consistency of a reaction dataset. J. Phys. Chem. A 108 (2004) 9573-9583
43. Frenklach M., Packard A., Seiler P., and Feeley R. Collaborative data processing in developing predictive models of complex reaction systems. Int. J. Chem. Kinet. 36 (2004) 57-66
44. -1. Mol. Phys. 32 (1976) 499-521
45. 17O. J. Mol. Spectry. 56 (1975) 138-145
46. 18O from 0.5 to 5 THz. J. Mol. Spectry. 193 (1999) 217-223
47. 18O. J. Mol. Spectry. 84 (1980) 405-423
48. SISAM database http://mark4sun.jpl.nasa.gov/
49. -1 spectral region. J. Mol. Spectry. 237 (2006) 53-62
50. -1 spectral region: the first decade of resonating states. J. Quant. Spectrosc. Rad. Transfer 61 (1999) 795-812
51. 17O in the 3 ν + δ and 4ν polyad region. J. Mol. Spectry. 234 (2005) 1-9
52. Tennyson J., Zobov N.F., Williamson R., Polyansky O.L., and Bernath P.F. Experimental energy levels of the water molecule. J. Phys. Chem. Ref. Data 30 (2001) 735-831
53. Császár A.G., and Mills I.M. Vibrational energy levels of water. Spectrochim. Acta 53A (1997) 1102-1122
54. Allen W.D., East A.L.L., and Császár A.G. Ab initio anharmonic vibrational analysis of non-rigid molecules. In: Laane J., Dakkouri M., van der Veken B., and Oberhammer H. (Eds). Structures and Conformations of Non-Rigid Molecules (1993), Kluwer, Dordrecht 343-373
55. Császár A.G., Allen W.D., and Schaefer III H.F. In pursuit of the ab initio limit for conformational energy prototypes. J. Chem. Phys. 108 (1998) 9751-9764
56. Dunning Jr. T.H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90 (1989) 1007-1023
57. The (aug-)cc-p(wC)VnZ basis sets can be obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 1.0, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory, which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, USA and funded by the U.S. Department of Energy. The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institute for the U.S. Department of Energy under contract DE-AC06-76RLO 1830
58. Note that the Hartree-Fock limit (HFL) can be achieved with just a few dozen Gaussian functions in a fully variational computation through optimization of the positions and the exponents of the Gaussians, as discussed in Tasi, G., Császár, A.G., Hartree-Fock-limit energies and structures with a few dozen distributed Gaussians, Chem. Phys. Lett., 2007, 438, 139-43
59. Hartree D.R. The wave mechanics of an atom with a non-Coulomb central field. Part I. Theory and methods. Proc. Cambridge Philos. Soc. 24 (1928) 89-110
60. Fock V. Naherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Z. Phys. 61 (1930) 126-148
61. Møller C., and Plesset M.S. Note on an approximation treatment for many-electron systems. Phys. Rev. 46 (1934) 618-622
62. Kállay M., and Surján P.R. Computing coupled-cluster wave functions with arbitrary excitations. J. Chem. Phys. 113 (2000) 1359-1365
63. Kállay M., Gauss J., and Szalay P.G. Analytic first derivatives for general coupled-cluster and configuration interaction models. J. Chem. Phys. 119 (2003) 2991-3004
64. Kállay M., and Gauss J. Analytic second derivatives for general coupled-cluster and configuration-interaction models. J. Chem. Phys. 120 (2004) 6841-6848
65. 2) saga: Ab initio excursions in the web of polytopism. J. Chem. Phys. 107 (1997) 1195-1211
66. Tarczay G., Császár A.G., Klopper W., Szalay V., Allen W.D., and Schaefer III H.F. The barrier to linearity of water. J. Chem. Phys. 110 (1999) 11971-11981
67. Barletta P., Shirin S.V., Zobov N.F., Polyansky O.L., Tennyson J., Valev E.F., and Császár A.G. CVRQD ab initio ground-state adiabatic potential energy surfaces for the water molecule. J. Chem. Phys. 125 (2006) 204307
68. Tarczay G., Császár A.G., Polyansky O.L., and Tennyson J. Ab initio rovibrational spectroscopy of hydrogen sulfide. J. Chem. Phys. 115 (2001) 1229-1242
69. -. J. Chem. Phys. 112 (2000) 4053-4063
70. Tarczay G., Császár A.G., Leininger M.L., and Klopper W. The barrier to linearity of hydrogen sulphide. Chem. Phys. Lett. 322 (2000) 119-128
71. Tajti A., Szalay P.G., Császár A.G., Kállay M., Gauss J., Valeev E.F., Flowers B.A., Vázquez J., and Stanton J.F. HEAT: High accuracy extrapolated ab initio thermochemistry. J. Chem. Phys. 121 (2004) 11599-11613
72. Bomble Y.J., Vázquez J., Kállay M., Michauk C., Szalay P.G., Császár A.G., Gauss J., and Stanton J.F. High accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification. J. Chem. Phys. 125 (2006) 064108
73. Boese A.D., Oren M., Atasoylu O., Martin J.M.L., Kállay M., and Gauss J. W3 theory: robust computational thermochemistry in the kJ/mol accuracy range. J. Chem. Phys. 120 (2004) 4129-4141
74. Karton A., Rabinovich E., Martin J.M.L., and Ruscic B. W4 theory for computational thermochemistry: in pursuit of confident sub-kJ-mol predictions. J. Chem. Phys. 125 (2006) 144108
75. Tasi G., Izsák R., Matisz G., Császár A.G., Kállay M., Ruscic B., and Stanton J.F. The origin of systematic error in the standard enthalpies of formation of hydrocarbons computed via atomization schemes. ChemPhysChem 7 (2006) 1664-1667
76. 2Π CH. Mol. Phys. 100 (2002) 3879-3883
77. 2. J. Chem. Phys. 118 (2003) 10631-10642
78. Császár A.G. Anharmonic molecular force fields. In: Schleyer P.v.R., Allinger N.L., Clark T., Gasteiger J., Kollman P.A., Schaefer III H.F., and Schreiner P.R. (Eds). The Encyclopedia of Computational Chemistry vol. 1 (2001), Wiley, Chichester 13-30
79. Sarka K., and Demaison J. Perturbation theory, effective Hamiltonians and force constants. In: Jensen P., and Bunker P.R. (Eds). Computational Molecular Spectroscopy (2000), Wiley, Chichester 255-303
80. Allen W.D., Czinki E., and Császár A.G. Molecular structure of proline. Chem. Eur. J. 10 (2004) 4512
81. th derivative of self-consistent-field energy. J. Chem. Phys. 95 (1991) 7409-7417
82. Yamaguchi Y., Osamura Y., Goddard J.D., and Schaefer III H.F. A New Dimension to Quantum Chemistry: Analytic Derivative Methods in Ab Initio Molecular Electronic Structure Theory (1994), Oxford University Press, New York
83. Kállay M., Gauss J., and Szalay P.G. Analytic first derivatives for general coupled-cluster and configuration interaction models. J. Chem. Phys. 119 (2003) 2991-3004
84. Kállay M., and Gauss J. Analytic second derivatives for general coupled-cluster and configuration-interaction models. J. Chem. Phys. 120 (2004) 6841-6848
85. Lacy M., and Whiffen D.H. The anharmonic force field of nitrous-oxide. Mol. Phys. 45 (1982) 241-252
86. 2O. J. Phys. Chem. 98 (1994) 8823-8826
87. Kobayashi M., and Suzuki I. Sextic force-field of nitrous-oxide. J. Mol. Spectry. 125 (1987) 24-42
88. Teffo J.-L., and Chédin A. Internuclear potential and equilibrium structure of the nitrous-oxide molecule from rovibrational data. J. Mol. Spectry. 135 (1989) 389-409
89. 2. J. Phys. Chem. 96 (1992) 7898-7904
90. Chédin A. Carbon-dioxide molecule-potential, spectroscopic, and molecular constants from its infrared spectrum. J. Mol. Spectry. 76 (1979) 430-491
91. Lacy M. The anharmonic force field of carbon-dioxide. Mol. Phys. 45 (1982) 253-258
92. Suzuki I. General anharmonic force constants of carbon dioxide. J. Mol. Spectry. 25 (1968) 479-500
93. Allen W.D., and Császár A.G. On the ab initio determination of higher-order force-constants at nonstationary reference geometries. J. Chem. Phys. 98 (1993) 2983-3015
94. 2O. J. Chem. Phys. 107 (1997) 8317
95. 4, by means of accurate ab initio calculations. J. Chem. Phys. 103 (1995) 2589-2602
96. Martin J.M.L., and Taylor P.R. Accurate ab initio quartic force field for trans-HNNH and treatment of resonance polyads. Spectrochim. Acta 53A (1997) 1039-1050
97. Watson J.K.G. Simplification of the molecular vibration-rotation Hamiltonian. Mol. Phys. 5 (1968) 479-490
98. Watson J.K.G. The vibration-rotation hamiltonian of linear molecules. Mol. Phys. 19 (1970) 465-487
99. van Mourik T., Harris G.J., Polyansky O.L., Tennyson J., Császár A.G., and Knowles P.J. Ab initio global potential, dipole, adiabatic, and relativistic correction surfaces for the HCN-HNC system. J. Chem. Phys. 115 (2001) 3706
100. Werner H.-J., and Knowles P.J. An efficient internally contracted multiconfiguration reference configuration-interaction method. J. Chem. Phys. 89 (1988) 5803-5814
101. Langhoff S., and Davidson E.R. Configuration-interaction calculations on the nitrogen molecule. Int. J. Quant. Chem. 8 (1974) 61-72
102. Gdanitz R.J., and Ahlrichs R. The averaged coupled-pair functional (ACPF)-a size-extensive modification of MR-CISD. Chem. Phys. Lett. 143 (1988) 413-420
103. Császár A.G., Kain J.S., Polyansky O.L., Zobov N.F., and Tennyson J. Relativistic correction to the potential energy surface and vibration-rotation levels of water. Chem. Phys. Lett. 293 (1998) 317-323
104. Császár A.G., Kain J.S., Polyansky O.L., Zobov N.F., and Tennyson J. Relativistic correction to the potential energy surface and vibration-rotation levels of water. Chem. Phys. Lett. 312 (1999) 613-616
105. Quiney H.M., Barletta P., Tarczay G., Császár A.G., Polyansky O.L., and Tennyson J. Two-electron relativistic corrections to the potential energy surface and vibration-rotation levels of water. Chem. Phys. Lett. 344 (2001) 413-420
106. Pyykkö P., Dyal K.G., Császár A.G., Tarczay G., Polyansky O.L., and Tennyson J. Estimation of Lamb-shift effects for molecules: Application to the rotation-vibration spectra of water. Phys. Rev. A 63 (2001) 024502
107. Partridge H., and Schwenke D.W. The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data. J. Chem. Phys. 106 (1997) 4618-4639
108. 18O isotopologues of water. J. Mol. Spectry. 236 (2006) 216-223
109. Callegari A., Theule P., Tolchenov R.N., Zobov N.F., Polyansky O.L., Tennyson J., Muenter J.S., and Rizzo T.R. Dipole moments of highly vibrationally excited water. Science 297 (2002) 993-995
110. 2O spectra measured by frequency-stabilized cavity ring-down spectroscopy. Phys. Rev. A 73 (2006) 012507
111. Schwenke D.W., and Partridge H. Convergence testing of the analytic representation of an ab initio dipole moment function for water: Improved fitting yields improved intensities. J. Chem. Phys. 113 (2000) 6592-6597
112. Lodi, L., Tolchenov, R.N., Tennyson, J., Lynas-Gray, A.-E., Shirin, S.V., Zobov, N.F., Polyansky, O.L., Császár, A.G., van Stralen, J.N.P., Visscher, L. A new ab initio ground state dipole moment surface for the water molecule, J. Chem. Phys. 2007, submitted
113. Bucknell M.G., Handy N.C., and Boys S.F. Vibration-rotation wavefunctions and energies for any molecule obtained by a variational method. Mol. Phys. 28 (1974) 759-776
114. Whitehead R.J., and Handy N.C. Variational calculation of vibration-rotation energy levels for triatomic molecules. J. Mol. Spectry. 55 (1975) 356-373
115. Sutcliffe B.T., and Tennyson J. A general treatment of vibration-rotation coordinates for triatomic-molecules. Int. J. Quant. Chem. 39 (1991) 183-196
116. Handy N.C. The derivation of vibration-rotation kinetic energy operators in internal coordinates. Mol. Phys. 61 (1987) 207-223
117. Császár A.G., and Handy N.C. Exact quantum-mechanical vibrational kinetic-energy operator of sequentially bonded molecules in valence internal coordinates. J. Chem. Phys. 102 (1995) 3962-3967
118. Lukka T.J. A simple method for the derivation of exact quantum-mechanical vibration-rotation Hamiltonians in terms of internal coordinates. J. Chem. Phys. 102 (1995) 3945-3955
119. Bowman J.M., Carter S., and Huang X. MULTIMODE: a code to calculate rovibrational energies of polyatomic molecules. Int. Rev. Phys. Chem. 22 (2003) 533-549
120. Harris D.O., Engerholm G.G., and Gwinn W.D. Calculation of matrix elements for one-dimensional quantum-mechanical problems and the application to anharmonic oscillators. J. Chem. Phys. 43 (1965) 1515-1517
121. Dickinson A.S., and Certain P.R. Calculation of matrix elements for one-dimensional quantum-mechanical problems. J. Chem. Phys. 49 (1968) 4209-4211
122. Light J.C., Hamilton I.P., and Lill J.V. Generalized discrete variable approximation in quantum-mechanics. J. Chem. Phys. 82 (1985) 1400-1409
123. Bačić Z., and Light J.C. Theoretical methods for rovibrational states of floppy molecules. Annu. Rev. Phys. Chem. 40 (1989) 469-498
124. Szalay V. Discrete variable representations of differential-operators. J. Chem. Phys. 99 (1993) 1978-1984
125. Szalay V. The generalized discrete variable representation. An optimal design. J. Chem. Phys. 105 (1996) 6940-6956
126. Light J.C., and Carrington Jr. T. Discrete-variable representations and their utilization. Adv. Chem. Phys. 114 (2000) 263-310
127. Szalay V., Czakó G., Nagy A., Furtenbacher T., and Császár A.G. On one-dimensional discrete variable representations with general basis functions. J. Chem. Phys. 119 (2003) 10512-10518
128. Bramley M.J., and Carrington Jr. T. A general discrete variable method to calculate vibrational-energy levels of 3-atom and 4-atom molecules. J. Chem. Phys. 99 (1993) 8519-8541
129. Mladenović M. Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. I. Orthogonal representations. J. Chem. Phys. 112 (2000) 1070-1081
130. Mladenović M. Discrete variable approaches to tetratomic molecules Part I: DVR(6) and DVR(3)+DGB methods. Spectrochim. Acta 58A (2002) 795-807
131. Antikainen J., Friesner R., and Leforestier C. Adiabatic pseudospectral calculation of vibrational-states of 4 atom molecules-application to hydrogen-peroxide. J. Chem. Phys. 102 (1995) 1270-1279
132. Schwenke D.W. Variational calculations of rovibrational energy levels and transition intensities for tetratomic molecules. J. Chem. Phys. 100 (1996) 2867-2884
133. Carter S., Pinnavaia N., and Handy N.C. The vibrations of formaldehyde. Chem. Phys. Lett. 240 (1995) 400-408
134. Luckhaus D. 6D vibrational quantum dynamics: Generalized coordinate discrete variable representation and (a)diabatic contraction. J. Chem. Phys. 113 (2000) 1329-1347
135. Handy N.C., Carter S., and Colwell S.M. The vibrational energy levels of ammonia. Mol. Phys. 96 (1999) 477-491
136. Koput J., Carter S., and Handy N.C. Potential energy surface and vibrational-rotational energy levels of hydrogen peroxide. J. Phys. Chem. A 102 (1998) 6325-6330
137. 2HF. J. Chem. Phys. 118 (2003) 4896-4904
138. 4 from an ab initio potential. Spectrochim. Acta 57A (2001) 887-895
139. Schwenke D.W. Towards accurate ab initio predictions of the vibrational spectrum of methane. Spectrochim. Acta 58A (2002) 849-861
140. Wang X.-G., and Carrington Jr. T. A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrodinger equation in nine dimensions. J. Chem. Phys. 119 (2003) 101-117
141. Yu H.-G. An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach. J. Chem. Phys. 117 (2002) 2030-2037
142. Yu H.-G. Two-layer Lanczos iteration approach to molecular spectroscopic calculation. J. Chem. Phys. 117 (2002) 8190-8196
143. Yu H.-G. Full-dimensional quantum calculations of vibrational spectra of six-atom molecules. I. Theory and numerical results. J. Chem. Phys. 120 (2004) 2270-2284
144. Carter S., and Handy N.C. The variational method for the calculation of ro-vibrational energy levels. Comp. Phys. Rep. 5 (1986) 115-172
145. +-Ab initio calculation of vibration spectrum. J. Chem. Phys. 65 (1976) 3547-3565
146. Tennyson J., Kostin M.A., Barletta P., Harris G.J., Polyansky O.L., Ramanlal J., and Zobov N.F. DVR3D: a program suite for the calculation of rotation-vibration spectra of triatomic molecules. Comp. Phys. Comm. 163 (2004) 85-116
147. Schwenke D.W. On the computation of ro-vibrational energy levels of triatomic molecules. Comp. Phys. Comm. 70 (1992) 1-14
148. - molecular anion: structural aspects, global surface, and vibrational eigenspectrum. J. Chem. Phys. 99 (1993) 3865-3897
149. Wang X.-G., and Carrington Jr. T. New ideas for using contracted basis functions with a Lanczos eigensolver for computing vibrational spectra of molecules with four or more atoms. J. Chem. Phys. 117 (2003) 6923-6934
150. Makarewicz J. Rovibrational Hamiltonian of a triatomic molecule in local and collective internal coordinates. J. Phys. B 21 (1988) 1803-1819
151. Lanczos C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stand. 45 (1950) 255-282
152. Czakó G., Furtenbacher T., Császár A.G., and Szalay V. Variational vibrational calculations using high-order anharmonic force fields. Mol. Phys. 102 (2004) 2411-2423
153. Sutcliffe B.T. The coupling of nuclear and electronic motions in molecules. J. Chem. Soc. Faraday Trans. 89 (1993) 2321-2335
154. Meremianin A.V., and Briggs J.S. The irreducible tensor approach in the separation of collective angles in the quantum N-body problem. Physics Rep. 384 (2003) 121-195
155. -1 including empirical corrections for the non-adiabatic effects, Mol. Phys. 2003, 101, 189-209
156. +-Explicit expressions for some vibrational matrix elements. J. Mol. Spectry. 134 (1987) 430-436
157. +-A reappraisal. J. Chem. Phys. 98 (1993) 7191-7203
158. + using a Morse-based discrete variable representation. Can. J. Phys. 72 (1994) 702-713
159. +. Chem. Phys. 190 (1995) 291-300
160. -1. J. Chem. Phys. 100 (1994) 6175-6194
161. + molecular ion for J = 0. An accurate calculation using filter diagonalization. J. Chem. Soc. Faraday Trans. 93 (1997) 847-860
162. Vincke M., Malegat L., and Baye D. Regularization of singularities in Lagrange-mesh calculations. J. Phys. B: At. Mol. Opt. Phys. 26 (1993) 811-826
163. Czakó G., Szalay V., Császár A.G., and Furtenbacher T. Treating singularities present in the Sutcliffe-Tennyson vibrational Hamiltonian in orthogonal internal coordinates. J. Chem. Phys. 122 (2005) 024101
164. Czakó G., Szalay V., and Császár A.G. Finite basis representations with nondirect product basis functions having structure similar to that of spherical harmonics. J. Chem. Phys. 124 (2006) 014110
165. Czakó G., Furtenbacher T., Barletta P., Császár A.G., Szalay V., and Sutcliffe B.T. Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations. Phys. Chem. Chem. Phys. 9 (2007) 3407-3415
166. Littlejohn R.G., and Cargo M. Bessel discrete variable representation bases. J. Chem. Phys. 117 (2002) 27-36
167. Dunn K., Boggs J.E., and Pulay P. Vibrational energy levels of methyl-fluoride. J. Chem. Phys. 86 (1987) 5088-5093
168. Leonard C., Handy N.C., Carter S., and Bowman J.M. The vibrational levels of ammonia. Spectrochim. Acta 58A (2002) 825-838
169. n, n = 2, 3, 4, 5): Vibrational self-consistent field with correlation corrections. J. Chem. Phys. 105 (1996) 10332-10348
170. Carter S., Culik S., and Bowman J.M. Vibrational self-consistent field method for many-mode systems: A new approach and application to the vibration of CO absorbed on Cu(100). J. Chem. Phys. 107 (1997) 10458-10469
171. Mátyus, E., Czakó, G., Sutcliffe, B.T. Császár, A.G. Vibrational energy levels with arbitrary potentials using the Eckart-Watson Hamiltonians and the discrete variable representation, J. Chem. Phys. 2007, in press
172. Sutcliffe B.T. Molecular Hamiltonians. In: Wilson S. (Ed). Handbook of Molecular Physics and Quantum Chemistry (2003), Wiley, Chichester