First-order nonadiabatic coupling matrix elements between excited states: A Lagrangian formulation at the CIS, RPA, TD-HF, and TD-DFT levels

Journal of Chemical Physics

Volumn 141, Issue 1, 2014, Pages

  Li, Zhendong ^a   Liu, Wenjian ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; EQUATIONS OF MOTION; LAGRANGE MULTIPLIERS; QUANTUM CHEMISTRY;

CONFIGURATION INTERACTION SINGLES; ELECTRONIC PERTURBATIONS; ELECTRONICALLY EXCITED STATE; LAGRANGIAN FORMULATIONS; NONADIABATIC COUPLING MATRIX ELEMENTS; RANDOM PHASE APPROXIMATIONS; TIME DEPENDENT DENSITY FUNCTIONAL THEORY; TIME-DEPENDENT RESPONSE;

EXCITED STATES;

EID: 84903978155     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4885817     Document Type: Article

References (54)

1. J. C. Tully, J. Chem. Phys. 137, 22A301 (2012). 10.1063/1.4757762
2. D. J. Thouless, The Quantum Mechanics of Many Body Systems (Academic, New York, 1972).
3. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984). 10.1103/PhysRevLett.52.997
4. M. E. Casida, in Recent Advances in Density Functional Methods, edited by D. P. Chang (World Scientific, Singapore, 1995), Vol. 1.
5. B. H. Lengsfield III, P. Saxe, and D. R. Yarkony, J. Chem. Phys. 81, 4549 (1984). 10.1063/1.447428
6. P. Saxe, B. H. Lengsfield III, and D. R. Yarkony, Chem. Phys. Lett. 113, 159 (1985). 10.1016/0009-2614(85)80935-0
7. K. L. Bak, P. Jørgensen, H. J. A. Jensen, J. Olsen, and T. Helgaker, J. Chem. Phys. 97, 7573 (1992). 10.1063/1.463477
8. H. Lischka, M. Dallos, P. G. Szalay, D. R. Yarkony, and R. Shepard, J. Chem. Phys. 120, 7322 (2004). 10.1063/1.1668615
9. Y. G. Khait, D. Theis, and M. R. Hoffmann, Mol. Phys. 108, 2703 (2010). 10.1080/00268976.2010.521777
10. Y. G. Khait, D. Theis, and M. R. Hoffmann, Chem. Phys. 401, 88 (2012). 10.1016/j.chemphys.2011.09.014
11. O. Christiansen, J. Chem. Phys. 110, 711 (1999). 10.1063/1.478179
12. A. Tajti and P. G. Szalay, J. Chem. Phys. 131, 124104 (2009). 10.1063/1.3232011
13. V. Chernyak and S. Mukamel, J. Chem. Phys. 112, 3572 (2000). 10.1063/1.480511
14. R. Baer, Chem. Phys. Lett. 364, 75 (2002). 10.1016/S0009-2614(02)01214-9
15. C. Hu, H. Hirai, and O. Sugino, J. Chem. Phys. 127, 064103 (2007). 10.1063/1.2755665
16. C. Hu, H. Hirai, and O. Sugino, J. Chem. Phys. 128, 154111 (2008). 10.1063/1.2900647
17. C. Hu, O. Sugino, and Y. Tateyama, J. Chem. Phys. 131, 114101 (2009). 10.1063/1.3226344
18. C. Hu, O. Sugino, H. Hirai, and Y. Tateyama, Phys. Rev. A 82, 062508 (2010). 10.1103/PhysRevA.82.062508
19. E. Tapavicza, I. Tavernelli, and U. Röthlisberger, Phys. Rev. Lett. 98, 023001 (2007). 10.1103/PhysRevLett.98.023001
20. I. Tavernelli, E. Tapavicza, and U. Röthllisberger, J. Chem. Phys. 130, 124107 (2009). 10.1063/1.3097192
21. I. Tavernelli, B. F. E. Curchod, and U. Röthlisberger, J. Chem. Phys. 131, 196101 (2009). 10.1063/1.3265858
22. I. Tavernelli, B. F. E. Curchod, A. Laktionov, and U. Röthlisberger, J. Chem. Phys. 133, 194104 (2010). 10.1063/1.3503765
23. R. Send and F. Furche, J. Chem. Phys. 132, 044107 (2010). 10.1063/1.3292571
24. F. Cordova, L. J. Doriol, A. Ipatov, M. E. Casida, C. Filippi, and A. Vela, J. Chem. Phys. 127, 164111 (2007). 10.1063/1.2786997
25. E. Tapavicza, I. Tavernelli, U. Rothlisberger, C. Filippi, and M. E. Casida, J. Chem. Phys. 129, 124108 (2008). 10.1063/1.2978380
26. M. E. Casida, B. Natarajan, and T. Deutsch, Fundamentals of Time-Dependent Density-Functional Theory, Lecture Notes in Physics Vol. 837, edited by M. A. L. Marques, N. T. Maitra, F. M. S. Noguiera, E. K. U. Gross, and A. Rubio (Springer-Verlag, 2011), p. 279.
27. B. G. Levine, C. Ko, J. Quenneville, and T. J. Martínez, Mol. Phys. 104, 1039 (2006). 10.1080/00268970500417762
28. S. L. Li, A. V. Marenich, X. Xu, and D. G. Truhlar, J. Phys. Chem. Lett. 5, 322 (2014). 10.1021/jz402549p
29. NB: CIS, TD-HF, and TD-DFT can describe the full coninical intersection space between excited states.
30. 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
31. N. Minezawa and M. S. Gordon, J. Phys. Chem. A 113, 12749 (2009). 10.1021/jp908032x
32. S. Gozem, F. Melaccio, A. Valentini, M. Filatov, M. Huix-Rotllant, N. Ferré, L. M. Frutos, C. Angeli, A. I. Krylov, A. A. Granovsky, R. Lindh, and M. Olivucci, " Shape of multireference, equation-of-motion coupled-cluster, and density functional theory potential energy surfaces at a conical intersection," J. Chem. Theory Comput. (published online, 2014). 10.1021/ct500154k
33. Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013). 10.1063/1.4834875
34. D. J. Rowe, Rev. Mod. Phys. 40, 153 (1968). 10.1103/RevModPhys.40.153
35. E. Dalgaard, Phys. Rev. A 26, 42 (1982). 10.1103/PhysRevA.26.42
36. J. Olsen and P. Jorgensen, J. Chem. Phys. 82, 3235 (1985). 10.1063/1.448223
37. K. Sasagane, F. Aiga, and R. Itoh, J. Chem. Phys. 99, 3738 (1993). 10.1063/1.466123
38. S. Fatehi, E. Alguire, Y. Shao, and J. E. Subotnik, J. Chem. Phys. 135, 234105 (2011). 10.1063/1.3665031
39. T. Helgaker and P. Jørgensen, Theor. Chim. Acta 75, 111 (1989). 10.1007/BF00527713
40. F. Furche, J. Chem. Phys. 114, 5982 (2001). 10.1063/1.1353585
41. F. Furche and R. Ahlrichs, J. Chem. Phys. 117, 7433 (2002). 10.1063/1.1508368
42. N. T. Maitra, J. Chem. Phys. 125, 014110 (2006). 10.1063/1.2210471
43. S. Fatehi, E. Alguire, and J. E. Subotnik, J. Chem. Phys. 139, 124112 (2013). 10.1063/1.4820485
44. J. Gerratt and I. M. Mills, J. Chem. Phys. 49, 1719 (1968). 10.1063/1.1670299
45. J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley, Int. J. Quantum Chem., Symp. 16, 225 (1979).
46. A. Dalgarno and A. L. Stewart, Proc. Roy. Soc. (London) A247, 245 (1958). 10.1098/rspa.1958.0182
47. J. R. Munkres, Analysis on Manifolds (Addison-Wesley, Reading, MA, 1991).
48. P. W. Langhoff, S. T. Epstein, and M. Karplus, Rev. Mod. Phys. 44, 602 (1972). 10.1103/RevModPhys.44.602
49. P. Jørgensen and J. Simons, Second Quantization-Based Methods in Quantum Chemistry (Academic, New York, 1981).
50. Z. Li, B. Suo, and W. Liu, " First-order nondiabatic coupling matrix elements between excited states at the TD-DFT and pp-RPA levels: II. Pilot applications " (unpublished).
51. Z. Li and W. Liu, J. Chem. Phys. 133, 064106 (2010). 10.1063/1.3463799
52. Z. Li, W. Liu, Y. Zhang, and B. Suo, J. Chem. Phys. 134, 134101 (2011). 10.1063/1.3573374
53. Z. Li and W. Liu, J. Chem. Phys. 135, 194106 (2011). 10.1063/1.3660688
54. Z. Li, B. Suo, Y. Zhang, Y. Xiao, and W. Liu, Mol. Phys. 111, 3741 (2013). 10.1080/00268976.2013.785611