Top Curr Chem (2016) 368: 61–96
DOI: 10.1007/128_2014_611
# Springer International Publishing Switzerland 2014
Published online: 20 March 2015
Constricted Variational Density Functional
Theory Approach to the Description
of Excited States
Tom Ziegler, Mykhaylo Krykunov, Issaka Seidu, and Young Choon Park
Abstract We review the theoretical foundation of constricted variational density
functional theory and illustrate its scope through applications.
Keywords Constricted variational density functional theory • Density functional
theory • Time-dependent density functional theory
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2 Constricted Variational Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 63
2.1 Second Order Constricted Variational Density Functional Theory . . . . . . . . . . . . . . . . . . . 64
2.2 Equivalence Between Adiabatic TDDFT and Second Order Constricted
Variational Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3 Perturbative All Order Constricted Variational Density Functional Theory . . . . . . . . . 67
2.4 Self-Consistent All Order Constricted Variational Density Functional Theory . . . . . . 75
2.5 Self-Consistent All Order Constricted Variational Density Functional Theory
with Orbital Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
1 Introduction
Excited states have been studied in wave function theory by both excited state
variational theories and ground state response methods [1, 2]. Either approach has
been used extensively and is considered complementary and, in principle, able to
T. Ziegler (*), M. Krykunov, I. Seidu, and Y.C. Park
Department of Chemistry, University of Calgary, Calgary, AB, Canada T2N1N4
e-mail: ziegler@ucalgary.ca
DOI: 10.1007/128_2014_611
# Springer International Publishing Switzerland 2014
Published online: 20 March 2015
Constricted Variational Density Functional
Theory Approach to the Description
of Excited States
Tom Ziegler, Mykhaylo Krykunov, Issaka Seidu, and Young Choon Park
Abstract We review the theoretical foundation of constricted variational density
functional theory and illustrate its scope through applications.
Keywords Constricted variational density functional theory • Density functional
theory • Time-dependent density functional theory
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2 Constricted Variational Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 63
2.1 Second Order Constricted Variational Density Functional Theory . . . . . . . . . . . . . . . . . . . 64
2.2 Equivalence Between Adiabatic TDDFT and Second Order Constricted
Variational Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3 Perturbative All Order Constricted Variational Density Functional Theory . . . . . . . . . 67
2.4 Self-Consistent All Order Constricted Variational Density Functional Theory . . . . . . 75
2.5 Self-Consistent All Order Constricted Variational Density Functional Theory
with Orbital Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
1 Introduction
Excited states have been studied in wave function theory by both excited state
variational theories and ground state response methods [1, 2]. Either approach has
been used extensively and is considered complementary and, in principle, able to
T. Ziegler (*), M. Krykunov, I. Seidu, and Y.C. Park
Department of Chemistry, University of Calgary, Calgary, AB, Canada T2N1N4
e-mail: ziegler@ucalgary.ca