Configuration State Function - A Genealogical Algorithm For CSF Construction

A Genealogical Algorithm For CSF Construction

At the most fundamental level, a configuration state function can be constructed

• from a set of orbitals

and

• a number of electrons

using the following genealogical algorithm:

1. distribute the over the set of orbitals giving a configuration
2. for each orbital the possible quantum number couplings (and therefore wavefunctions for the individual orbitals) are known from basic quantum mechanics; for each orbital choose one of the permitted couplings but leave the z-component of the total spin, undefined.
3. check that the spatial coupling of all orbitals matches that required for the system wavefunction. For a molecule exhibiting or this is achieved by a simple linear summation of the coupled

value for each orbital; for molecules whose nuclear framework transforms according to symmetry, or one of its sub-groups, the group product table has to be used to find the product of the irreducible representation of all orbitals.

1. couple the total spins of the orbitals from left to right; this means we have to choose a fixed for each orbital.
2. test the final total spin and its z-projection against the values required for the system wavefunction

The above steps will need to be repeated many times to elucidate the total set of CSFs that can be derived from the electrons and orbitals.