Top Curr Chem (2016) 368: 125–184
DOI: 10.1007/128_2015_624
# Springer International Publishing Switzerland 2015
Published online: 14 May 2015
Reduced Density Matrix Functional Theory
(RDMFT) and Linear Response
Time-Dependent RDMFT (TD-RDMFT)
Katarzyna Pernal and Klaas J.H. Giesbertz
Abstract Recent advances in reduced density matrix functional theory (RDMFT)
and linear response time-dependent reduced density matrix functional theory
(TD-RDMFT) are reviewed. In particular, we present various approaches to
develop approximate density matrix functionals which have been employed in
RDMFT. We discuss the properties and performance of most available density
matrix functionals. Progress in the development of functionals has been paralleled
by formulation of novel RDMFT-based methods for predicting properties of
molecular systems and solids. We give an overview of these methods. The
time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting
practical and generally useful functionals which would work within the adiabatic
approximation. In this chapter we concentrate on the formulation of TD-RDMFT
response equations and various adiabatic approximations. None of the adiabatic
approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals
(PINOs). We focus on applications of the linear response formulations to
two-electron systems, for which the (almost) exact functional is known.
Keywords Density matrix functional Á Reduced density matrix Á Density matrix
functional theory Á Time-dependent density matrix functional Á Electron correlation
K. Pernal (*)
Institute of Physics, ul. Wolczanska 219, 90-924 Lodz, Poland
e-mail: pernalk@gmail.com
K.J.H. Giesbertz
Theoretical Chemistry, VU University, De Boelelaan 1083, 1081 HV Amsterdam,
The Netherlands
e-mail: k.j.h.giesbertz@vu.nl
DOI: 10.1007/128_2015_624
# Springer International Publishing Switzerland 2015
Published online: 14 May 2015
Reduced Density Matrix Functional Theory
(RDMFT) and Linear Response
Time-Dependent RDMFT (TD-RDMFT)
Katarzyna Pernal and Klaas J.H. Giesbertz
Abstract Recent advances in reduced density matrix functional theory (RDMFT)
and linear response time-dependent reduced density matrix functional theory
(TD-RDMFT) are reviewed. In particular, we present various approaches to
develop approximate density matrix functionals which have been employed in
RDMFT. We discuss the properties and performance of most available density
matrix functionals. Progress in the development of functionals has been paralleled
by formulation of novel RDMFT-based methods for predicting properties of
molecular systems and solids. We give an overview of these methods. The
time-dependent extension, TD-RDMFT, is a relatively new theory still awaiting
practical and generally useful functionals which would work within the adiabatic
approximation. In this chapter we concentrate on the formulation of TD-RDMFT
response equations and various adiabatic approximations. None of the adiabatic
approximations is fully satisfactory, so we also discuss a phase-dependent extension to TD-RDMFT employing the concept of phase-including-natural-spinorbitals
(PINOs). We focus on applications of the linear response formulations to
two-electron systems, for which the (almost) exact functional is known.
Keywords Density matrix functional Á Reduced density matrix Á Density matrix
functional theory Á Time-dependent density matrix functional Á Electron correlation
K. Pernal (*)
Institute of Physics, ul. Wolczanska 219, 90-924 Lodz, Poland
e-mail: pernalk@gmail.com
K.J.H. Giesbertz
Theoretical Chemistry, VU University, De Boelelaan 1083, 1081 HV Amsterdam,
The Netherlands
e-mail: k.j.h.giesbertz@vu.nl