Complete set of solutions of the generalized Bloch equation

The genuine multireference approaches, including multireference coupled-clu ster (MRCC) methods of the state-universal and valence-universal type, are based on the generalized Bloch equation. Unlike the Schrodinger equation, t he Bloch equation is nonlinear and has multiple solutions. In this study, t he homotopy method is used to obtain complete sets of solutions of the exac t and approximate Bloch equations for a four-electron model system consisti ng of four hydrogen atoms. Different geometries of the model and different choices of the multidimensional reference space are investigated. The rigor ous relationships between the solutions of the Bloch equation corresponding to approximate and exact cases are established by extending the procedure of beta -nested equations to multireference case. It is argued that the non linear nature of the Bloch equation and the asymmetric treatment of the exc itation manifolds corresponding to different reference configurations in th e Bloch wave operator formalism are the primary reasons for the emergence o f various problems plaguing genuine MRCC calculations, including the recent ly discovered intruder solution problem [K. Kowalski and P. Piecuch, Phys. Rev. A til, 052506 (2000)]. (C) 2000 John Wiley & Sons, Inc.