Cumulant approach to the direct calculation of reduced density matrices: A critical analysis

Journal of Chemical Physics

Volumn 118, Issue 11, 2003, Pages 4832-4848

  Nooijen, Marcel ^a   Wladyslawski, Mark ^a   Hazra, Anirban ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; ALGORITHMS; CHARGED PARTICLES; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRONIC DENSITY OF STATES; HAMILTONIANS; MATHEMATICAL OPERATORS; PARAMETER ESTIMATION;

CRITICAL ANALYSIS; CUMULANT APPROACH; GENERALIZED COUPLED CLUSTER; NEWTON-RAPHSON SCHEME; SCHRODINGER EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0037444582     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1545779     Document Type: Article

References (83)

1. C. A. Coulson, Rev. Mod. Phys. 32, 175 (1960).
2. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson's Challenge (Springer-Verlag, New York, 2000).
3. Reduced Density Operators with Applications to Physical and Chemical Systems II, edited by R. M. Erdahl, Queens Papers in Pure and Applied Mathematics No. 44 (Queens University Press, Kingston, Ontario, 1974).
4. J. Cioslowski, Many-Electron Densities and Density Matrices (Kluwer, Boston, 2000).
5. R. H. Tredgold, Phys. Rev. 105, 1421 (1957).
6. Y. Mizuno and T. Izuyama, Prog. Theor. Phys. 18, 33 (1957).
7. A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963).
8. C. Garrod and J. Percus, J. Math. Phys. 5, 1756 (1964).
9. L. Cohen and C. Frishberg, Phys. Rev. A 13, 927 (1976).
10. H. Nakatsuji, Phys. Rev. A 14, 41 (1976).
11. F. Colmenero, C. Perez, and C. Valdemoro, Phys. Rev. A 47, 971 (1993).
12. F. Colmenero and C. Valdemoro, Phys. Rev. A 47, 979 (1993).
13. F. Colmenero and C. Valdemoro, Int. J. Quantum Chem. 51, 369 (1994).
14. C. Valdemoro, L. M. Tel, and E. P. Romero, Adv. Quantum Chem. 28, 33 (1997).
15. C. Valdemoro, M. P. De Lara-Castells, E. P. Romero, and L. M. Tel, Adv. Quantum Chem, 31, 37 (1999).
16. H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996).
17. K. Yasuda and H. Nakatsuji, Phys. Rev. A 56, 2648 (1997).
18. M. Ehara, M. Nakata, H. Kou, K. Yasuda, and H. Nakatsuji, Chem. Phys. Lett. 305, 483 (1999).
19. M. Nakata, M. Ehara, K. Yasuda, and H. Nakatsuji, J. Chem. Phys. 112, 8772 (2000).
20. D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998).
21. D. A. Mazziotti, Chem. Phys. Lett. 289, 419 (1998).
22. D. A. Mazziotti, Int. J. Quantum Chem. 70, 557 (1998).
23. R. Kubo, J. Phys. Soc. Jpn. 17, 1100 (1962).
24. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997).
25. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 110, 2800 (1999).
26. W. Kutzelnigg and D. Mukherjee, Chem. Phys. Lett. 317, 567 (2000).
27. D. Mukherjee and W. Kutzelnigg, J. Chem. Phys. 114, 8226 (2001).
28. W. Kutzelnigg, Chem. Phys. Lett. 64, 383 (1979).
29. W. Kutzelnigg, Int. J. Quantum Chem. 18, 3 (1980).
30. F. Coester, Nucl. Phys. 7, 421 (1958).
31. J. Cizek, J. Chem. Phys. 45, 4256 (1966).
32. R. J. Bartlett and J. F. Stanton, Rev. Comput. Chem. 5, 65 (1994).
33. T. D. Crawford and H. F. Schaefer, Rev. Comput. Chem. 14, 33 (2000).
34. D. A. Mazziotti, Phys. Rev. A 60, 4396 (1999).
35. D. A. Mazziotti, Phys. Rev. A 60, 3618 (1999).
36. K. Yasuda, Phys. Rev. A 59, 4133 (1999).
37. D. A. Mazziotti, Chem. Phys. Lett. 326, 212 (2000).
38. M. Nooijen, Phys. Rev. Lett. 84, 2108 (2000).
39. M. Nooijen and V. Lotrich, J. Chem. Phys. 113, 4549 (2000).
40. T. Van Voorhis and V. Head-Gordon, J. Chem. Phys. 115, 5033 (2001).
41. H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000).
42. H. Nakatsuji, J. Chem. Phys. 115, 2465 (2001).
43. H. Nakatsuji and E. R. Davidson, J. Chem. Phys. 115, 2000 (2001).
44. P. Piecuch (private communication).
45. M. Nooijen, J. Chem. Phys. 104, 2638 (1996).
46. M. Nooijen and R. J. Bartlett, J. Chem. Phys. 107, 6812 (1997).
47. T. J. Lee and G. E. Scuseria, in Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, edited by S. R. Langhoff (Kluwer Academic, Dordrecht, 1995), p. 47.
48. D. A. Mazziotti, J. Chem. Phys. 116, 1239 (2002).
49. C. Valdemoro, L. M. Tel, and E. Perez-Romero, Phys. Rev. A 61, 032507 (2000).
50. D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001).
51. W. Kutzelnigg, J. Chem. Phys. 77, 3081 (1982).
52. P. O. Lowdin, Phys. Rev. A 97, 1474 (1955).
53. R. McWeeny, Methods of Molecular Quantum Mechanics (Academic, London, 1992).
54. N. H. March, W. H. Young, and S. Samphantar, The Many-Body Problem in Quantum Mechanics (Cambridge University Press, London, 1967).
55. M. Wladyslawski and M. Nooijen (unpublished).
56. A. L. Fetter and J. D. Walecka, The Quantum Mechanics of Many Particle Systems (McGraw-Hill, New York, 1971).
57. F. E. Harris (private communication).
58. J. Noga, R. J. Bartlett, and M. Urban, Chem. Phys. Lett. 134, 146 (1987).
59. P. Pulay, Chem. Phys. Lett. 73, 393 (1980).
60. P. Pulay, J. Comput. Chem. 3, 556 (1982).
61. P. Pulay, J. Comput. Chem. 3, 556 (1982).
62. K. Kowalski and P. Piecuch, Chem. Phys. Lett. 347, 237 (2001).
63. J. F. Stanton, J. Gauss, J. D. Watts, and R. J. Bartlett, J. Chem. Phys. 94, 4334 (1990).
64. M. Nooijen and R. J. Bartlett, J. Chem. Phys. 106, 6441 (1997).
65. M. Nooijen and R. J. Bartlett, J. Chem. Phys. 106, 6449 (1997).
66. M. Nooijen and V. Lotrich, J. Chem. Phys. 113, 494 (2000).
67. J. F. Stanton, J. Gauss, J. D. Watts et al., ACES II is a program product of the Quantum Theory project, University of Florida, Integral packages included are VMOL (J. Almlof and P. R. Taylor), VPROPS (P. R. Taylor), ABACUS (T. Helgaker, H. J. Aa Jensen, P. Jorgensen, and P. R. Taylor).
68. A. Banerjee, N. Adams, J. Simons, and R. Shepard, J. Phys. Chem. 89, 52 (1985).
69. T. Helgaker, in Lecture Notes in Quantum Chemistry, edited by B. O. Roos (Springer-Verlag, Berlin, 1992), Vol. 58, 295.
70. W. J. Hehre, R. Ditchfield, and J. A. Pople, J. Chem. Phys. 56, 2257 (1972).
71. P. C. Hariharan and J. A. Pople, Theor. Chim. Acta 28, 213 (1973).
72. J. Noga and R. J. Bartlett, J. Chem. Phys. 86, 7041 (1987).
73. J. D. Watts and R. J. Bartlett, J. Chem. Phys. 93, 6104 (1990).
74. K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, Chem. Phys. Lett. 157, 479 (1989).
75. R. J. Bartlett, J. D. Watts, S. A. Kucharski, and J. Noga, Chem. Phys. Lett. 165, 513 (1990).
76. C. Valdemoro, L. M. Tel, and E. Perez-Romero, Adv. Quantum Chem. 28, 33 (1997).
77. C. Valdemoro, Top. Curr. Chem. 203, 187 (1999).
78. C. Valdemoro, L. M. Tel, E. Perez-Romero, and A. Torre, J. Mol. Struct.: THEOCHEM 574, 255 (2001).
79. C. Valdemoro, D. R. Alcoba, L. M. Tel, and E. Perez-Romero, Int. J. Quantum Chem. 85, 214 (2001).
80. D. A. Mazziotti and R. M. Erdahl, Phys. Rev. A 63, 042113 (2001).
81. D. A. Mazziotti, J. Chem. Phys. 112, 10125 (2000).
82. S. Goedecker and C. J. Umrigat, Phys. Rev. Lett. 81, 866 (1998).
83. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys. 114, 8282 (2001).