3. Runge, E., Gross, E.: Density-functional theory for time-dependent systems. Phys. Rev. Lett.
52, 997 (1984)
4. Castro, A., Appel, H., Oliveira, M., Rozzi, C., Andrade, X., Lorenzen, F., Marques, M.,
Gross, E., Rubio, A.: Octopus: a tool for the application of time-dependent density functional
theory. Physica Status Solidi B 243, 2465–2488 (2006)
5. Casida, M.E.: Time-dependent density functional response theories of molecules. In: Chong,
D.P. (ed.) Recent Advances in Density Functional Methods, Part 1. Recent Advances in
Computational Chemistry, vol. 1. World Scientific, Singapore (1995)
6. Furche, F.: On the density matrix based approach to time-dependent density functional
response theory. J. Chem. Phys. 114(14), 5982–5992 (2001)
7. Furche, F., Ahlrichs, R.: Adiabatic time-dependent density functional methods for excited
state properties. J. Chem. Phys. 117(16), 7433–7447 (2002)
8. Baerends, E.J.: Exact exchange-correlation treatment of dissociated H 2 in density functional
theory. Phys. Rev. Lett. 87(13), 133004 (2001)
9. Gritsenko, O.V., van Gisbergen, S.J.A., Go ¨rling, A., Baerends, E.J.: Excitation energies of
dissociating H 2 : a problematic case for the adiabatic approximation of time-dependent
density functional theory. J. Chem. Phys. 113(19), 8478–8489 (2000)
10. Gru ¨ning, M., Gritsenko, O.V., Baerends, E.J.: Exchange-correlation energy and potential as
approximate functionals of occupied and virtual Kohn-Sham orbitals: application to
dissociating H2. J. Chem. Phys. 118(16), 7183–7192 (2003)
11. Gru ¨ning, M., Gritsenko, O.V., van Gisbergen, S.J.A., Baerends, E.J.: The failure of
generalized gradient approximations (GGAs) and meta-GGAs for the two-center threeelectron bonds in He 2
+ , (H 2 O) 2
+ , and (NH 3 ) 2
+ . J. Phys. Chem. A 105(40), 9211–9218 (2001)
12. Cizek, J., Paldus, J.: Stability conditions for solutions of Hartree-Fock equations for atomic
and molecular systems. Application to pi-electron model of cyclic polyenes. J. Chem. Phys.
47(10), 3976–3985 (1967)
13. Cordova, F., Doriol, L.J., Ipatov, A., Casida, M.E., Filippi, C., Vela, A.: Troubleshooting
time-dependent density-functional theory for photochemical applications: oxirane. J. Chem.
Phys. 127(16), 164111 (2007). doi:10.1063/1.2786997
14. Levine, B.G., Ko, C., Quenneville, J., Martinez, T.J.: Conical intersections and double
excitations in time-dependent density functional theory. Mol. Phys. 104(5–7), 1039–1051
(2006)
15. Casida, M.E., Jamorski, C., Casida, K.C., 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(11), 4439–4449 (1998)
16. Tozer, D., Handy, N.C.: Improving virtual Kohn-Sham orbitals and eigenvalues: application
to excitation energies and static polarizabilities. J. Chem. Phys. 109(23), 10180 (1998)
17. Gru ¨ning, M., Gritsenko, O.V., van Gisbergen, S.J.A., Baerends, E.J.: Shape corrections to
exchange-correlation potentials by gradient-regulated seamless connection of model
potentials for inner and outer region. J. Chem. Phys. 114(2), 652–660 (2001)
18. van Leeuwen, R., Baerends, E.J.: Exchange-correlation potential with correct asymptotic
behavior. Phys. Rev. A 49, 2421–2431 (1994)
19. Dreuw, A., Head-Gordon, M.: Failure of time-dependent density functional theory for longrange charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and
bacteriochlorophyll-spheroidene complexes. J. Am. Chem. Soc. 126, 4007–4016 (2004)
20. Tozer, D.J.: Relationship between long-range charge-transfer excitation energy error and
integer discontinuity in Kohn-Sham theory. J. Chem. Phys. 119(24), 12697–12699 (2003)
21. Hellgren, M., Gross, E.K.U.: Discontinuities of the exchange-correlation kernel and chargetransfer excitations in time-dependent density-functional theory. Phys. Rev. A 85(2), 022514
(2012)
4 Theoretical Methods
59
52, 997 (1984)
4. Castro, A., Appel, H., Oliveira, M., Rozzi, C., Andrade, X., Lorenzen, F., Marques, M.,
Gross, E., Rubio, A.: Octopus: a tool for the application of time-dependent density functional
theory. Physica Status Solidi B 243, 2465–2488 (2006)
5. Casida, M.E.: Time-dependent density functional response theories of molecules. In: Chong,
D.P. (ed.) Recent Advances in Density Functional Methods, Part 1. Recent Advances in
Computational Chemistry, vol. 1. World Scientific, Singapore (1995)
6. Furche, F.: On the density matrix based approach to time-dependent density functional
response theory. J. Chem. Phys. 114(14), 5982–5992 (2001)
7. Furche, F., Ahlrichs, R.: Adiabatic time-dependent density functional methods for excited
state properties. J. Chem. Phys. 117(16), 7433–7447 (2002)
8. Baerends, E.J.: Exact exchange-correlation treatment of dissociated H 2 in density functional
theory. Phys. Rev. Lett. 87(13), 133004 (2001)
9. Gritsenko, O.V., van Gisbergen, S.J.A., Go ¨rling, A., Baerends, E.J.: Excitation energies of
dissociating H 2 : a problematic case for the adiabatic approximation of time-dependent
density functional theory. J. Chem. Phys. 113(19), 8478–8489 (2000)
10. Gru ¨ning, M., Gritsenko, O.V., Baerends, E.J.: Exchange-correlation energy and potential as
approximate functionals of occupied and virtual Kohn-Sham orbitals: application to
dissociating H2. J. Chem. Phys. 118(16), 7183–7192 (2003)
11. Gru ¨ning, M., Gritsenko, O.V., van Gisbergen, S.J.A., Baerends, E.J.: The failure of
generalized gradient approximations (GGAs) and meta-GGAs for the two-center threeelectron bonds in He 2
+ , (H 2 O) 2
+ , and (NH 3 ) 2
+ . J. Phys. Chem. A 105(40), 9211–9218 (2001)
12. Cizek, J., Paldus, J.: Stability conditions for solutions of Hartree-Fock equations for atomic
and molecular systems. Application to pi-electron model of cyclic polyenes. J. Chem. Phys.
47(10), 3976–3985 (1967)
13. Cordova, F., Doriol, L.J., Ipatov, A., Casida, M.E., Filippi, C., Vela, A.: Troubleshooting
time-dependent density-functional theory for photochemical applications: oxirane. J. Chem.
Phys. 127(16), 164111 (2007). doi:10.1063/1.2786997
14. Levine, B.G., Ko, C., Quenneville, J., Martinez, T.J.: Conical intersections and double
excitations in time-dependent density functional theory. Mol. Phys. 104(5–7), 1039–1051
(2006)
15. Casida, M.E., Jamorski, C., Casida, K.C., 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(11), 4439–4449 (1998)
16. Tozer, D., Handy, N.C.: Improving virtual Kohn-Sham orbitals and eigenvalues: application
to excitation energies and static polarizabilities. J. Chem. Phys. 109(23), 10180 (1998)
17. Gru ¨ning, M., Gritsenko, O.V., van Gisbergen, S.J.A., Baerends, E.J.: Shape corrections to
exchange-correlation potentials by gradient-regulated seamless connection of model
potentials for inner and outer region. J. Chem. Phys. 114(2), 652–660 (2001)
18. van Leeuwen, R., Baerends, E.J.: Exchange-correlation potential with correct asymptotic
behavior. Phys. Rev. A 49, 2421–2431 (1994)
19. Dreuw, A., Head-Gordon, M.: Failure of time-dependent density functional theory for longrange charge-transfer excited states: the zincbacteriochlorin-bacteriochlorin and
bacteriochlorophyll-spheroidene complexes. J. Am. Chem. Soc. 126, 4007–4016 (2004)
20. Tozer, D.J.: Relationship between long-range charge-transfer excitation energy error and
integer discontinuity in Kohn-Sham theory. J. Chem. Phys. 119(24), 12697–12699 (2003)
21. Hellgren, M., Gross, E.K.U.: Discontinuities of the exchange-correlation kernel and chargetransfer excitations in time-dependent density-functional theory. Phys. Rev. A 85(2), 022514
(2012)
4 Theoretical Methods
59