Complete set of solutions of the generalized Bloch equation

✍ Scribed by K. Kowalski; P. Piecuch

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 397 KB
• Volume: 80
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/1097-461x(2000)80:4/5<757::aid-qua25>3.0.co;2-a

✦ Synopsis

The genuine multireference approaches, including multireference coupled-cluster (MRCC) methods of the state-universal and valence-universal type, are based on the generalized Bloch equation. Unlike the Schrödinger equation, the Bloch equation is nonlinear and has multiple solutions. In this study, the homotopy method is used to obtain complete sets of solutions of the exact and approximate Bloch equations for a four-electron model system consisting of four hydrogen atoms. Different geometries of the model and different choices of the multidimensional reference space are investigated. The rigorous relationships between the solutions of the Bloch equation corresponding to approximate and exact cases are established by extending the procedure of β-nested equations to multireference case. It is argued that the nonlinear nature of the Bloch equation and the asymmetric treatment of the excitation manifolds corresponding to different reference configurations in the Bloch wave operator formalism are the primary reasons for the emergence of various problems plaguing genuine MRCC calculations, including the recently discovered intruder solution problem [K. Kowalski and P. Piecuch, Phys. Rev. A 61, 052506 (2000)].