1 3
Theor Chem Acc (2015) 134:74
DOI 10.1007/s00214-015-1670-2
REGULAR ARTICLE
Unconventional bond functions for quantum chemical
calculations
Dávid Mester
1 · József Csontos
1 · Mihály Kállay
1
Received: 30 March 2015 / Accepted: 16 April 2015 / Published online: 15 May 2015
© Springer-Verlag Berlin Heidelberg 2015
sets is signifi cantly lower. The accuracy of the computed
energies can be further increased by about 15 % if EGTO
BFs are used.
Keywords Bond functions · Ellipsoidal Gaussian
functions · Polarization functions · Unconventional basis
functions
1 Introduction
In quantum chemistry, the computational cost of a theoretical investigation is substantially infl uenced by the size of
the basis set selected. On the other hand, the “goodness” of
the basis set for a given property can decide about the quality of the work. The most frequently used basis sets, such as
those developed by Pople et al. [ 1 – 6 ], Ahlrichs et al. [ 7 – 9 ],
and Dunning et al. [ 10 – 13 ], consist of atom-centered (AC)
Gaussian-type orbitals (GTO), which were proposed by
Boys [ 14 ]. Polarization functions fi rst have been introduced
to help in describing the non-spherical symmetry of the
atoms in the molecular environment [ 15 ]. However, beside
characterizing molecular polarization effects, their use is
also inevitable in the accurate treatment of the electron correlation problem [ 16 , 17 ]. Nevertheless, their addition to
the basis set, due to their higher angular momentum, considerably increases the number and the computational complexity of the evaluation of molecular integrals. It is reasonable to assume that the substitution of AC polarization
functions with bond-centered (BC) s - and p -type Gaussians
(bond functions, BFs) may provide a more natural account
of the polarized molecular environment, and less BC than
AC functions are needed to achieve the same effect.
Several studies with BF basis sets have been reported
about replacing the polarization basis functions with BC
Abstract New types of bond function (BF) basis sets are
proposed and tested for quantum chemical applications.
First, BF basis sets constituted of conventional Gaussiantype orbitals (GTO) are considered. Both the exponents
and the positions of the BFs are optimized, but, in contrast
to previous studies, the position of each BF shell is varied
separately. Second, new types of basis functions, the general ellipsoidal Gaussian-type orbitals (EGTOs), are proposed for quantum chemical applications. The EGTOs are
distorted spherical GTOs and, as such, are expected to be
well suited for describing the polarized charge densities
in molecular environments. EGTOs can be used either as
atom-centered (AC) basis functions or as BFs. In this study,
the latter possibility is explored, and BF basis sets including EGTOs are optimized and compared to those containing only conventional GTO BFs. The performance of the
developed GTO and EGTO BF basis sets is assessed for
Hartree–Fock and density functional calculations against
conventional AC GTO basis sets. Our results show that
using GTO BF basis sets, the results are signifi cantly
improved, while the number of the basis functions can be
decreased by about 10 %, which is not dramatic; however,
the average angular momentum quantum number in the BF
Published as part of the special collection of articles “Festschrift
in honour of P. R. Surjan.”
This paper is dedicated to Professor Péter R. Surján on the happy
occasion of his 60th birthday.
* Mihály Kállay
kallay@mail.bme.hu
1
MTA-BME Lendület Quantum Chemistry Research Group,
Department of Physical Chemistry and Materials Science ,
Budapest University of Technology and Economics ,
P.O. Box 91 , Budapest 1521 , Hungary
205
Reprinted from the journal
Theor Chem Acc (2015) 134:74
DOI 10.1007/s00214-015-1670-2
REGULAR ARTICLE
Unconventional bond functions for quantum chemical
calculations
Dávid Mester
1 · József Csontos
1 · Mihály Kállay
1
Received: 30 March 2015 / Accepted: 16 April 2015 / Published online: 15 May 2015
© Springer-Verlag Berlin Heidelberg 2015
sets is signifi cantly lower. The accuracy of the computed
energies can be further increased by about 15 % if EGTO
BFs are used.
Keywords Bond functions · Ellipsoidal Gaussian
functions · Polarization functions · Unconventional basis
functions
1 Introduction
In quantum chemistry, the computational cost of a theoretical investigation is substantially infl uenced by the size of
the basis set selected. On the other hand, the “goodness” of
the basis set for a given property can decide about the quality of the work. The most frequently used basis sets, such as
those developed by Pople et al. [ 1 – 6 ], Ahlrichs et al. [ 7 – 9 ],
and Dunning et al. [ 10 – 13 ], consist of atom-centered (AC)
Gaussian-type orbitals (GTO), which were proposed by
Boys [ 14 ]. Polarization functions fi rst have been introduced
to help in describing the non-spherical symmetry of the
atoms in the molecular environment [ 15 ]. However, beside
characterizing molecular polarization effects, their use is
also inevitable in the accurate treatment of the electron correlation problem [ 16 , 17 ]. Nevertheless, their addition to
the basis set, due to their higher angular momentum, considerably increases the number and the computational complexity of the evaluation of molecular integrals. It is reasonable to assume that the substitution of AC polarization
functions with bond-centered (BC) s - and p -type Gaussians
(bond functions, BFs) may provide a more natural account
of the polarized molecular environment, and less BC than
AC functions are needed to achieve the same effect.
Several studies with BF basis sets have been reported
about replacing the polarization basis functions with BC
Abstract New types of bond function (BF) basis sets are
proposed and tested for quantum chemical applications.
First, BF basis sets constituted of conventional Gaussiantype orbitals (GTO) are considered. Both the exponents
and the positions of the BFs are optimized, but, in contrast
to previous studies, the position of each BF shell is varied
separately. Second, new types of basis functions, the general ellipsoidal Gaussian-type orbitals (EGTOs), are proposed for quantum chemical applications. The EGTOs are
distorted spherical GTOs and, as such, are expected to be
well suited for describing the polarized charge densities
in molecular environments. EGTOs can be used either as
atom-centered (AC) basis functions or as BFs. In this study,
the latter possibility is explored, and BF basis sets including EGTOs are optimized and compared to those containing only conventional GTO BFs. The performance of the
developed GTO and EGTO BF basis sets is assessed for
Hartree–Fock and density functional calculations against
conventional AC GTO basis sets. Our results show that
using GTO BF basis sets, the results are signifi cantly
improved, while the number of the basis functions can be
decreased by about 10 %, which is not dramatic; however,
the average angular momentum quantum number in the BF
Published as part of the special collection of articles “Festschrift
in honour of P. R. Surjan.”
This paper is dedicated to Professor Péter R. Surján on the happy
occasion of his 60th birthday.
* Mihály Kállay
kallay@mail.bme.hu
1
MTA-BME Lendület Quantum Chemistry Research Group,
Department of Physical Chemistry and Materials Science ,
Budapest University of Technology and Economics ,
P.O. Box 91 , Budapest 1521 , Hungary
205
Reprinted from the journal