130. Neugebauer J, Baerends E (2004) Vibronic coupling and double excitations in linear response
time-dependent density functional calculations: dipole allowed states of N 2 . J Chem Phys 121
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131. Yvon J (1935) Theorie statistique des fluides et l’equation et l’equation d’etat (French). In:
Actes Sientifique et Industrie, vol. 203. Hermann, Paris
132. Bogoliubov NN (1946) Kinetic equations. J Phys USSR 10(3):265 (in English)
133. Bogoliubov NN (1946) Kinetic equations. J Exp Theor Phys 16(8):691 (in Russian)
134. Kirkwood JG (1946) The statistical mechanical theory of transport processes I. General
theory. J Chem Phys 14(3):180
135. Born M, Green HS (1946) A general kinetic theory of liquids. I. The molecular distribution
functions. Proc R Soc Med 188(1012):10–18
136. Kirkwood JG (1947) The statistical mechanical theory of transport processes II. Transport in
gases. J Chem Phys 15(1):72
137. Bogoliubov NN, Gurov KP (1947) Kinetic equations in quantum mechanics (rus.). J Exp
Theor Phys 17(7):614
138. Runge E, Gross EKU (1984) Density-functional theory for time-dependent systems. Phys
Rev Lett 52(12):997. doi:10.1103/PhysRevLett.52.997
139. Ruggenthaler M, van Leeuwen R (2011) Global fixed-point proof of time-dependent densityfunctional theory. Europhys Lett 95(1):13001. doi:10.1209/0295-5075/95/13001
140. Ruggenthaler M, Giesbertz KJH, Penz M, van Leeuwen R (2012) Density-potential mappings
in quantum dynamics. Phys Rev A 85(5):052504. doi:10.1103/PhysRevA.85.052504
141. Giesbertz KJH, Baerends EJ, Gritsenko OV (2008) Charge transfer, double and bondbreaking excitations with time-dependent density matrix functional theory. Phys Rev Lett
101:033004. doi:10.1103/PhysRevLett.101.033004
142. Giesbertz KJH, Pernal K, Gritsenko OV, Baerends EJ (2009) Excitation energies with timedependent density matrix functional theory: singlet two-electron systems. J Chem Phys 130
(11):114104. doi:10.1063/1.3079821
143. Peuckert V (1978) A new approximation method for electron systems. J Phys C 11(24):4945
144. Giesbertz KJH, Gritsenko OV, Baerends EJ (2010) Response calculations with an independent particle system with an exact one-particle density matrix. Phys Rev Lett 105(1):013002.
doi:10.1103/PhysRevLett.105.013002
145. Giesbertz KJH, Gritsenko OV, Baerends EJ (2010) The adiabatic approximation in timedependent density matrix functional theory: response properties from dynamics of phaseincluding natural orbitals. J Chem Phys 133(17):174119. doi:10.1063/1.3499601
146. Requist R, Pankratov O (2011) Time-dependent occupation numbers in reduced-densitymatrix-functional theory: application to an interacting Landau–Zener model. Phys Rev A 83
(5):052510. doi:10.1103/PhysRevA.83.052510
147. Giesbertz KJH, Gritsenko OV, Baerends EJ (2014) Response calculations based on an
independent particle system with the exact one-particle density matrix: polarizabilities.
J Chem Phys 140(18):18A517. doi:10.1063/1.4867000
148. Giesbertz KJH, Gritsenko OV, Baerends EJ (2012) Time-dependent reduced density matrix
functional theory. In: Marques MAL, Maitra N, Nogueira F, Gross EKU, Rubio A (eds)
Fundamentals of time-dependent density functional theory, vol 837, Lecture notes in physics.
Springer, Berlin, pp 485–498. doi:10.1007/978-3-642-23518-4
149. Requist R, Pankratov O (2010) Adiabatic approximation in time-dependent reduced-densitymatrix functional theory. Phys Rev A 81(4):042519. doi:10.1103/PhysRevA.81.042519
150. Lehmann H (1954) U ¨ ber Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder. Nuovo Cimento 11(4):342
151. Requist R (2012) Hamiltonian formulation of nonequilibrium quantum dynamics: geometric
structure of the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy. Phys Rev A 86
(2):022117. doi:10.1103/PhysRevA.86.02211
182
K. Pernal and K.J.H. Giesbertz
time-dependent density functional calculations: dipole allowed states of N 2 . J Chem Phys 121
(13):6155. doi:10.1063/1.1785775
131. Yvon J (1935) Theorie statistique des fluides et l’equation et l’equation d’etat (French). In:
Actes Sientifique et Industrie, vol. 203. Hermann, Paris
132. Bogoliubov NN (1946) Kinetic equations. J Phys USSR 10(3):265 (in English)
133. Bogoliubov NN (1946) Kinetic equations. J Exp Theor Phys 16(8):691 (in Russian)
134. Kirkwood JG (1946) The statistical mechanical theory of transport processes I. General
theory. J Chem Phys 14(3):180
135. Born M, Green HS (1946) A general kinetic theory of liquids. I. The molecular distribution
functions. Proc R Soc Med 188(1012):10–18
136. Kirkwood JG (1947) The statistical mechanical theory of transport processes II. Transport in
gases. J Chem Phys 15(1):72
137. Bogoliubov NN, Gurov KP (1947) Kinetic equations in quantum mechanics (rus.). J Exp
Theor Phys 17(7):614
138. Runge E, Gross EKU (1984) Density-functional theory for time-dependent systems. Phys
Rev Lett 52(12):997. doi:10.1103/PhysRevLett.52.997
139. Ruggenthaler M, van Leeuwen R (2011) Global fixed-point proof of time-dependent densityfunctional theory. Europhys Lett 95(1):13001. doi:10.1209/0295-5075/95/13001
140. Ruggenthaler M, Giesbertz KJH, Penz M, van Leeuwen R (2012) Density-potential mappings
in quantum dynamics. Phys Rev A 85(5):052504. doi:10.1103/PhysRevA.85.052504
141. Giesbertz KJH, Baerends EJ, Gritsenko OV (2008) Charge transfer, double and bondbreaking excitations with time-dependent density matrix functional theory. Phys Rev Lett
101:033004. doi:10.1103/PhysRevLett.101.033004
142. Giesbertz KJH, Pernal K, Gritsenko OV, Baerends EJ (2009) Excitation energies with timedependent density matrix functional theory: singlet two-electron systems. J Chem Phys 130
(11):114104. doi:10.1063/1.3079821
143. Peuckert V (1978) A new approximation method for electron systems. J Phys C 11(24):4945
144. Giesbertz KJH, Gritsenko OV, Baerends EJ (2010) Response calculations with an independent particle system with an exact one-particle density matrix. Phys Rev Lett 105(1):013002.
doi:10.1103/PhysRevLett.105.013002
145. Giesbertz KJH, Gritsenko OV, Baerends EJ (2010) The adiabatic approximation in timedependent density matrix functional theory: response properties from dynamics of phaseincluding natural orbitals. J Chem Phys 133(17):174119. doi:10.1063/1.3499601
146. Requist R, Pankratov O (2011) Time-dependent occupation numbers in reduced-densitymatrix-functional theory: application to an interacting Landau–Zener model. Phys Rev A 83
(5):052510. doi:10.1103/PhysRevA.83.052510
147. Giesbertz KJH, Gritsenko OV, Baerends EJ (2014) Response calculations based on an
independent particle system with the exact one-particle density matrix: polarizabilities.
J Chem Phys 140(18):18A517. doi:10.1063/1.4867000
148. Giesbertz KJH, Gritsenko OV, Baerends EJ (2012) Time-dependent reduced density matrix
functional theory. In: Marques MAL, Maitra N, Nogueira F, Gross EKU, Rubio A (eds)
Fundamentals of time-dependent density functional theory, vol 837, Lecture notes in physics.
Springer, Berlin, pp 485–498. doi:10.1007/978-3-642-23518-4
149. Requist R, Pankratov O (2010) Adiabatic approximation in time-dependent reduced-densitymatrix functional theory. Phys Rev A 81(4):042519. doi:10.1103/PhysRevA.81.042519
150. Lehmann H (1954) U ¨ ber Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder. Nuovo Cimento 11(4):342
151. Requist R (2012) Hamiltonian formulation of nonequilibrium quantum dynamics: geometric
structure of the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy. Phys Rev A 86
(2):022117. doi:10.1103/PhysRevA.86.02211
182
K. Pernal and K.J.H. Giesbertz