Self-interaction correction in a real-time Kohn-Sham scheme: Access to difficult excitations in time-dependent density functional theory

Journal of Chemical Physics

Volumn 137, Issue 6, 2012, Pages

  Hofmann, D ^a   Kummel S ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EXCHANGE-CORRELATION POTENTIAL; HYDROGEN-TERMINATED SILICON; KOHN-SHAM POTENTIAL; KOHN-SHAM SCHEME; MOLECULAR CHAINS; OPTIMIZED EFFECTIVE POTENTIAL; REAL-SPACE; SELF-INTERACTION CORRECTIONS; TEST SYSTEMS; TIME DEPENDENT DENSITY FUNCTIONAL THEORY; TIME EVOLUTIONS; TIME-DEPENDENT; TRANSITION DENSITY;

CHARGE TRANSFER; HYDROGEN;

DENSITY FUNCTIONAL THEORY;

EID: 84865177389     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4742763     Document Type: Article

References (127)

1. J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). 10.1103/PhysRevB.23.5048
2. Y. Zhang and W. Yang, J. Chem. Phys. 109, 2604 (1998). 10.1063/1.476859 (Pubitemid 128678150)
3. S. J. A. van Gisbergen, P. R. T. Schipper, O. V. Gritsenko, E. J. Baerends, J. G. Snijders, B. Champagne, and B. Kirtman, Phys. Rev. Lett. 83, 694 (1999). 10.1103/PhysRevLett.83.694
4. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). 10.1103/RevModPhys.74.601
5. S. Öüt, J. R. Chelikowsky, and S. G. Louie, Phys. Rev. Lett. 79, 1770 (1997). 10.1103/PhysRevLett.79.1770
6. M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 80, 3320 (1998). 10.1103/PhysRevLett.80.3320
7. M. Rohlfing and S. G. Louie, Phys. Rev. B 62, 4927 (2000). 10.1103/PhysRevB.62.4927
8. I. Vasiliev, S. Öüt, and J. R. Chelikowsky, Phys. Rev. B 65, 115416 (2002). 10.1103/PhysRevB.65.115416
9. M. L. Tiago and J. R. Chelikowsky, Phys. Rev. B 73, 205334 (2006). 10.1103/PhysRevB.73.205334 (Pubitemid 43752535)
10. M. A. L. Marques, A. Castro, and A. Rubio, J. Chem. Phys. 115, 3006 (2001). 10.1063/1.1385368 (Pubitemid 32796741)
11. C. Toher, A. Filippetti, S. Sanvito, and K. Burke, Phys. Rev. Lett. 95, 146402 (2005). 10.1103/PhysRevLett.95.146402 (Pubitemid 41777596)
12. A. Dreuw, J. Weisman, and M. Head-Gordon, J. Chem. Phys. 119, 2943 (2003). 10.1063/1.1590951
13. D. J. Tozer, J. Chem. Phys. 119, 12697 (2003). 10.1063/1.1633756
14. S. Kümmel, L. Kronik, and J. P. Perdew, Phys. Rev. Lett. 93, 213002 (2004). 10.1103/PhysRevLett.93.213002 (Pubitemid 40011377)
15. T. Yanai, D. P. Tew, and N. C. Handy, Chem. Phys. Lett. 393, 51 (2004). 10.1016/j.cplett.2004.06.011
16. J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008). 10.1063/1.2834918 (Pubitemid 351328681)
17. E. Livshits and R. Baer, Phys. Chem. Chem. Phys. 9, 2932 (2007). 10.1039/b617919c
18. T. Stein, L. Kronik, and R. Baer, J. Am. Chem. Soc. 131, 2818 (2009). 10.1021/ja8087482
19. A. Karolewski, T. Stein, R. Baer, and S. Kümmel, J. Chem. Phys. 134, 151101 (2011). 10.1063/1.3581788
20. T. Körzdörfer, J. S. Sears, C. Sutton, and J.-L. Brédas, J. Chem. Phys. 135, 204107 (2011). 10.1063/1.3663856
21. A. Karolewski, L. Kronik, and S. Kümmel, A perspective on tuned range-separated hybrid functionals. (unpublished).
22. C. D. Pemmaraju, S. Sanvito, and K. Burke, Phys. Rev. B 77, 121204(R) (2008). 10.1103/PhysRevB.77.121204
23. A. Ruzsinszky, J. P. Perdew, G. I. Csonka, G. E. Scuseria, and O. A. Vydrov, Phys. Rev. A 77, 060502(R) (2008). 10.1103/PhysRevA.77.060502
24. T. Körzdörfer, M. Mundt, and S. Kümmel, Phys. Rev. Lett. 100, 133004 (2008). 10.1103/PhysRevLett.100.133004 (Pubitemid 351490849)
25. T. Grabo, T. Kreibich, and E. K. U Gross, in Strong Coulomb Correlation in Electronic Structure: Beyond the Local Density Approximation, edited by, V. Anisimov, (Gordon and Breach, Tokyo, 2000).
26. J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Phys. Rev. Lett. 49, 1691 (1982). 10.1103/PhysRevLett.49.1691
27. J. P. Perdew, Adv. Quantum Chem. 21, 113 (1990). 10.1016/S0065-3276(08) 60594-8
28. T. Körzdörfer and S. Kümmel, in Theoretical and Computational Developments in Modern Density Functional Theory, edited by, A. K. Roy, (Nova Science, New York, 2012).
29. N. T. Maitra, K. Burke, and C. Woodward, Phys. Rev. Lett. 89, 023002 (2002). 10.1103/PhysRevLett.89.023002
30. E. K. U. Gross, J. F. Dobson, and M. Petersilka, in Density Functional Theory, edited by, R. F. Nalewajski, Topics in Current Chemistry Vol. 181 (Springer, Berlin, 1996), p. 81.
31. S. Kümmel, in Fundamentals of Time-Dependent Density Functional Theory, edited by, M. A. L. Marques, N. T. Maitra, F. M. S. Nogueria, E. K. U. Gross, and, A. Rubio, (Springer-Verlag, Berlin, 2012), Chap., pp. 125-138.
32. N. T. Maitra and D. G. Tempel, J. Chem. Phys. 125, 184111 (2006). 10.1063/1.2387951 (Pubitemid 44749467)
33. N. T. Maitra, J. Chem. Phys. 122, 234104 (2005). 10.1063/1.1924599 (Pubitemid 41100392)
34. M. Hellgren and E. K. U. Gross, Phys. Rev. A 85, 022514 (2011). 10.1103/PhysRevA.85.022514
35. T. Körzdörfer, S. Kümmel, and M. Mundt, J. Chem. Phys. 129, 014110 (2008). 10.1063/1.2944272
36. M. R. Pederson, R. A. Heaton, and C. C. Lin, J. Chem. Phys. 80, 1972 (1984). 10.1063/1.446959
37. M. R. Pederson, R. A. Heaton, and C. C. Lin, J. Chem. Phys. 82, 2688 (1985). 10.1063/1.448266
38. M. R. Pederson and C. C. Lin, J. Chem. Phys. 88, 1807 (1988). 10.1063/1.454104
39. J. Garza, J. A. Nichols, and D. A. Dixon, J. Chem. Phys. 112, 7880 (2000). 10.1063/1.481421
40. S. Patchkovskii, J. Autschbach, and T. Zieger, J. Chem. Phys. 115, 26 (2001). 10.1063/1.1370527 (Pubitemid 32639793)
41. J. Messud, P. M. Dinh, P.-G. Reinhard, and E. Suraud, Phys. Rev. Lett. 101, 096404 (2008). 10.1103/PhysRevLett.101.096404
42. J. Messud, P. M. Dinh, P.-G. Reinhard, and E. Suraud, Ann. Phys. 324, 955 (2009). 10.1016/j.aop.2008.12.001
43. S. Kümmel and J. P. Perdew, Mol. Phys. 101, 1363 (2003). 10.1080/0026897031000094506
44. M. Dauth, T. Körzdörfer, S. Kümmel, J. Ziroff, M. Wiessner, A. Schöll, F. Reinert, M. Arita, and K. Shimada, Phys. Rev. Lett. 107, 193002 (2011). 10.1103/PhysRevLett.107.193002
45. S. Klüpfel, P. Klüpfel, and H. Jónsson, Phys. Rev. A 84, 050501(R) (2011). 10.1103/PhysRevA.84.050501
46. D. Hofmann, S. Klüpfel, P. Klüpfel, and S. Kümmel, Phys. Rev. A 85, 062514 (2012). 10.1103/PhysRevA.85.062514
47. O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976). 10.1103/PhysRevB.13.4274
48. O. A. Vydrov, G. E. Scuseria, J. P. Perdew, A. Ruzsinszky, and G. I. Csonka, J. Chem. Phys. 124, 094108 (2006). 10.1063/1.2176608 (Pubitemid 43346523)
49. J. F. Janak, Phys. Rev. B 18, 7165 (1978). 10.1103/PhysRevB.18.7165
50. D. P. Chong, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 116, 1760 (2002). 10.1063/1.1430255 (Pubitemid 34159892)
51. S. Kümmel and L. Kronik, Rev. Mod. Phys. 80, 3 (2008). 10.1103/RevModPhys.80.3
52. C. A. Ullrich, U. J. Grossmann, and E. K. U. Gross, Phys. Rev. Lett. 74, 872 (1995). 10.1103/PhysRevLett.74.872
53. M. Mundt and S. Kümmel, Phys. Rev. A 74, 022511 (2006). 10.1103/PhysRevA.74.022511 (Pubitemid 44277916)
54. H. O. Wijewardane and C. A. Ullrich, Phys. Rev. Lett. 100, 056404 (2008). 10.1103/PhysRevLett.100.056404 (Pubitemid 351230682)
55. S. Kümmel and J. P. Perdew, Phys. Rev. B 68, 035103 (2003). 10.1103/PhysRevB.68.035103
56. J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Rev. A 46, 5453 (1992). 10.1103/PhysRevA.46.5453
57. M. Mundt, S. Kümmel, R. van Leeuwen, and P.-G. Reinhard, Phys. Rev. A 75, 050501(R) (2007). 10.1103/PhysRevA.75.050501 (Pubitemid 47014646)
58. X.-M. Tong and S.-I. Chu, Phys. Rev. A 57, 452 (1998). 10.1103/PhysRevA.57.452
59. X.-M. Tong and S.-I. Chu, Int. J. Quantum Chem. 69, 293 (1998). 10.1002/(SICI)1097-461X(1998)69:3293::AID-QUA8>3.0.CO;2-Q
60. J. Messud, P. M. Dinh, P.-G. Reinhard, and E. Suraud, Phys. Rev. A 80, 044503 (2009). 10.1103/PhysRevA.80.044503
61. P. M. Dinh, J. Messud, P.-G. Reinhard, and E. Suraud, J. Phys.: Conf. Ser. 248, 012024 (2010). 10.1088/1742-6596/248/1/012024
62. J. Messud, P. M. Dinh, P.-G. Reinhard, and E. Suraud, Ann. Phys. 523, 270 (2011). 10.1002/andp.201100002
63. T. Körzdörfer, S. Kümmel, N. Marom, and L. Kronik, Phys. Rev. B 79, 201205(R) (2009). 10.1103/PhysRevB.79.201205
64. C. A. Ullrich, P.-G. Reinhard, and E. Suraud, J. Phys. B 31, 1871 (1998). 10.1088/0953-4075/31/9/006
65. S.-I. Chu, J. Chem. Phys. 123, 062207 (2005). 10.1063/1.1904587 (Pubitemid 41231965)
66. S. I. Chu and D. A. Telnov, Intense Ultrashort Laser Fields in Computational Studies of New Materials II: From Ultrafast Processes and Nanostructures to Optoelectronics, Energy Storage and Nanomedicine, edited by, T. F. George, D. Jelski, R. R. Letfullin, and, G. Zhang, (World Scientific, 2011), pp. 75-101.
67. J. C. Slater, Phys. Rev. 81, 385 (1951). 10.1103/PhysRev.81.385
68. C. A. Ullrich, P.-G. Reinhard, and E. Suraud, Phys. Rev. A 62, 053202 (2000). 10.1103/PhysRevA.62.053202 (Pubitemid 32023329)
69. D. Hofmann, T. Körzdörfer, and S. Kümmel, Phys. Rev. Lett. 108, 146401 (2012). 10.1103/PhysRevLett.108.146401
70. C.-H. Park, A. Ferretti, I. Dabo, N. Poilvert, and N. Marzari, e-print arXiv:1108.5726v1.
71. S. F. Boys, Rev. Mod. Phys. 32, 296 (1960). 10.1103/RevModPhys.32.296
72. J. M. Foster and S. F. Boys, Rev. Mod. Phys. 32, 300 (1960). 10.1103/RevModPhys.32.300
73. J. Pipek and P. G. Mezey, J. Chem. Phys. 90, 4916 (1989). 10.1063/1.456588
74. K. Yabana and G. F. Bertsch, Phys. Rev. B 54, 4484 (1996). 10.1103/PhysRevB.54.4484
75. K. Yabana and G. F. Bertsch, Int. J. Quantum Chem. 75, 55 (1999). 10.1002/(SICI)1097-461X(1999)75:155::AID-QUA6>3.0.CO;2-K
76. M. Mundt and S. Kümmel, Phys. Rev. B 76, 035413 (2007). 10.1103/PhysRevB.76.035413
77. M. Mundt, J. Theor. Comput. Chem. 8, 561 (2009). 10.1142/ S0219633609004915
78. L. Kronik, A. Makmal, M. L. Tiago, M. M. G. Alemany, M. Jain, X. Huang, Y. Saad, and J. R. Chelikowsky, Phys. Status Solidi B 243, 1063 (2006). 10.1002/pssb.200541463 (Pubitemid 43633041)
79. A. Castro, M. A. L. Marques, and A. Rubio, J. Chem. Phys. 121, 3425 (2004). 10.1063/1.1774980
80. E. S. Fois, J. I. Penman, and P. A. Madden, J. Chem. Phys. 98, 6352 (1993). 10.1063/1.464828
81. T. Abrudan, J. Eriksson, and V. Koivunen, Signal Process. 89, 1704 (2009). 10.1016/j.sigpro.2009.03.015
82. M. E. Casida, Recent Advances in Density Functional Methods, Part I, edited by, D. P Chong, (Word Scientific, Singapore, 1995), Vol. 1, Chap., pp. 155-192.
83. S. Kümmel, K. Andrae, and P.-G. Reinhard, Appl. Phys. B 73, 293 (2001). 10.1007/s003400100679 (Pubitemid 33091171)
84. R. A. Broglia, G. Colò, G. Onida, and H. E. Roman, Solid State Physics of Finite Systems (Springer, Berlin, 2004), pp. 68-70.
85. M. Thiele and S. Kümmel, Phys. Chem. Chem. Phys. 11, 4631 (2009). 10.1039/b902567g
86. C. B. Bulliard, M. Allen, G. Wirtz, E. Haselbach, K. A. Zachariasse, N. Detzer, and S. Grimme, J. Phys. Chem. A 103, 7766 (1999). 10.1021/jp990922s
87. C. Jamorski, J. B. Foresman, C. Thilgen, and H.-P. Lüthi, J. Chem. Phys. 116, 8761 (2002). 10.1063/1.1465404 (Pubitemid 34631423)
88. M. J. G. Peach, P. Benfield, T. Helgaker, and D. J. Tozer, J. Chem. Phys. 128, 044118 (2008). 10.1063/1.2831900 (Pubitemid 351200451)
89. 12, 0.5 bohr for the hydrogenated silicon clusters, and 0.7 bohr for the Na clusters.
90. N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 (1991). 10.1103/PhysRevB.43.1993
91. c(C)=1.60 bohrs.
92. B. Champagne, D. H. Mosley, M. Vrako, and J.-M. André, Phys. Rev. A 52, 178 (1995). 10.1103/PhysRevA.52.178
93. P. Mori-Sánchez, Q. Wu, and W. Yang, J. Chem. Phys. 119, 11001 (2003). 10.1063/1.1630011
94. S. Kümmel and L. Kronik, Comput. Mater. Sci. 35, 321 (2006). 10.1016/j.commatsci.2004.09.057 (Pubitemid 41737491)
95. R. Armiento, S. Kümmel, and T. Körzdörfer, Phys. Rev. B 77, 165106 (2008). 10.1103/PhysRevB.77.165106
96. B. Champagne and B. Kirtman, Int. J. Quantum Chem. 109, 3103 (2009). 10.1002/qua.22177
97. O. V. Gritsenko, S. J. A. van Gisbergen, P. R. T. Schipper, and E. J. Baerends, Phys. Rev. A 62, 012507 (2000). 10.1103/PhysRevA.62.012507
98. O. Christiansen, H. Koch, and P. Jorgensen, Chem. Phys. Lett. 243, 409 (1995). 10.1016/0009-2614(95)00841-Q
99. D. Varsano, A. Marini, and A. Rubio, Phys. Rev. Lett. 101, 133002 (2008). 10.1103/PhysRevLett.101.133002
100. TURBOMOLE V6.0 2009, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989-2007, TURBOMOLE GmbH, 2007, see http://www.turbomole.com.
101. Ch. Haettig and F. Weigend, J. Chem. Phys. 113, 5154 (2000). 10.1063/1.1290013
102. F. Weigend, F. Furche, and R. Ahlrichs, J. Chem. Phys. 119, 12753 (2003). 10.1063/1.1627293
103. M. Schreiber, M. R. Silva-Junior, S. P. A. Sauer, and W. Thiel, J. Chem. Phys. 128, 134110 (2008). 10.1063/1.2889385 (Pubitemid 351506424)
104. M. van Faassen, P. L. de Boeij, R. van Leeuwen, J. A. Berger, and J. G. Snijders, Phys. Rev. Lett. 88, 186401 (2002). 10.1103/PhysRevLett.88.186401
105. D. Rocca, D. Lu, and G. Galli, J. Chem. Phys. 133, 164109 (2010). 10.1063/1.3494540
106. U. Itoh, Y. Toyoshima, and H. Onuki, J. Chem. Phys. 85, 4867 (1986). 10.1063/1.451721
107. D. R. J. Boyd, J. Chem. Phys. 23, 922 (1955). 10.1063/1.1742148
108. G. W. Bethke and M. K. Wilson, J. Chem. Phys. 26, 1107 (1957). 10.1063/1.1743480
109. H. Shirakawa, E. J. Louis, A. G. MacDiarmid, C. K. Chiang, and A. J. Heeger, J. Chem. Soc., Chem. Commun. 1977, 578. 10.1039/c39770000578
110. C. K. Chiang, C. R. Fincher, Y. W. Park, A. J. Heeger, H. Shirakawa, E. J. Louis, S. C. Gau, and A. G. MacDiarmid, Phys. Rev. Lett. 39, 1098 (1977). 10.1103/PhysRevLett.39.1098
111. B. Champagne, E. A. Perpète, S. J. A. van Gisbergen, E. J. Baerends, J. G. Snijders, C. Soubra-Ghaoui, K. A. Robins, and B. Kirtman, J. Chem. Phys. 109, 10489 (1998). 10.1063/1.477731 (Pubitemid 128678486)
112. M. J. G. Peach, E. I. Tellgren, P. Saek, T. Helgaker, and D. J. Tozer, J. Phys. Chem. 111, 11930 (2007). 10.1021/jp0754839 (Pubitemid 350247214)
113. A. Karolewski, R. Armiento, and S. Kümmel, J. Chem. Theory Comput. 5, 712 (2009). 10.1021/ct8005198
114. 12 at 3.98 eV.
115. W. C. Price and A. D. Walsh, Proc. R. Soc. A 174, 220 (1940). 10.1098/rspa.1940.0016
116. R. M. Gavin Jr., S. Risemberg, and S. A. Rice, J. Chem. Phys. 58, 3160 (1973); 10.1063/1.1679637
117. W. C. Price and A. D. Walsh, Proc. R. Soc. A 185, 182 (1946). 10.1098/rspa.1946.0012
118. K. L. DAmico, C. Manos, and R. L. Christensen, J. Am. Chem. Soc. 102, 1777 (1980). 10.1021/ja00526a003
119. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 10.1103/PhysRevLett.77.3865
120. L. Serrano-Andrés and M. P. Fülscher, J. Am. Chem. Soc. 120, 10912 (1998). 10.1021/ja981148+ (Pubitemid 28507437)
121. D. J. Tozer, R. D. Amos, N. C. Handy, B. O. Roos, and L. Serrano-Andrés, Mol. Phys. 97, 859 (1999). 10.1080/00268979909482888
122. We optimized the geometry with the TURBOMOLE (Ref.) program package using the B3LYP and Fully Optimized Contracted Gaussian Basis Sets of Triple Zeta Valance Quality (def2-TZVP).
123. As an aside we note that the dipeptide provides more examples of the serious failures of TD LDA as there is another CT excitation which TD LDA seriously underestimates. However, in contrast to the TD LDA excitation at 5.15 eV the latter carries practically no oscillator strength and is therefore less interesting and less suited for RT investigation.
124. A. Schäfer, C. Huber, and R. Ahlrichs, J. Chem. Phys. 100, 5829 (1994). 10.1063/1.467146
125. D. A. Telnov, J. T. Heslar, and S. Chu, Chem. Phys. 391, 88 (2011). 10.1016/j.chemphys.2011.03.023
126. D. A. Telnov and S. Chu, Phys. Rev. A 80, 043412 (2009). 10.1103/PhysRevA.80.043412
127. X. Andrade, J. N. Sanders, and A. Aspuru-Guzik, e-print arXiv:1205.6485v1.