91. Pernal K, Baerends EJ (2006) Coupled-perturbed density-matrix functional theory equations.
Application to static polarizabilities. J Chem Phys 124(1):14102. doi:10.1063/1.2137325
92. Lopez X, Piris M, Nakano M, Champagne B (2014) Natural orbital functional calculations of
molecular polarizabilities and second hyperpolarizabilities. The hydrogen molecule as a test
case. J Phys B At Mol Opt Phys 47(1):015101. doi:10.1088/0953-4075/47/1/015101
93. Leiva P, Piris M (2005) Assessment of a new approach for the two-electron cumulant in
natural-orbital-functional theory. J Chem Phys 123(21):214102. doi:10.1063/1.2135289
94. Leiva P, Piris M (2005) Natural orbital functional theory: ionization potentials, equilibrium
geometries and vibrational frequencies. J Mol Struct (THEOCHEM) 719(1–3):63–67.
doi:10.1016/j.theochem.2005.01.023
95. Zarkadoula EN, Sharma S, Dewhurst JK, Gross EKU, Lathiotakis NN (2012) Ionization
potentials and electron affinities from reduced-density-matrix functional theory. Phys Rev A
85(3):032504. doi:10.1103/PhysRevA.85.032504
96. Smith DW, Day OW (1975) Extension of Koopmans theorem. I. Derivation. J Chem Phys 62
(1):113–114. doi:10.1063/1.430253
97. Day OW, Smith DW, Morrison RC (1975) Extension of Koopmans theorem. II. Accurate
ionization energies from correlated wavefunctions for closed-shell atoms. J Chem Phys 62
(1):115–119. doi:10.1063/1.430254
98. Morrell MM, Parr RG, Levy M (1975) Calculation of ionization-potentials from density
matrices and natural functions, and long-range behavior of natural orbitals and electrondensity. J Chem Phys 62(2):549–554. doi:10.1063/1.430509
99. Pernal K, Cioslowski J (2005) Ionization potentials from the extended Koopmans’ theorem
applied to density matrix functional theory. Chem Phys Lett 412(1–3):71–75. doi:10.1016/j.
cplett.2005.06.103
100. Piris M, Matxain JM, Lopez X, Ugalde JM (2012) The extended Koopmans’ theorem:
vertical ionization potentials from natural orbital functional theory. J Chem Phys 136
(17):174116. doi:10.1063/1.4709769
101. Gritsenko OV, Braida B, Baerends EJ (2003) Physical interpretation and evaluation of the
Kohn-Sham and Dyson components of the ε-I relations between the Kohn-Sham orbital
energies and the ionization potentials. J Chem Phys 119(4):1937–1950. doi:10.1063/1.
1582839
102. Chong DP, Gritsenko OV, Baerends EJ (2002) Interpretation of the Kohn-Sham orbital
energies as approximate vertical ionization potentials. J Chem Phys 116(5):1760–1772.
doi:10.1063/1.1430255
103. Pernal K (2005) Effective potential for natural spin orbitals. Phys Rev Lett 94(23):233002.
doi:10.1103/PhysRevLett.94.233002
104. Lathiotakis NN, Helbig N, Rubio A, Gidopoulos NI (2014) Local reduced-density-matrixfunctional theory: incorporating static correlation effects in Kohn-Sham equations. Phys Rev
A 90(3):032511. doi:10.1103/PhysRevA.90.032511
105. Lathiotakis NN, Helbig N, Rubio A, Gidopoulos NI (2014) Quasi-particle energy spectra in
local reduced density matrix functional theory. J Chem Phys 141(16):164120
106. Helbig N, Lathiotakis NN, Albrecht M, Gross EKU (2007) Discontinuity of the chemical
potential in reduced-density-matrix-functional theory. EPL 77(6):67003. doi:10.1209/02955075/77/67003
107. Helbig N, Lathiotakis NN, Gross EKU (2009) Discontinuity of the chemical potential in
reduced-density-matrix-functional theory for open-shell systems. Phys Rev A 79(2):022504.
doi:10.1103/PhysRevA.79.022504
108. Lathiotakis NN, Sharma S, Helbig N, Dewhurst JK, Marques MAL, Eich F, Baldsiefen T,
Zacarias A, Gross EKU (2010) Discontinuities of the chemical potential in reduced density
matrix functional theory. Z Phys Chem 224(3–4, SI):467–480. doi:10.1524/zpch.2010.6118
109. Cance `s E, Pernal K (2008) Projected gradient algorithms for Hartree-Fock and density matrix
functional theory calculations. J Chem Phys 128(13):134108. doi:10.1063/1.2888550
180
K. Pernal and K.J.H. Giesbertz
Application to static polarizabilities. J Chem Phys 124(1):14102. doi:10.1063/1.2137325
92. Lopez X, Piris M, Nakano M, Champagne B (2014) Natural orbital functional calculations of
molecular polarizabilities and second hyperpolarizabilities. The hydrogen molecule as a test
case. J Phys B At Mol Opt Phys 47(1):015101. doi:10.1088/0953-4075/47/1/015101
93. Leiva P, Piris M (2005) Assessment of a new approach for the two-electron cumulant in
natural-orbital-functional theory. J Chem Phys 123(21):214102. doi:10.1063/1.2135289
94. Leiva P, Piris M (2005) Natural orbital functional theory: ionization potentials, equilibrium
geometries and vibrational frequencies. J Mol Struct (THEOCHEM) 719(1–3):63–67.
doi:10.1016/j.theochem.2005.01.023
95. Zarkadoula EN, Sharma S, Dewhurst JK, Gross EKU, Lathiotakis NN (2012) Ionization
potentials and electron affinities from reduced-density-matrix functional theory. Phys Rev A
85(3):032504. doi:10.1103/PhysRevA.85.032504
96. Smith DW, Day OW (1975) Extension of Koopmans theorem. I. Derivation. J Chem Phys 62
(1):113–114. doi:10.1063/1.430253
97. Day OW, Smith DW, Morrison RC (1975) Extension of Koopmans theorem. II. Accurate
ionization energies from correlated wavefunctions for closed-shell atoms. J Chem Phys 62
(1):115–119. doi:10.1063/1.430254
98. Morrell MM, Parr RG, Levy M (1975) Calculation of ionization-potentials from density
matrices and natural functions, and long-range behavior of natural orbitals and electrondensity. J Chem Phys 62(2):549–554. doi:10.1063/1.430509
99. Pernal K, Cioslowski J (2005) Ionization potentials from the extended Koopmans’ theorem
applied to density matrix functional theory. Chem Phys Lett 412(1–3):71–75. doi:10.1016/j.
cplett.2005.06.103
100. Piris M, Matxain JM, Lopez X, Ugalde JM (2012) The extended Koopmans’ theorem:
vertical ionization potentials from natural orbital functional theory. J Chem Phys 136
(17):174116. doi:10.1063/1.4709769
101. Gritsenko OV, Braida B, Baerends EJ (2003) Physical interpretation and evaluation of the
Kohn-Sham and Dyson components of the ε-I relations between the Kohn-Sham orbital
energies and the ionization potentials. J Chem Phys 119(4):1937–1950. doi:10.1063/1.
1582839
102. Chong DP, Gritsenko OV, Baerends EJ (2002) Interpretation of the Kohn-Sham orbital
energies as approximate vertical ionization potentials. J Chem Phys 116(5):1760–1772.
doi:10.1063/1.1430255
103. Pernal K (2005) Effective potential for natural spin orbitals. Phys Rev Lett 94(23):233002.
doi:10.1103/PhysRevLett.94.233002
104. Lathiotakis NN, Helbig N, Rubio A, Gidopoulos NI (2014) Local reduced-density-matrixfunctional theory: incorporating static correlation effects in Kohn-Sham equations. Phys Rev
A 90(3):032511. doi:10.1103/PhysRevA.90.032511
105. Lathiotakis NN, Helbig N, Rubio A, Gidopoulos NI (2014) Quasi-particle energy spectra in
local reduced density matrix functional theory. J Chem Phys 141(16):164120
106. Helbig N, Lathiotakis NN, Albrecht M, Gross EKU (2007) Discontinuity of the chemical
potential in reduced-density-matrix-functional theory. EPL 77(6):67003. doi:10.1209/02955075/77/67003
107. Helbig N, Lathiotakis NN, Gross EKU (2009) Discontinuity of the chemical potential in
reduced-density-matrix-functional theory for open-shell systems. Phys Rev A 79(2):022504.
doi:10.1103/PhysRevA.79.022504
108. Lathiotakis NN, Sharma S, Helbig N, Dewhurst JK, Marques MAL, Eich F, Baldsiefen T,
Zacarias A, Gross EKU (2010) Discontinuities of the chemical potential in reduced density
matrix functional theory. Z Phys Chem 224(3–4, SI):467–480. doi:10.1524/zpch.2010.6118
109. Cance `s E, Pernal K (2008) Projected gradient algorithms for Hartree-Fock and density matrix
functional theory calculations. J Chem Phys 128(13):134108. doi:10.1063/1.2888550
180
K. Pernal and K.J.H. Giesbertz