Complete set of solutions of multireference coupled-cluster equations: The state-universal formalism

The homotopy method is used to obtain a complete set of solutions of multireference coupled-cluster equations within the framework of the state-universal coupled-cluster (SUCC) formalism. The solutions are obtained for an ab initio four-electron model system consisting of four hydrogen atoms in rectangular arrangement. Essential information about the structure of solutions of nonlinear SUCC equations is provided and analyzed, both numerically and analytically, in the form of two theorems. The existence of multiple solutions of SUCC equations provides new insights into the nature of convergence problems often encountered in SUCC calculations. The evidence for the possible association of some solutions of the SUCC equations with the intruder-state problem is presented and briefly discussed.