Gaussian orbital

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In molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals in the LCAO method for the computation of electron orbitals in molecules.

[edit] 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.

Correct form of atomic orbitals:

R(r) = Ar^le ^{− αr}

GTO:

R(r) = Ar^le ^{− αr * r}

[edit] External links

• A visualization of all common and uncommon atomic orbitals, from 1s to 7g (Note that the radial part of the expressions given corresponds to Slater orbitals rather than Gaussians. The angular parts, and hence their shapes as displayed in figures, are the same as those of spherical Gaussians.)