Exact and constrained kinetic energy operators for polyatomic molecules: The polyspherical approach

Physics Reports

Volumn 484, Issue 1-2, 2009, Pages 1-69

  Gatti, Fabien ^a   Iung, Christophe ^a  

^a UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

Curvilinear coordinates; Kinetic energy operator; Polyspherical coordinates; Quantum molecular dynamics

Indexed keywords

EID: 70449367070     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2009.05.003     Document Type: Review

References (204)

1. In: Chergui M. (Ed). Femtochemistry (1996), World Scientific, Singapore
2. Zewail A.H. Femtochemistry-Ultrafast Dynamics of the Chemical Bond (1994), World Scientific, Singapore
3. Ihee H., Lobastov V., Gomez U., Goodson B., Srinivasan R., Ruan C.-Y., and Zewail A.H. Science 291 (2001) 385
4. Fellers R.S., Braly L.B., Saykally R.J., and Leforestier C. Science 284 (1999) 6306
5. Saykally R.J., and Blake G.A. Science 259 (1993) 1570
6. 3H. J. Chem. Phys. 118 (2003) 93
7. 3. Chem. Phys. Lett. 254 (1996) 52
8. Espinosa-García J., Corchado J.C., and Truhlar D.G. The importance of quantum effects for C-H bond activation reactions. J. Am. Chem. Soc. 119 (1997) 9891
9. Truhlar D.G., Gao J., Alhambra C., Garcia-Viloca M., Corchado J., Sánchez M.L., and Villà J. The incorporation of quantum effects in enzyme kinetics modeling. Acc. Chem. Res. 35 (2002) 341
10. Truhlar D.G., Gao J., Alhambra C., Garcia-Viloca M., Corchado J., Sánchez M.L., and Villà J. Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions. Int. J. Quant. Chem. 100 (2004) 1136
11. Meyer H.-D., and Worth G.A. Quantum molecular dynamics: Propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree (MCTDH) method. Theor. Chem. Acc. 109 (2003) 251-267
12. In: Meyer H.-D., Gatti F., and Worth G.A. (Eds). Multidimensional Quantum Dynamics: MCTDH Theory and Applications (2009), Wiley-VCH, Weinheim
13. Meyer H.-D., Manthe U., and Cederbaum L.S. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 165 (1990) 73-78
14. Manthe U., Meyer H.-D., and Cederbaum L.S. Wave-packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl. J. Chem. Phys. 97 (1992) 3199-3213
15. Beck M.H., Jäckle A., Worth G.A., and Meyer H.-D. The multi-configuration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propagating wave packets. Phys. Rep 324 (2000) 1-105
16. Manthe U. A time-dependent discrete variable representation for (multi-configuration) Hartree methods. J. Chem. Phys. 105 (1996) 6989
17. Manthe U. Reaction Rates: Accurat quantum dynamical calculations for polyatomic systems. J. Theor. Comp. Chem. 1 (2002) 153
18. Manthe U. The state averaged multi-configurational time-dependent Hartree approach: Vibrational state and reaction rate calculations. J. Chem. Phys. 128 (2008) 064108
19. Worth G.A. Accurate wave packet propagation for large molecular systems: The multi-configuration time-dependent Hartree (MCTDH) method with selected configurations. J. Chem. Phys. 112 (2000) 8322-8329
20. Worth G.A. Quantum dynamics using pseudo-particle trajectories: A new approach based on the multi-configuration time-dependent Hartree method. J. Chem. Phys. 114 (2001) 1524-1532
21. Bowman J.M., Huang X., Handy N.C., and Carter S. Vibrational levels of methanol calculated by the reaction path version of MULTIMODE, using an ab initio, full-dimensional potential. J. Phys. Chem. A 111 (2007) 7317
22. Bowman J.M. The self-consistent-field approach to polyatomic vibrations. Acc. Chem. Res. 19 (1986) 202
23. Carter S., Culik S.J., and Bowman J.M. Vibrational self-consistent field method for many-mode systems: A new approach and application to the vibrations of CO adsorbed on Cu(100). J. Chem. Phys. 107 (1997) 10458
24. 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
25. Chakraborty A., Truhlar D.G., Bowman J.M., and Carter S. J. Chem. Phys. 121 (2004) 2071
26. Bégué D., Gohaud N., Pouchan C., Cassam-Chenaï P., and Liévin J. A comparison of two methods for selecting vibrational configuration interaction spaces on a heptatomic system: Ethylene oxide. J. Chem. Phys. 127 (2007) 164115
27. Heislbetz S., Schwerdtfeger P., and Rauhut G. Mol. Phys. 105 (2007) 1385
28. Cassam-Chenaï P., and Scribano J.L.Y. Chem. Phys. Lett. 466 (2008) 16
29. Pfluger K., Paulus M., Jagiella S., Burkert T., and Rauhut G. Theor. Chem. Acc. 114 (2005) 327
30. Hrenar T., Werner H.-J., and Rauhut G. Accurate calculation of anharmonic vibrational frequencies of medium sized molecules using local coupled cluster methods. J. Chem. Phys. 126 (2007) 134108
31. Rauhut G. Configuration selection as a route towards efficient vibrational configuration interaction calculations. J. Chem. Phys. 127 (2007) 184109
32. Benoit D.M. J. Chem. Phys. 125 (2006) 244110
33. Wyatt R.E., Iung C., and Leforestier C. Quantum dynamics of overtone relaxation in benzene. I. 5 and 9 modes models for relaxation from CH (ν = 3). J. Chem. Phys. 97 (1992) 3458
34. Wyatt R.E., Iung C., and Leforestier C. Quantum dynamics of overtone relaxation in benzene. II. 16 mode models for relaxation from CH (ν = 3). J. Chem. Phys. 97 (1992) 3477
35. Iung C., Leforestier C., and Wyatt R.E. J. Chem. Phys. 98 (1993) 6722
36. Iung C., and Wyatt R.E. Time-dependent quantum mechanical studyy of intramolecular vibrational energy redistribution in benzene. J. Chem. Phys. 99 (1993) 2261-2264
37. Hougen J.T., Bunker P.R., and Johns J.W.C. J. Mol. Spectrosc. 34 (1970) 136
38. Bunker P.R., and Stone J.M.R. J. Mol. Spectrosc. 41 (1972) 310
39. Hoy A., and Bunker P.R. J. Mol. Spectrosc. 67 (1979) 439
40. Bunker P.R., and Landsberg B.M. J. Mol. Spectrosc. 67 (1979) 374
41. Jensen P., and Bunker P.R. J. Mol. Spectrosc. 118 (1986) 18
42. Miller W.H., Handy N.C., and Adams J.E. Reaction path hamiltonian for polyatomic molecules. J. Chem. Phys. 72 (1980) 99
43. Ruf B.A., and Miller W.H. J. Chem. Soc. Faraday. Trans. 84 (1988) 1523
44. Carrington Jr. T., and Miller W.H. J. Chem. Phys. 81 (1984) 3942
45. Carrington Jr. T., and Miller W.H. J. Chem. Phys. 84 (1986) 4364
46. Köppel H., Domcke W., and Cederbaum L.S. Multimode molecular dynamics beyond the Born-Oppenheimer approximation. Adv. Chem. Phys. 57 (1984) 59
47. Cederbaum L.S. Born-oppenheimer approximation and beyond. In: Domcke W., Yarkony D.R., and Köppel H. (Eds). Conical Intersections. (Singapore, 2004) (2004), World Scientific Co. 3-40
48. Köppel H. Diabatic representation: Methods for the construction of diabatic states. In: Domcke W., Yarkony D.R., and Köppel H. (Eds). Conical Intersections. (Singapore, 2004) (2004), World Scientific Co. 175-204
49. Cederbaum L.S., Domcke W., Köppel H., and von Niessen W. Strong vibronic coupling effects in ionization spectra: The "mystery band" of butatriene. Chem. Phys. 26 (1977) 169
50. Cederbaum L.S., Köppel H., and Domcke W. Multimode vibronic coupling effects in molecules. Int. J. Quant. Chem. S15 (1981) 251
51. Jackels C.F., Gu Z., and Truhlar D.G. Reaction-path potential and vibrational frequencies in terms of curvilinear internal coordinates. J. Chem. Phys. 102 (1995) 3188
52. Nguyen K.A., Jackels C.F., and Truhlar D.G. Reaction-path dynamics in curvilinear internal coordinates including torsions. J. Chem. Phys. 104 (1996) 6491
53. Atchity G.J., Xantheas S.S., and Ruendenberg K. Potential energy surfaces near intersections. J. Chem. Phys. 95 (1991) 1862-1876
54. Yarkony D.R. Diabolical conical intersections. Rev. Modern. Phys. 68 (1996) 985-1013
55. Paterson M.J., Bearpark M.J., Robb M.A., and Blancafort L. J. Chem. Phys. 121 (2004) 11562
56. Sicilia F., Blancafort L., Bearpark M.J., and Robb M.A. Quadratic description of conical intersections: Characterization of critical points on the extended seam. J. Phys. Chem. A 111 (2007) 2182
57. Podolsky B. Quantum-mechanically correct form of hamiltonian function for conservative systems. Phys. Rev. 32 (1928) 812
58. Nauts A., and Chapuisat X. Momentum, quasi-momentum and hamiltonian operators in terms of arbitrary curvilinear coordinates, with special emphasis on molecular hamiltonians. Mol. Phys. 55 (1985) 1287
59. Chapuisat X., Nauts A., and Brunet J.-P. Exact quantum molecular hamiltonians: Part I. Application to the dynamics of three particles. Mol. Phys. 72 (1991) 1-31
60. Brocks G., Avoird A.V.D., Sutcliffe B.T., and Tennyson J. Mol. Phys. 50 (1983) 1025
61. Tennyson J., and Sutcliffe B.T. J. Chem. Phys. 77 (1982) 4061
62. Sutcliffe B.T., and Tennyson J. A generalized approach to the calculation of ro-vibrational spectra of triatomic molecules. Mol. Phys. 58 (1986) 1053-1066
63. Handy N.C. Mol. Phys. 61 (1987) 207
64. Bramley M.J., and Handy N.C. Efficient calculation of rovibrational eigenstates of sequentially bonded four-atom molecules. J. Chem. Phys. 98 (1993) 1378-1397
65. Bramley M.J., and Carrington Jr. T. J. Chem. Phys. 99 (1993) 8519
66. Wei H., and Carrington Jr. T. Chem. Phys. Lett. 287 (1998) 289
67. Wolfram S. Mathematica, a system for doing mathematics by computer. 2nd ed. (1991), Addison-Wesley, Reading, Mass
68. Lauvergnat D., and Nauts A. Exact numerical computation of a kinetic energy operator in curvilinear coordinates. J. Chem. Phys. 116 (2002) 8560
69. Lauvergnat D., Nauts A., Justum Y., and Chapuisat X. A harmonic adiabatic approximation to calculate highly excited vibrational levels of "floppy molecules". J. Chem. Phys. 114 (2001) 6592
70. Menou M., and Chapuisat X. Quantum-mechanical hamiltonians for constrained systems: Application to four-body systems. J. Mol. Spectrosc. 159 (1993) 300-328
71. Lauvergnat D., and Nauts A. A harmonic adiabatic approximation to calculate vibrational states of ammonia. Chem. Phys. 305 (2004) 105
72. Gatti F., Justum Y., Menou M., Nauts A., and Chapuisat X. Quantum-mechanical description of rigidly or adiabatically constrained molecular systems. J. Mol. Spectrosc. 181 (1997) 403
73. Chapuisat X., and Iung C. Vector parametrization of the N-body problem in quantum mechanics: Polyspherical coordinates. Phys. Rev. A 45 (1992) 6217-6235
74. Gatti F., Iung C., Menou M., Justum Y., Nauts A., and Chapuisat X. Vector parametrization of the n-atom problem in quantum mechanics. I. Jacobi vectors. J. Chem. Phys. 108 (1998) 8804
75. Gatti F., Iung C., Menou M., and Chapuisat X. Vector parametrization of the n-atom problem in quantum mechanics. II. Coupled-angular-momentun spectral representations for four atom systems. J. Chem. Phys. 108 (1998) 8821
76. F. Gatti, Approche vectorielle des Hamiltoniens moléculaires, Application au spectre rovibrationnel excité de l'Ammoniac. Ph.D. Thesis, Université Montpellier, 1999
77. Gatti F. Vector parametrization of the n-atom problem in quantum mechanics. III. Separation into two sub-systems. J. Chem. Phys. 111 (1999) 7225
78. Iung C., Gatti F., Viel A., and Chapuisat X. Vector parametrization of the n-atom problem in quantum mechanics. non-orthogonal coordinates. Phys. Chem. Chem. Phys. 1 (1999) 3377
79. Mladenović M. Rovibrational hamiltonians for general polyatomic molecules in spherical polar parametrization. I. Orthogonal representations. J. Chem. Phys. 112 (2000) 1070-1081
80. Gatti F., Munoz C., and Iung C. A general expression of the exact kinetic energy operator in polyspherical coordinates. J. Chem. Phys. 114 (2001) 8275
81. Gatti F., and Nauts A. Vector parametrization, partial angular momenta and unusual commutation relations in molecular physics. Chem. Phys. 295 (2003) 167-174
82. Gatti F., and Iung C. Exact and constrained kinetic energy operators in polyspherical coordinates. J. Theor. Comp. Chem. 2 (2003) 507-522
83. Iung C., and Gatti F. Polyspherical parametrization of a n-atom system: Principles and applications. Int. J. Quant. Chem. 106 (2006) 130
84. Brillouin L. Les tenseurs en mécanique et en électricité (1938), Masson, Paris
85. Wilson E., and Howard J. J. Chem. Phys. 4 (1936) 260
86. Pickett H. J. Chem. Phys. 56 (1972) 1715
87. Chapuisat X., Belfhal A., and Nauts A. J. Mol. Spectrosc. 149 (1991) 274
88. Watson J.K.G. Simplification of the molecular vibration-rotation hamiltonian. Mol. Phys. 15 (1968) 479
89. Watson J.K.G. The vibration-rotation hamiltonian of linear molecules. Mol. Phys. 19 (1970) 465
90. Sutcliffe B.T., and Tennyson J. Int. J. Quant. Chem. 39 (1991) 183
91. Xantheas S.S., and Sutcliffe B.T. J. Chem. Phys. 103 (1995) 8022
92. Sutcliffe B.T. Current Aspects of Quantum Chemistry. In: Carbo R. (Ed). Studies in Theoretical and Physical Chemistry vol. 21 (1982), Elsevier, Amsterdam
93. 3 fragment: A curvilinear coordinate system and kinetic energy operators. J. Chem. Phys. 127 (2007) 144302
94. Lukka T.J. J. Chem. Phys. 102 (1995) 3945
95. Pesonen J. J. Chem. Phys. 112 (2000) 3121
96. Pesonen J. J. Chem. Phys. 114 (2001) 10598
97. Pesonen J. J. Chem. Phys. 128 (2008) 044319
98. Wilson E., Decius J., and Cross P. Molecular Vibrations (1955), McGraw-Hill, New York
99. Frederick J.H., and Woywod C. J. Chem. Phys. 111 (1999) 7255
100. Ramesh S.G., and Sibert E.L. Combined perturbative-variational investigation of the vibrations of CHBr and CDBr. J. Chem. Phys. 120 (2004) 11011
101. Sibert E.L., and Castillo-Chara J. Theoretical studies of the potential surface and vibrational spectroscopy of ch3oh and its deuterated analogs. J. Chem. Phys. 122 (2005) 194306
102. Ramesh S.G., and Sibert E.L. Mol. Phys. 103 (2005) 149
103. Ramesh S.G., and Sibert E.L. Combination of perturbative and variational methods for calculating molecular spectra: Calculation of the ν = 3-5 ch stretch overtone spectrum of chf3. J. Chem. Phys. 103 (2006) 114307
104. Gu X.-Y., Duan B., and Ma Z.-Q. Phys. Lett. A 281 (2001) 168
105. Gu X.-Y., Duan B., and Ma Z.-Q. Phys. Lett. A 289 (2001) 82
106. Mladenović M. Rovibrational hamiltonians for general polyatomic molecules in spherical polar parametrization. II. Nonorthogonal descriptions of internal molecular geometry. J. Chem. Phys. 112 (2000) 1082-1095
107. Hirschfelder J.O. Coordinates which diagonalize the kinetic energy of relative motion. Int. J. Quant. Chem. 3S (1969) 17-31
108. Messiah A. Quantum Mechanics, vol. 1 (1962), John Wiley, New York
109. Zare R.N. Angular momentum (1988), Wiley, New York
110. Biedenharn L.C., and Louck J.D. Angular Momentum in Quantum Mechanics (1981), Addison-Wesley, Reading, Ma
111. Eckart C. Some studies concerning rotating axes and polyatomic molecules. Phys. Rev. 47 (1935) 552-558
112. Wang X.-G., and Carrington Jr. T. A simple method for deriving kinetic energy operators. J. Chem. Phys. 113 17 (2000) 7097-7101
113. Schwenke D.W. J. Chem. Phys. 118 (2003) 10431
114. Van Vleck J.H. The coupling of angular momentum vectors in molecules. Rev. Modern. Phys. 23 (1951) 213-227
115. Lemoine D. The discrete bessel transform algorithm. J. Chem. Phys. 101 (1994) 3936
116. Corey G.C., Tromp J.W., and Lemoine D. Fast pseudospectral algorithm in curvilinear coordinates. In: Cerjan C. (Ed). Numerical Grid Methods and Their Application to Schrödinger's Equation (1993), Kluwer Academic Publishers, Netherlands 1-23
117. Corey G.C., and Lemoine D. Pseudospectral method for solving the time-dependent Schrödinger equation in spherical coordinates. J. Chem. Phys. 97 (1992) 4115
118. 2 reactive scattering systems. J. Phys. Chem. A 105 (2001) 2604-2611
119. 0=1)→DH+H systems. A multi-configuration time-dependent Hartree (MCTDH) wave-packet propagation study. J. Chem. Phys. 116 (2002) 10641-10647
120. Wang X., and Carrington Jr. T. Using a nondirect product discrete variable representation for angular coordinates to compute vibrational levels of polyatomic molecules. J. Chem. Phys. 128 19 (2008) 194109
121. i = cos φ. J. Chem. Phys. 112 (2000) 4413
122. Leforestier C., Viel A., Gatti F., Munoz C., and Iung C. The Jacobi-Wilson method: A new approach to the description of polyatomic molecules. J. Chem. Phys. 114 (2001) 2099
123. McCoy A.B., and Sibert E.L. Canonical van vleck perturbation theory and its application to studies of higly vibrationally excited states of polyatomic molecules. In: Wyatt R.E., and Zhang J.Z.H. (Eds). Dynamics of Molecules and Chemical Reactions. (New York, 1996) (1996), Marcel Dekker 151-184
124. Rempe S.B., and Watts R.O. J. Chem. Phys. 108 (1998) 10084
125. X. Chapuisat, private communication, 1998
126. Brill M.R., Gatti F., Lauvergnat D., and Meyer H.-D. Photoinduced nonadiabatic dynamics of ethene: Six dimensional wave packet propagations using two different approximations of the kinetic energy operator. Chem. Phys. 338 (2007) 186-199
127. D. Lauvergnat, private communication, 2008
128. Vendrell O., Gatti F., Lauvergnat D., and Meyer H.-D. Full dimensional (15D) quantum-dynamical simulation of the protonated water dimer I: Hamiltonian setup and analysis of the ground vibrational state. J. Chem. Phys. 127 (2007) 184302
129. G.A. Worth, M.H. Beck, A. Jäckle, H.-D. Meyer, The MCTDH Package, Version 8.2, (2000). H.-D. Meyer, Version 8.3 (2002), Version 8.4 (2007). See http://mctdh.uni-hd.de/
130. Gatti F., Iung C., Leforestier C., Menou M., Justum Y., Nauts A., and Chapuisat X. J. Mol. Struct. (Theochem) 424 (1998) 181
131. Gatti F., Iung C., and Chapuisat X. J. Mol. Struct. (Theochem) 424 (1998) 201
132. 2 collisions. A full-dimensional wave packet propagation study using an exact form of the kinetic energy. J. Chem. Phys. 123 (2005) 174311
133. 2HBr complex. J. Chem. Phys. 122 (2005) 184313
134. 2O+H. J. Chem. Phys. 95 (1991) 7298
135. 2+OH reaction. J. Chem. Phys. 104 (1996) 4544
136. 2+OH reaction in six dimensions. J. Chem. Phys. 105 (1996) 1291
137. Qiu Y., and Bac ̌ić. J. Chem. Phys. 106 (1997) 2158
138. Costa L.S., and Clary D.C. Calculation of the energy levels of weakly bound molecular trimers: Application to (h - 2)(3). J. Chem. Phys. 117 (2002) 7512
139. 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
140. Wang X., and Carrington Jr. T. Vibrational energy levels of ch5+. J. Chem. Phys. 129 (2008) 234102
141. Smith F.T. Modified heliocentric coordinates for particle dynamics. Phys. Rev. Lett. 45 (1980) 1157
142. 2 during and after coherent infrared excitation. J. Chem. Phys. 118 (2003) 643-658
143. Richter F., Hochlaf M., Rosmus P., Gatti F., and Meyer H.-D. A study of mode-selective trans-cis isomerisation in HONO using ab initio methodology. J. Chem. Phys. 120 (2004) 1306-1317
144. Richter F., Rosmus P., Gatti F., and Meyer H.-D. Time-dependent wavepacket study on trans-cis isomerisation of HONO. J. Chem. Phys. 120 (2004) 6072-6084
145. Richter F., Gatti F., Léonard C., Le Quéré F., and Meyer H.-D. Time-dependent wave packet study on trans-cis isomerisation of HONO driven by an external field. J. Chem. Phys. 127 (2007) 164315
146. Pasin G., Gatti F., Iung C., and Meyer H.-D. Theoretical investigation of Intramolecular Vibrational Energy Redistribution in highly excited HFCO. J. Chem. Phys. 124 (2006) 194304
147. Pasin G., Iung C., Gatti F., and Meyer H.-D. Theoretical investigation of highly excited vibrational states in DFCO: Calculation of the out-of-plane bending states and simulation of the intramolecular vibrational energy redistribution. J. Chem. Phys. 126 (2007) 024302
148. Pasin G., Iung C., Gatti F., Richter F., Léonard C., and Meyer H.-D. Theoretical investigation of intramolecular vibrational energy redistribution in HFCO and DFCO induced by an external field. J. Chem. Phys. 129 (2008) 144304
149. Meyer H.-D., Le Quéré F., Léonard C., and Gatti F. Calculation and selective population of vibrational levels with the Multiconfiguration Time-Dependent Hartree (MCTDH) algorithm. Chem. Phys. 329 (2006) 179-192
150. Yu H.-G. An exact variational method to calculate vibrational energies of five at om molecules beyond the normal mode approach. J. Chem. Phys. 117 (2002) 2030
151. Wang X.-G., and Carrington Jr. T. A finite basis representation Lanczos calculation of the bend energy levels of methane. J. Chem. Phys. 118 (2003) 6946
152. Wang X.-G., and Carrington Jr. T. Contracted basis lanczos methods for computing numerically exact rovibrational levels of methane. J. Chem. Phys. 121 7 (2004) 2937-2954
153. Vendrell O., Gatti F., and Meyer H.-D. Dynamics and infrared spectroscopy of the protonated water dimer. Angew. Chem. Int. Ed. 46 (2007) 6918-6921
154. Vendrell O., Gatti F., and Meyer H.-D. Full dimensional (15D) quantum-dynamical simulation of the protonated water dimer II: Infrared spectrum and vibrational dynamics. J. Chem. Phys. 127 (2007) 184303
155. Vendrell O., Gatti F., and Meyer H.-D. Strong isotope effects in the infrared spectrum of the zundel cation. Angew. Chem. Int. Ed. 48 (2009) 352-355
156. Gatti F. Novel perspectives in quantum dynamics. Theor. Chem. Acc. 116 (2006) 60
157. Bowman J.M., Carrington Jr. T., and Meyer H.-D. Variational quantum approaches for computing vibrational energies of polyatomic molecules. Mol. Phys. 106 (2008) 2145-2182
158. Manthe U. Layered discrete variable representations and their application within the multiconfigurational time-dependent hartree approach. J. Chem. Phys. 130 (2009) 054109
159. Wang H., and Thoss M. Multilayer formulation of the multiconfiguration time-dependent Hartree theory. J. Chem. Phys. 119 (2003) 1289-1299
160. Wang H., and Thoss M. Quantum dynamical simulation of electron-transfer reactions in an anharmonic environment. J. Phys. Chem. A 111 (2007) 10369
161. Manthe U. A multilayer multiconfigurational time-dependent hartree approach for quantum dynamics on general potential energy surfaces. J. Chem. Phys. 128 (2008) 164116
162. Truhlar D.G., Steckler R., and Gordon M.S. Potential energy surfaces for polyatomic reaction dynamics. Chem. Rev. 87 (1987) 217-236
163. Thompson K.C., Jordan M.J.T., and Collins M.A. Molecular potential energy surfaces by interpolation in cartesian coordinates. J. Chem. Phys. 108 (1998) 564-578
164. Thompson K.C., Jordan M.J.T., and Collins M.A. Polyatomic molecular potential energy surfaces by interpolation in local internal coordinates. J. Chem. Phys. 108 (1998) 8302-8316
165. Varandas A.J.C. Modeling and interpolation of global multi-sheeted potential energy surfaces. In: Domcke W., Yarkony D.R., and Köppel H. (Eds). Conical Intersections (2004), World Scientific Co., Singapore 205
166. Bettens R.P.A., and Collins M.A. Learning to interpolate molecular potential energy surfaces with confidence: A Bayesian approach. J. Chem. Phys. 111 (1999) 816-826
167. Collins M.A., and Zhang D.H. Application of interpolated potential energy surfaces to quantum reactive scattering. J. Chem. Phys. 111 (1999) 9924-9931
168. +. J. Chem. Phys. 122 (2005) 044308
169. Ischtwan J., and Collins M.A. Molecular potential energy surfaces by interpolation. J. Chem. Phys. 100 (1994) 8080-8088
170. + using an ab initio potential energy surface. J. Chem. Phys. 122 (2005) 061101
171. Evenhuis C.R., and Manthe U. Calculating vibrational spectra using modified shepard interpolated potential energy surfaces. J. Chem. Phys. 129 (2008) 024104
172. Bowman J.M., and Gazdy B. J. Chem. Phys. 93 (1990) 1774
173. Shibl M.F., Pietrzak M., Limbach H.-H., and Kühn O. Geometric H/D isotope effects and cooperativity of the hydrogen bonds in porphycene. Chem. Phys. Chem. 8 (2007) 315-321
174. Giese K., Petković M., Naundorf H., and Kühn O. Multidimensional quantum dynamics and infrared spectroscopy of hydrogen bonds. Phys. Rep. 430 (2006) 211
175. - and its isotopomers. Z. Phys. Chem. 222 (2008) 1375-1387
176. 2 absorption spectrum of pyrazine: A wavepacket study treating all 24 vibrational modes. J. Chem. Phys. 105 (1996) 4412
177. 2 electronic state using a realistic 24-mode model Hamiltonian. J. Chem. Phys. 110 (1999) 936-946
178. Cattarius C., Worth G.A., Meyer H.-D., and Cederbaum L.S. All mode dynamics at the conical intersection of an octa-atomic molecule: Multi-configuration time-dependent Hartree (MCTDH) investigation on the butatriene cation. J. Chem. Phys. 115 (2001) 2088-2100
179. Cederbaum L.S., Gindensperger E., and Burghardt I. Short-time dynamics through conical intersections in macrosystems. Phys. Rev. Lett. 94 (2005) 113003
180. Gindensperger E., Burghardt I., and Cederbaum L.S. Short-time dynamics through conical intersections in macrosystems. I. Theory: Effective-mode formulation. J. Chem. Phys. 124 (2006) 144103
181. Nauts A., and Chapuisat X. Hamiltonians for constrained n-particle systems. Chem. Phys. Lett. 136 (1987) 164
182. Hadder J.E., and Frederick J.H. J. Chem. Phys. 97 (1992) 3500
183. van der Avoird A., Wormer P.E.S., and Moszynski R. Chem. Rev. 94 (1994) 1931
184. Meyer H. The molecular hamiltonian. Ann. Rev. Phys. Chem. 53 (2002) 141-172
185. Gatti F. Flexible monomer formulation for non-rigid systems. Chem. Phys. Lett. 373 (2003) 146-152
186. Yang Y., and Kühn O. Mol. Phys. 106 (2008) 2445
187. Meyer R., and Guenthard H.H. J. Chem. Phys. 49 (1968) 1510
188. Light J.C., and Bac ̌ić Z. J. Chem. Phys. 87 (1987) 4008
189. Bowman J.M. Chem. Phys. Lett. 217 (1994) 36
190. Antikainen J., Friesner R., and Leforestier C. Adiabatic pseudospectral calculation of vibrational states of four atom molecules: Application to hydrogen peroxide. J. Chem. Phys. 102 (1995) 1270
191. McCoy A.B., and Sibert E.L. J. Chem. Phys. 105 (1996) 459
192. Leforestier C., Gatti F., Fellers R.S., and Saykally R.J. Determination of a flexible (12D) water dimer potential via direct inversion of spectroscopic data. J. Chem. Phys. 117 (2002) 8710
193. Leforestier C., Braly L.B., Liu K., Matthew M.J., and Saykally R.J. Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with a split wigner pseudo spectral approach. J. Chem. Phys. 106 (1997) 8527
194. Justum Y., Gatti F., and Chapuisat X. J. Mol. Struct. (Theochem) 453 (1998) 131
195. Justum Y., Gatti F., Lauvergnat D., Nauts A., and Chapuisat X. One-dimensional quantum description of the bending of hcn/cnh for high values of the total angular momentuim. Spectrochimica Acta 58 (2002) 649
196. Krawczyk R.P., Viel A., Manthe U., and Domcke W. Photoinduced dynamics of the valence states of ethene: A six-dimensional potential-energy surface of three electronic states with several conical intersections. J. Chem. Phys. 119 (2003) 1397-1411
197. Viel A., Krawczyk R.P., Manthe U., and Domcke W. Photoinduced dynamics of ethene in the N, V and Z valence states: A six-dimensional nonadiabatic quantum dynamics investigation. J. Chem. Phys. 120 (2004) 11000-11010
198. Bittner M., Köppel H., and Gatti F. A multi-dimensional quantum dynamical study of beta-hydrogen transfer in a cationic rhodium complex. J. Phys. Chem. A 111 (2007) 2407
199. Gatti F., Iung C., Leforestier C., and Chapuisat X. Fully coupled 6d calculations of the ammonia vibration-inversion-tunneling states with a split hamiltonian pseudospectral approach. J. Chem. Phys. 111 (1999) 7236-7243
200. Pack R.T., and Parker G. J. Chem. Phys. 87 (1987) 3888
201. Pack R.T., and Parker G. J. Chem. Phys. 90 (1989) 3511
202. Bunker P.R., and Jensen P. Molecular Symmetry and Spectroscopy (1998), NRC Research press, Ottawa
203. Wang X.-G., and Carrington Jr. T. J. Chem. Phys. 115 (2001) 9781
204. Wang X.-G., and Carrington Jr. T. Can. J. Phys. 114 4 (2001) 1473-1477