Gaussian orbital

In molecules.

Rationale

The principal reason for the use of Gaussian 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.

Correct form of atomic orbitals:

GTO:

Molecular integrals

Molecular integrals over cartesian gaussian functions were first proposed by Boys^[1] in 1950. Since then much work has been done to speed up the evaluation of these integrals which are the slowest part of many quantum chemical calculations. McMurchie and Davidson (1978) introduced Hermite Gaussian functions to take advantage of differential relations. Pople and Hehre (1978) developed a local coordinate method. Obara and Saika introduced efficient recursion relations in 1985, which was followed by the development of other important recurrence relations. Gill and Pople (1990) introduced a 'prism' algorithm which allowed efficient use of 20 different calculation paths.

References