A novel interpretation of reduced density matrix and cumulant for electronic structure theories

Journal of Chemical Physics

Volumn 134, Issue 21, 2011, Pages

  Kong, Liguo ^a   Valeev, Edward F ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONFIGURATION INTERACTIONS; CORRELATED FLUCTUATIONS; CROSS-CORRELATIONS; CUMULANTS; DIAGONAL ELEMENTS; ELECTRONIC STRUCTURE THEORY; NOVEL INTERPRETATION; ORBITAL OCCUPATION; ORBITALS; PARAMETRIZATIONS; REDUCED-DENSITY MATRIX; SPIN-ORBITALS; STATISTICAL AVERAGE; STRONG CORRELATION; WEIGHTED AVERAGES;

ELECTRONIC STRUCTURE; EMPLOYMENT; LINEAR ALGEBRA; SPIN FLUCTUATIONS;

QUANTUM THEORY;

EID: 79958802412     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3596948     Document Type: Article

References (94)

1. K. Husimi, Proc. Phys.-Math. Soc. Jpn. 22, 264 (1940).
2. P.-O. Lwdin, Phys. Rev. 97, 1474 (1955). 10.1103/PhysRev.97.1474
3. E. Davidson, Reduced Density Matrices in Quantum Chemistry (Academic, New York, 1976).
4. D. A. Mazziotti, Many-Electron Densities and Reduced Density-Matrices (Plenum, New York, 2000), p. 139.
5. H. Nakatsuji, Many-Electron Densities and Reduced Density-Matrices (Plenum, New York, 2000), p. 85.
6. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulsons Challenge, Lecture Notes in Chemistry Vol. 72 (Springer, Berlin, 2000).
7. P. Dirac, Math. Proc. Cambridge Philos. Soc. 25, 62 (1929). 10.1017/S0305004100018570
8. P. Dirac, Math. Proc. Cambridge Philos. Soc. 26, 376 (1930). 10.1017/S0305004100016108
9. P. Dirac, Math. Proc. Cambridge Philos. Soc. 27, 240 (1931). 10.1017/S0305004100010343
10. J. E. Mayer, Phys. Rev. 100, 1579 (1955). 10.1103/PhysRev.100.1579
11. R. H. Tredgold, Phys. Rev. 105, 1421 (1957). 10.1103/PhysRev.105.1421
12. A. Coleman, Rev. Mod. Phys. 35, 668 (1963). 10.1103/RevModPhys.35.668
13. S. Cho, Sci. Rep. Gunma Univ. 11, 1 (1962).
14. L. Cohen and C. Frishberg, Phys. Rev. A 13, 927 (1976). 10.1103/PhysRevA.13.927
15. H. Nakatsuji, Phys. Rev. A 14, 41 (1976). 10.1103/PhysRevA.14.41
16. C. Garrod, M. V. Mihailovi, and M. Rosina, J. Math. Phys. 16, 868 (1975). 10.1063/1.522634
17. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys. 114, 8282 (2001). 10.1063/1.1360199 (Pubitemid 32512374)
18. D. A. Mazziotti, Phys. Rev. A 65, 062511 (2002). 10.1103/PhysRevA.65. 062511
19. T. Juhasz and D. A. Mazziotti, J. Chem. Phys. 121, 1201 (2004). 10.1063/1.1760748
20. G. Gidofalvi and D. A. Mazziotti, Chem. Phys. Lett. 398, 434 (2004). 10.1016/j.cplett.2004.09.086
21. J. R. Hammond and D. A. Mazziotti, Phys. Rev. A 71, 062503 (2005). 10.1103/PhysRevA.71.062503 (Pubitemid 41481211)
22. D. A. Mazziotti, Acc. Chem. Res. 39, 207 (2006). 10.1021/ar050029d
23. D. A. Mazziotti, Phys. Rev. A 74, 032501 (2006). 10.1103/PhysRevA.74. 032501 (Pubitemid 44330449)
24. D. A. Mazziotti, Adv. Chem. Phys. 134, 19 (2007). 10.1002/9780470106600. ch3
25. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 127, 244105 (2007). 10.1063/1.2817602
26. A. E. DePrince, E. Kamarchik, and D. A. Mazziotti, J. Chem. Phys. 128, 234103 (2008). 10.1063/1.2937454
27. M. Nakata and K. Yasuda, Phys. Rev. A 80, 042109 (2009). 10.1103/PhysRevA.80.042109
28. H. V. Aggelen, P. Bultinck, B. Verstichel, D. V. Neck, and P. W. Ayers, Phys. Chem. Chem. Phys. 128, 5558 (2009). 10.1039/b907624g
29. B. Verstichel, H. V. Aggelen, D. V. Neck, P. W. Ayers, and P. Bultinck, J. Chem. Phys. 132, 114113 (2010). 10.1063/1.3354911
30. N. Shenvi and A. F. Izmaylov, Phys. Rev. Lett. 105, 213003 (2010). 10.1103/PhysRevLett.105.213003
31. A. E. DePrince and D. A. Mazziotti, Phys. Rev. A 76, 042501 (2007). 10.1103/PhysRevA.76.042501 (Pubitemid 47531654)
32. D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008). 10.1103/PhysRevLett.101.253002
33. A. E. DePrince and I. D.A. Mazziotti, J. Chem. Phys. 133, 034112 (2010). 10.1063/1.3458641
34. D. A. Mazziotti, Adv. Chem. Phys. 134, 165 (2007). 10.1002/9780470106600. ch8
35. C. Valdemoro, Adv. Chem. Phys. 134, 119 (2007). 10.1002/9780470106600.ch7
36. J. Herbert and J. E. Harriman, Adv. Chem. Phys. 134, 261 (2007). 10.1002/9780470106600.ch10
37. C. Valdemoro, Phys. Rev. A 45, 4462 (1992). 10.1103/PhysRevA.45.4462
38. F. Colmenero, C. Delvalle, and C. Valdemoro, Phys. Rev. A 47, 971 (1993). 10.1103/PhysRevA.47.971
39. H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996). 10.1103/PhysRevLett.76.1039
40. D. A. Mazziotti, Int. J. Quantum Chem. 70, 557 (1998). 10.1002/(SICI)1097-461X(1998)70:4/5557::AID-QUA23.0.CO;2-U
41. D. A. Mazziotti, Chem. Phys. Lett. 289, 419 (1998). 10.1016/S0009- 2614(98)00470-9
42. D. A. Mazziotti, Phys. Rev. A 57, 4219 (1998). 10.1103/PhysRevA.57.4219
43. K. Yasuda, Phys. Rev. A 59, 4133 (1999). 10.1103/PhysRevA.59.4133
44. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 110, 2800 (1999). 10.1063/1.478189
45. C. Valdemoro, L. Tel, and E. Perez-Romero, Phys. Rev. A 61, 032507 (2000). 10.1103/PhysRevA.61.032507
46. D. A. Mazziotti, Chem. Phys. Lett. 326, 212 (2000). 10.1016/S0009- 2614(00)00773-9
47. C. Valdemoro, L. M. Tel, E. Perez-Romero, and A. Torre, J. Mol. Struct.: THEOCHEM 537, 1 (2001). 10.1016/S0166-1280(00)00657-6 (Pubitemid 32118551)
48. D. A. Mazziotti, Phys. Rev. A 66, 062503 (2002). 10.1103/PhysRevA.66. 062503
49. J. M. Herbert and J. E. Harriman, Phys. Rev. A 65, 022511 (2002). 10.1103/PhysRevA.65.022511
50. D. A. Mazziotti, Phys. Rev. E 65, 026704 (2002). 10.1103/PhysRevE.65. 026704 (Pubitemid 40619537)
51. F. Harris, Int. J. Quantum Chem. 90, 105 (2002). 10.1002/qua.997
52. J. E. Harriman, Phys. Rev. A 65, 052507 (2002). 10.1103/PhysRevA.65. 052507
53. J. M. Herbert and J. E. Harriman, J. Chem. Phys. 117, 7464 (2002). 10.1063/1.1508369 (Pubitemid 35354309)
54. M. Nooijen, M. Wladyslawski, and A. Hazra, J. Chem. Phys. 118, 4832 (2003). 10.1063/1.1545779
55. C. Valdemoro, D. Alcoba, and L. Tel, Int. J. Quantum Chem. 93, 212 (2003). 10.1002/qua.10553
56. D. R. Alcoba, C. Valdemoro, L. M. Tel, and E. Perez-Romero, Phys. Rev. A 77, 042508 (2008). 10.1103/PhysRevA.77.042508 (Pubitemid 351561887)
57. R. Kubo, J. Phys. Soc. Jpn. 17, 1100 (1962). 10.1143/JPSJ.17.1100
58. K. W. Becke and P. Fulde, Z. Phys. B 72, 423 (1988). 10.1007/BF01314521
59. K. W. Becke and P. Fulde, J. Chem. Phys. 91, 4223 (1989). 10.1063/1.456801
60. T. Schork and P. Fulde, J. Chem. Phys. 97, 9195 (1992). 10.1063/1.463295
61. D. Mukherjee, Chem. Phys. Lett. 274, 561 (1997). 10.1016/S0009-2614(97) 00714-8
62. T. Korona, J. Chem. Phys. 128, 224104 (2008). 10.1063/1.2933312
63. M. Piris, Int. J. Quantum Chem. 106, 1093 (2006). 10.1002/qua.20858
64. K. R. Shamasundar, J. Chem. Phys. 131, 174109 (2009). 10.1063/1.3256237
65. L. Kong, Extension of the cumulant definition for low particle number systems., Int. J. Quant. Chem. (in press); see http://onlinelibrary.wiley.com/ doi/10.1002/qua.22832/abstract.
66. D. R. Alcoba, R. C. Bochicchio, L. Lain, and A. Torre, J. Chem. Phys. 133, 144104 (2010). 10.1063/1.3503766
67. D. A. Mazziotti, Phys. Rev. A 68, 052501 (2003). 10.1103/PhysRevA.68. 052501
68. J. D. Farnum and D. A. Mazziotti, Chem. Phys. Lett. 400, 90 (2004). 10.1016/j.cplett.2004.10.075
69. L. Greenman and D. A. Mazziotti, J. Chem. Phys. 128, 114109 (2008). 10.1063/1.2890961 (Pubitemid 351423188)
70. M. Nooijen, K. R. Shamasundar, and D. Mukherjee, Mol. Phys. 103, 2277 (2005). 10.1080/00268970500083952 (Pubitemid 41647964)
71. D. Mukherjee and W. Kutzelnigg, J. Chem. Phys. 114, 2047 (2001). 10.1063/1.1337058
72. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 116, 4787 (2002). 10.1063/1.1448827 (Pubitemid 34923838)
73. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 120, 7350 (2004). 10.1063/1.1652490
74. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 120, 7340 (2004). 10.1063/1.1652465
75. W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006). 10.1063/1.2387955 (Pubitemid 44707810)
76. A. C. Simmonett, J. J. Wilke, H. F. Schaefer III, and W. Kutzelnigg, J. Chem. Phys. 133, 174122 (2010). 10.1063/1.3503657
77. T. Yanai and G. K.-L. Chan, J. Chem. Phys. 127, 104107 (2007). 10.1063/1.2761870 (Pubitemid 47421918)
78. E. Neuscamman, T. Yanai, and G. K.-L. Chan, Int. Rev. Phys. Chem. 29, 231 (2010). 10.1080/01442351003620540
79. E. Neuscamman, T. Yanai, and G. K.-L. Chan, J. Chem. Phys. 130, 124102 (2009). 10.1063/1.3086932
80. T. Yanai, Y. Kurashige, E. Neuscamman, and G. K.-L. Chan, J. Chem. Phys. 132, 024105 (2010). 10.1063/1.3275806
81. D. A. Mazziotti, Adv. Chem. Phys. 134, 331 (2007). 10.1002/9780470106600. ch12
82. A. E. DePrince and D. A. Mazziotti, J. Chem. Phys. 127, 104104 (2007). 10.1063/1.2768354 (Pubitemid 47416068)
83. D. A. Mazziotti, Phys. Rev. A 76, 052502 (2007). 10.1103/PhysRevA.76. 052502 (Pubitemid 350085079)
84. J. J. Foley IV, A. E. Rothman, and D. A. Mazziotti, J. Chem. Phys. 134, 034111 (2011). 10.1063/1.3526298
85. L. Kong, K. Shamasundar, O. Demel, and M. Nooijenn, J. Chem. Phys. 130, 114101 (2009). 10.1063/1.3089302
86. M. Torheyden and E. F. Valeev, J. Chem. Phys. 131, 171103 (2009). 10.1063/1.3254836
87. U. S. Mahapatra, B. Datta, B. Bandyopadhyay, and D. Mukherjee, Adv. Quantum Chem. 30, 163 (1998). 10.1016/S0065-3276(08)60507-9
88. R. Bartlett and M. Musia, Rev. Mod. Phys. 79, 291 (2007). 10.1103/RevModPhys.79.291 (Pubitemid 46346056)
89. D. A. Mazziotti, Phys. Rev. A 60, 4396 (1999). 10.1103/PhysRevA.60.4396
90. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997). 10.1063/1.474405
91. M. B. Plenio and S. Virmani, Quantum Inf. Comput. 7, 1 (2007).
92. D. Zgid, D. Ghosh, E. Neuscamman, and G. K.-L. Chan, J. Chem. Phys. 130, 194107 (2009). 10.1063/1.3132922
93. C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger, and J.-P. Malrieu, J. Chem. Phys. 114, 10252 (2001). 10.1063/1.1361246 (Pubitemid 32616407)
94. C. Angeli, B. Bories, A. Cavallini, and R. Cimiraglia, J. Chem. Phys. 124, 054108 (2006). 10.1063/1.2148946 (Pubitemid 43204509)