Time-dependent density-functional theory for molecules and molecular solids

Journal of Molecular Structure: THEOCHEM

Volumn 914, Issue 1-3, 2009, Pages 3-18

  Casida, Mark E ^a  

^a Centre National de la Recherche Scientifique   (France)

Author keywords

Density functional theory; Excited states; Optical properties; Time dependent density functional theory

Indexed keywords

EID: 70349748795     PISSN: 01661280     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.theochem.2009.08.018     Document Type: Review

References (195)

1. Hohenberg P., and Kohn W. Inhomogenous electron gas. Phys. Rev. 136 (1964) B864
2. Kohn W., and Sham L.J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (1965) A1133
3. Zangwill A., and Soven P. Density-functional approach to local-field effects in finite systems: photoabsorption in the rare gases. Phys. Rev. A 21 (1980) 1561
4. Runge E., and Gross E.K.U. Density-functional theory for time-dependent systems. Phys. Rev. Lett. 52 (1984) 997
5. Casida M.E. Time-dependent density-functional response theory for molecules. In: Chong D.P. (Ed). Recent Advances in Density Functional Methods Part I (1995), World Scientific, Singapore 155
6. Gross E.K.U., and Kohn W. Time-dependent density functional theory. Adv. Quant. Chem. 21 (1990) 255
7. Gross E.K.U., Ullrich C.A., and Gossmann U.J. Density functional theory of time-dependent systems. In: Gross E.K.U., and Dreizler R.M. (Eds). Density Functional Theory (1994), Plenum, New York 149-171
8. Gross E.K.U., Dobson J.F., and Petersilka M. Density-functional theory of time-dependent phenomena. Top. Curr. Chem. 181 (1996) 81
9. Casida M.E. Time-dependent density functional response theory of molecular systems: theory, computational methods, and functionals. In: Seminario J.M. (Ed). Recent Developments and Applications of Modern Density Functional Theory (1996), Elsevier, Amsterdam 391
10. Burke K., and Gross E.K.U. A guided tour of time-dependent density functional theory. In: Joubert D. (Ed). Density Functionals: Theory and Applications. Springer Lecture Notes in Physics vol. 500 (1998), Springer 116-146
11. van Leeuwen R. Key concepts in time-dependent density-functional theory. Int. J. Mod. Phys. B 15 (2001) 1969
12. te Velde G., et al. Chemistry with adf. J. Comput. Chem. 22 (2001) 931
13. Casida M.E. Jacob's ladder for time-dependent density-functional theory: some rungs on the way to photochemical heaven. In: Hoffmann M.R.H., and Dyall K.G. (Eds). Accurate Description of Low-Lying Molecular States and Potential Energy Surfaces (2002), ACS Press, Washington, DC 199
14. Daniel C. Electronic spectroscopy and photoreactivity in transition metal complexes. Coord. Chem. Rev. 238-239 (2003) 141
15. Marques M.A.L., and Gross E.K.U. Time-dependent density functional theory. In: Fiolhais C., Nogueira F., and Marques M.A.L. (Eds). A Primer in Density Functional Theory. Springer Lecture Notes in Physics vol. 620 (2003), Springer 144-184
16. Marques M.A.L., and Gross E.K.U. Time-dependent density-functional theory. Annu. Rev. Phys. Chem. 55 (2004) 427
17. Burke K., Werschnik J., and Gross E.K.U. Time-dependent density functional theory: past, present and future. J. Chem. Phys. 123 (2005) 062206
18. Dreuw A., and Head-Gordon M. Single-reference ab initio methods for the calculation of excited states of large molecules. Chem. Rev. 105 (2005) 4009
19. Castro A., et al. Octopus: a tool for the application of time-dependent density functional theory. Phys. Status Solidi 243 (2006) 2465
20. P. Elliott, K. Burke, F. Furche, Excited states from time-dependent density functional theory, 2007, arXiv:cond-mat/0703590v1.
21. Casida M.E. TDDFT for excited states. In: Sautet P., and van Santen R.A. (Eds). Computational Methods in Catalysis and Materials Science (2008), Wiley-VCH, Weinheim, Germany 33
22. Mahan G.D., and Subbaswamy K.R. Local Density Theory of Polarizability (1990), Plenum, New York
23. In: Marques M.A.L., Ullrich C., Nogueira F., Rubio A., and Gross E.K.U. (Eds). Time-Dependent Density-Functional Theory. Lecture Notes in Physics vol. 706 (2006), Springer, Berlin
24. Marques M.A.L., and Rubio A. Time-Dependent Density-Functional Theory. Phys. Chem. Chem. Phys. 11 22 (2009) 4421-4688 (special issue)
25. Perdew J.P., and Schmidt K. Jacob's ladder of density functional approximations for the exchange-correlation energy. In: Doren V.E.V., Alseoy K.V., and Geerlings P. (Eds). Density Functional Theory and its Applications to Materials (2001), American Institute of Physics, Melville, New York 1
26. Perdew J.P., Ruzsinsky A., Constantin L.A., Sun J., and Csonka G.I. Some fundamental issues in ground-state density functional theory: a guide for the perplexed. J. Chem. Theor. Comput. 5 (2009) 902
27. Perdew J.P., and Constantin L.A. Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy. Phys. Rev. B 75 (2007) 155109
28. Ahlberg R., and Goscinski O. Atomic polarizabilities and shielding factors with a local linear response method. J. Phys. B 6 (1973) 2254
29. Stott M.J., and Zaremba E. Linear-response theory within the density-functional formalism: application to atomic polarizabilities. Phys. Rev. A 21 (1980) 12 Erratum 22 (1980) 2293
30. Mahan G.D. Modified Sternheimer equation for polarizability. Phys. Rev. A 22 (1980) 1780
31. Bauernschmitt R., and Ahlrichs R. Stability analysis for solutions of the closed shell Kohn-Sham equation. J. Chem. Phys. 104 (1996) 9047
32. Rajagopal A.K. Time-dependent variational principle and the effective action in density-functional theory and Berry's phase. Phys. Rev. A 54 (1996) 3916
33. Görling A. Exact exchange kernel for time-dependent density-functional theory. Int. J. Quant. Chem. 69 (1998) 265
34. Casida M.E., Jamorski C., Casida K.C., and Salahub D.R. Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: characterization and correction of the time-dependent local density approximation ionization threshold. J. Chem. Phys. 108 (1998) 4439
35. Champagne B., Perpète E.A., van Gisbergen S.J.A., Baerends E.-J., and Snijders J.G. Assessment of conventional density functional schemes for computing the polarizabilities and hyperpolarizabilities of conjugated oligomers: an ab initio investigation of polyacetylene chains. J. Chem. Phys. 109 (1998) 10489 Erratum 110 (1999) 11664
36. Hirata S., and Head-Gordon M. Time-dependent density functional theory within the Tamm-Dancoff approximation. Chem. Phys. Lett. 314 (1999) 291
37. Caillie C.V., and Amos R.D. Geometric derivatives of excitation energies using SCF and DFT. Chem. Phys. Lett. 308 (1999) 249
38. Adamo C., and Barone V. A TDDFT study of the electronic spectrum of s-tetrazine in the gas-phase and in aqueous solution. Chem. Phys. Lett. 330 (2000) 152
39. Dreuw A., Weisman J.L., and Head-Gordon M. Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange. J. Chem. Phys. 119 (2003) 2943
40. Tunell I., et al. Density functional theory of nonlinear triplet response properties with applications to phosphorescence. J. Chem. Phys. 119 (2003) 11024
41. Shao Y., Head-Gordon M., and Krylov A.I. The spin-flip approach within time-dependent density functional theory: theory and applications to diradicals. J. Chem. Phys. 118 (2003) 4807
42. Maitra N.T., Zhang F., Cave F.J., and Burke K. Double excitations within time-dependent density functional theory linear response. J. Chem. Phys. 120 (2004) 5932
43. Casida M.E., and Wesołowski T.A. Generalization of the Kohn-Sham equations with constrained electron density (KSCED) formalism and its time-dependent response theory formulation. Int. J. Quant. Chem. 96 (2004) 577
44. Tawada Y., Tsuneda T., Yanagisawa S., Yanai T., and Hirao K. A long-range-corrected time-dependent density functional theory. J. Chem. Phys. 120 (2004) 8425
45. Dierksen M., and Grimme S. Density functional calculations of the vibronic structure of electronic absorption spectra. J. Chem. Phys. 120 (2004) 3544
46. Wang F., and Ziegler T. The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculation of excitation energies. J. Chem. Phys. 122 (2005) 074109
47. Wang F., Ziegler T., van Lenthe E., van Gisbergen S., and Baerends E.J. The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry. J. Chem. Phys. 122 (2005) 204103
48. Wang F., and Ziegler T. Theoretical study of the electronic spectra of square-planar platinum (II) complexes based on the two-component relativistic time-dependent density-functional theory. J. Chem. Phys. 123 (2005) 194102
49. Mukamel S. Generalized time-dependent density-functional-theory response functions for spontaneous density fluctuations and nonlinear response: resolving the causality paradox in real time. Phys. Rev. A 71 (2005) 024503
50. Tapavicza E., Tavernelli I., and Rothlisberger U. Trajectory surface hopping within linear response time-dependent density-functional theory. Phys. Rev. Lett. 98 (2007) 023001
51. Vignale G. Real-time resolution of the causality paradox of time-dependent density-functional theory. Phys. Rev. A 77 (2008) 062511
52. Schreiber M., Silva-Junior M.R., Sauer S.P.A., and Thiel W. Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. J. Chem. Phys. 128 (2008) 134110
53. Silva-Junior M.R., Schreiber M., Sauer S.P.A., and Thiel W. Benchmarks for electronically excited states: time-dependent density functional theory and density functional theory based multireference configuration interaction. J. Chem. Phys. 129 (2008) 104103
54. Heßelmann A., and Görling A. Blindness of the exact density response function to certain types of electronic excitations: implications for time-dependent density-functional theory. Phys. Rev. Lett. 102 (2009) 233003
55. Baer R. Prevalence of the adiabatic exchange-correlation potential approximation in time-dependent density functional theory. J. Mol. Struct. Theochem. 914 (2009) 19
56. Hanke W., and Sham L.J. Dielectric response in the Wannier representation: application to the optical spectrum of diamond. Phys. Rev. Lett. 33 (1974) 582
57. Hanke W., and Sham L.J. Local-field and excitonic effects in the optical spectrum of a covalent crystal. Phys. Rev. B 12 (1975) 4501
58. Hanke W., and Sham L.J. Many-particle effects in the optical excitations of a semiconductor. Phys. Rev. Lett. 43 (1979) 387
59. Hanke W., and Sham L.J. Many-particle effects in the optical spectrum of a semiconductor. Phys. Rev. B 21 (1980) 4656
60. Casida M.E., and Chong D.P. Physical interpretation and assessment of the Coulomb-hole and screened-exchange approximation for molecules. Phys. Rev. A 44 (1991) 4837 Erratum 44 (1991) 5773
61. Casida M.E., and Chong D.P. Simplified Green-function approximations: further assessment of a polarization model for second-order calculation of outer-valence ionization potentials in molecules. Phys. Rev. A 44 (1991) 5773
62. Yamaguchi Y., Osamura Y., Goddard J.D., and Schaefer III H.F. A New Dimension to Quantum Chemistry: Analytic Derivative Methods in Ab Initio Molecular Electronic Structure Theory (1994), Oxford University Press, Oxford
63. Fournier R. Second and third derivatives of the linear combination of Gaussian type orbitals local spin density energy. J. Chem. Phys. 92 (1990) 5422
64. Dunlap B.I., and Andzelm J. Second derivatives of the local-density-functional total energy when the local potential is fitted. Phys. Rev. A 45 (1992) 81
65. Kormornicki A., and Fitzgerald G. Molecular gradients and hessians implemented in density functional theory. J. Chem. Phys. 98 (1993) 1398
66. Colwell S.M., Murray C.W., Handy N.C., and Amos R.D. The determination of hyperpolarisabilities using density functional theory. Chem. Phys. Lett. 210 (1993) 261
67. Chakravarty S., Fogel M.B., and Kohn W. Dynamic response of inhomogeneous Fermi systems. Phys. Rev. Lett. 43 (1979) 775
68. Deb B.M., and Ghosh S.K. Schrödinger fluid dynamics of many-electron systems in a time-dependent density-functional framework. J. Chem. Phys. 77 (1982) 342
69. Ghosh S.K., and Deb B.M. Dynamic polarizability of many-electron systems within a time-dependent density-functional theory. Chem. Phys. 71 (1982) 295
70. Bartolotti L.J. Time-dependent extension of the Hohenberg-Kohn-Levy energy-density functional. Phys. Rev. A 24 (1981) 1661
71. Bartolotti L.J. Time-dependent Kohn-Sham density-functional theory. Phys. Rev. A 26 (1982) 2243
72. Rajam A.K., Hessler P., Gaun C., and Maitra N.T. Phase-space explorations in time-dependent density functional theory. J. Mol. Struct. Theochem. 914 (2009) 30
73. Schirmer J., and Dreuw A. Critique of the foundations of time-dependent density-functional theory. Phys. Rev. A 75 (2007) 022513
74. N.T. Maitra, K. Burke, R. van Leeuwen, Comment on 'Critique of the foundations of time-dependent density functional theory', Phys. Rev. A 75 (2007) 022513.
75. Schirmer J., and Dreuw A. Reply to "Comment on 'Critique of the foundations of time-dependent density functional theory"'. Phys. Rev. A 78 (2008) 056502
76. Gross E.K.U., and Kohn W. Local density-functional theory of frequency-dependent linear response. Phys. Rev. Lett. 55 (1985) 2850
77. Dobson J.F. Harmonic-potential theorem: implications for approximate many-body theories. Phys. Rev. Lett. 73 (1994) 2244
78. Kurzweil Y., and Baer R. Time-dependent exchange-correlation current density functionals with memory. J. Chem. Phys. 121 (2004) 8731
79. Kurzweil Y., and Baer R. Generic Galilean-invariant exchange-correlation functionals with quantum memory. Phys. Rev. B 72 (2006) 035106
80. Kurzweil Y., and Baer R. Quantum memory effects in the dynamics of electrons in gold clusters. Phys. Rev. B 73 (2006) 075413
81. Kurzweil Y., and Baer R. Adapting approximate-memory potentials for time-dependent density functional theory. Phys. Rev. B 77 (2008) 085121
82. Vignale G., and Kohn W. Current-dependent exchange-correlation potential for dynamical linear response theory. Phys. Rev. Lett. 77 (1996) 2037
83. Vignale G., Ullrich C.A., and Conti S. Time-dependent density functional theory beyond the adiabatic local density approximation. Phys. Rev. Lett. 79 (1997) 4878
84. Ullrich C.A., and Tokatly I.V. Nonadiabatic electron dynamics in time-dependent density-functional theory. Phys. Rev. B 73 (2006) 235102
85. Hirata S., Ivanov S., Grabowski I., and Bartlett R.J. Time-dependent density functional theory employing optimized effective potentials. J. Chem. Phys. 116 (2002) 6468
86. Onida G., Reining L., and Rubio A. Electronic excitations: density-functional versus many-body Green's-function approaches. Rev. Mod. Phys. 74 (2002) 601
87. g states of butadiene and hexatriene. Chem. Phys. Lett. 389 (2004) 39
88. Casida M.E. Propagator corrections to adiabatic time-dependent density-functional theory linear response theory. J. Chem. Phys. 122 (2005) 054111
89. Romaniello P., et al. Double excitations in finite systems. J. Chem. Phys. 130 (2009) 044108
90. Mazur G., and Włodarczyk R. Application of the dressed time-dependent density functional theory for the excited states of linear polyenes. J. Comput. Chem. 30 (2009) 811
91. Gritsenko O.V., and Baerends E.J. Double excitation effect in non-adiabatic time-dependent density functional theory with an analytic construction of the exchange-correlation kernel in the common energy denominator approximation. Phys. Chem. Chem. Phys. 11 (2009) 4640
92. Singh R., and Deb B.M. Developments in excited-state density-functional theory. Phys. Reps. 311 (1999) 50
93. Petersilka M., Gossmann U.J., and Gross E.K.U. Excitation energies from time-dependent density-functional theory. Phys. Rev. Lett. 76 (1996) 1212
94. Rinkevicius Z., Vahtras O., and Ågren H. Time-dependent closed and open-shell density functional theory from the perspective of partitioning techniques and projections. J. Mol. Struct. Theochem. 914 (2009) 50
95. 2 as a case study. J. Chem. Phys. 104 (1996) 5134
96. Maurice D., and Head-Gordon M. Configuration interaction with single substitutions for excited states of open-shell molecules. Int. J. Quant. Chem. Symp. 29 (1995) 361
97. 2 and LiH. J. Chem. Phys. 113 (2000) 7062
98. Casida M.E., Ipatov A., and Cordova F. Linear-response time-dependent density-functional theory for open-shell molecules. In: Marques M.A.L., Ullrich C., Nogueira F., Rubio A., and Gross E.K.U. (Eds). Time-Dependent Density-Functional Theory. Lecture Notes in Physics vol. 706 (2006), Springer 243
99. Cordova F., Doriol L.J., Ipatov A., Casida M.E., Filippi C., and Vela A. Troubleshooting time-dependent density-functional theory for photochemical applications: oxirane. J. Chem. Phys. 127 (2007) 164111
100. Tapavicza E., Tavernelli I., Rothlisberger U., Filippi C., and Casida M.E. Mixed time-dependent density-functional theory/classical surface hopping study of oxirane photochemistry. J. Chem. Phys. 129 (2008) 124108
101. Ipatov A., Cordova F., Doriol L.J., and Casida M.E. Excited-state spin-contamination in time-dependent density-functional theory for molecules with open-shell ground states. J. Mol. Struct. Theochem. 914 (2009) 60
102. Caillie C.V., and Amos R.D. Geometric derivatives of density functional theory excitation energies using gradient-corrected functionals. Chem. Phys. Lett. 317 (2000) 159
103. Furche F., and Ahlrichs R. Adiabatic time-dependent density functional methods for excited state properties. J. Chem. Phys. 117 (2002) 7433
104. Hutter J. Excited state nuclear forces from the Tamm-Dancoff approximation to time-dependent density functional theory within the plane wave basis set framework. J. Chem. Phys. 118 (2003) 3928
105. Rappoport D., and Furche F. Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules. J. Chem. Phys. 122 (2005) 064105
106. Doltsinis N.L., and Kosov D.S. Plane wave/pseudopotential implementation of excited state gradients in density functional linear response theory: a new route via implicit differentiation. J. Chem. Phys. 122 (2005) 144101
107. Scalmani G., et al. Geometries and properties of excited states in the gas phase and in solution: theory and application of a time-dependent density functional theory polarizable continuum model. J. Chem. Phys. 124 (2006) 094107
108. Wasserman A., Maitra N.T., and Burke K. Accurate Rydberg excitations from the local density approximation. Phys. Rev. Lett. 91 (2003) 263001
109. Wasserman A., and Burke K. Rydberg transition frequencies from the local density approximation. Phys. Rev. Lett. 95 (2005) 163006
110. 1 manifold. Int. J. Quant. Chem. 70 (1998) 933
111. Tozer D.J., and Handy N.C. Improving virtual Kohn-Sham orbitals and eigenvalues: application to excitation energies and static polarizabilities. J. Chem. Phys. 109 (1998) 10180
112. Casida M.E., and Salahub D.R. Asymptotic correction approach to improving approximate exchange-correlation potentials: time-dependent density-functional theory calculations of molecular excitation spectra. J. Chem. Phys. 113 (2000) 8918
113. Hirata S., Zhan C.G., Apra E., Windlus T.L., and Dixon D.A. A new, self-contained asymptotic correction scheme to exchange-correlation potentials for time-dependent density functional theory. J. Phys. Chem. A 107 (2003) 10154
114. Sharp R.T., and Horton G. A variational approach to the unipotential many-electron problem. Phys. Rev. 90 (1953) 317
115. Talman J.D., and Shadwick W.F. Optimized effective atomic central potential. Phys. Rev. A 14 (1976) 36
116. Görling A. New KS method for molecules based on an exchange charge density generating the exact local KS exchange potential. Phys. Rev. Lett. 83 (1999) 5462
117. Ivanov S., Hirata S., and Bartlett R.J. Exact exchange treatment for molecules in finite-basis-set Kohn-Sham theory. Phys. Rev. Lett. 83 (1999) 5455
118. Hamel S., Duffy P., Casida M.E., and Salahub D.R. Kohn-Sham orbitals and orbital energies: fictitious constructs but good approximations all the same. J. Electron. Spectrosc. Relat. Phenom. 123 (2002) 345
119. Hamel S., Casida M.E., and Salahub D.R. Exchange-only optimized effective potential for molecules from resolution-of-the-identity techniques: comparison with the local density approximation, with and without asymptotic correction. J. Chem. Phys. 116 (2002) 8276
120. Tozer D.J., Amos R.D., Handy N.C., Roos B.O., and Serrano-Andrés L. Does density functional theory contribute to the understanding of excited states of unsaturated organic compounds?. Mol. Phys. 97 (1999) 859
121. Hu C., Sugino O., and Miyamoto Y. Modified linear response for time-dependent density-functional theory: application to Rydberg and charge-transfer excitations. Phys. Rev. A 74 (2006) 032508
122. Hu C., and Sugino O. Average excitation energies from time-dependent density-functional theory. J. Chem. Phys. 126 (2007) 074112
123. Tokura S., Tsuneda T., and Hirao K. Long-range-corrected time-dependent density functional study on electronic spectra of five-membered ring compounds and free-base porphyrin. J. Theor. Comput. Chem. 5 (2006) 925
124. Vydrov O.A., and Scuseria G.E. Assessment of a long-range corrected hybrid functional. J. Chem. Phys. 125 (2006) 234109
125. Peach M.J.G., Tellgrent E.I., Sałek P., Helgaker T., and Tozer D.J. Structural and electronic properties of polvacetylene and polyyne from hybrid and coulomb-attenuated density functionals. J. Phys. Chem. A 111 (2007) 11930
126. Livshits E., and Baer R. A well-tempered density functional theory of molecules. Phys. Chem. Chem. Phys. 9 (2007) 2932
127. Rohrdanz M.A., Martins K.M., and Herbert J.M. A long-range-corrected density functional that performs well for both ground-state properties and time-dependent density functional theory excitation energies, including charge-transfer excited states. J. Chem. Phys. 130 (2009) 054112
128. Livshits E., and Baer R. A density functional theory for symmetric radical cations from bonding to dissociation. J. Phys. Chem. A 112 (2008) 12789
129. Stein T., Kronik L., and Baer R. Reliable prediction of charge transfer excitations in molecular complexes using time-dependent density functional theory. J. Am. Chem. Soc. 131 (2009) 2818
130. Gimon T., Ipatov A., Heßelmann A., and Görling A. Qualitatively correct charge-transfer excitation energies in HeH by time-dependent density-functional theory due to exact exchange Kohn-Sham eigenvalue differences. J. Chem. Theor. Comput. 5 (2009) 781
131. Heßelmann A., Ipatov A., and Görling A. Charge-transfer excitation energies with a time-dependent density-functional method suitable for orbital-dependent exchange-correlation functionals. Phys. Rev. A 80 (2009) 012507
132. * excited singlet states of linear polyenes: time-dependent density-functional theory versus multiconfigurational methods. Phys. Rev. A 77 (2008) 012510
133. Tretiak S., and Chernyak V. Resonant nonlinear polarizabilities in the time-dependent density functional theory. J. Chem. Phys. 119 (2003) 8809
134. Isborn C.M., and Li X. Modeling the doubly excited state with time-dependent Hartree-Fock and density functional theories. J. Chem. Phys. 129 (2007) 204107
135. Hirata S., Head-Gordon M., and Bartlett R.J. Configuration interaction singles, time-dependent Hartree-Fock, and time-dependent density functional theory for the electronic excited states of extended systems. J. Chem. Phys. 111 (1999) 10774
136. Champagne B., et al. Assessment of conventional density functional schemes for computing the dipole moment and (hyper)polarizabilities of push-pull π-conjugated systems. J. Phys. Chem. A 104 (2000) 4755
137. Petersilka M., Gross E.K.U., and Burke K. Excitation energies from time-dependent density functional theory using exact and approximate potentials. Int. J. Quant. Chem. 80 (2000) 534
138. van Gisbergen S.J.A., et al. Electric field dependence of the exchange-correlation potential in molecular chains. Phys. Rev. Lett. 83 (1999) 694
139. Wesołowski T.A. Hydrogen bonding induced shifts of the excitation energies in nucleic acid bases: an interplay between electrostatic and electron density overlap effect. J. Am. Chem. Soc. 126 (2004) 11444
140. Neugebauer J., Louwerse M.J., Baerends E.J., and Wesołowski T.A. The merits of the frozen density embedding scheme to model solvachromic shifts. J. Chem. Phys. 122 (2005) 094115
141. Qian Z., Constantinescu A., and Vignale G. Solving the ultranonlocality problem in time-dependent spin-density-functional theory. Phys. Rev. Lett. 90 (2003) 066402
142. Faassen M.V. Time-dependent current-density-functional theory applied to atoms and molecules. Int. J. Mod. Phys. B 20 (2006) 3419
143. Reining L., Olevano V., Rubio A., and Onida G. Excitonic effects in solids described by time-dependent density-functional theory. Phys. Rev. Lett. 88 (2002) 066404
144. Marini A., Sole R.D., and Rubio A. Bound excitations in time-dependent density-functional theory: optical and energy-loss spectra. Phys. Rev. Lett. 91 (2003) 256402
145. Varsano D., Marini A., and Rubio A. Optical saturation driven by exciton confinement in molecular chains: a time-dependent density-functional theory approach. Phys. Rev. Lett. 101 (2008) 133002
146. Perpète E.A., and Jacquemin D. TD-DFT benchmark for indigoïd dyes. J. Mol. Struct. Theochem. 914 (2009) 100
147. Hu C., Hirai H., and Sugino O. Nonadiabatic couplings from time-dependent density functional theory: formulation in the Casida formalism and practical scheme within modified linear response. J. Chem. Phys. 127 (2007) 064103
148. Ziegler T., Seth M., Krykunov M., Autschbach J., and Wang F. On the relation between time-dependent and variational density functional theory approaches for the determination of excitation energies and transition moments. J. Chem. Phys. 130 (2009) 154102
149. M. Casida, Reconciling of the ΔSCF and TDDFT approaches to excitation energies in DFT: a charge-transfer correction for TDDFT with GGA functionals, in: The On-line Workshop Proceedings of the Joint ITP/INT Workshop on Time-Dependent Density Functional Theory, 15-17 April 1999, Institute for Theoretical Physics, University of California at Santa, Barbara. Available from: .
150. Ziegler T., Seth M., Krykunov M., Autschbach J., and Wang F. Is charge transfer transitions really too difficult for standard density functionals or are they just a problem for time-dependent density functional theory based on a linear response approach. J. Mol. Struct. Theochem. 914 (2009) 106
151. * transitions in organic dyes. J. Chem. Phys. 127 (2007) 094102
152. Jacquemin D., Perpète E.A., Scuseria G.E., Ciofini I., and Adamo C. TD-DFT performance for the visible absorption spectra of organic dyes: conventional versus long-range hybrids. J. Chem. Theor. Comput. 4 (2008) 123
153. Peach M.J.G., Benfield P., Helgaker T., and Tozer D.J. Excitation energies in density functional theory: an evaluation and a diagnostic test. J. Chem. Phys. 128 (2008) 044118
154. Peach M.J.G., and Tozer D.J. Illustration of a TDDFT spatial overlap diagnostic by basis function exponent scaling. J. Mol. Struct. Theochem. 914 (2009) 110
155. Santoro F., Improta R., Lami A., Bloino J., and Barone V. Effective method to compute Franck-Condon integrals for optical spectra of large molecules in solution. J. Chem. Phys. 126 (2007) 084509 Erratum 126 (2007) 169903
156. Santoro F., Improta R., Lami A., and Barone V. Effective method to compute vibrationally resolved optical spectra of large molecules at finite temperature in the gas phase and in solution. J. Chem. Phys. 126 (2007) 184102
157. x band of porphyrin as a case study. J. Chem. Phys. 128 (2008) 224311
158. FClasses code. Available from: .
159. De Angelis F., and Fantacci S. Spectroscopic properties of cyclometallated iridium complexes by TDDFT. J. Mol. Struct. Theochem. 914 (2009) 74
160. Peltier C., et al. Environmental effects on electronic absorption spectra using DFT: an organic and positively charged fused polycyclic chromophore as a case study. J. Mol. Struct. Theochem. 914 (2009) 94
161. Cossi M., and Barone V. Solvent effect on vertical electronic transitions by the polarizable continuum model. J. Chem. Phys. 112 (2000) 2427
162. Sałek P., Vahtras O., Helgaker T., and Ågren H. Density-functional theory of linear and nonlinear time-dependent molecular properties. J. Chem. Phys. 117 (2002) 9630
163. Rinkevicius Z., Telyatnyk L., Vahtras O., and Ågren H. Density functional theory for hyperfine coupling constants with a restricted-unrestricted approach. J. Chem. Phys. 121 (2004) 7614
164. Oprea C.I., Telyatnyk L., Rinkevicius Z., Vahtras O., and Ågren H. Time-dependent density functional theory with the generalized restricted-unrestricted approach. J. Chem. Phys. 124 (2006) 174103
165. Rinkevicius Z., de Almeida K.J., and Vahtras O. Density functional restricted-unrestricted approach for nonlinear properties: application to electronic paramagnetic resonance parameters of square planar copper complexes. J. Chem. Phys. 129 (2008) 064109
166. Vahtras O., and Rinkevicius Z. General excitations in time-dependent density functional theory. J. Chem. Phys. 126 (2007) 114101
167. Rinkevicius Z., Jha P.C., Oprea C.I., Vahtras O., and Ågren H. Time-dependent density functional theory for nonlinear properties of open-shell systems. J. Chem. Phys. 127 (2007) 114101
168. 1 surface. ChemPhysChem 2 (2001) 273
169. 1 surface. ChemPhysChem 2 (2001) 294
170. Diau E.W.-G., Kötting C., Sølling T.I., and Zewail A.H. Femtochemistry of Norrish type-I reactions: III. Highly excited ketones-theoretical. ChemPhysChem 3 (2002) 57
171. Sølling T.I., Diau E.W.-G., Kötting C., Feyter S.D., and Zewail A.H. Femtochemistry of Norrish type-I reactions: IV. Highly excited ketones-experimental. ChemPhysChem 3 (2002) 79
172. Doltsinis N.L., and Marx D. First principles molecular dynamics involving excited states and nonadiabatic transitions. J. Theor. Comput. Chem. 1 (2002) 319
173. Ipatov A.N., Reinhard P., and Suraud E. A microscopic study of sodium cluster deposition on an insulating surface. Int. J. Mol. Sci. 4 (2003) 301
174. Ipatov A.N., Reinhard P., and Suraud E. Velocity dependence of metal cluster deposition on an insulating surface. Eur. Phys. J. D 30 (2004) 65
175. Gervais B., et al. Spectroscopic properties of Na clusters embedded in a rare-gas matrix. Phys. Rev. A 71 (2005) 015201
176. Gervais B., et al. Simple DFT model of clusters embedded in rare gas matrix: trapping sites and spectroscopic properties of Na embedded in Ar. J. Chem. Phys. 121 (2004) 8466
177. Fehrer F., et al. Linear and non-linear response of embedded Na clusters. Appl. Phys. A 92 (2006) 151
178. Burnus T., Marques M.A.L., and Gross E.K.U. Time-dependent electron localization function. Phys. Rev. A 71 (2005) 010501
179. Tully J.C. Molecular dynamics with electronic transitions. J. Chem. Phys. 93 (1990) 1061
180. Tully J.C. Nonadiabatic dynamics. In: Thompson D.L. (Ed). Modern Methods in Multidimensional Dynamics Computations in Chemistry (1998), World Scientific, Singapore 34
181. Werner U., Mitrić R., Suzuki T., and Bonačić-Koutecký V. Nonadiabatic dynamics within the time dependent density functional theory: ultrafast photodynamics in pyrazine. Chem. Phys. 249 (2008) 319
182. Mirić R., Werner U., and Bonačić-Koutecký V. Nonadiabatic dynamics and simulation of time resolved photoelectron spectra within time-dependent density functional theory: ultrafast photoswitching in benzylideneaniline. J. Chem. Phys. 129 (2008) 164118
183. Niehaus T.A. Approximate time-dependent density functional theory. J. Mol. Struct. Theochem. 914 (2009) 38
184. Tavernelli I., Tapavicza E., and Rothlisberger U. Nonadiabatic coupling vectors within linear response time-dependent density functional theory. J. Chem. Phys. 130 (2009) 124107
185. Tavernelli I., Tapavicza E., and Rothlisberger U. Non-adiabatic dynamics using time-dependent density functional theory: assessing the coupling strengths. J. Mol. Struct. Theochem. 914 (2009) 22
186. Levine B.G., Ko C., Quenneville J., and Martinez T.J. Conical intersections and double excitations in density functional theory. Mol. Phys. 104 (2006) 1039
187. Vasiliev I., del Puerto M.L., Jain M., Lugo-Solis A., and Chelikowsky J.R. Application of time-dependent density-functional theory to molecules and nanostructures. J. Mol. Struct. Theochem. 914 (2009) 115
188. 60 in the time-dependent density functional theory. J. Mol. Struct. Theochem. 914 (2009) 130
189. Levine Z.H., and Allan D.C. Optical second-harmonic generation in III-V semiconductors: detailed formulation and computational results. Phys. Rev. B 44 (1991) 12781
190. Levine Z.H. Optical second-harmonic susceptibilities: frequency-dependent formulation with results for GaP and GaAs. Phys. Rev. B 49 (1994) 4532
191. Corso A.D., Mauri F., and Rubio A. Density-functional theory of the nonlinear optical susceptibility: application to cubic semiconductors. Phys. Rev. B 53 (1996) 15638
192. Bertsch G.F., Iwata J.-I., Rubio A., and Yabana K. Real-space, real-time method for the dielectric function. Phys. Rev. B 62 (2000) 7998
193. Perdew J.P., and Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23 (1981) 5048
194. Langreth D.C., and Perdew J.P. Theory of nonuniform electronic systems. I. Analysis of the gradient approximation and a generalization that works. Phys. Rev. B 21 (1980) 5469
195. Langreth D.C., and Mel M.J. Beyond the local-density approximation in calculations of ground-state electronic properties. Phys. Rev. B 28 (1983) 1809