Configuration State Function - Definition

Definition

In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants. It is constructed to have the same quantum numbers as the wavefunction, of the system being studied. In the method of configuration interaction the wavefunction can be expressed as a linear combination of CSFs, that is in the form

where denotes the set of CSFs. The coefficients, are found by using the expansion of to compute a Hamiltonian matrix. When this is diagonalized, the eigenvectors are chosen as the expansion coefficients. CSFs rather than just Slater determinants can also be used as a basis in Multi-configurational self-consistent field computations.

In atomic structure, a CSF is an eigenstate of

• the square of the angular momentum operator, .
• the z-projection of angular momentum
• the square of the spin operator .
• the z-projection of the spin operator

In linear molecules, does not commute with the Hamiltonian for the system and therefore CSFs are not eigenstates of . However, the z-projection of angular momentum is still a good quantum number and CSFs are constructed to be eigenstates of and . In non-linear (which implies polyatomic) molecules, neither nor commute with the Hamiltonian. The CSFs are constructed to have the spatial transformation properties of one of the irreducible representations of the point group to which the nuclear framework belongs. This is because the Hamiltonian operator transforms in the same way. and are still valid quantum numbers and CSFs are built to be eigenfunctions of these operators.