Quasi-random integration in quantum chemistry: Efficiency, stability, and application to the study of small atoms and molecules constrained in spherical boxes

International Journal of Quantum Chemistry

Volumn 107, Issue 4, 2007, Pages 879-893

  Cuenca, D Zorrilla ^a   Márquez, J Sánchez ^a   Núñez, M Fernández ^a   Huertas, R Rodríguez ^a  

^a UNIVERSITY OF CÁDIZ   (Spain)

Author keywords

Atom in a box; Atomic integrals; Molecular integrals; Monte carlo integration; Pseudo random integration; Quasi random integration

Indexed keywords

ELECTRONS; FUNCTIONS; INTEGRATION; MOLECULAR STRUCTURE; MONTE CARLO METHODS; POLYNOMIALS;

ATOM IN A BOX; ATOMIC INTEGRALS; MOLECULAR INTEGRALS; PSEUDO-RANDOM INTEGRATION; QUASI-RANDOM INTEGRATION;

QUANTUM THEORY;

EID: 33846706352     PISSN: 00207608     EISSN: 1097461X     Source Type: Journal    
DOI: 10.1002/qua.21221     Document Type: Article

References (70)

1. Fabbri, M.; Perondi, L. F. Int J Quantum Chem 1984, 26, 1029.
2. Becke, A. D. J Chem Phys 1988, 88, 2547.
3. Murray, C. W.; Handy, N. C.; Laming, G. J Mol Phys 1993, 78, 997.
4. Treutler, O.; Ahlrichs, R. J Chem Phys 1995, 102, 346.
5. Cesco, J. C.; Denner, C. C.; Rosso, A. E.; Perez, J. E.; Ortiz, F. S.; Contreras, R. H.; Giribert, C. G.; Azúa, M. C. J Comp Chem 1995, 16, 1507.
6. Alexander, S. A.; Coldwell, R. L. J Comp Phys 2001, 172, 908.
7. Rodríguez, R.; Infante, R.; Zorrilla, D.; Fernańdez, M. An Quim Int Ed 1998, 94, 201.
8. Software UCA-CMC: Fernández, M.; Zorrilla, M. HF and MP2 Atomic and Molecular Calculations with Space Restricted Basis Functions (http://www.uca.es/dept/quimica_fisica/,>Software>ProgramasCTPM).
9. Neiderreiter, H. Bull Am Math Soc 1987, 84, 957.
10. (a) Halton, J. H. Num Math 1960, 2, 84;
11. (b) Halton, J. H. Berichtigung 1960, 2, 196.
12. Haselgrove, C. B. Math Comp 1960, 15, 323.
13. Korobov, H. M. Dokl Akad Nauk SSSR 1959, 124, 1207.
14. Hammersley, J. M. Ann NY Acad Sci 1960, 86, 884.
15. Berblinger, M.; Schlier, C. Comput Phys Commun 1991, 66, 157.
16. Rodríguez, R. Doctoral thesis; Universidad de Sevilla Sevilla, Spain 1995 (PDF at: http://www.uca.es/dept/quimica_fisica/, >investigación>CTPM>publicaciones).
17. Zorrilla, D. Doctoral thesis; Universidad de Cadiz: Cadiz, Spain, 2001 (PDF at: http://www.uca.es/dept/quimica_fisica/, >investigación>CTPM>publicaciqnes).
18. Fernández, M.; Rodríguez, R.; Infante, R. Fol Chim Theor Lat 1994, 22, 129.
19. Baker, C. T. H. Can J Math 1965, 17, 616.
20. Press, W. H.; Flannery, B. P.; Teulkowsky, S. A.; Vetterling, W. T. Numerical Recipes; Cambridge University Press: New York, 1987.
21. Hehre, J.; Stewart, R. F.; Pople, J. A. J Chem Phys 1979, 52, 2235.
22. Daudel, R.; Leroy, G.; Peeters, D.; Sana, M. Quantum Chemistry; John Wiley & Sons, 1983; Section 5.2.
23. Clementi, E.; Raimondi, D. L. J Chem Phys 1963, 38, 11.
24. Ransil, B. J. Rev Mod Phys 1960, 32, 245.
25. Michels, A.; de Boer, J.; Bijl, A. Physica 1937, 4, 981.
26. Sommerfeld, A.; Welker, H. Ann Phys 1938, 32, 56.
27. de Groot, S. R.; ten Seldam, C. A. Physica 1946, 12, 669; ten Seldam, C. A.; de Groot, S. R. Physica 1952, 18, 891.
28. Cottrell, T. L. Trans Faraday Soc 1951, 47, 337.
29. Gimarc, B. M. J Chem Phys 1966, 44, 373.
30. Ludeña, E. V. J Chem Phys 1977, 66, 468.
31. Suryanarayana, D.; Weil, J. A. J Chem Phys 1976, 64, 510.
32. Ley-Koo, E.; Rubinstein, S. J Chem Phys 1979, 71, 351.
33. Fernandez, F. M.; Castro, E. A. Int J Quantum Chem 1982, 21, 741.
34. Arteca, G. A.; Fernandez, F. M.; Castro, E. A. J Chem Phys 1984, 80, 1569.
35. (a) Fröman, P. O.; Yngve, S.; Fröman, N. J Math Phys 1987, 28, 1813;
36. (b) Yngve, S. J Math Phys 1988, 29, 931.
37. Gorecki, J.; Byers Brown, W. J Phys B: At Mol Phys 1987, 20, 5953.
38. Goodfriend, P. L. J Phys B: At Mol Opt Phys 1990, 23, 1373.
39. Marin, J. L.; Cruz, S. A. J Phys B: At Mol Opt Phys 1991, 24, 2899; Marin, J. L.; Cruz, S. A. Am J Phys 1991, 59, 931.
40. Goldman, S.; Joslin, C. J Phys Chem 1992, 96, 6021.
41. Brownstein, K. R. Phys Rev Lett 1993, 71, 1427.
42. Dutt, R.; Mukherjee, A.; Varshni, Y. P. Phys Rev A 1995, 52, 1750.
43. Levelt, J. M. H.; Hurst, R. P. J Chem Phys 1960, 32, 96.
44. Hillier, I. H.; Walkley, J. J Chem Phys 1964, 41, 3205.
45. (a) Zhu, J. L.; Xiong, J. J.; Gu, B. L. Phys Rev B 1990, 41, 6001;
46. (b) Chuu, D. S.; Hsiao, C. M.; Mei, W. N. Phys Rev B 1992, 46, 3898;
47. (c) Zhu, J. L.; Zhao, J. H.; Duan, W. H.; Gu, B. L. Phys Rev B 1992, 46, 7546;
48. (d) Porras-Montenegro, N.; Perez-Merchancano, S. T. Phys Rev B 1992, 46, 9780;
49. (e) Zhu, J. L.; Zhao, J. H.; Xiong, J. J. J Phys: Condens Matter 1994, 6, 5097;
50. (f) Zhu, J. L.; Zhao, J. H.; Xiong, J. J. Phys Rev B 1994, 50, 1832;
51. (g) Zhu, J. L.; Xi Chen, X. J Phys: Condens Matter 1994, 6, L123;
52. (h) Zhu, J. L.; Xi Chen, X. Phys Rev B 1994, 50, 4497;
53. (i) Deng, Z. Y.; Guo, J. K.; Lai, T. R. Phys Rev B 1994, 50, 5736;
54. (j) Parades-Gutierrez, H.; Cuero-Yepez, J. C.; Porras-Montenegro, N. J Appl Phys 1994, 75, 5150.
55. Tomasi, J. Theor Chem Acc 2004, 112, 184.
56. Varshni, Y. P. J Phys B: At Mol Opt Phys 1997, 30, L589.
57. Suryanarayana, D.; Weyl, J. A. J Chem Phys 1976, 64, 510.
58. LeSar, R.; Herschbach, D. R. J Phys Chem 1981, 85, 2798.
59. LeSar, R.; Herschbach, D. R. J Phys Chem 1983, 87, 5202.
60. Marín, J. L.; Cruz, S. A. J Phys B: At Mol Opt Phys 1992, 25, 4365.
61. Marín, J. L.; Muñoz, G. J Mol Struct (Theochem) 1993, 287, 281.
62. Marin, J. L.; R.; Uribe, A. Am J Phys 1995, 63, 460.
63. Corella-Madueño, A.; Rosas, R.; Marín, J. L.; Riera, R. Phys Low-Dimens Struct 1999, 5/6, 75.
64. Ludeña, E. V. J Chem Phys 1978, 69, 1770.
65. Ludeña, E. V.; Gregori, M. J Chem Phys 1979, 71, 2235.
66. Gorecki, J.; Byers Brown, W. J Phys B: At Mol Opt Phys 1988, 21, 403.
67. Ley-Koo, E.; Flores-Flores, A. Int J Quantum Chem 1998, 66, 123.
68. Ley-Koo, E.; Volke-Sepúlveda, K. P. Int J Quantum Chem 1997, 65, 269.
69. Corella-Madueño, A.; Rosas, R.; Marin, J. L.; Riera, R. Int J Quantum Chem 2000, 77, 509.
70. Aguilar Peris, J. Termodinámica; Alhambra-Longmans: Madrid, Spain, 1995; Chapter 10.