MC-SCF. I. The multi-configuration self-consistent-field method

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Abstract
The general multi-configuration self-consistent-field (MC-SCF) method is presented with no restrictions on the types of configurations participating in the expansion of the total wavefunction. The general coupled Fock-like equations for the ``best'' orbitals to be used in such a multi-configuration wavefunction are derived. Formally these coupled nonlinear equations are decoupled with the use of projection operators and transformed into a pseudoeigenvalue problem. Several general methods, based on orbital transformations and on the use of the generalized Brillouin theorem, are presented for solving the coupled nonlinear Fock like equations for the determination of the MC-SCF orbitals. The formalism presented is applicable not only to the ground state of a given system, but also to any excited state, yielding an upper bound to the true energy of the desired state.