Susi Lehtola
April 23, 2019
Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1),
FI-00014 University of Helsinki, Finland
Abstract
The need for accurate calculations on atoms and diatomic molecules is motivated
by the opportunities and challenges of such studies. The most commonly-used approach for all-electron electronic structure calculations in general – the linear combination of atomic orbitals (LCAO) method – is discussed in combination with Gaussian,
Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical
approaches based on, e.g. finite differences, finite elements, or the discrete variable
representation, which are also briefly introduced.
Applications of fully numerical approaches for general molecules are briefly reviewed,
and their challenges are discussed. It is pointed out that the high level of symmetry
present in atoms and diatomic molecules can be exploited to fashion more efficient fully
numerical approaches for these special cases, after which it is possible to routinely perform all-electron Hartree–Fock and density functional calculations directly at the basis
set limit on such systems. Applications of fully numerical approaches to calculations
on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook
is given.
https://arxiv.org/pdf/1902.01431.pdf
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