Electronic Fock Spaces: Phase Prefactors and Hidden Symmetry

Many years ago in paper [1] some special set-theoretical operation ∆K was introduced. It was used to reduce manipulations with phase prefactors in the Fock space ( Grassmann algebra) to pure set theoretical ones. More detailed discussion of this operation was given in [2], Appendix A. The main purpose of this paper is to show that the operation mentioned makes it easy to obtain very complicated analytic expressions in effective and uniform manner. In addition, this technique helps to reveal hidden symmetry of the electronic Fock space. Fock space equipped with new algebraic structure can be considered as a natural domain for a certain class of Post Hartree-Fock (HF) methods. In Section I we discuss properties of the operation ∆K both for the case of molecular spin orbital (MSO) basis and molecular orbital (MO) basis. Section II is dedicated to classic configuration interaction (CI) matrix elements. It does not contain any new results and is included only as simple but important application of our technique of manipulations with phase prefactors. In Section III excitation operators and coupled cluster (CC) approach [4] [10] are discussed. General analytic expression for CI expansion of CC wave function is given. For the CC CI coefficients recurrence relations are derived. Analytic expressions for derivatives of CC CI coefficients with respect to CC