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A full set of uncontracted configurations can be obtained by applying the excitation operators EaiEkjto all individual reference configurations. If the labels k a n d j correspond to orbitals of the same symmetry, the operator E k j only creates a particular configuration (or a linear combination of some configurations) of the complete internal space. Therefore, these operators can be omitted. If k and j have different symmetries, internal N-electron states which do not have the symmetry of the reference wavefunction are generated.
First we consider the core orbitals, which are not correlated. By partitioning the summations in the Hamiltonian (Eq. (1 18)) it is easy to show that in this case one has simply to replace the one-electron Hamiltonian h by the core Fock matrix F’ (Eq. (84)) and to add the core energy E, = 1 (hii + FZ) i(corc) to the total energy. Furthermore, all summations then exclude the core orbitals. Hence, the operators Jk’and Kk’are only needed for the correlated orbitals. Next we consider excitations from the valence orbitals.
For longer CASSCF expansions the only remedy is to recalculate the coupling coefficients each time they are needed. Clearly, this requires a particularly efficient algorithm. I(l'O5) where the summation runs over the full spin-eigenfunction basis. This factorization follows from the anticommutation relations in Eqs (lo)-( 12). The formula tape then need only contain the one-particle matrix elements (@, I Eijl OK), ordered after the intermediate state label K . Even though this greatly reduces the number of stored coupling coefficients, the length of the formula tape can still be rather large.