Chemistry Reference
In-Depth Information
3
Atomic Orbitals
3.1 ATOMICORBITALS AS ABASIS FORMOLECULAR
CALCULATIONS
We saw in Chapter 1 that AOs are one-electron one-centre functions
needed for describing the probability of finding the electron at any given
point in space. They are, therefore, the building blocks of any theory
that can be devised inside the orbital model. In practical applications,
we shall see in Chapter 4 that appropriate orbitals will be the basis of all
approximation methods resting on the variation theorem. A particular
type of AO is obtained from the solution of the atomic one-electron
problem, the so-called hydrogen-like atomic orbitals (HAOs). Even if
the HAOs are of no interest in practice, they are important in that they
are exact solutions of the corresponding Schroedinger equation and,
therefore, are useful for testing the accuracy of approximate calcula-
tions. The great majority of quantum chemical calculations on atoms
and molecules are based on the use of basis AOs that have a radial
dependence different from that of the HAOs. They can be separated into
two classes according to whether their decay with the radial variable r is
exponential (Slater-type orbitals or STOs, by far the best) or Gaussian
(Gaussian-type orbitals or GTOs).
In the following, we shall first introduce the HAOs mostly with the aim
of (i) illustrating the general techniques of solution of one of the exactly
solvable Schroedinger eigenvalue equations and (ii) explaining from first
