For differences greater than δ ↑ + δ ↓ ≥ 3, have a matrix-element is 0 (rule 3). This yields 7 Slater-Condon rules in U-CI. For each of the 6 terms above (plus rule 3) apply a partition of the entire CI matrix. This may be seen by the example on fig. , for 4 Slater-Condon rules (each column above, in eq. 2). The CI Hamiltonian matrix-elements may be partitioned into seven 1-dimensional arrays. The value of these matrix-elements are determined by a formula on the next page. As the 0-difference rule is always located on the matrix-diagonal It may be used to initialize the CI Hamiltonian with 0s in the off diagonal (covering rule 3). Next, for the remaining 5 rules, the indices of the CI Hamiltonian for their applicability are determined by (determined by the Spin-Difference Matrix):