Exponentially generated wave functions

Abstract

We consider several generalizations of the exponential ansatz in a rather formal way, giving several new wave functions which we call exponentially generated (EG) wave functions. There are three distinct ways of the exponential-type generations of the wave functions, two of which are new. They are named ESAC (extended symmetry-adapted-cluster) wave function and exponentially generated CI (EGCI) wave function. The ESAC wave function is a simple extension of the SAC wave function and is applicable even when the Hartree–Fock reference configuration is not dominant. The EGCI wave function is a CI wave function constructed in the spirit of the cluster expansion theory. Formally, it has the merits of both the CI theory and the cluster expansion theory; for example, the upper bound nature, size consistency, and the applicability to quasidegenerate states and excited states. We then introduce several new wave functions by a multiple and mixed use of the exponential-type operators. We call such a class of wave functions multiexponentially generated (MEG) wave functions. There are many possibilities for the MEG wave functions, and the MR-SAC wave function proposed previously is one of them. When the system involves several classes of electron correlations, the MEG wave function permits an optimal (physically and practically) use of the exponential-type operators for the distinct classes of electron correlations. We described the method of solution of the EG and MEG wave functions and examined size consistency and some other properties.