Slater – Condon rules for integrals involving determinantal wave functions

Sometimes we need to evaluate matrix elements of one- and two-electron operators. The following rules are readily derived based on the properties of the determinants and orthonormality of the orbitals in them – try it!

Consider three functions,

Then,

1e-integrals:

(If the two determinants differ by more than one orbital, the integral is zero)

2e-integrals:

(If the two determinants differ by more than two orbitals, the integral is zero)