Propagators for the time-dependent Kohn-Sham equations

Journal of Chemical Physics

Volumn 121, Issue 8, 2004, Pages 3425-3433

  Castro, Alberto ^a,b   Marques, Miguel A L ^c   Rubio, Angel ^b,d  

^a UNIVERSITY OF VALLADOLID   (Spain)

^b DONOSTIA INTERNATIONAL PHYSICS CENTER DIPC   (Spain)

^c FREIE UNIVERSITÄT BERLIN   (Germany)

^d CENTRO MIXTO CSIC UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; ELECTROMAGNETIC FIELD EFFECTS; ELECTRON ENERGY LEVELS; FUNCTIONS; HAMILTONIANS; INTEGRAL EQUATIONS; MOLECULAR DYNAMICS; PHOTOEMISSION; POLYNOMIALS; PROBLEM SOLVING; TRANSPORT PROPERTIES;

KOHN-SHAM EQUATIONS; OPEN QUANTUM SYSTEMS; POLYNOMIAL EXPANSIONS; TIME-DEPENDENT DENSITY FUNCTIONAL THEORY (TDDFT);

QUANTUM THEORY;

EID: 4444265781     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1774980     Document Type: Article

References (46)

1. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); E. K. U. Gross, J. Dobson, and M. Petersilka, in Density Functional Theory II, Topics in Current Chemistry Vol. 18, edited by R. F. Nalewajski (Springer, Berlin, 1986), p. 81; R. van Leeuwen, Int. J. Mod. Phys. B 15, 1969 (2001); K. Burke, M. Petersilka, and E. K. U. Gross, in Recent Advances in Density Functional Methods, edited by P. Fantucci and A. Bencini (World Scientific, Singapore, 2002), p. 67.
2. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); E. K. U. Gross, J. Dobson, and M. Petersilka, in Density Functional Theory II, Topics in Current Chemistry Vol. 18, edited by R. F. Nalewajski (Springer, Berlin, 1986), p. 81; R. van Leeuwen, Int. J. Mod. Phys. B 15, 1969 (2001); K. Burke, M. Petersilka, and E. K. U. Gross, in Recent Advances in Density Functional Methods, edited by P. Fantucci and A. Bencini (World Scientific, Singapore, 2002), p. 67.
3. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); E. K. U. Gross, J. Dobson, and M. Petersilka, in Density Functional Theory II, Topics in Current Chemistry Vol. 18, edited by R. F. Nalewajski (Springer, Berlin, 1986), p. 81; R. van Leeuwen, Int. J. Mod. Phys. B 15, 1969 (2001); K. Burke, M. Petersilka, and E. K. U. Gross, in Recent Advances in Density Functional Methods, edited by P. Fantucci and A. Bencini (World Scientific, Singapore, 2002), p. 67.
4. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984); E. K. U. Gross, J. Dobson, and M. Petersilka, in Density Functional Theory II, Topics in Current Chemistry Vol. 18, edited by R. F. Nalewajski (Springer, Berlin, 1986), p. 81; R. van Leeuwen, Int. J. Mod. Phys. B 15, 1969 (2001); K. Burke, M. Petersilka, and E. K. U. Gross, in Recent Advances in Density Functional Methods, edited by P. Fantucci and A. Bencini (World Scientific, Singapore, 2002), p. 67.
5. A. Castro, M. A. L. Marques, J. A. Alonso, and A. Rubio, J. Comp. Theor. Nanoscience (in press); M. A. L. Marques and E. K. U. Gross, Annu. Rev. Phys. Chem. 55, 427 (2004).
6. A. Castro, M. A. L. Marques, J. A. Alonso, and A. Rubio, J. Comp. Theor. Nanoscience (in press); M. A. L. Marques and E. K. U. Gross, Annu. Rev. Phys. Chem. 55, 427 (2004).
7. Fetter and Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).
8. R. Kosloff, J. Phys. Chem. 92, 2087 (1988).
9. C. Lubich, in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, edited by J. Grotendorst, D. Marx, and A. Muramatsu (John von Neumann Institute for Computing, Jülich, 2002), Vol. 10, p. 459.
10. M. Hochbruck, C. Lubich, and H. Selhofer, SIAM J. Sci. Comput. (USA) 19, 1552 (1998).
11. M. Hochbruck and C. Lubich, BIT 39, 620 (1999).
12. T. N. Truong, J. J. Tanner, P. Bala, and J. A. McCammon, J. Chem. Phys. 96, 2077 (1992).
13. O. Sugino and Y. Miyamoto, Phys. Rev. B 59, 2579 (1999); 66, 8990(E) (2002).
14. O. Sugino and Y. Miyamoto, Phys. Rev. B 59, 2579 (1999); 66, 8990(E) (2002).
15. R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).
16. M. R. Tuckerman and M. Parrinello, J. Chem. Phys. 101, 1302 (1994); 101, 1316 (1994).
17. M. R. Tuckerman and M. Parrinello, J. Chem. Phys. 101, 1302 (1994); 101, 1316 (1994).
18. The octopus project is aimed at describing the electron-ion dynamics in finite and extended systems under the influence of time-dependent electromagnetic fields. The program can be freely downloaded from http://www.tddft.org/programs/octopus. For details see M. A. L. Marques, A. Castro, G. F. Bertsch and A. Rubio, Comput. Phys. Commun. 151, 60 (2003).
19. T. L. Beck, Rev. Mod. Phys. 72, 1041 (2000), and references therein.
20. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002).
21. C. Moler and C. van Loan, SIAM Rev. 45, 3 (2003).
22. J. Giansiracusa (private communication).
23. K. Yabana and G. F. Bertsch, Phys. Rev. B 54, 4484 (1996).
24. H. Tal-Ezer and R. Kosloff, J. Chem. Phys. 81, 3967 (1984).
25. C. W. Clenshaw, MTAC 9, 118 (1955).
26. R. Baer and R. Gould, J. Chem. Phys. 114, 3385 (2001).
27. R. Chen and H. Guo, Comput. Phys. Commun. 119, 19 (1999).
28. Y. Saad, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 209 (1992).
29. T. J. Park and J. C. Light, J. Chem. Phys. 85, 5870 (1986).
30. M. Hochbruck and C. Lubich, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 34, 1911 (1997).
31. M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 47, 412 (1982).
32. M. D. Feit and J. A. Fleck, J. Chem. Phys. 78, 301 (1982).
33. M. Suzuki, J. Phys. Soc. Jpn. 61, L3015 (1993).
34. M. Suzuki and T. Yamauchi, J. Math. Phys. 34, 4892 (1992).
35. T. Y. Mikhailova and V. I. Pupyshev, Phys. Lett. A 257, 1 (1999); A. D. Bandrauk and H. Shen, J. Chem. Phys. 99, 1185 (1993).
36. T. Y. Mikhailova and V. I. Pupyshev, Phys. Lett. A 257, 1 (1999); A. D. Bandrauk and H. Shen, J. Chem. Phys. 99, 1185 (1993).
37. N. Watanabe and M. Tsukada, Phys. Rev. E 65, 036705 (2002).
38. W. Magnus, Pure Appl. Math. 7, 649 (1954).
39. S. Klarsfeld and J. A. Oteo, Phys. Rev. A 39, 3270 (1989).
40. S. Blanes, F. Casas, and J. Ros, BIT 40, 434 (2000).
41. M. Hochbruck and C. Lubich, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 41, 945 (2003).
42. K. F. Milfeld and R. E. Wyatt, Phys. Rev. A 27, 72 (1983).
43. M. Nooijen, Phys. Rev. Lett. 84, 2108 (2000); H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000); T. van Voorhis and M. Head-Gordon, ibid. 115, 5033 (2001); P. Piecuch, K. Kowalski, P. D. Fang, and K. Jedziniak, Phys. Rev. Lett. 90, 113001 (2003).
44. M. Nooijen, Phys. Rev. Lett. 84, 2108 (2000); H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000); T. van Voorhis and M. Head-Gordon, ibid. 115, 5033 (2001); P. Piecuch, K. Kowalski, P. D. Fang, and K. Jedziniak, Phys. Rev. Lett. 90, 113001 (2003).
45. M. Nooijen, Phys. Rev. Lett. 84, 2108 (2000); H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000); T. van Voorhis and M. Head-Gordon, ibid. 115, 5033 (2001); P. Piecuch, K. Kowalski, P. D. Fang, and K. Jedziniak, Phys. Rev. Lett. 90, 113001 (2003).
46. M. Nooijen, Phys. Rev. Lett. 84, 2108 (2000); H. Nakatsuji, J. Chem. Phys. 113, 2949 (2000); T. van Voorhis and M. Head-Gordon, ibid. 115, 5033 (2001); P. Piecuch, K. Kowalski, P. D. Fang, and K. Jedziniak, Phys. Rev. Lett. 90, 113001 (2003).