Slater-type Orbital - Definition

Definition

STOs have the following radial part:

where

n is a natural number that plays the role of principal quantum number, n = 1,2,...,
N is a normalizing constant,
r is the distance of the electron from the atomic nucleus, and
is a constant related to the effective charge of the nucleus, the nuclear charge being partly shielded by electrons. Historically, the effective nuclear charge was estimated by Slater's rules.

The normalization constant is computed from the integral

\int_0^\infty x^n e^{-\alpha x} dx = \frac{n!}{\alpha^{n+1}}.

Hence

N^2 \int_0^\infty \left(r^{n-1}e^{-\zeta r}\right)^2 r^2 dr =1 \Longrightarrow N= (2\zeta)^n \sqrt{\frac{2\zeta}{(2n)!}}.

It is common to use the spherical harmonics depending on the polar coordinates of the position vector as the angular part of the Slater orbital.

Read more about this topic:  Slater-type Orbital

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