A VALENCE-UNIVERSAL COUPLED-CLUSTER SINGLE-EXCITATIONS AND DOUBLE-EXCITATIONS METHOD FOR ATOMS .3. SOLVABILITY PROBLEMS IN THE PRESENCE OF INTRUDER STATES

To better understand the problems met when solving the equations of VU-CC approaches in the presence of intruder states, we are concerned with the following aspects of the solvability problem for sets of non-linear equations: the existence and properties of multiple solutions and the attainability of these solutions by means of various numerical methods. Our study is concentrated on the equations obtained for Be within the framework of the recently formulated atomically oriented form of the valence-universal coupled-cluster theory accounting for one- and two-electron excitations (VU-CCSD/R) and based on the complete model space (2s2, 2p2). Six pairs of multiple solutions representing four S-1 states are found and discussed. Three of these solutions provide amplitudes describing the 2p2 S-1 state for which the intruder state problem has been considered as extremely serious. Several known numerical methods have been applied to solve the same set of non-linear equations for the two-valence cluster amplitudes. It is shown that these methods perform quite differently in the presence of intruder states, which seems to indicate that the intruder state problem for VU-CC methods is partly caused by the commonly used methods of solving the non-linear equations.