The first step can take as input an initial Slater determinant (whose position in the list of basis Slater determinants is \( \alpha \)) written as an ordered listed of occupied single-particle states, e.g. \( 1,2,5,8 \), and the indices \( p,q,r,s \) from the two-body operator.

It will return another final Slater determinant if the single-particle states \( r \) and \( s \) are occupied, else it will return an empty Slater determinant (all zeroes).

If \( r \) and \( s \) are in the list of occupied single particle states, then replace the initial single-particle states \( ij \) as \( i \rightarrow r \) and \( j \rightarrow r \).