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1. M. E. Casida, in Recent Advances in Density Functional Methods, Part I, edited by D. P. Chong (World Scientific, Singapore, 1995);
1.M. E. Casida, in Recent Developments and Applications in Density Functional Theory, edited by J. M. Seminario (Elsevier, Amsterdam, 1996).
2. M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996).
3. S. J. A. van Gisbergen, J. G. Snijders, and E. J. Baerends, Comput. Phys. Commun. 118, 119 (1999).
4. N. T. Maitra, K. Burke, H. Appel, E. K. U. Gross, and R. van Leeuwen, in Reviews in Modern Quantum Chemistry: A Celebration of the Contributions of R. G. Parr, edited by K. D. Sen (World Scientific, Singapore, 2001).
5. S. Hirata and M. Head-Gordon, Chem. Phys. Lett. 314, 291 (1999).
6. M. A. L. Marques and E. K. U. Gross, Annu. Rev. Phys. Chem. 55, 427 (2004).
7. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).
8. J. B. Foresman, M. Head-Gordon, J. A. Pople, and M. J. Frisch, J. Phys. Chem. 96, 135 (1992).
9. J. Oddershede, Adv. Chem. Phys. 69, 201 (1987).
10. F. Furche and R. Ahlrichs, J. Chem. Phys. 117, 7433 (2002);
10.F. Furche and R. Ahlrichs, J. Chem. Phys. 121, 12772E (2004).
11. D. Maurice and M. Head-Gordon, Mol. Phys. 96, 1533 (1999).
12. J. F. Stanton, J. Chem. Phys. 99, 8840 (1993).
13. J. F. Stanton and J. Gauss, J. Chem. Phys. 103, 8931 (1995).
14. Y. Osamura, Theor. Chim. Acta 76, 113 (1989).
15. G. Scalmani, M. J. Frisch, B. Mennucci, J. Tomasi, R. Cammi, and V. Barone, J. Chem. Phys. 124, 094107 (2006).
16. F. Liu, Z. Gan, Y. Shao, C.-P. Hsu, A. Dreuw, M. Head-Gordon, B. T. Miller, B. R. Brooks, J.-G. Yu, T. R. Furlani, and J. Kong, Mol. Phys. 108, 2791 (2010).
17. C. V. Caillie and R. D. Amos, Chem. Phys. Lett. 308, 249 (1999);
17.C. V. Caillie and R. D. Amos, Chem. Phys. Lett. 317, 159 (2000).
18. J. Gerratt and I. M. Mills, J. Chem. Phys. 49, 1749 (1968).
19. N. C. Handy and H. F. Schaefer III, J. Chem. Phys. 81, 5031 (1984).
20. M. Chiba, T. Tsuneda, and K. Hirao, J. Chem. Phys. 124, 144106 (2006).
21. R. Cammi, B. Mennucci, and J. Tomasi, J. Phys. Chem. A 104, 5631 (2000).
22. J. Liu and W. Z. Liang, J. Chem. Phys. 134, 044114 (2011).
23. J. A. Pople , R. Krishnan , H. B. Schlegel, and J. S. Binkley, Int. J. Quantum Chem. Symp. 13, 255 (1979).
24. N. C. Handy, R. D. Amos, J. F. Gaw, J. E. Rice, and E. D. Simandiras, Chem. Phys. Lett. 120, 151 (1985).
25. D. J. Fox, Y. Osamura, M. R. Hoffmann, J. F. Gaw, G. Fitzgerald, Y. Yamaguchi, and H. F. Schaefer, Chem. Phys. Lett. 102, 17 (1983).
26. H. Koch, H. J. A. Jensen, P. Jørgensen, T. Helgaker, G. E. Scuseria, and H. F. Schaefer, J. Chem. Phys. 92, 4924 (1990).
27. J. Gauss, J. F. Stanton, and R. J. Bartlett, J. Chem. Phys. 97, 7825 (1992).
28. M. Kállay and J. Gauss, J. Chem. Phys. 120, 6841 (2004).
29. W. Z. Liang, Y. Zhao, and M. Head-Gordon, J. Chem. Phys. 123, 194106 (2005).
30. Y. Yamaguchi, O. Osamura, J. D. Goddard, and H. F. Schaefer III, A New Dimension to Quantum Mechanics: Analytical Derivative Methods in Ab Initio Molecular Electronic Structure Theory (Oxford University Press, Oxford, 1994).
31. A. D. Becke, J. Chem. Phys. 98, 5648 (1993).
32. A. D. Becke, J. Chem. Phys. 98, 1672 (1993).
33. U. Ekström, L. Visscher, R. Bast, A. J. Thorvaldsen, and K. Ruud, J. Chem. Theory Comput. 6, 1971 (2010).
34. A. D. Becke, J. Chem. Phys. 88, 2547 (1988).
35. M. B. Monagan, K. O. Geddes, K. M. Heal, G. Labahn, S. M. Vorkoetter, J. McCarron, and P. DeMarco, Maple 10 Programming Guide (2005). See
36. Y. Shao, L. F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. T. Brown, A. T. B. Gilbert, L. V. Slipchenko, S. V. Levchenko, D. P. O’Neill, R. A. DiStasio, Jr., R. C. Lochan, T. Wang, G. J. O. Beran, N. A. Besley, J. M. Herbert, C. Y. Lin, T. V. Voorhis, S. H. Chien, A. Sodt, R. P. Steele, V. A. Rassolov, P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin, J. Baker, E. F. C. Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw, B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney, A. Heyden, S. Hirata, C. Hsu, G. Kedziora, R. Z. Khalliulin, P. Klunzinger, A. M. Lee, M. S. Lee, W. Z. Liang, I. Lotan, N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee, J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett, J. E. Subotnik, H. L. Woodcock III, W. Zhang, A. T. Bell, A. K. Chakraborty, and M. Head-Gordon, Phys. Chem. Chem. Phys. 8, 3172 (2006).
37. P. A. M. Dirac, Proc. Cambridge Philos. Soc. 26, 376 (1930);
37.S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).
38. A. D. Becke, Phys. Rev. A 38, 3098 (1988);
38.C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988).
39. K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1979), Vol. IV.
40. G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1966), Vol. II.

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We present the analytical expression and computer implementation for the second-order energy derivatives of the electronic excited state with respect to the nuclear coordinates in the time-dependent density functional theory (TDDFT) with Gaussian atomic orbital basis sets. Here, the Tamm-Dancoff approximation to the full TDDFT is adopted, and therefore the formulation process of TDDFT excited-state Hessian is similar to that of configuration interaction singles (CIS) Hessian. However, due to the replacement of the Hartree-Fock exchange integrals in CIS with the exchange-correlation kernels in TDDFT, many quantitative changes in the derived equations are arisen. The replacement also causes additional technical difficulties associated with the calculation of a large number of multiple-order functional derivatives with respect to the density variables and the nuclear coordinates. Numerical tests on a set of test molecules are performed. The simulated excited-state vibrational frequencies by the analytical Hessian approach are compared with those computed by CIS and the finite-difference method. It is found that the analytical Hessian method is superior to the finite-difference method in terms of the computational accuracy and efficiency. The numerical differentiation can be difficult due to root flipping for excited states that are close in energy. TDDFT yields more exact excited-state vibrational frequencies than CIS, which usually overestimates the values.


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