We have adapted the algorithm to evaluate the first two terms from Ref. 82. The sigma vector corresponding to bilinear coupling terms can be calculated in a similar fashion to the one-electron part of (σ e ) 1 and (σ e ) 2 . The last term is simply a product of scalars and the CI vector. The construction of σ 3 is the most time-consuming step in the Olsen method. We use the algorithm for building σ 3 described in Ref. 83 by rewriting Eqn.29 as follows: