ALGEBRAIC PROPAGATOR APPROACHES AND INTERMEDIATE-STATE REPRESENTATIONS .2. THE EQUATION-OF-MOTION METHODS FOR N, N+ -1, AND N+/-2 ELECTRONS/

The equation-of-motion (EOM) method and the equivalent superoperator p ropagator approach, used in studies of (generalized) electronic excita tions, are analyzed with respect to two basic properties referred to a s separability and compactness. The separability property ensures that the computed excitation energies and transition moments are size cons istent; compactness means that the secular configuration spaces used i n the EOM and propagator schemes can be systematically smaller than th ose of comparable configuration-interaction (CI) expansions. The valid ity of these properties depends critically on an appropriate orthonorm alization of the operator manifolds used in the EOM and propagator sch emes. Separable and compact EOM versions are obtained by generalizing the excitation class orthogonalization procedure discussed in the prec eding paper [Phys. Rev. A 53, 2140 (1996)] to the basis operators. Mor eover, it is shown that the EOM secular equations for N+/-1,N+/-2,..., electron systems can be formulated as state representations of a gene ralized Hamiltonian in terms of ''intermediate'' Fock space states. Th ese intermediate-state representations (ISR's) give some interesting i nsight complementing the usual operator based derivation of the EOM pr opagator schemes. In particular, the ISR formulation allows for a tran sparent discussion of the relationship between the (N+/-1)-electron EO M scheme and the Dyson equation for the electron propagator. Some pote ntially useful EOM variants are proposed.