Top Curr Chem (2016) 368: 97–124
DOI: 10.1007/128_2015_630
# Springer International Publishing Switzerland 2015
Published online: 24 April 2015
Ensemble DFT Approach to Excited States
of Strongly Correlated Molecular Systems
Michael Filatov
Abstract Ensemble density functional theory (DFT) is a novel time-independent
formalism for obtaining excitation energies of many-body fermionic systems. A
considerable advantage of ensemble DFT over the more common Kohn–Sham
(KS) DFT and time-dependent DFT formalisms is that it enables one to account
for strong non-dynamic electron correlation in the ground and excited states of
molecular systems in a transparent and accurate fashion. Despite its positive aspects,
ensemble DFT has not so far found its way into the repertoire of methods of modern
computational chemistry, probably because of the perceived lack of practically
affordable implementations of the theory. The spin-restricted ensemble-referenced
KS (REKS) method is perhaps the first computationally feasible implementation of
the ideas behind ensemble DFT which enables one to describe accurately electronic
transitions in a wide class of molecular systems, including strongly correlated
molecules (biradicals, molecules undergoing bond breaking/formation), extended
π-conjugated systems, donor–acceptor charge transfer adducts, etc.
Keywords Charge transfer excitation energies Á Ensemble density functional
theory Á Excited electronic states Á Non-dynamic electron correlation
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2 Ensemble DFT . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 99
3 REKS Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.1 REKS Method for Ground States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.2 REKS Method for Excited States: SA-REKS and SI-SA-REKS . . . . . . . . . . . . . . . . . . . . 111
4 Applications of the REKS Method to Excited States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
M. Filatov (*)
Institut fu ¨r Physikalische und Theoretische Chemie, Universita ¨t Bonn, Beringstr. 4, 53115
Bonn, Germany
e-mail: mike.filatov@gmail.com
DOI: 10.1007/128_2015_630
# Springer International Publishing Switzerland 2015
Published online: 24 April 2015
Ensemble DFT Approach to Excited States
of Strongly Correlated Molecular Systems
Michael Filatov
Abstract Ensemble density functional theory (DFT) is a novel time-independent
formalism for obtaining excitation energies of many-body fermionic systems. A
considerable advantage of ensemble DFT over the more common Kohn–Sham
(KS) DFT and time-dependent DFT formalisms is that it enables one to account
for strong non-dynamic electron correlation in the ground and excited states of
molecular systems in a transparent and accurate fashion. Despite its positive aspects,
ensemble DFT has not so far found its way into the repertoire of methods of modern
computational chemistry, probably because of the perceived lack of practically
affordable implementations of the theory. The spin-restricted ensemble-referenced
KS (REKS) method is perhaps the first computationally feasible implementation of
the ideas behind ensemble DFT which enables one to describe accurately electronic
transitions in a wide class of molecular systems, including strongly correlated
molecules (biradicals, molecules undergoing bond breaking/formation), extended
π-conjugated systems, donor–acceptor charge transfer adducts, etc.
Keywords Charge transfer excitation energies Á Ensemble density functional
theory Á Excited electronic states Á Non-dynamic electron correlation
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
2 Ensemble DFT . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 99
3 REKS Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.1 REKS Method for Ground States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.2 REKS Method for Excited States: SA-REKS and SI-SA-REKS . . . . . . . . . . . . . . . . . . . . 111
4 Applications of the REKS Method to Excited States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
M. Filatov (*)
Institut fu ¨r Physikalische und Theoretische Chemie, Universita ¨t Bonn, Beringstr. 4, 53115
Bonn, Germany
e-mail: mike.filatov@gmail.com