Scaling properties of exchange and correlation holes of the valence shell of second-row atoms

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 85, Issue 4, 2012, Pages

  Cancio, A C ^a   Fong, C Y ^b  

^a BALL STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION HOLES; EXCHANGE AND CORRELATION; EXCHANGE-CORRELATIONS; FINITE SIZE; GENERALIZED GRADIENT APPROXIMATIONS; HIGH DENSITY; NORM-CONSERVING PSEUDOPOTENTIALS; PARTICLE NUMBERS; PERDEW-BURKE-ERNZERHOF; SCALING PROPERTIES; SCALING TRENDS; SELF-INTERACTIONS; TEST MODELS; VALENCE SHELLS; VARIATIONAL MONTE CARLO;

ATOMS; MONTE CARLO METHODS;

DENSITY FUNCTIONAL THEORY;

EID: 84860341366     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.85.042515     Document Type: Article

References (85)

1. P. Hohenberg and W. Kohn, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.136.B864 136, B864 (1964).
2. R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.61.689 61, 689 (1989).
3. M. Levy and J. P. Perdew, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.2010 32, 2010 (1985).
4. M. Levy, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.43.4637 43, 4637 (1991).
5. J. Harris and R. O. Jones, J. Phys. F: Met. Phys. JPFMAT 0305-4608 10.1088/0305-4608/4/8/013 4, 1170 (1974);
6. D. C. Langreth and J. P. Perdew, Solid State Commun. 0038-1098 10.1016/0038-1098(75)90618-3 17, 1425 (1975);
7. O. Gunnarson and B. I. Lundqvist, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.13.4274 13, 4274 (1976).
8. J. M. C. Scott, Philos. Mag. series 7 43, 859 (1952).
9. N. H. March, Adv. Phys. ADPHAH 0001-8732 10.1080/00018735700101156 6, 1 (1957).
10. J. P. Perdew, L. A. Constantin, E. Sagvolden, and K. Burke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.223002 97, 223002 (2006). (Pubitemid 44853871)
11. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.136406 100, 136406 (2008). (Pubitemid 351503187)
12. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, L. A. Constantin, and J. Sun, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.026403 103, 026403 (2009).
13. J. P. Perdew, in Electronic Structure of Solids '91, edited by, P. Ziesche, and, H. Eschrig, (Akademie Verlag, Berlin, 1991).
14. J. P. Perdew, K. Burke, and Y. Wang, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.54.16533 54, 16533 (1996).
15. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3865 77, 3865 (1996);
16. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.1396 78, 1396 (E) (1997).
17. A. D. Becke, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.464913 98, 5648 (1993).
18. L. A. Constantin, J. P. Perdew, and J. Tao, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.73.205104 73, 205104 (2006). (Pubitemid 43660037)
19. C. A. Coulson and A. H. Neilson, Proc. Phys. Soc. PPSOAU 0370-1328 10.1088/0370-1328/78/5/328 78, 831 (1961).
20. T. Koga and H. Matsuyama, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.475002 107, 8510 (1997).
21. H. Matsuyama, T. Koga, E. Romera, and J. S. Dehesa, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.1759 57, 1759 (1998).
22. T. Koga, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.481294 112, 6966 (2000).
23. K. E. Banyard and R. J. Mobbs, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.442452 75, 3433 (1981).
24. X. Fradera, M. Duran, and J. Mestres, J. Chem. Phys. 0021-9606 10.1063/1.1305920 113, 2530 (2000).
25. X. Fradera, M. Duran, E. Valderrama, and J. M. Ugalde, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.034502 62, 034502 (2000).
26. J. Wang, A. N. Tripathi, and V. H. Smith, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.463294 97, 9188 (1992).
27. J. Wang, A. N. Tripathi, and V. H. Smith, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.467407 101, 4842 (1994).
28. J. Cioslowski and G. Liu, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.477484 109, 8225 (1998). (Pubitemid 128672180)
29. J. Cioslowski and G. Liu, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.477854 110, 1882 (1999).
30. A. C. Cancio, C. Y. Fong, and J. S. Nelson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062507 62, 062507 (2000). (Pubitemid 32076648)
31. F. J. Gálvez, E. Buendía, and A. Sarsa, J. Chem. Phys. 0021-9606 10.1063/1.1961384 123, 034302 (2005); (Pubitemid 41117891)
32. F. J. Gálvez, E. Buendía, and A. Sarsa, J. Chem. Phys. 0021-9606 10.1063/1.2150822 124, 044319 (2006). (Pubitemid 43166329)
33. J. Toulouse, R. Assaraf, and C. J. Umrigar, J. Chem. Phys. 0021-9606 10.1063/1.2746029 126, 244112 (2007). (Pubitemid 47141408)
34. A. J. Thakkar, A. N. Tripathi, and V. H. Smith, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.560260202 26, 157 (1984).
35. P. Gori-Giorgi and A. Savin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032513 71, 032513 (2005). (Pubitemid 40648472)
36. A. Nagy, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2370948 125, 184104 (2006). (Pubitemid 44749460)
37. M. A. Buijse and E. J. Baerends, in Density Functional Theory of Molecules, Clusters and Solids, edited by, D. E. Ellis, (Kluwer Academic, Dordrecht, 1995).
38. S. Fahy, X. W. Wang, and S. G. Louie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.1478 65, 1478 (1990).
39. R. Q. Hood, M. Y. Chou, A. J. Williamson, G. Rajagopal, R. J. Needs, and W. M. C. Foulkes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.3350 78, 3350 (1997).
40. R. Q. Hood, M. Y. Chou, A. J. Williamson, G. Rajagopal, and R. J. Needs, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.57.8972 57, 8972 (1998).
41. Maziar Nekovee, W. M. C. Foulkes, and R. J. Needs, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.036401 87, 036401 (2001);
42. Maziar Nekovee, W. M. C. Foulkes, and R. J. Needs, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.68.235108 68, 235108 (2003).
43. A. C. Cancio, M. Y. Chou, and R. Q. Hood, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.64.115112 64, 115112 (2001).
44. A. Puzder, M. Y. Chou, and R. Q. Hood, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.022501 64, 022501 (2001).
45. C. R. Hsing, M. Y. Chou, and T. K. Lee, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.032507 74, 032507 (2006). (Pubitemid 44465435)
46. J. C. Slater, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.36.57 36, 57 (1930).
47. W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.73.33 73, 33 (2001).
48. W. Kohn and L. J. Sham, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.140. A1133 140, A1133 (1965).
49. Note that the variation of the XC hole with coupling constant λ is equivalent to the variation of the hole under uniform scaling of the density. A study of this variation with λ, as in Ref., would be a useful complement to ours.
50. U. von Barth and L. Hedin, J. Phys. C 0022-3719 10.1088/0022-3719/5/13/ 012 5, 1629 (1972).
51. A. D. Becke, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.3098 38, 3098 (1988).
52. C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.37.785 37, 785 (1988).
53. R. Armiento and A. E. Mattsson, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.72.085108 72, 085108 (2005). (Pubitemid 43406100)
54. Y. Zhao and D. G. Truhlar, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2912068 128, 184109 (2008). (Pubitemid 351707231)
55. A. D. Becke, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.476722 109, 2092 (1998). (Pubitemid 128678085)
56. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.146401 91, 146401 (2003).
57. H. L. Schmider and A. D. Becke, J. Mol. Struct.: THEOCHEM THEODJ 0166-1280 10.1016/S0166-1280(00)00477-2 527, 51 (2000).
58. Y. Zhao and D. G. Truhlar, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2370993 125, 194101 (2006). (Pubitemid 44867314)
59. J. P. Perdew and L. A. Constantin, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.75.155109 75, 155109 (2007).
60. A. C. Cancio and M. Y. Chou, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.74.081202 74, 081202 (R) (2006). (Pubitemid 44310600)
61. M. Ernzerhof and J. P. Perdew, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.476928 109, 3313 (1998). (Pubitemid 128678234)
62. J. P. Perdew and Y. Wang, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.46.12947 46, 12947 (1992).
63. K. Burke, J. P. Perdew, and M. Ernzerhof, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.476976 109, 3760 (1998). (Pubitemid 128678583)
64. The presence of self-interaction error in the Hartree energy is what forces the constant term A in this expression, and spoils a purely power-law behavior as seen in Thomas-Fermi scaling of the all-electron density.
65. G. L. Oliver and J. P. Perdew, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.20.397 20, 397 (1979).
66. The analogous relationship for the correlation hole is used to derive the scaling formula for the hole at full coupling [Eq.].
67. D. R. Hamann, M. Schlüter, and C. Chiang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.43.1494 43, 1494 (1979);
68. G. B. Bachelet, D. R. Hamann, and M. Schlüter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.26.4199 26, 4199 (1982).
69. N. C. Handy, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1678918 58, 279 (1973).
70. K. E. Schmidt and J. W. Moskowitz, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.458750 93, 4172 (1990).
71. T. Kato, Commun. Pure Appl. Math. 0010-3640 10.1002/cpa.3160100201 10, 151 (1957).
72. R. J. Harrison and N. C. Handy, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/0009-2614(85)80255-4 113, 257 (1985).
73. C. Filippi and C. J. Umrigar, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.471865 105, 213 (1996).
74. R. N. Barnett, Z. Sun, and W. A. Lester, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1335596 114, 2013 (2001). (Pubitemid 32873179)
75. W. L. McMillan, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.138.A442 138, A442 (1965).
76. D. Ceperley and M. H. Kalos, in Monte Carlo Methods in Statistical Physics, edited by, K. Binder, (Springer Verlag, Berlin, 1979).
77. S. Fahy, X. W. Wang, and S. G. Louie, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.1631 61, 1631 (1988);
78. S. Fahy, X. W. Wang, and S. G. Louie, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.42.3503 42, 3503 (1990).
79. L. Mitár̊, E. L. Shirley, and D. M. Ceperley, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.460849 95, 3467 (1991).
80. C. J. Umrigar, K. G. Wilson, and J. W. Wilkins, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60.1719 60, 1719 (1988).
81. M. Kalos and P. Whitlock, Monte Carlo Methods, Vol. I (Wiley and Sons, New York, 1986).
82. D. Ceperley, Lecture notes on Computational Statistical Mechanics, University of Illinois, 1990 (unpublished).
83. G. Ortiz and P. Ballone, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.50.1391 50, 1391 (1994).
84. J. M. del Campo, J. L. Gazquez, S. B. Trickey, and A. Vela, J. Chem. Phys. 0021-9606 10.1063/1.3691197 136, 104108 (2012).
85. J. C. Kimball, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.7.1648 7, 1648 (1973).