Gaussian Approximations to 1s Slater-Type Orbitals

level of approximation

STO-1G

STO-2G

STO-3G

function plotted

ϕ(r)

RDF

α

1

0.25

α

2

0.55

α

3

2

The most natural basis functions in atomic structure computations are hydrogen-like exponentials of the form

-ζr

e

, which are known as Slater-type orbitals (STOs). Most current molecular structure computations, realized in software packages such as GAUSSIAN 03, make use of Gaussian approximations to atomic orbitals, functions of the form

-α

2

r



. Although these do not produce optimal atomic orbitals, they enable the large number of multicenter integrals involved in molecular computations to be evaluated with much greater facility. The key property is that the product of two Gaussians on different centers reduces to a single Gaussian about a shifted center. (See the Demonstration "Product of Two Gaussians".) In this Demonstration the red curve represents the simplest 1s STO. The black curve represents its approximation by a superposition of

n=1

, 2, or 3 Gaussians, designated STO-

n

G basis functions, with

n=1,2,3

. You can vary the exponential parameters

α

1

,

α

2

, and

α

3

to maximize the integral

S

(the overlap between the STO and its Gaussian approximation) with a maximum attainable value

S=1

. You can plot either the orbital function

ϕ(r)

or the radial distribution function (RDF)

4π

2

r

2

ϕ(r)

.