In order to implement an accurate theory of electronic structure we need a good estimate of atomic properties. A "basis set" is such an estimate. It is a collection of radial functions for each orbital on each atom that best describes the atomic radius. The problem is the same as that seen for the He atom where the two electrons screen each other. The screening results in a net expansion of the size of the atom relative to the estimate in the absence of screening. Since each electron blocks the nucleus some percentage of the time, the effective charge seen by the other electron is less than Z = 2 in He. The same concept applies to all atoms. However, the effect is dependent on the orbital. Screening is greatest in s orbitals and screening decreases in the order s > p > d > f. The reason for this that the increased angular momentum and sharpness of the orbital results in less of an opportunity for screening. Consequently, we observe a contraction of the radii of atoms as we move from left to right across the transition metals, lanthanides or actinides. In each case the increase in orbital occupancy results in an increase in nuclear charge that is not effectively screened.
The Gaussian-type orbitals have become the most widely used approach based on the commercial code Guassian. This method does have some advantages since it permits rapid computation of many molecules. Gaussian functions have been the most widely used in Hartree-Fock calculations and post-Hartree-Fock calculations using configuration interaction. However, exponential radial functions can be computed in an efficient manner using all-numerical methods in density functional theory. These methods have been discussed in a previous lecture and are applicable to the calculation of spectra using time-dependent density functional theory (TD-DFT) methods.
