Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach: General formulation and removal of singularities

Journal of Chemical Physics

Volumn 139, Issue 20, 2013, Pages

  Ndong, Mamadou ^a   Nauts, André ^b,c   Joubert Doriol, Loïc ^d   Meyer, Hans Dieter ^e   Gatti, Fabien ^d   Lauvergnat, David ^a  

^a CNRS   (France)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c UNIVERSITÉ PARIS SUD   (France)

^d UNIVERSITÉ DE MONTPELLIER   (France)

^e UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; ANALYTICAL FORMS; AUTOMATIC COMPUTATIONS; AUTOMATIC PROCEDURES; CARTESIAN COORDINATE; CYCLIC COMPOUNDS; KINETIC-ENERGY OPERATOR; SYMBOLIC CALCULATION;

KINETICS; QUANTUM CHEMISTRY;

KINETIC ENERGY;

EID: 84903362038     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4828729     Document Type: Article

References (53)

1. J. M. Bowman, T. Carrington, Jr., and H.-D. Meyer, Mol. Phys. 106, 2145 (2008). 10.1080/00268970802258609
2. G. Ávila and T. Carrington, Jr., J. Chem. Phys. 135, 064101 (2011). 10.1063/1.3617249
3. X. Wang and T. Carrington, Jr., J. Chem. Phys. 129, 234102 (2008). 10.1063/1.3027825
4. Y. Wang, S. Carter, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 128, 071101 (2008). 10.1063/1.2839303
5. J. M. Bowman, X. Huang, N. C. Handy, and S. Carter, J. Phys. Chem. A 111, 7317 (2007). 10.1021/jp070398m
6. T. Hammer and U. Manthe, J. Chem. Phys. 134, 224305 (2011). 10.1063/1.3598110
7. G. Schiffel and U. Manthe, J. Chem. Phys. 132, 084103 (2010). 10.1063/1.3304920
8. O. Vendrell, M. Brill, F. Gatti, D. Lauvergnat, and H.-D. Meyer, J. Chem. Phys. 130, 234305 (2009). 10.1063/1.3152488
9. O. Vendrell, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 131, 034308 (2009). 10.1063/1.3183166
10. M. Schröder, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 134, 234307 (2011). 10.1063/1.3600343
11. H.-D. Meyer, U. Manthe, and L. S. Cederbaum, Chem. Phys. Lett. 165, 73 (1990). 10.1016/0009-2614(90)87014-I
12. U. Manthe, H.-D. Meyer, and L. S. Cederbaum, J. Chem. Phys. 97, 3199 (1992). 10.1063/1.463007
13. M. H. Beck and H.-D. Meyer, J. Chem. Phys. 114, 2036 (2001). 10.1063/1.1334618
14. Multidimensional Quantum Dynamics: MCTDH Theory and Applications, edited by, H.-D. Meyer, F. Gatti, and, G. A. Worth, (Wiley-VCH, Weinheim, 2009).
15. H.-D. Meyer, WIREs: Comput. Mol. Sci. 2, 351 (2012). 10.1002/wcms.87
16. G. A. Worth, M. H. Beck, A. Jäckle, and H.-D. Meyer, The MCTDH Package, Version 8.2, 2000;
17. H.-D. Meyer, Version 8.3, 2002; Version 8.4, 2007. See http://mctdh.uni-hd.de/.
18. Y. G. Smeyers, F. J. Melendez, and M. L. Senent, J. Chem. Phys. 106, 1709 (1997). 10.1063/1.473975
19. A. Niño and C. Muñoz-Caro, Comput. Chem. 18, 27 (1994). 10.1016/0097-8485(94)80020-0
20. M. L. Senent, Chem. Phys. Lett. 296, 299 (1998). 10.1016/S0009-2614(98) 01052-5
21. D. J. Rush and K. B. Wiberg, J. Phys. Chem. A 101, 3143 (1997). 10.1021/jp9624358
22. D. Luckhaus, J. Chem. Phys. 113, 1329 (2000). 10.1063/1.481924
23. D. Lauvergnat and A. Nauts, J. Chem. Phys. 116, 8560 (2002). 10.1063/1.1469019
24. E. Mátyus, G. Czakó, and A. G. Császár, J. Chem. Phys. 130, 134112 (2009). 10.1063/1.3076742
25. J. E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill, 1955).
26. J. H. Frederick and C. Woywod, J. Chem. Phys. 111, 7255 (1999). 10.1063/1.480101
27. X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 113, 7097 (2000). 10.1063/1.1313544
28. X. Chapuisat and C. Iung, Phys. Rev. A 45, 6217 (1992). 10.1103/PhysRevA.45.6217
29. F. Gatti, C. Munoz, and C. Iung, J. Chem. Phys. 114, 8275 (2001). 10.1063/1.1361069
30. F. Gatti and C. Iung, Phys. Rep. 484, 1 (2009). 10.1016/j.physrep.2009. 05.003
31. X.-G. Wang and T. Carrington, Jr., Can. J. Phys. 79, 623 (2001). 10.1139/p01-012
32. M. Ndong, L. Joubert-Doriol, H.-D. Meyer, A. Nauts, F. Gatti, and D. Lauvergnat, J. Chem. Phys. 136, 034107 (2012). 10.1063/1.3675163
33. M. Mladenović, J. Chem. Phys. 112, 1082 (2000). 10.1063/1.480663
34. F. Gatti, C. Iung, M. Menou, and X. Chapuisat, J. Chem. Phys. 108, 8821 (1998). 10.1063/1.476328
35. C. Iung and F. Gatti, Int. J. Quantum Chem. 106, 130 (2006). 10.1002/qua.20728
36. F. Gatti, J. Chem. Phys. 111, 7225 (1999). 10.1063/1.480051
37. F. Gatti and C. Iung, J. Theor. Comput. Chem. 2, 507 (2003). 10.1142/S0219633603000653
38. T. Carrington and X.-G. Wang, WIREs: Comput. Mol. Sci. 1, 952 (2011). 10.1002/wcms.73
39. O. Vendrell, F. Gatti, D. Lauvergnat, and H.-D. Meyer, J. Chem. Phys. 127, 184302 (2007). 10.1063/1.2787588
40. See supplementary material at http://dx.doi.org/10.1063/1.4828729 E-JCPSA6-139-050342 for the derivation of the kinetic energy operator with polyspherical coordinates and subsystems.
41. F. Gatti, C. Iung, M. Menou, Y. Justum, A. Nauts, and X. Chapuisat, J. Chem. Phys. 108, 8804 (1998). 10.1063/1.476327
42. A. Nauts and X. Chapuisat, Mol. Phys. 55, 1287 (1985). 10.1080/00268978500102031
43. C. Iung, F. Gatti, A. Viel, and X. Chapuisat, Phys. Chem. Chem. Phys. 1, 3377 (1999). 10.1039/a903466h
44. F. Otto, F. Gatti, and H.-D. Meyer, J. Chem. Phys. 128, 064305 (2008). 10.1063/1.2826379
45. S. Sukiasyan and H.-D. Meyer, J. Phys. Chem. A 105, 2604 (2001). 10.1021/jp003767m
46. C. Leforestier, F. Gatti, R. S. Fellers, and R. J. Saykally, J. Chem. Phys. 117, 8710 (2002). 10.1063/1.1514977
47. E. V. Gromov, A. B. Trofimov, F. Gatti, and H. Köppel, J. Chem. Phys. 133, 164309 (2010). 10.1063/1.3493451
48. E. V. Gromov, C. Leveque, F. Gatti, I. Burghardt, and H. Köppel, J. Chem. Phys. 135, 164305 (2011). 10.1063/1.3653792
49. P. Celani, F. Bernardi, M. Olivucci, and M. A. Robb, J. Am. Chem. Soc. 119, 10815 (1997). 10.1021/ja9717323
50. M. Tanaka and Y. Yonezawa, J. Chem. Phys. 100, 5160 (1996). 10.1021/jp953340t
51. T. Ikeda and O. Tsutsumi, Science 268, 1873 (1995). 10.1126/science.268. 5219.1873
52. L. Joubert-Doriol, Ph.D. thesis, Université de Montpellier, 2012.
53. L. Joubert-Doriol, B. Lasorne, F. Gatti, M. Schröder, O. Vendrell, and H.-D. Meyer, Comput. Theor. Chem. 990, 75 (2012). 10.1016/j.comptc.2011.12. 015