9. Furche F, Ahlrichs R (2002) Adiabatic time-dependent density functional methods for
excited state properties. J Chem Phys 117:7433
10. Romaniello P, Sangalli D, Berger JA, Sottile F, Molinari LG, Reining L, Onida G (2009)
Double excitations in finite systems. J Chem Phys 130:044108
11. Gritsenko O, Baerends EJ (2009) Double excitation effects in non-adiabatic time-dependent
theory with an analytic construction of the exchange correlation kernel in the common energy
denominator energy approximation. Phys Chem 11:4640
12. Jacquemin D, Wathelet V, Perpe `te EA, Adamo C (2009) Extensive TD-DFT benchmark:
singlet excited states of organic molecules. J Chem Theory Comput 5:2420
13. Jacquemin D, Perpe `te EA, Ciofini I, Adamo C (2009) Accurate simulation of optical
properties in dyes. Acc Chem Res 42:326
14. Jacquemin D, Perpete EA, Scuseria GE, Ciofini I, Adamo C (2008) TD-DFT performance for
the visible absorption spectra of organic dyes: conventional versus long range hybrids. J
Chem Theory Comput 4:123–135
15. Grimme S, Neese F (2007) Double-hybrid density functional theory for excited electronic
states of molecules. J Chem Phys 127:154116
16. Send R, Valsson O, Filippi C (2011) Electronic excitations of simple cyanine dyes: reconciling density functional and wave function methods. J Chem Theory Comput 7:444
17. Jacquemin D, Perpete EA, Ciofini I, Adamo C, Valero R, Zhao Y, Truhlar DG (2010) On the
performances of the M06 family of density functionals for electronic excitation energies. J
Chem Theory Comput 6:2071
18. Moore B II, Autschbach J (2013) Longest-wavelength electronic excitations of linear cyanines: the role of electron delocalization and of approximations in time-dependent density
functional theory. J Chem Theory Comput 9:4991
19. Schipper PRT, Gritsenko OV, van Gisberger SJA, Baerends EJ (2000) Molecular calculations
of excitation energies and (hyper)polarizabilities with a statistical average of orbital model
exchange-correlation potentials. J Chem Phys 112:1344
20. Likura H, Tsuneda T, Tanai T, Hirao K (2001) A long-range correction scheme for
generalized-gradient-approximation exchange functionals. J Chem Phys 115:3540
21. Song J-W, Watson MA, Hirao K (2009) An improved long-range corrected hybrid functional
with vanishing Hartree–Fock exchange at zero interelectronic distance (LC2gau-BOP). J
Chem Phys 131:144108
22. Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb
potential. J Chem Phys 118:8207
23. Baer R, Neuhauser D (2005) Density functional theory with correct long-range asymptotic
behavior. Phys Rev Lett 94:043002
24. Dreuw A, Weisman J, Head-Gordon M (2003) Long-range charge-transfer excited states in
time-dependent density functional theory require non-local exchange. J Chem Phys 119:2943
25. Tozer D (2003) Relationship between long-range charge transfer error and integer discontinuity error in Kohn Sham theory. J Chem Phys 119:12697
26. Krykunov M, Ziegler T (2013) Self-consistent formulation of constricted variational density
functional theory with orbital relaxation. Implementation and application. J Chem Theory
Comput 9:2761
27. Ziegler T, Krykunov M, Cullen J (2012) The implementation of a self-consistent constricted
variational density functional theory for the description of excited states. J Chem Phys
136:124107
28. Cullen J, Krykunov M, Ziegler T (2011) The formulation of a self-consistent constricted
variational density functional theory for the description of excited states. Chem Phys 391:11
29. Ziegler T, Seth M, Krykunov M, Autschbach J, Wang F (2009) On the relation between timedependent and variational density functional theory approaches for the determination of
excitation energies and transition moments. J Chem Phys 130:154102
30. Krykunov M, Seth M, Ziegler T (2014) Derivation of the RPA (random phase approximation)
equation of ATDDFT (adiabatic time dependent density functional ground state response
92
T. Ziegler et al.
excited state properties. J Chem Phys 117:7433
10. Romaniello P, Sangalli D, Berger JA, Sottile F, Molinari LG, Reining L, Onida G (2009)
Double excitations in finite systems. J Chem Phys 130:044108
11. Gritsenko O, Baerends EJ (2009) Double excitation effects in non-adiabatic time-dependent
theory with an analytic construction of the exchange correlation kernel in the common energy
denominator energy approximation. Phys Chem 11:4640
12. Jacquemin D, Wathelet V, Perpe `te EA, Adamo C (2009) Extensive TD-DFT benchmark:
singlet excited states of organic molecules. J Chem Theory Comput 5:2420
13. Jacquemin D, Perpe `te EA, Ciofini I, Adamo C (2009) Accurate simulation of optical
properties in dyes. Acc Chem Res 42:326
14. Jacquemin D, Perpete EA, Scuseria GE, Ciofini I, Adamo C (2008) TD-DFT performance for
the visible absorption spectra of organic dyes: conventional versus long range hybrids. J
Chem Theory Comput 4:123–135
15. Grimme S, Neese F (2007) Double-hybrid density functional theory for excited electronic
states of molecules. J Chem Phys 127:154116
16. Send R, Valsson O, Filippi C (2011) Electronic excitations of simple cyanine dyes: reconciling density functional and wave function methods. J Chem Theory Comput 7:444
17. Jacquemin D, Perpete EA, Ciofini I, Adamo C, Valero R, Zhao Y, Truhlar DG (2010) On the
performances of the M06 family of density functionals for electronic excitation energies. J
Chem Theory Comput 6:2071
18. Moore B II, Autschbach J (2013) Longest-wavelength electronic excitations of linear cyanines: the role of electron delocalization and of approximations in time-dependent density
functional theory. J Chem Theory Comput 9:4991
19. Schipper PRT, Gritsenko OV, van Gisberger SJA, Baerends EJ (2000) Molecular calculations
of excitation energies and (hyper)polarizabilities with a statistical average of orbital model
exchange-correlation potentials. J Chem Phys 112:1344
20. Likura H, Tsuneda T, Tanai T, Hirao K (2001) A long-range correction scheme for
generalized-gradient-approximation exchange functionals. J Chem Phys 115:3540
21. Song J-W, Watson MA, Hirao K (2009) An improved long-range corrected hybrid functional
with vanishing Hartree–Fock exchange at zero interelectronic distance (LC2gau-BOP). J
Chem Phys 131:144108
22. Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb
potential. J Chem Phys 118:8207
23. Baer R, Neuhauser D (2005) Density functional theory with correct long-range asymptotic
behavior. Phys Rev Lett 94:043002
24. Dreuw A, Weisman J, Head-Gordon M (2003) Long-range charge-transfer excited states in
time-dependent density functional theory require non-local exchange. J Chem Phys 119:2943
25. Tozer D (2003) Relationship between long-range charge transfer error and integer discontinuity error in Kohn Sham theory. J Chem Phys 119:12697
26. Krykunov M, Ziegler T (2013) Self-consistent formulation of constricted variational density
functional theory with orbital relaxation. Implementation and application. J Chem Theory
Comput 9:2761
27. Ziegler T, Krykunov M, Cullen J (2012) The implementation of a self-consistent constricted
variational density functional theory for the description of excited states. J Chem Phys
136:124107
28. Cullen J, Krykunov M, Ziegler T (2011) The formulation of a self-consistent constricted
variational density functional theory for the description of excited states. Chem Phys 391:11
29. Ziegler T, Seth M, Krykunov M, Autschbach J, Wang F (2009) On the relation between timedependent and variational density functional theory approaches for the determination of
excitation energies and transition moments. J Chem Phys 130:154102
30. Krykunov M, Seth M, Ziegler T (2014) Derivation of the RPA (random phase approximation)
equation of ATDDFT (adiabatic time dependent density functional ground state response
92
T. Ziegler et al.