Basis set (chemistry)

Basis Set (Chemistry)

Basis set (chemistry)

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A basis set in chemistry is a set of functions used to create the molecular orbitals, which are expanded as a linear combination of such functions with the weights or coefficients to be determined. Usually these functions are atomic orbitals, in that they are centered on atoms. Otherwise, the functions are centered on bonds or lone pairs. Pairs of functions centered in the two lobes of a p orbital have also been used. Additionally, basis sets composed of sets of plane waves down to a cutoff wavelength are often used, especially in calculations involving systems with periodic boundary conditions.

Introduction

In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. In these cases, the wavefunctions under consideration are all represented as vector, the components of which correspond to coefficients in a linear combination of the basis functions in the basis set used. The operators are then represented as matrices, (rank two tensors), in this finite basis. In this article, basis function and atomic orbital are sometimes used interchangeably, although it should be noted that these basis functions are usually not actually the exact atomic orbitals, even for the corresponding hydrogen-like atoms, due to approximations and simplifications of their analytic formulas. If the finite basis is expanded towards an infinite complete set of functions, calculations using such a basis set are said to approach the...
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