Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities

Journal of Chemical Physics

Volumn 126, Issue 18, 2007, Pages

  Andrade, Xavier ^a,b   Botti, Silvana ^b,c   Marques, Miguel A L ^c,d   Rubio, Angel ^a  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b LABORATOIRE DES SOLIDES IRRADIÉS   (France)

^c UNIVERSITY OF COIMBRA   (Portugal)

^d European Theoretical Spectroscopy Facility ETSF   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY FUNCTIONAL THEORY; MOLECULAR DYNAMICS; PERTURBATION TECHNIQUES; POLARIZATION;

DYNAMIC POLARIZABILITY; STERNHEIMER EQUATION;

ELECTRONIC STATES;

EID: 34248348289     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2733666     Document Type: Article

References (75)

1. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, Cambridge, 1990).
2. N. Bloembergen, Nonlinear Optics (Benjamin, New York, 1965).
3. K. D. Bonin and V. V. Kresinq, Electric-Dipole Polarizabilities of Atoms, Molecules and Clusters (World Scientific, Singapore, 1997).
4. A. Dalgarno, in Perturbation Theory and Its Applications in Quantum Mechanics, edited by, C. H. Wilcox, (Wiley, New York, 1996), p. 162; P. W. Langhoff, S. T. Epstein, and M. Karplusaroni, Rev. Mod. Phys. 44, 602 (1972).
5. A. Dalgarno, in Perturbation Theory and Its Applications in Quantum Mechanics, edited by, C. H. Wilcox, (Wiley, New York, 1996), p. 162; P. W. Langhoff, S. T. Epstein, and M. Karplusaroni, Rev. Mod. Phys. 44, 602 (1972).
6. D. P. Shelton and J. E. Rice, Chem. Rev. (Washington, D.C.) 94, 3 (1994).
7. D. M. Bishop and P. Norman, in Handbook of Advanced Electric and Photonic Materials and Devices: Nonlinear Optical Materials, edited by, H. S. Nalwa, (Academic, San Diego, 2000), Vol. 9, Chap..
8. S. Baroni, S. de Gironcoli, A. D. Corso, and P. Gianozzi, Rev. Mod. Phys. 73, 515 (2001), and references therein.
9. C. Cardoso, F. Nogueira, and M. A. L. Marques (unpublished).
10. See, for example, J. E. Gready, G. B. Backsay, and N. S. Hush, Chem. Phys. 22, 141 (1977), this method is widely used in the chemistry and physics communities.
11. B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971).
12. A. Zangwill, J. Chem. Phys. 0021-9606 10.1063/1.444598 78, 5926 (1983); K. R. Subbaswamy and G. D. Mahan, J. Chem. Phys. 0021-9606 10.1063/1.450264 84, 3317 (1986); G. Senatore and K. R. Subbaswamy, Phys. Rev. A 34, 3619 (1986).
13. A. Zangwill, J. Chem. Phys. 0021-9606 10.1063/1.444598 78, 5926 (1983); K. R. Subbaswamy and G. D. Mahan, J. Chem. Phys. 0021-9606 10.1063/1.450264 84, 3317 (1986); G. Senatore and K. R. Subbaswamy, Phys. Rev. A 34, 3619 (1986).
14. A. Zangwill, J. Chem. Phys. 0021-9606 10.1063/1.444598 78, 5926 (1983); K. R. Subbaswamy and G. D. Mahan, J. Chem. Phys. 0021-9606 10.1063/1.450264 84, 3317 (1986); G. Senatore and K. R. Subbaswamy, Phys. Rev. A 34, 3619 (1986).
15. K. Yabana and G. F. Bertsch, Phys. Rev. B 54, 4484 (1996).
16. R. Sternheimer, Phys. Rev. 84, 244 (1951).
17. G. Senatore and K. R. Subbaswamy, Phys. Rev. A 35, 2440 (1987).
18. S. P. Karna and M. Dupuis, Chem. Phys. Lett. 171, 201 (1990).
19. S. J. A. van Gisbergen, J. G. Snijders, and E. J. Baerends, Phys. Rev. Lett. 78, 3097 (1997).
20. J.-I. Iwata, K. Yabana, and G. F. Bertsch, J. Chem. Phys. 115, 8773 (2001).
21. B. Walker, A. M. Saitta, R. Gebauer, and S. Baroni, Phys. Rev. Lett. 96, 113001 (2006).
22. P. Hohenberg and W. Kohn, Phys. Rev. 0096-8269 10.1103/PhysRev.136.B864 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
23. P. Hohenberg and W. Kohn, Phys. Rev. 0096-8269 10.1103/PhysRev.136.B864 136, B864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
24. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); Time-Dependent Density Functional Theory, edited by, M. A. L. Marques, C. A. Ullrich, F. Nogueira, A. Rubio, K. Burke, and, E. K. U. Gross, (Springer, Heidelberg, 2006).
25. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); Time-Dependent Density Functional Theory, edited by, M. A. L. Marques, C. A. Ullrich, F. Nogueira, A. Rubio, K. Burke, and, E. K. U. Gross, (Springer, Heidelberg, 2006).
26. A. D. Corso, F. Mauri, and A. Rubio, Phys. Rev. B 53, 15638 (1996).
27. X. Gonze, Phys. Rev. A 52, 1086 (1995).
28. A. Willetts, J. E. Rice, D. M. Burland, and D. P. Shelton, J. Chem. Phys. 97, 7590 (1992).
29. X. Gonze and J.-P. Vigneron, Phys. Rev. B 39, 13120 (1989).
30. M. A. L. Marques, A. Castro, G. F. Bertsch, and A. Rubio, Comput. Phys. Commun. 0010-4655 10.1016/S0010-4655(02)00686-0 151, 60 (2003); A. Castro, H. Appel, M. Oliveira, C. A. Rozzi, X. Andrade, F. Lorenzen, M. A. L. Marques, E. K. U. Gross, and A. Rubio, Phys. Status Solidi B 243, 2465 (2006).
31. M. A. L. Marques, A. Castro, G. F. Bertsch, and A. Rubio, Comput. Phys. Commun. 0010-4655 10.1016/S0010-4655(02)00686-0 151, 60 (2003); A. Castro, H. Appel, M. Oliveira, C. A. Rozzi, X. Andrade, F. Lorenzen, M. A. L. Marques, E. K. U. Gross, and A. Rubio, Phys. Status Solidi B 243, 2465 (2006).
32. G. E. Scuseria and V. N. Staroverov, in Theory and Applications of Computational Chemistry: The First Forty Years, edited by, C. E. Dykstra, G. Frenking, K. S. Kim, and, G. E. Scuseria, (Elsevier, Amsterdam, 2005), pp. 669-724.
33. S. van Gisbergen, P. Schipper, O. Gritsenko, E. Baerends, J. Snijders, B. Champagne, and B. Kirtman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.83. 694 83, 694 (1999); P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1385370 115, 1995 (2001); M. van Faassen, P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1529679 118, 1044 (2003); P. Mori-Sánchez, Q. Wu, and W. Yang, J. Chem. Phys. 0021-9606 10.1063/1.1630011 119, 11001 (2003); S. Kümmel, L. Kronik, and J. P. Perdew, Phys. Rev. Lett. 93, 213002 (2004).
34. S. van Gisbergen, P. Schipper, O. Gritsenko, E. Baerends, J. Snijders, B. Champagne, and B. Kirtman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.83. 694 83, 694 (1999); P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1385370 115, 1995 (2001); M. van Faassen, P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1529679 118, 1044 (2003); P. Mori-Sánchez, Q. Wu, and W. Yang, J. Chem. Phys. 0021-9606 10.1063/1.1630011 119, 11001 (2003); S. Kümmel, L. Kronik, and J. P. Perdew, Phys. Rev. Lett. 93, 213002 (2004).
35. S. van Gisbergen, P. Schipper, O. Gritsenko, E. Baerends, J. Snijders, B. Champagne, and B. Kirtman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.83. 694 83, 694 (1999); P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1385370 115, 1995 (2001); M. van Faassen, P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1529679 118, 1044 (2003); P. Mori-Sánchez, Q. Wu, and W. Yang, J. Chem. Phys. 0021-9606 10.1063/1.1630011 119, 11001 (2003); S. Kümmel, L. Kronik, and J. P. Perdew, Phys. Rev. Lett. 93, 213002 (2004).
36. S. van Gisbergen, P. Schipper, O. Gritsenko, E. Baerends, J. Snijders, B. Champagne, and B. Kirtman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.83. 694 83, 694 (1999); P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1385370 115, 1995 (2001); M. van Faassen, P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1529679 118, 1044 (2003); P. Mori-Sánchez, Q. Wu, and W. Yang, J. Chem. Phys. 0021-9606 10.1063/1.1630011 119, 11001 (2003); S. Kümmel, L. Kronik, and J. P. Perdew, Phys. Rev. Lett. 93, 213002 (2004).
37. S. van Gisbergen, P. Schipper, O. Gritsenko, E. Baerends, J. Snijders, B. Champagne, and B. Kirtman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.83. 694 83, 694 (1999); P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1385370 115, 1995 (2001); M. van Faassen, P. de Boeij, F. Kootstra, J. Berger, R. van Leeuwen, and J. Snijders, J. Chem. Phys. 0021-9606 10.1063/1.1529679 118, 1044 (2003); P. Mori-Sánchez, Q. Wu, and W. Yang, J. Chem. Phys. 0021-9606 10.1063/1.1630011 119, 11001 (2003); S. Kümmel, L. Kronik, and J. P. Perdew, Phys. Rev. Lett. 93, 213002 (2004).
38. M. Stener, P. Decleva, and A. Grling, J. Chem. Phys. 114, 7816 (2001).
39. M. E. Casida and D. R. Salahub, J. Chem. Phys. 0021-9606 10.1063/1.1319649 113, 8918 (2000); M. A. L. Marques, A. Castro, and A. Rubio, J. Chem. Phys. 0021-9606 10.1063/1.1385368 115, 3006 (2001); F. A. Bulat, A. Toro-Labb́, B. Champagne, B. Kirtman, and W. Yang, J. Chem. Phys. 123, 014319 (2005).
40. M. E. Casida and D. R. Salahub, J. Chem. Phys. 0021-9606 10.1063/1.1319649 113, 8918 (2000); M. A. L. Marques, A. Castro, and A. Rubio, J. Chem. Phys. 0021-9606 10.1063/1.1385368 115, 3006 (2001); F. A. Bulat, A. Toro-Labb́, B. Champagne, B. Kirtman, and W. Yang, J. Chem. Phys. 123, 014319 (2005).
41. M. E. Casida and D. R. Salahub, J. Chem. Phys. 0021-9606 10.1063/1.1319649 113, 8918 (2000); M. A. L. Marques, A. Castro, and A. Rubio, J. Chem. Phys. 0021-9606 10.1063/1.1385368 115, 3006 (2001); F. A. Bulat, A. Toro-Labb́, B. Champagne, B. Kirtman, and W. Yang, J. Chem. Phys. 123, 014319 (2005).
42. J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
43. A. Görling and M. Levy, Phys. Rev. A 50, 196 (1994).
44. J. B. Krieger, Y. Li, and G. J. Iafrate, Phys. Lett. A 146, 256 (1990).
45. Y. Saad, Iterative Method for Sparse Linear Systems (Pws, Boston, 1996).
46. Y. Saad, A. Stathopoulos, J. Chelikowsky, K. Wu, and S. Öǧüt, BIT 36, 563 (1996).
47. C. G. Broyden, Math. Comput. 0025-5718 10.2307/2003941 19, 577 (1965); D. D. Johnson, Phys. Rev. B 38, 12807 (1988).
48. C. G. Broyden, Math. Comput. 0025-5718 10.2307/2003941 19, 577 (1965); D. D. Johnson, Phys. Rev. B 38, 12807 (1988).
49. L. Genovese, T. Deutsch, A. Neelov, S. Goedecker, and G. Beylkin, J. Chem. Phys. 125, 074105 (2006), we use the free implementation of this solver provided by the authors.
50. S. Goedecker, Rev. Mod. Phys. 71, 1085 (1999).
51. H. J. Xiang, J. Yang, J. G. Hou, and Q. Zhu, Phys. Rev. Lett. 97, 266402 (2006).
52. W. Kohn, Phys. Rev. Lett. 76, 3168 (1996).
53. W. Yang, Phys. Rev. Lett. 66, 1438 (1991).
54. F. Bertinelli, P. Palmieri, A. Brillante, and C. Taliani, Chem. Phys. 25, 333 (1977).
55. P. Salek, T. Helgaker, O. Vahtras, H. Ågren, D. Jonsson, and J. Gauss, Mol. Phys. 103, 439 (2005).
56. S. P. Karna, P. N. Prasad, and M. Dupuis, J. Chem. Phys. 94, 1171 (1991).
57. G. Maroulis, J. Phys. Chem. 100, 13466 (1996).
58. J. S. Muenter, J. Mol. Spectrosc. 55, 490 (1975).
59. S. J. A. van Gisbergen, F. Kootstra, P. R. T. Schipper, O. V. Gritsenko, J. G. Snijders, and E. J. Baerends, Phys. Rev. A 57, 2556 (1998).
60. G. A. Parker and R. T. Pack, J. Chem. Phys. 64, 2010 (1976).
61. S. J. A. van Gisbergen, J. G. Snijders, and E. J. Baerends, J. Chem. Phys. 0021-9606 10.1063/1.477762 109, 10644 (1998); S. J. A. van Gisbergen, J. G. Snijders, and E. J. Baerends, J. Chem. Phys. 111, 6652 (E) (1999).
62. S. J. A. van Gisbergen, J. G. Snijders, and E. J. Baerends, J. Chem. Phys. 0021-9606 10.1063/1.477762 109, 10644 (1998); S. J. A. van Gisbergen, J. G. Snijders, and E. J. Baerends, J. Chem. Phys. 111, 6652 (E) (1999).
63. W. Chan, G. Cooper, and C. Brion, Chem. Phys. 170, 123 (1993).
64. E. S. Nielsen, P. Jørgensen, and J. Oddershede, J. Chem. Phys. 0021-9606 10.1063/1.440119 73, 6238 (1980); E. S. Nielsen, P. Jørgensen, and J. Oddershede, J. Chem. Phys. 75, 499 (E) (1981).
65. E. S. Nielsen, P. Jørgensen, and J. Oddershede, J. Chem. Phys. 0021-9606 10.1063/1.440119 73, 6238 (1980); E. S. Nielsen, P. Jørgensen, and J. Oddershede, J. Chem. Phys. 75, 499 (E) (1981).
66. A. Becke, Phys. Rev. A 38, 3098 (1988).
67. C. Lee, W. Yang, and R. Parr, Phys. Rev. B 0163-1829 10.1103/PhysRevB.37. 785 37, 785 (1988); B. Miehlich, A. Savin, H. Stoll, and H. Preuss, Chem. Phys. Lett. 157, 200 (1989).
68. C. Lee, W. Yang, and R. Parr, Phys. Rev. B 0163-1829 10.1103/PhysRevB.37. 785 37, 785 (1988); B. Miehlich, A. Savin, H. Stoll, and H. Preuss, Chem. Phys. Lett. 157, 200 (1989).
69. A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
70. H. Sekino and R. Bartlett, J. Chem. Phys. 98, 3022 (1993).
71. M. A. Spackman, J. Phys. Chem. 93, 7594 (1989).
72. J. F. Ward and C. K. Miller, Phys. Rev. A 19, 826 (1979).
73. P. Kaatz, E. A. Donley, and D. P. Shelton, J. Chem. Phys. 108, 849 (1998).
74. C. C. Teng and A. F. Garito, Phys. Rev. B 28, 6766 (1983).
75. P. Salek, O. Vahtras, T. Helgaker, and H. Ågren, J. Chem. Phys. 117, 9630 (2002).