Correspondence between physical states and solutions to the coupled-cluster equations

Abstract

To discuss the usefulness of the entries of the complete set of solutions to approximate coupled-cluster (CC) equations for the description of the states of many-electron systems, one has to be able to establish a correspondence between the states and solutions. The authors have explored four methods of finding links between the states (represented for the model by the full configuration interaction wave functions and energies) and solutions to the CC equations. Numerical studies for the P4 model, which belongs to the simplest realistic many-electron model systems, show that the states-solutions correspondence pattern strongly depends on the method employed. Only for a few states all methods considered have assigned the same solutions. Among these states are those that are energetically the closest to the reference determinants. For the remaining states the assignment is not unique and the accuracy of description depends on the physical features considered. The article is concluded with a comparison of the present results and results of the most recent studies on the structure of the complete sets of solutions to the CC equations with the findings and intuitions being the content of the work by Zivkovic and Monkhorst (J Math Phys 1978, 19, 1007).