The final step is to generate the set of \( N \)-particle Slater determinants with fixed \( M \). The Slater determinants will be stored in occupation representation. Although in many codes this representation is done compactly in bit notation with ones and zeros, but for greater transparency and simplicity we will list the occupied single particle states.

Hence we can store the Slater determinant basis states as \( sd(i,j) \), that is an array of dimension \( N_{SD} \), the number of Slater determinants, by \( N \), the number of occupied state. So if for the 7th Slater determinant the 2nd, 3rd, and 9th single-particle states are occupied, then \( sd(7,1) = 2 \), \( sd(7,2) = 3 \), and \( sd(7,3) = 9 \).