Linear-scaling implementation of the direct random-phase approximation

Journal of Chemical Physics

Volumn 142, Issue 20, 2015, Pages

  Kállay, Mihály ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR ORBITALS;

AUXILIARY FUNCTIONS; BENCHMARK CALCULATIONS; ENERGY DIFFERENCES; INCREMENTAL SCHEME; LINEAR SCALING ALGORITHM; LOCAL CORRELATIONS; RANDOM PHASE APPROXIMATIONS; SCREENED EXCHANGES;

APPROXIMATION ALGORITHMS;

EID: 84930632027     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4921542     Document Type: Article

References (138)

1. D. Bohm and D. Pines, Phys. Rev. 82, 625 (1951). 10.1103/PhysRev.82.625
2. P. Nozières and D. Pines, Phys. Rev. 111, 442 (1958). 10.1103/PhysRev.111.442
3. A. D. McLachlan and A. M. Ball, Rev. Mod. Phys. 36, 844 (1964). 10.1103/RevModPhys.36.844
4. J. Oddershede, Adv. Quantum Chem. 11, 275 (1978). 10.1016/S0065-3276(08)60240-3
5. D. C. Langreth and J. P. Perdew, Solid State Commun. 17, 1425 (1975). 10.1016/0038-1098(75)90618-3
6. D. C. Langreth and J. P. Perdew, Phys. Rev. B 15, 2884 (1977). 10.1103/PhysRevB.15.2884
7. O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976). 10.1103/PhysRevB.13.4274
8. J. F. Dobson and J. Wang, Phys. Rev. Lett. 82, 2123 (1999). 10.1103/PhysRevLett.82.2123
9. F. Furche, Phys. Rev. B 64, 195120 (2001). 10.1103/PhysRevB.64.195120
10. A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977). 10.1063/1.434580
11. H. Eshuis, J. E. Bates, and F. Furche, Theor. Chem. Acc. 131, 1084 (2012). 10.1007/s00214-011-1084-8
12. H. Eshuis and F. Furche, J. Chem. Phys. 136, 084105 (2012). 10.1063/1.3687005
13. H. Eshuis and F. Furche, J. Phys. Chem. Lett. 2, 983 (2011). 10.1021/jz200238f
14. J. Paier, X. Ren, P. Rinke, G. E. Scuseria, A. Grüneis, G. Kresse, and M. Scheffler, New J. Phys. 14, 043002 (2012). 10.1088/1367-2630/14/4/043002
15. D. L. Freeman, Phys. Rev. B 15, 5512 (1977). 10.1103/PhysRevB.15.5512
16. A. Grüneis, M. Marsman, J. Harl, L. Schimka, and G. Kresse, J. Chem. Phys. 131, 154115 (2009). 10.1063/1.3250347
17. M. Hellgren and U. von Barth, Phys. Rev. B 78, 115107 (2008). 10.1103/PhysRevB.78.115107
18. A. Heßelmann and A. Görling, Phys. Rev. Lett. 106, 093001 (2011). 10.1103/PhysRevLett.106.093001
19. P. Bleiziffer, A. Heßelmann, and A. Görling, J. Chem. Phys. 139, 084113 (2013). 10.1063/1.4818984
20. A. Heßelmann, Phys. Rev. A 85, 012517 (2012). 10.1103/PhysRevA.85.012517
21. H. Jiang and E. Engel, J. Chem. Phys. 127, 184108 (2007). 10.1063/1.2795707
22. V. Lotrich and R. J. Bartlett, J. Chem. Phys. 134, 184108 (2011). 10.1063/1.3570573
23. A. Heßelmann and A. Görling, Mol. Phys. 109, 2473 (2011). 10.1080/00268976.2011.614282
24. J. E. Bates and F. Furche, J. Chem. Phys. 139, 171103 (2013). 10.1063/1.4827254
25. J. G. Ángyán, I. C. Gerber, A. Savin, and J. Toulouse, Phys. Rev. A 72, 012510 (2005). 10.1103/PhysRevA.72.012510
26. J. Toulouse, I. C. Gerber, G. Jansen, A. Savin, and J. G. Ángyán, Phys. Rev. Lett. 102, 096404 (2009). 10.1103/PhysRevLett.102.096404
27. B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 131, 034110 (2009). 10.1063/1.3176514
28. J. Toulouse, W. Zhu, A. Savin, G. Jansen, and J. G. Ángyán, J. Chem. Phys. 135, 084119 (2011). 10.1063/1.3626551
29. F. Furche, J. Chem. Phys. 114, 5982 (2001). 10.1063/1.1353585
30. G. E. Scuseria, T. M. Henderson, and D. C. Sorensen, J. Chem. Phys. 129, 231101 (2008). 10.1063/1.3043729
31. G. Jansen, R.-F. Liu, and J. G. Ángyán, J. Chem. Phys. 133, 154106 (2010). 10.1063/1.3481575
32. G. E. Scuseria, T. M. Henderson, and I. W. Bulik, J. Chem. Phys. 139, 104113 (2013). 10.1063/1.4820557
33. H. Eshuis, J. Yarkony, and F. Furche, J. Chem. Phys. 132, 234114 (2010). 10.1063/1.3442749
34. M. Del Ben, O. Schütt, T. Wentz, P. Messmer, J. Hutter, and J. VandeVondele, Comput. Phys. Commun. 187, 120 (2015). 10.1016/j.cpc.2014.10.021
35. X. Ren, P. Rinke, V. Blum, J. Wieferink, A. Tkatchenko, A. Sanfilippo, K. Reuter, and M. Scheffler, New J. Phys. 14, 053020 (2012). 10.1088/1367-2630/14/5/053020
36. D. Rocca, J. Chem. Phys. 140, 18A501 (2014). 10.1063/1.4849416
37. T. Olsen and K. S. Thygesen, Phys. Rev. B 87, 075111 (2013). 10.1103/PhysRevB.87.075111
38. M. Kaltak, J. Klimeš, and G. Kresse, J. Chem. Theory Comput. 10, 2498 (2014). 10.1021/ct5001268
39. J. E. Moussa, J. Chem. Phys. 140, 014107 (2014). 10.1063/1.4855255
40. M. Kaltak, J. Klimeš, and G. Kresse, Phys. Rev. B 90, 054115 (2014). 10.1103/PhysRevB.90.054115
41. D. Neuhauser, E. Rabani, and R. Baer, J. Phys. Chem. Lett. 4, 1172 (2013). 10.1021/jz3021606
42. Y. Gao, D. Neuhauser, R. Baer, and E. Rabani, J. Chem. Phys. 142, 034106 (2015). 10.1063/1.4905568
43. P. Pulay, Chem. Phys. Lett. 100, 151 (1983). 10.1016/0009-2614(83)80703-9
44. E. Kapuy, Z. Csépes, and C. Kozmutza, Int. J. Quantum Chem. 23, 981 (1983). 10.1002/qua.560230321
45. W. Förner, J. Ladik, P. Otto, and J. Cizek, Chem. Phys. 97, 251 (1985). 10.1016/0301-0104(85)87035-X
46. C. Hampel and H.-J. Werner, J. Chem. Phys. 104, 6286 (1996). 10.1063/1.471289
47. M. Schütz and H.-J. Werner, Chem. Phys. Lett. 318, 370 (2000). 10.1016/S0009-2614(00)00066-X
48. H.-J. Werner and M. Schütz, J. Chem. Phys. 135, 144116 (2011). 10.1063/1.3641642
49. T. B. Adler and H.-J. Werner, J. Chem. Phys. 135, 144117 (2011). 10.1063/1.3647565
50. T. B. Adler, H.-J. Werner, and F. R. Manby, J. Chem. Phys. 130, 054106 (2009). 10.1063/1.3040174
51. C. Krause and H.-J. Werner, Phys. Chem. Chem. Phys. 14, 7591 (2012). 10.1039/c2cp40231a
52. M. Schütz, J. Chem. Phys. 113, 9986 (2000). 10.1063/1.1323265
53. M. Schütz, J. Chem. Phys. 116, 8772 (2002). 10.1063/1.1470497
54. M. Schütz, Phys. Chem. Chem. Phys. 4, 3941 (2002). 10.1039/b203994j
55. M. Schütz and F. R. Manby, Phys. Chem. Chem. Phys. 5, 3349 (2003). 10.1039/b304550a
56. D. Kats, T. Korona, and M. Schütz, J. Chem. Phys. 125, 104106 (2006). 10.1063/1.2339021
57. O. Masur, D. Usvyat, and M. Schütz, J. Chem. Phys. 139, 164116 (2013). 10.1063/1.4826534
58. F. Neese, F. Wennmohs, and A. Hansen, J. Chem. Phys. 130, 114108 (2009). 10.1063/1.3086717
59. F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009). 10.1063/1.3173827
60. A. Hansen, D. G. Liakos, and F. Neese, J. Chem. Phys. 135, 214102 (2011). 10.1063/1.3663855
61. C. Riplinger and F. Neese, J. Chem. Phys. 138, 034106 (2013). 10.1063/1.4773581
62. C. Riplinger, B. Sandhoefer, A. Hansen, and F. Neese, J. Chem. Phys. 139, 134101 (2013). 10.1063/1.4821834
63. J. Yang, Y. Kurashige, F. R. Manby, and G. K.-L. Chan, J. Chem. Phys. 134, 044123 (2011). 10.1063/1.3528935
64. J. Yang, G. K.-L. Chan, F. R. Manby, M. Schütz, and H.-J. Werner, J. Chem. Phys. 136, 144105 (2012). 10.1063/1.3696963
65. M. Schütz, J. Yang, G. K.-L. Chan, F. R. Manby, and H.-J. Werner, J. Chem. Phys. 138, 054109 (2013). 10.1063/1.4789415
66. Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011). 10.1063/1.3632085
67. Z. Rolik, L. Szegedy, I. Ladjánszki, B. Ladóczki, and M. Kállay, J. Chem. Phys. 139, 094105 (2013). 10.1063/1.4819401
68. H.-J. Werner, G. Knizia, C. Krause, M. Schwilk, and M. Dornbach, J. Chem. Theory Comput. 11, 484 (2015). 10.1021/ct500725e
69. H. Stoll, Phys. Rev. B 46, 6700 (1992). 10.1103/PhysRevB.46.6700
70. M. Yu, S. Kalvoda, and M. Dolg, Chem. Phys. 224, 121 (1997). 10.1016/S0301-0104(97)00257-7
71. K. Ro'ciszewski, K. Doll, B. Paulus, P. Fulde, and H. Stoll, Phys. Rev. B 57, 14667 (1998). 10.1103/PhysRevB.57.14667
72. C. Willnauer and U. Birkenheuer, J. Chem. Phys. 120, 11910 (2004). 10.1063/1.1740748
73. J. Friedrich and M. Dolg, J. Chem. Theory Comput. 5, 287 (2009). 10.1021/ct800355e
74. J. Friedrich and K. Walczak, J. Chem. Theory Comput. 9, 408 (2013). 10.1021/ct300938w
75. S. Li, J. Ma, and Y. Jiang, J. Comput. Chem. 23, 237 (2002). 10.1002/jcc.10003
76. S. Li, W. Li, and J. Ma, Chin. J. Chem. 21, 1422 (2003). 10.1002/cjoc.20030211106
77. S. Li, J. Shen, W. Li, and Y. Jiang, J. Chem. Phys. 125, 074109 (2006). 10.1063/1.2244566
78. W. Li, P. Piecuch, J. R. Gour, and S. Li, J. Chem. Phys. 131, 114109 (2009). 10.1063/1.3218842
79. W. Li and P. Piecuch, J. Phys. Chem. A 114, 6721 (2010). 10.1021/jp1038738
80. W. Li and P. Piecuch, J. Phys. Chem. A 114, 8644 (2010). 10.1021/jp100782u
81. P. Arora, W. Li, P. Piecuch, J. W. Evans, M. Albao, and M. S. Gordon, J. Phys. Chem. C 114, 12649 (2010). 10.1021/jp102998y
82. D. G. Federov and K. Kitaura, J. Chem. Phys. 123, 134103 (2005). 10.1063/1.2007588
83. W. Li and S. Li, J. Chem. Phys. 121, 6649 (2004). 10.1063/1.1792051
84. M. Ziółkowski, B. Jansík, T. Kjærgaard, and P. Jørgensen, J. Chem. Phys. 133, 014107 (2010). 10.1063/1.3456535
85. K. Kristensen, I.-M. Høyvik, B. Jansík, P. Jørgensen, T. Kjærgaard, S. Reine, and J. Jakowski, Phys. Chem. Chem. Phys. 14, 15706 (2012). 10.1039/c2cp41958k
86. N. Flocke and R. J. Bartlett, J. Chem. Phys. 121, 10935 (2004). 10.1063/1.1811606
87. P. Y. Ayala and G. E. Scuseria, J. Chem. Phys. 110, 3660 (1999). 10.1063/1.478256
88. G. E. Scuseria and P. Y. Ayala, J. Chem. Phys. 111, 8330 (1999). 10.1063/1.480174
89. P. E. Maslen and M. Head-Gordon, Chem. Phys. Lett. 283, 102 (1998). 10.1016/S0009-2614(97)01333-X
90. B. Doser, D. S. Lambrecht, J. Kussmann, and C. Ochsenfeld, J. Chem. Phys. 130, 064107 (2009). 10.1063/1.3072903
91. J. Zienau, L. Clin, B. Doser, and C. Ochsenfeld, J. Chem. Phys. 130, 204112 (2009). 10.1063/1.3142592
92. M. Del Ben, J. Hutter, and J. VandeVondele, J. Chem. Theory Comput. 8, 4177 (2012). 10.1021/ct300531w
93. E. Chermak, B. Mussard, J. G. Ángyán, and P. Reinhardt, Chem. Phys. Lett. 550, 162 (2012). 10.1016/j.cplett.2012.08.073
94. M. Schütz, O. Masur, and D. Usvyat, J. Chem. Phys. 140, 244107 (2014). 10.1063/1.4884156
95. J. G. Ángyán, R.-F. Liu, J. Toulouse, and G. Jansen, J. Chem. Theory Comput. 7, 3116 (2011). 10.1021/ct200501r
96. J. L. Whitten, J. Chem. Phys. 58, 4496 (1973). 10.1063/1.1679012
97. M. Feyereisen, G. Fitzgerald, and A. Komornicki, Chem. Phys. Lett. 208, 359 (1993). 10.1016/0009-2614(93)87156-W
98. H. Koch and A. M. Sánchez de Merás, J. Chem. Phys. 113, 508 (2000). 10.1063/1.481910
99. J. Almlöf, Chem. Phys. Lett. 176, 319 (1991). 10.1016/0009-2614(91)80078-C
100. A. Takatsuka, S. Ten-no, and W. Hackbusch, J. Chem. Phys. 129, 044112 (2008). 10.1063/1.2958921
101. P. Pulay, Chem. Phys. Lett. 73, 393 (1980). 10.1016/0009-2614(80)80396-4
102. G. E. Scuseria, T. J. Lee, and H. F. Schaefer III, Chem. Phys. Lett. 130, 236 (1986). 10.1016/0009-2614(86)80461-4
103. J. Rekkedal, S. Coriani, M. F. Iozzi, A. M. Teale, T. Helgaker, and T. B. Pedersen, J. Chem. Phys. 139, 081101 (2013). 10.1063/1.4819399
104. J. Willems, IEEE Trans. Autom. Control 16, 621 (1971). 10.1109/TAC.1971.1099831
105. B. P. Molinari, SIAM J. Control 11, 262 (1973). 10.1137/0311021
106. A. D. Becke, J. Chem. Phys. 88, 2547 (1988). 10.1063/1.454033
107. C. W. Murray, N. C. Handy, and G. J. Laming, Mol. Phys. 78, 997 (1993). 10.1080/00268979300100651
108. M. Krack and A. M. Köster, J. Chem. Phys. 108, 3226 (1998). 10.1063/1.475719
109. Functionals were obtained from the Density Functional Repository as developed and distributed by the Quantum Chemistry Group, CCLRC Daresbury Laboratory, Daresbury, Cheshire WA4 4AD, United Kingdom. Contact Huub van Dam (h.j.j.vandam@dl.ac.uk) or Paul Sherwood for further information.
110. R. Strange, F. R. Manby, and P. J. Knowles, Comput. Phys. Commun. 136, 310 (2001). 10.1016/S0010-4655(01)00148-5
111. R. Polly, H.-J. Werner, F. R. Manby, and P. J. Knowles, Mol. Phys. 102, 2311 (2004). 10.1080/0026897042000274801
112. Y. Jung, R. C. Lochan, A. D. Dutoi, and M. Head-Gordon, J. Chem. Phys. 121, 9793 (2004). 10.1063/1.1809602
113. Y. Jung, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 1953 (2007). 10.1002/jcc.20590
114. B. G. Janesko and G. E. Scuseria, Phys. Chem. Chem. Phys. 11, 9677 (2009). 10.1039/b910905f
115. M. Kállay, J. Chem. Phys. 141, 244113 (2014). 10.1063/1.4905005
116. J. M. Foster and S. F. Boys, Rev. Mod. Phys. 32, 300 (1960). 10.1103/RevModPhys.32.300
117. J. Pipek and P. Mezey, J. Chem. Phys. 90, 4916 (1989). 10.1063/1.456588
118. See supplementary material at http://dx.doi.org/10.1063/1.4921542 E-JCPSA6-142-020521 for the pseudocode of the dRPA algorithm and the scaling of the various steps.
119. J. W. Boughton and P. Pulay, J. Comput. Chem. 14, 736 (1993). 10.1002/jcc.540140615
120. G. Hetzer, P. Pulay, and H.-J. Werner, Chem. Phys. Lett. 290, 143 (1998). 10.1016/S0009-2614(98)00491-6
121. S. Grimme, J. Chem. Phys. 118, 9095 (2003). 10.1063/1.1569242
122. Mrcc, a quantum chemical program suite written by M. Kállay, Z. Rolik, J. Csontos, I. Ladjánszki, L. Szegedy, B. Ladóczki, and G. Samu. See also Ref. 67as well as http://www.mrcc.hu/.
123. T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989). 10.1063/1.456153
124. R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. Phys. 96, 6796 (1992). 10.1063/1.462569
125. D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 98, 1358 (1993). 10.1063/1.464303
126. F. Weigend, J. Comput. Chem. 29, 167 (2008). 10.1002/jcc.20702
127. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 10.1103/PhysRevLett.77.3865
128. P. A. M. Dirac, Proc. R. Soc. London, Ser. A 123, 714 (1929). 10.1098/rspa.1929.0094
129. J. C. Slater, Phys. Rev. 81, 385 (1951). 10.1103/PhysRev.81.385
130. R. Huenerbein, B. Schirmer, J. Moellmann, and S. Grimme, Phys. Chem. Chem. Phys. 12, 6940 (2010). 10.1039/c003951a
131. S. A. Maurer, D. S. Lambrecht, D. Flaig, and C. Ochsenfeld, J. Chem. Phys. 136, 144107 (2012). 10.1063/1.3693908
132. C. Baerlocher and L. B. McCusker, Database of Zeolite Structures, http://www.iza-structure.org/databases/.
133. J. Cezáč, K. E. Riley, and P. Hobza, J. Chem. Theory Comput. 7, 2427 (2011). 10.1021/ct2002946
134. J. Csontos, M. Kálmán, and G. Tasi, J. Mol. Struct.: THEOCHEM 640, 69 (2003). 10.1016/j.theochem.2003.08.005
135. J. Csontos, M. Kálmán, and G. Tasi, J. Mol. Struct.: THEOCHEM 666, 515 (2003). 10.1016/j.theochem.2003.08.075
136. J. Csontos, P. Kálmán, G. Tasi, M. Kálmán, R. F. Murphy, and S. Lovas, J. Comput. Chem. 29, 1466 (2008). 10.1002/jcc.20907
137. U. R. Fogueri, S. Kozuch, A. Karton, and J. M. L. Martin, J. Phys. Chem. A 117, 2269 (2013). 10.1021/jp312644t
138. J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 127, 054103 (2007). 10.1063/1.2749509