Basis set superposition error || basis set part 5 || BSSE

Basis set superposition error (BSSE) is a systematic error that arises when performing quantum chemical calculations on molecular systems using a basis set approach. It occurs when the basis set used to describe the electronic structure of a molecule is not large enough to accurately represent the electronic wavefunctions of molecules in close proximity to one another.

In many quantum chemical calculations, it is necessary to consider the interaction between two or more molecules or fragments. When two or more molecules are brought close together, the basis sets used to describe their electronic wavefunctions can overlap. This overlap can result in the same electron density being described twice, which can lead to an overestimation of the interaction energy between the molecules. This overestimation is referred to as the basis set superposition error.

There are several methods to correct for BSSE, including the counterpoise (CP) correction method, which was first proposed by Boys and Bernardi in 1970. The CP method involves performing calculations on each fragment separately and then combining them to obtain the interaction energy. The method corrects for BSSE by subtracting the contribution of the basis functions shared between the fragments from the total energy.

Another method to correct for BSSE is the basis set extrapolation method, where calculations are performed using a sequence of basis sets of increasing size, and the energy differences are extrapolated to the complete basis set limit. Other methods include the ghost atom approach and the Morokuma-Zwanzig method.

It is important to correct for BSSE when performing quantum chemical calculations on molecular systems to ensure accurate results.