Economical basis sets and their uses in ab initio calculations

Abstract

The roles of the particular functions composing a basis set, including the polarization and diffuse functions, as well as the nature and environment of each atom in a molecule need to be considered to choose the most appropriate basis in ab initio calculations. The number and level of basis functions required to describe an atom should increase from left to right in terms of its appearance in the periodic table and the relative increase in electronegativity. In this article, we review a practical and effective scheme proposed by one of the authors for choosing basis sets in ab initio calculations and assess its efficiency in selected applications. In the scheme, we consider the different roles of the particular functions, including the polarization and diffuse functions, adopted in the basis set, as well as the nature and environment of the atom. The number and level of basis functions required to describe an atom should be determined according to its relative order in the periodic table and/or electronegativity. For an atom with a relatively higher electronegativity, larger basis functions including polarization and diffuse functions should be used, while the basis functions for a less electronegative atom or positively charged atom can be reduced and may not adopt any polarization and diffuse functions. For systems involving hydrogen bonding, weak interactions, functional groups, metallic bonding with zero or low-positive valence, and other sensitive interactions, both the polarization and diffuse functions may need to be used. These economical composite basis sets are applied to a variety of systems, from small to very large compounds. Compared with the calculations required for conventional basis set schemes at different levels, the economical composite basis set can accurately predict the structures and properties of compounds while saving significant CPU. A single-point calculation using the geometric structure determined using the economical composite basis set can further improve the accuracy of calculating certain properties.