54. Oliveira LN, Gross EKU, Kohn W (1988) Density-functional theory for ensembles of
fractionally occupied states. II. Application to the He atom. Phys Rev A 37:2821
55. Filatov M, Shaik S (1998) Spin-restricted density functional approach to the open-shell
problem. Chem Phys Lett 288:689
56. Filatov M, Shaik S (1999) Spin-restricted density functional approach to the open-shell
problem. Chem Phys Lett 304:429
57. Filatov M, Huix-Rotllant M (2014) Description of electron transfer in the ground and excited
states of organic donor–acceptor systems by single-reference and multi-reference density
functional methods. J Chem Phys 141:024112
58. Gidopoulos NI, Papaconstantinou PG, Gross EKU (2002) Density-functional theory for
ensembles of fractionally occupied states. II. Application to the He atom. Phys Rev Lett
88:03300
59. Gross EKU, Oliveira LN, Kohn W (1988) Spurious interactions, and their correction, in the
ensemble-Kohn-Sham scheme for excited states. Phys Rev A 37:2809
60. Levy M, Nagy A (1999) Variational density-functional theory for an individual excited state.
Phys Rev Lett 83:4361
61. Go ¨rling A, Levy M (1993) Correlation-energy functional and its high-density limit obtained
from a coupling-constant perturbation expansion. Phys Rev B 47:13105
62. Ziegler T, Krykunov M, Autschbach J (2014) Derivation of the RPA (random phase approximation) equation of ATDDFT (adiabatic time dependent density functional ground state
response theory) from an excited state variational approach based on the ground state
functional. J Chem Theory Comput 10:3980
63. Ziegler T, Krykunov M, Cullen J (2011) The application of constricted variational density
functional theory to excitations involving electron transitions from occupied lone-pair
orbitals to virtual π* orbitals. J Chem Theory Comput 7:2485
64. Krykunov M, Grimme S, Ziegler T (2012) Accurate theoretical description of the
1
L a and
1
L b
excited states in acenes using the all order constricted variational density functional theory
method and the local density approximation. J Chem Theory Comput 8:4434
65. Zhekova H, Krykunov M, Autschbach J, Ziegler T (2014) Applications of time dependent
and time independent density functional theory to the first π to π* transition in cyanine dyes. J
Chem Theory Comput 10:3299
66. Seidu I, Krykunov M, Ziegler T (2014) Applications of time--dependent and time-- independent density functional theory to Rydberg transitions. J Phys Chem A ASAP. doi:10.1021/
jp5082802
67. Wang F, Ziegler T (2004) Time-dependent density functional theory based on a noncollinear
formulation of the exchange-correlation potential. J Chem Phys 121:12191-1
68. Wang F, Ziegler T (2005) The performance of time-dependent density functional theory
based on a noncollinear exchange-correlation potential in the calculations of excitation
energies. J Chem Phys 122:074109-1
69. Wang F, Ziegler T (2006) Use of noncollinear exchange-correlation potentials in multiplet
resolutions by time-dependent density functional theory. Int J Quant Chem 106:2545–2550
70. Hirata S, Head-Gordon M (1999) Time-dependent density functional theory within the
Tamm-Dancoff approximation. Chem Phys Lett 291:314
71. Amos AT, Hall GG (1961) Single determinant wave functions. Proc R Soc A 263:483
72. Martin RLJ (2003) Natural transition orbitals. J Chem Phys 118:4775
73. Schreiber M, Silva-Junior M, Sauer S, Thiel W (2008) Benchmarks for electronically excited
states: CASPT2, CC2, CCSD, and CC3. J Chem Phys 128:134110
74. Platt JR (1949) Classification of spectra of Cata condensed hydrocarbons. J Chem Phys
17:484
75. Grimme S, Parac M (2003) Substantial errors from time-dependent density functional theory
for the calculation of excited states of large π systems. Chemphyschem 4:292
76. Parac M, Grimme S (2003) TDDFT of the lowest excitation energies of polycyclic aromatic
hydrocarbons. Chem Phys 292:11
94
T. Ziegler et al.
fractionally occupied states. II. Application to the He atom. Phys Rev A 37:2821
55. Filatov M, Shaik S (1998) Spin-restricted density functional approach to the open-shell
problem. Chem Phys Lett 288:689
56. Filatov M, Shaik S (1999) Spin-restricted density functional approach to the open-shell
problem. Chem Phys Lett 304:429
57. Filatov M, Huix-Rotllant M (2014) Description of electron transfer in the ground and excited
states of organic donor–acceptor systems by single-reference and multi-reference density
functional methods. J Chem Phys 141:024112
58. Gidopoulos NI, Papaconstantinou PG, Gross EKU (2002) Density-functional theory for
ensembles of fractionally occupied states. II. Application to the He atom. Phys Rev Lett
88:03300
59. Gross EKU, Oliveira LN, Kohn W (1988) Spurious interactions, and their correction, in the
ensemble-Kohn-Sham scheme for excited states. Phys Rev A 37:2809
60. Levy M, Nagy A (1999) Variational density-functional theory for an individual excited state.
Phys Rev Lett 83:4361
61. Go ¨rling A, Levy M (1993) Correlation-energy functional and its high-density limit obtained
from a coupling-constant perturbation expansion. Phys Rev B 47:13105
62. Ziegler T, Krykunov M, Autschbach J (2014) Derivation of the RPA (random phase approximation) equation of ATDDFT (adiabatic time dependent density functional ground state
response theory) from an excited state variational approach based on the ground state
functional. J Chem Theory Comput 10:3980
63. Ziegler T, Krykunov M, Cullen J (2011) The application of constricted variational density
functional theory to excitations involving electron transitions from occupied lone-pair
orbitals to virtual π* orbitals. J Chem Theory Comput 7:2485
64. Krykunov M, Grimme S, Ziegler T (2012) Accurate theoretical description of the
1
L a and
1
L b
excited states in acenes using the all order constricted variational density functional theory
method and the local density approximation. J Chem Theory Comput 8:4434
65. Zhekova H, Krykunov M, Autschbach J, Ziegler T (2014) Applications of time dependent
and time independent density functional theory to the first π to π* transition in cyanine dyes. J
Chem Theory Comput 10:3299
66. Seidu I, Krykunov M, Ziegler T (2014) Applications of time--dependent and time-- independent density functional theory to Rydberg transitions. J Phys Chem A ASAP. doi:10.1021/
jp5082802
67. Wang F, Ziegler T (2004) Time-dependent density functional theory based on a noncollinear
formulation of the exchange-correlation potential. J Chem Phys 121:12191-1
68. Wang F, Ziegler T (2005) The performance of time-dependent density functional theory
based on a noncollinear exchange-correlation potential in the calculations of excitation
energies. J Chem Phys 122:074109-1
69. Wang F, Ziegler T (2006) Use of noncollinear exchange-correlation potentials in multiplet
resolutions by time-dependent density functional theory. Int J Quant Chem 106:2545–2550
70. Hirata S, Head-Gordon M (1999) Time-dependent density functional theory within the
Tamm-Dancoff approximation. Chem Phys Lett 291:314
71. Amos AT, Hall GG (1961) Single determinant wave functions. Proc R Soc A 263:483
72. Martin RLJ (2003) Natural transition orbitals. J Chem Phys 118:4775
73. Schreiber M, Silva-Junior M, Sauer S, Thiel W (2008) Benchmarks for electronically excited
states: CASPT2, CC2, CCSD, and CC3. J Chem Phys 128:134110
74. Platt JR (1949) Classification of spectra of Cata condensed hydrocarbons. J Chem Phys
17:484
75. Grimme S, Parac M (2003) Substantial errors from time-dependent density functional theory
for the calculation of excited states of large π systems. Chemphyschem 4:292
76. Parac M, Grimme S (2003) TDDFT of the lowest excitation energies of polycyclic aromatic
hydrocarbons. Chem Phys 292:11
94
T. Ziegler et al.