Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation

Journal of Chemical Physics

Volumn 139, Issue 15, 2013, Pages

  Zhang, Du ^a   Steinmann, Stephan N ^a   Yang, Weitao ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY FUNCTIONAL THEORY; EQUATIONS OF MOTION; NUMERICAL METHODS; QUANTUM CHEMISTRY;

ADIABATIC APPROXIMATIONS; BETHE-SALPETER EQUATION; CONFIGURATION INTERACTION SINGLES; ELECTRONIC EXCITATION ENERGY; EQUATION OF MOTION COUPLED CLUSTERS; PERTURBATIVE CALCULATIONS; TIME DEPENDENT DENSITY FUNCTIONAL THEORY; TIME-DEPENDENT HARTREE-FOCK;

HARTREE APPROXIMATION;

ARTICLE; ELECTRON; QUANTUM THEORY; TIME;

ELECTRONS; QUANTUM THEORY; TIME FACTORS;

EID: 84886571404     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4824907     Document Type: Article

References (126)

1. M. R. Wasielewski, J. Org. Chem. 71, 5051 (2006). 10.1021/jo060225d
2. M. R. Wasielewski, Chem. Rev. 92, 435 (1992). 10.1021/cr00011a005
3. Y.-C. Cheng and G. R. Fleming, Annu. Rev. Phys. Chem. 60, 241 (2009). 10.1146/annurev.physchem.040808.090259
4. J. Jortner, M. Bixon, T. Langenbacher, and M. E. Michel-Beyerle, Proc. Natl. Acad. Sci. U.S.A. 95, 12759 (1998). 10.1073/pnas.95.22.12759
5. M. S. Kaczmarski, Y. Ma, and M. Rohlfing, Phys. Rev. B 81, 115433 (2010). 10.1103/PhysRevB.81.115433
6. B. Kohler, J. Phys. Chem. Lett. 1, 2047 (2010). 10.1021/jz100491x
7. J. Bisquert, D. Cahen, G. Hodes, S. Rühle, and A. Zaban, J. Phys. Chem. B 108, 8106 (2004). 10.1021/jp0359283
8. D. Kuciauskas, M. S. Freund, H. B. Gray, J. R. Winkler, and N. S. Lewis, J. Phys. Chem. B 105, 392 (2001). 10.1021/jp002545l
9. A. Yamakata, T.-a. Ishibashi, and H. Onishi, J. Mol. Catal. A: Chem. 199, 85 (2003). 10.1016/S1381-1169(03)00021-9
10. J. Liu, G. Chen, Z. Li, and Z. Zhang, J. Solid State Chem. 179, 3704 (2006). 10.1016/j.jssc.2006.08.014
11. J. B. Foresman, M. Head-Gordon, J. A. Pople, and M. J. Frisch, J. Phys. Chem. 96, 135 (1992). 10.1021/j100180a030
12. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984). 10.1103/PhysRevLett.52.997
13. R. Bauernschmitt and R. Ahlrichs, Chem. Phys. Lett. 256, 454 (1996). 10.1016/0009-2614(96)00440-X
14. F. Furche and R. Ahlrichs, J. Chem. Phys. 117, 7433 (2002). 10.1063/1.1508368
15. R. E. Stratmann, G. E. Scuseria, and M. J. Frisch, J. Chem. Phys. 109, 8218 (1998). 10.1063/1.477483
16. I. Shavitt in Methods of Electronic Structure Theory, edited by, H. F. Schaeffer III, (Plenum, New York, 1977), p. 189.
17. F. Neese, T. Petrenko, D. Ganyushin, and G. Olbrich, Coord. Chem. Rev. 251, 288 (2007). 10.1016/j.ccr.2006.05.019
18. B. O. Roos, P. Linse, P. E. Siegbahn, and M. R. Blomberg, Chem. Phys. 66, 197 (1982). 10.1016/0301-0104(82)88019-1
19. K. Wolinski, H. L. Sellers, and P. Pulay, Chem. Phys. Lett. 140, 225 (1987). 10.1016/0009-2614(87)80448-7
20. B. O. Roos, K. Andersson, M. P. Fulscher, L. Serrano-Andres, K. Pierloot, M. Merchon, and V. Molina, J. Mol. Struct.: THEOCHEM 388, 257 (1996). 10.1016/S0166-1280(96)80039-X
21. J. F. Stanton and R. J. Bartlett, J. Chem. Phys. 98, 7029 (1993). 10.1063/1.464746
22. K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 8490 (2000). 10.1063/1.1318757
23. A. I. Krylov, Annu. Rev. Phys. Chem. 59, 433 (2008). 10.1146/annurev. physchem.59.032607.093602
24. G. Strinati, Riv. Nuovo Cimento 11, 1 (1988). 10.1007/BF02725962
25. M. Rohlfing and S. G. Louie, Phys. Rev. B 62, 4927 (2000). 10.1103/PhysRevB.62.4927
26. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). 10.1103/RevModPhys.74.601
27. A. J. Cohen, P. Mori-Sánchez, and W. Yang, Chem. Rev. 112, 289 (2012). 10.1021/cr200107z
28. S. R. Gwaltney and R. J. Bartlett, Chem. Phys. Lett. 241, 26 (1995). 10.1016/0009-2614(95)00608-7
29. N. T. Maitra, F. Zhang, R. J. Cave, and K. Burke, J. Chem. Phys. 120, 5932 (2004). 10.1063/1.1651060
30. J. H. Starcke, M. Wormit, J. Schirmer, and A. Dreuw, Chem. Phys. 329, 39 (2006). 10.1016/j.chemphys.2006.07.020
31. M. Head-Gordon, R. J. Rico, M. Oumi, and T. J. Lee, Chem. Phys. Lett. 219, 21 (1994). 10.1016/0009-2614(94)00070-0
32. M. Head-Gordon, D. Maurice, and M. Oumi, Chem. Phys. Lett. 246, 114 (1995). 10.1016/0009-2614(95)01111-L
33. Y. M. Rhee and M. Head-Gordon, J. Phys. Chem. A 111, 5314 (2007). 10.1021/jp068409j
34. D. Casanova, Y. M. Rhee, and M. Head-Gordon, J. Chem. Phys. 128, 164106 (2008). 10.1063/1.2907724
35. S. Chattopadhyay, U. S. Mahapatra, and D. Mukherjee, J. Chem. Phys. 111, 3820 (1999). 10.1063/1.479685
36. S. Chattopadhyay, D. Pahari, D. Mukherjee, and U. S. Mahapatra, J. Chem. Phys. 120, 5968 (2004). 10.1063/1.1650328
37. J. Cizek, Advances in Chemical Physics, edited by, P. C. Hariharan, (Wiley Interscience, New York, 1969), p. 35.
38. G. D. Purvis III and R. J. Bartlett, J. Chem. Phys. 76, 1910 (1982). 10.1063/1.443164
39. G. E. Scuseria, C. L. Janssen, and H. F. Schaefer, J. Chem. Phys. 89, 7382 (1988). 10.1063/1.455269
40. G. E. Scuseria and H. F. Schaefer, J. Chem. Phys. 90, 3700 (1989). 10.1063/1.455827
41. R. J. Bartlett, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2, 126 (2012). 10.1002/wcms.76
42. A. Banerjee and J. Simons, Int. J. Quantum Chem. 19, 207 (1981). 10.1002/qua.560190203
43. C. Rittby and R. Bartlett, Theor. Chim. Acta 80, 469 (1991). 10.1007/BF01119666
44. A. Balkova and R. J. Bartlett, J. Chem. Phys. 101, 8972 (1994). 10.1063/1.468025
45. K. Kowalski and P. Piecuch, Phys. Rev. A 61, 052506 (2000). 10.1103/PhysRevA.61.052506
46. K. Bhaskaran-Nair, O. Demel, and J. Pittner, J. Chem. Phys. 129, 184105 (2008). 10.1063/1.3006401
47. D. Hegarty and M. A. Robb, Mol. Phys. 38, 1795 (1979). 10.1080/00268977900102871
48. R. H. Eade and M. A. Robb, Chem. Phys. Lett. 83, 362 (1981). 10.1016/0009-2614(81)85480-2
49. F. Bernardi, A. Bottoni, J. J. McDouall, M. A. Robb, and H. B. Schlegel, Faraday Symposia of the Chemical Society (The Royal Society of Chemistry, 1984), Vol. 19, pp. 137-147.
50. M. Frisch, I. N. Ragazos, M. A. Robb, and H. Bernhard Schlegel, Chem. Phys. Lett. 189, 524 (1992). 10.1016/0009-2614(92)85244-5
51. A. I. Krylov, C. D. Sherrill, E. F. C. Byrd, and M. Head-Gordon, J. Chem. Phys. 109, 10669 (1998). 10.1063/1.477764
52. C. Møller and M. S. Plesset, Phys. Rev. 46, 618 (1934). 10.1103/PhysRev.46.618
53. M. Head-Gordon, J. A. Pople, and M. J. Frisch, Chem. Phys. Lett. 153, 503 (1988). 10.1016/0009-2614(88)85250-3
54. E. Salpeter and H. Bethe, Phys. Rev. 84, 1232 (1951). 10.1103/PhysRev.84.1232
55. L. Sham and T. Rice, Phys. Rev. 144, 708 (1966). 10.1103/PhysRev.144.708
56. Y. Ma, M. Rohlfing, and C. Molteni, Phys. Rev. B 80, 241405 (R) (2009). 10.1103/PhysRevB.80.241405
57. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). 10.1103/PhysRev.136.B864
58. K. Burke, J. Werschnik, and E. K. U. Gross, J. Chem. Phys. 123, 062206 (2005). 10.1063/1.1904586
59. S. Botti, A. Schindlmayr, R. Del Sole, and L. Reining, Rep. Prog. Phys. 70, 357 (2007). 10.1088/0034-4885/70/3/R02
60. M. Casida, in Recent Advances in Density Functional Methods Part A, edited by, P. D. Chong, (World Scientific, 1995), pp. 155-192.
61. D. Peng and W. Yang, J. Chem. Phys. 138, 184108 (2013). 10.1063/1.4803101
62. J. F. Dobson, M. J. Bünner, and E. K. U. Gross, Phys. Rev. Lett. 79, 1905 (1997). 10.1103/PhysRevLett.79.1905
63. N. T. Maitra, K. Burke, and C. Woodward, Phys. Rev. Lett. 89, 023002 (2002). 10.1103/PhysRevLett.89.023002
64. C. A. Ullrich and K. Burke, J. Chem. Phys. 121, 28 (2004). 10.1063/1.1756865
65. A. Heßelmann and A. Görling, J. Chem. Phys. 134, 034120 (2011). 10.1063/1.3517312
66. M. E. Casida, J. Chem. Phys. 122, 054111 (2005). 10.1063/1.1836757
67. M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996). 10.1103/PhysRevLett.76.1212
68. S. Albrecht, L. Reining, R. Del Sole, and G. Onida, Phys. Rev. Lett. 80, 4510 (1998). 10.1103/PhysRevLett.80.4510
69. D. Rocca, D. Lu, and G. Galli, J. Chem. Phys. 133, 164109 (2010). 10.1063/1.3494540
70. L. Hedin, Phys. Rev. 139, A796 (1965). 10.1103/PhysRev.139.A796
71. R. W. Godby, M. Schluter, and L. J. Sham, Phys. Rev. B 37, 10159 (1988). 10.1103/PhysRevB.37.10159
72. M. S. Hybertsen and S. G. Louie, Phys. Rev. B 34, 5390 (1986). 10.1103/PhysRevB.34.5390
73. M. van Schilfgaarde, T. Kotani, and S. Faleev, Phys. Rev. Lett. 96, 226402 (2006). 10.1103/PhysRevLett.96.226402
74. S. V. Faleev, M. Van Schilfgaarde, and T. Kotani, Phys. Rev. Lett. 93, 126406 (2004). 10.1103/PhysRevLett.93.126406
75. See supplementary material at http://dx.doi.org/10.1063/1.4824907 E-JCPSA6-139-020340 for background information, detailed derivations, and extra results.
76. B. Baumeier, D. Andrienko, Y. Ma, and M. Rohlfing, J. Chem. Theory Comput. 8, 997 (2012). 10.1021/ct2008999
77. B. Baumeier, D. Andrienko, and M. Rohlfing, J. Chem. Theory Comput. 8, 2790 (2012). 10.1021/ct300311x
78. A. Marini and R. Del Sole, Phys. Rev. Lett. 91, 176402 (2003). 10.1103/PhysRevLett.91.176402
79. G. Strinati, Phys. Rev. B 29, 5718 (1984). 10.1103/PhysRevB.29.5718
80. F. Sottile, V. Olevano, and L. Reining, Phys. Rev. Lett. 91, 056402 (2003). 10.1103/PhysRevLett.91.056402
81. A. Marini, R. Del Sole, and A. Rubio, Phys. Rev. Lett. 91, 256402 (2003). 10.1103/PhysRevLett.91.256402
82. P. Romaniello, D. Sangalli, J. A. Berger, F. Sottile, L. G. Molinari, L. Reining, and G. Onida, J. Chem. Phys. 130, 044108 (2009). 10.1063/1.3065669
83. D. Sangalli, P. Romaniello, G. Onida, and A. Marini, J. Chem. Phys. 134, 034115 (2011). 10.1063/1.3518705
84. P. Myöhänen, A. Stan, G. Stefanucci, and R. van Leeuwen, Europhys. Lett. 84, 67001 (2008). 10.1209/0295-5075/84/67001
85. N. Sakkinen, M. Manninen, and R. van Leeuwen, New J. Phys. 14, 013032 (2012). 10.1088/1367-2630/14/1/013032
86. M. Gruning, A. Marini, and X. Gonze, Nano Lett. 9, 2820 (2009). 10.1021/nl803717g
87. M. Huix-Rotllant, B. Natarajan, A. Ipatov, C. M. Wawire, T. Deutsch, and M. E. Casida, Phys. Chem. Chem. Phys. 12, 12811 (2010). 10.1039/c0cp00273a
88. S. Hirata and M. Head-Gordon, Chem. Phys. Lett. 314, 291 (1999). 10.1016/S0009-2614(99)01149-5
89. A. J. Cohen, P. Mori-Sanchez, and W. Yang, J. Chem. Theory Comput. 5, 786 (2009). 10.1021/ct8005419
90. A. Beste, Álvaro Vázquez-Mayagoitia, and J. V. Ortiz, J. Chem. Phys. 138, 074101 (2013). 10.1063/1.4790626
91. See http://www.qm4d.info for an in-house program for QM/MM simulations.
92. C. C. J. Roothaan, Rev. Mod. Phys. 23, 69 (1951). 10.1103/RevModPhys.23. 69
93. J. A. Pople and R. K. Nesbet, J. Chem. Phys. 22, 571 (1954). 10.1063/1.1740120
94. R. McWeeny and G. Diercksen, J. Chem. Phys. 49, 4852 (1968). 10.1063/1.1669970
95. C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988). 10.1103/PhysRevB.37.785
96. A. D. Becke, J. Chem. Phys. 96, 2155 (1992). 10.1063/1.462066
97. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 10.1103/PhysRevLett.77.3865
98. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78, 1396 (1997). 10.1103/PhysRevLett.78.1396
99. J. Geertsen, M. Rittby, and R. J. Bartlett, Chem. Phys. Lett. 164, 57 (1989). 10.1016/0009-2614(89)85202-9
100. D. C. Comeau and R. J. Bartlett, Chem. Phys. Lett. 207, 414 (1993). 10.1016/0009-2614(93)89023-B
101. M. J. Frisch, G. W. Trucks, H. B. Schlegel, Gaussian 09, Revision A.1, Gaussian, Inc., 2009.
102. O. Christiansen, H. Koch, and P. Jorgensen, Chem. Phys. Lett. 243, 409 (1995). 10.1016/0009-2614(95)00841-Q
103. CFour, Coupled-cluster techniques for computational chemistry, a quantum-chemical program package by J. F. Stanton, J. Gauss, M. E. Harding, P. G. Szalay with contributions from A. A. Auer, R. J. Bartlett, U. Benedikt, C. Berger, D. E. Bernholdt, Y. J. Bomble, L. Cheng, O. Christiansen, M. Heckert, O. Heun, C. Huber, T.-C. Jagau, D. Jonsson, J. Juselius, K. Klein, W. J. Lauderdale, D. A. Matthews, T. Metzroth, L. A. Muck, D. P. O'Neill, D. R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F. Schiffmann, W. Schwalbach, S. Stopkowicz, A. Tajti, J. Vazquez, F. Wang, and J. D. Watts; the integral packages: MOLECULE by J. Almlof and P. R. Taylor, PROPS by P. R. Taylor, ABACUS by T. Helgaker, H. J. Aa. Jensen, P. Jorgensen, and J. Olsen, and ECP routines by A. V. Mitin and C. van Wullen, see http://www.cfour.de.
104. K. Kowalski and P. Piecuch, J. Chem. Phys. 120, 1715 (2004). 10.1063/1.1632474
105. M. Valiev, E. Bylaska, N. Govind, K. Kowalski, T. Straatsma, H. Van Dam, D. Wang, J. Nieplocha, E. Apra, T. Windus, and W. de Jong, Comput. Phys. Commun. 181, 1477 (2010). 10.1016/j.cpc.2010.04.018
106. Thom H. Dunning, J. Chem. Phys. 90, 1007 (1989). 10.1063/1.456153
107. R. A. Kendall, Thom H. Dunning, and R. J. Harrison, J. Chem. Phys. 96, 6796 (1992). 10.1063/1.462569
108. D. E. Woon and Thom H. Dunning, J. Chem. Phys. 98, 1358 (1993). 10.1063/1.464303
109. K. A. Peterson, D. E. Woon, and Thom H. Dunning, J. Chem. Phys. 100, 7410 (1994). 10.1063/1.466884
110. A. Kramida and W. Martin, J. Phys. Chem. Ref. Data 26, 1185 (1997). 10.1063/1.555999
111. C. E. Moore, Atomic Energy Levels, NBS Circular 467 (National Bureau of Standards, U.S. Government Printing Office, Washington, D.C., 1949).
112. M. J. G. Peach, M. J. Williamson, and D. J. Tozer, J. Chem. Theory Comput. 7, 3578 (2011). 10.1021/ct200651r
113. K. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Vol. IV. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).
114. S. Bauer, G. Herzberg, and J. Johns, J. Mol. Spectrosc. 13, 256 (1964). 10.1016/0022-2852(64)90071-2
115. J. Johns, F. Grimm, and R. Porter, J. Mol. Spectrosc. 22, 435 (1967). 10.1016/0022-2852(67)90190-7
116. J. D. Watts and R. J. Bartlett, Chem. Phys. Lett. 233, 81 (1995). 10.1016/0009-2614(94)01434-W
117. L. A. Curtiss, K. Raghavachari, P. C. Redfern, and J. A. Pople, J. Chem. Phys. 112, 7374 (2000). 10.1063/1.481336
118. L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys. 123, 124107 (2005). 10.1063/1.2039080
119. K. B. Wiberg, C. M. Hadad, J. B. Foresman, and W. A. Chupka, J. Phys. Chem. 96, 10756 (1992). 10.1021/j100205a032
120. M. E. Casida, C. Jamorski, K. C. Casida, and D. R. Salahub, J. Chem. Phys. 108, 4439 (1998). 10.1063/1.475855
121. A. Dreuw, J. L. Weisman, and M. Head-Gordon, J. Chem. Phys. 119, 2943 (2003). 10.1063/1.1590951
122. Y. Zhao and D. G. Truhlar, Theor. Chem. Acc. 120, 215 (2008). 10.1007/s00214-007-0310-x
123. W. J. Hehre, R. Ditchfield, and J. A. Pople, J. Chem. Phys. 56, 2257 (1972). 10.1063/1.1677527
124. T. Clark, J. Chandrasekhar, G. W. Spitznagel, and P. V. R. Schleyer, J. Comput. Chem. 4, 294 (1983). 10.1002/jcc.540040303
125. A. J. Cohen, P. Mori-Sanchez, and W. Yang, Phys. Rev. B 77, 115123 (2008). 10.1103/PhysRevB.77.115123
126. R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994). 10.1103/PhysRevA.49.2421