1 3
Theor Chem Acc (2016) 135:3
DOI 10.1007/s00214-015-1759-7
REGULAR ARTICLE
Orthogonality-constrained Hartree–Fock and perturbation
theory for high-spin open-shell excited states
V. N. Glushkov
1 · X. Assfeld
2
Received: 12 June 2015 / Accepted: 7 November 2015 / Published online: 10 December 2015
© Springer-Verlag Berlin Heidelberg 2015
1 Introduction
It is well known that Hartree–Fock (HF) theory not only
has been proven to be quite suitable for calculations of
ground state (GS) properties of electronic systems, but
has also served as a starting point to develop many-particle approaches which deal with electronic correlation, like
perturbation theory, confi guration interaction methods and
so on (see e.g., [ 1 ]). Therefore, a large number of sophisticated computational approaches have been developed
for the description of the ground states based on the HF
approximation. One of the most popular computational
tools in quantum chemistry for GS calculations is based on
the effectiveness of the HF approximation and the computational advantages of the widely used many-body Møller–
Plesset perturbation theory (MPPT) for correlation effects.
We designate this scheme as “HF + MPPT,” here after
denoted “HF + MP2.”
There is far less reported experience for the HF studies
of electronic excited states (ESs). Especially, highly, doubly
and core hole excited (ionized) states are not often studied.
It is clear that existing ground state self-consistent fi eld
(SCF) methods cannot be directly applied to excited states
of the same symmetry or of the same spin multiplicity as a
lower state because of the so-called variational collapse i.e.,
the optimization procedure will fi nd only the lowest solution
of a given symmetry or a given spin multiplicity. Therefore,
such calculations for ES cannot be considered as routine.
The most powerful scheme for accurate treatment of ESs is
based on multireference methods [ 2 – 8 ]. They typically provide an accuracy of about 0.1 eV but require the expense
of much computational cost. Thus, it can be quite diffi cult
to carry out the corresponding calculations. Such methods are, however, indispensable to study systems where
Abstract We present the orthogonality-constrained Hartree–Fock (HF) method for excited states in a combination
with the Møller–Plesset-like perturbation theory for the
correlation energy. This developed “HF + MP2” formalism
for excited states allows for the treatment of both ground
and excited states in a balanced manner. Unlike a previous
work (Glushkov in Chem Phys Lett 287:189, 1998 ), our
interest has shifted toward highly doubly excited states of
atoms and doubly ionized core hole molecular states which
are attractive from the experimental point of view. The
accuracy of the method is demonstrated by calculations of
more than 30 highly excited states of the He and Li atoms
and about 10 doubly excited core hole states of some diatomic molecules (CO, NO and LiF).
Keywords Excited states · Constrained Hartree–Fock ·
Perturbation theory · Double core hole states · Frozen
orbitals
Published as part of the special collection of articles “Festschrift
in honour of P. R. Surjan.”
* X. Assfeld
xavier.assfeld@univ-lorraine.fr
1
Department of Physics, Electronics and Computer Systems ,
Oles Gonchar Dnipropetrovsk National University ,
Dnipropetrovsk , Ukraine
2
Université de Lorraine Nancy, CNRS, Théorie-ModélisationSimulation, SRSMC , Boulevard des Aiguillettes ,
54506 Vandoeuvre-lès-Nancy , France
189
Reprinted from the journal
Theor Chem Acc (2016) 135:3
DOI 10.1007/s00214-015-1759-7
REGULAR ARTICLE
Orthogonality-constrained Hartree–Fock and perturbation
theory for high-spin open-shell excited states
V. N. Glushkov
1 · X. Assfeld
2
Received: 12 June 2015 / Accepted: 7 November 2015 / Published online: 10 December 2015
© Springer-Verlag Berlin Heidelberg 2015
1 Introduction
It is well known that Hartree–Fock (HF) theory not only
has been proven to be quite suitable for calculations of
ground state (GS) properties of electronic systems, but
has also served as a starting point to develop many-particle approaches which deal with electronic correlation, like
perturbation theory, confi guration interaction methods and
so on (see e.g., [ 1 ]). Therefore, a large number of sophisticated computational approaches have been developed
for the description of the ground states based on the HF
approximation. One of the most popular computational
tools in quantum chemistry for GS calculations is based on
the effectiveness of the HF approximation and the computational advantages of the widely used many-body Møller–
Plesset perturbation theory (MPPT) for correlation effects.
We designate this scheme as “HF + MPPT,” here after
denoted “HF + MP2.”
There is far less reported experience for the HF studies
of electronic excited states (ESs). Especially, highly, doubly
and core hole excited (ionized) states are not often studied.
It is clear that existing ground state self-consistent fi eld
(SCF) methods cannot be directly applied to excited states
of the same symmetry or of the same spin multiplicity as a
lower state because of the so-called variational collapse i.e.,
the optimization procedure will fi nd only the lowest solution
of a given symmetry or a given spin multiplicity. Therefore,
such calculations for ES cannot be considered as routine.
The most powerful scheme for accurate treatment of ESs is
based on multireference methods [ 2 – 8 ]. They typically provide an accuracy of about 0.1 eV but require the expense
of much computational cost. Thus, it can be quite diffi cult
to carry out the corresponding calculations. Such methods are, however, indispensable to study systems where
Abstract We present the orthogonality-constrained Hartree–Fock (HF) method for excited states in a combination
with the Møller–Plesset-like perturbation theory for the
correlation energy. This developed “HF + MP2” formalism
for excited states allows for the treatment of both ground
and excited states in a balanced manner. Unlike a previous
work (Glushkov in Chem Phys Lett 287:189, 1998 ), our
interest has shifted toward highly doubly excited states of
atoms and doubly ionized core hole molecular states which
are attractive from the experimental point of view. The
accuracy of the method is demonstrated by calculations of
more than 30 highly excited states of the He and Li atoms
and about 10 doubly excited core hole states of some diatomic molecules (CO, NO and LiF).
Keywords Excited states · Constrained Hartree–Fock ·
Perturbation theory · Double core hole states · Frozen
orbitals
Published as part of the special collection of articles “Festschrift
in honour of P. R. Surjan.”
* X. Assfeld
xavier.assfeld@univ-lorraine.fr
1
Department of Physics, Electronics and Computer Systems ,
Oles Gonchar Dnipropetrovsk National University ,
Dnipropetrovsk , Ukraine
2
Université de Lorraine Nancy, CNRS, Théorie-ModélisationSimulation, SRSMC , Boulevard des Aiguillettes ,
54506 Vandoeuvre-lès-Nancy , France
189
Reprinted from the journal