Matrix elements between determinantal wavefunctions of non-orthogonal orbitals

Expressions are given for the matrix elements of one- and two-electron operators between determinants composed of non-orthogonal orbitals, in the case (relevant to perturbation theory) where the determinants are obtained by single or double replacement of orbitals in a reference determinant. The matrix elements can all be expressed in terms of cofactors of the overlap matrix of the orbitals contained in the reference determinant.