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Theoretical Chemistry Accounts (2019) 138:9
https://doi.org/10.1007/s00214-018-2386-x
REGULAR ARTICLE
Atomic orbitals revisited: generalized hydrogen‑like basis sets
for2nd‑row elements
IlyaV.Popov1,2· AndreiL.Tchougrée1,2,3
Received: 16 June 2018 / Accepted: 15 November 2018 / Published online: 4 December 2018
© Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract
In the present work, we revisit the problem of atomic orbitals from the positions mostly dictated by semiempirical approaches
in quantum chemistry. To construct basis set, having proper nodal structure and simple functional form of orbitals and repre-
senting atomic properties with reasonable accuracy, authors propose an Ansatz based on gradual improvement of hydrogen
atomic orbitals. According to it, several basis sets with different numbers of variable parameters are considered and forms
of orbitals are obtained for the 2nd-row elements either by minimization of their ground state energy (direct problem) or by
extracting from atomic spectra (inverse problem). It is shown that so-derived three- and four-parametric basis sets provide
accurate description of atomic properties, being, however, substantially provident for computational requirements and, what
is more important, simple to handle in analytic models of quantum chemistry. Since the discussed Ansatz allows a generaliza-
tion for heavier atoms, our results may be considered not only as a solution for light elements, but also as a proof of concept
with possible further extension to a wider range of elements.
Keywords Atomic orbitals· Atoms· Analytic models· Semiempirical methods
1 Introduction
Quantum chemical description of molecules involves one-
electron states, expanded against finite sets of basis func-
tions. Quality and efficiency of electronic structure calcula-
tions and f eatures of their computational implementation
substantially rely on the properties of the underlying basis
set. This fact is emphasized in almost each handbook on
quantum chemistry (see, e.g., [1]) and reflected in the huge
number of basis sets available in the literature for description
of various objects and properties [2, 3]. Two major classes
of basis functions (coming from two main types of objects in
theoretical chemistry) are local (atomic) basis functions and
plane waves. Although using the latter is extremely efficient
numerically, the incurred loss of local chemical information
generated demand for a posteriori analysis tools projecting
the results obtained in the plane wave basis onto local basis
sets as successfully implemented, e.g., in the LOBSTER
package [4–6]. In this work, we focus only on local atomic
orbitals, and thus our further discussion will be restricted
to them.
Atomic functions appear in either numerical (tabular) or
analytic form [1]. Numerical atomic orbitals (for example,
Ref.[7]) come from accurate ab initio calculations on many-
electron atoms, but their actual application is restricted to
very simple and highly symmetric (usually linear) mol-
ecules. By contrast, analytic atomic orbitals (AOs) are the
main tool of quantum chemistry. Analytic AOs are in their
turn linear combinations of primitives, the latter being either
Slater-type (STO) [8] or Gaussian-type functions [9]. The
numbers of primitives and variable parameters are deter-
mined by two target characteristics of a basis set: flexibil-
ity (growing with number of primitives and parameters)
and efficiency in computational and analytic applications
Published as part of the special collection of articles In Memoriam
of János Ángyán.
Electronic supplementary material The online version of this
article (https ://doi.org/10.1007/s0021 4-018-2386-x) contains
supplementary material, which is available to authorized users.
* Andrei L. Tchougréeff
andrei.tchougreeff@ac.rwth-aachen.de
1 A.N. Frumkin Institute ofPhysical Chemistry
andElectrochemistry ofRAS, Moscow, Russia
2 Independent University ofMoscow, Moscow, Russia
3 Chair ofSolid State andQuantum Chemistry, RWTH
- Aachen University, Aachen, Germany
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