Gaussian Orbital - Rationale

Rationale

The principal reason for the use of Gaussian basis functions in molecular quantum chemical calculations is the 'Gaussian Product Theorem', which guarantees that the product of two GTOs centered on two different atoms is a finite sum of Gaussians centered on a point along the axis connecting them. In this manner, four-center integrals can be reduced to finite sums of two-center integrals, and in a next step to finite sums of one-center integrals. The speedup by 4--5 orders of magnitude compared to Slater orbitals more than outweighs the extra cost entailed by the larger number of basis functions generally required in a Gaussian calculation.

For reasons of convenience, many Gaussian integral evaluation programs work in a basis of Cartesian Gaussians even when spherical Gaussians are requested: the 'contaminants' are deleted a posteriori.

Slater radial orbitals read

Gaussian primitives for radial orbitals read

where is normalisation constant.