An ab-initio derivation of the pi-electron Hamiltonian by a non-perturbative open-shell formalism

Abstract

A method for generating a pi-electron hamiltonian in an ab-initio manner using the non-perturbative open-shell many-body formalism recently developed by us is presented. The _π-hamiltonian thus derived is energy-independent, and is also proved to be spin-independent. A recipe is given with the help of which Goldstone-like matrix-elements of H_π can be extracted up to three body terms. It has been demonstrated that the use of diagrammatics considerably simplifies the algebra and allows one to keep track of the various quantities involved. Up to a given order of approximation, an explicit form of H_π containing up to the three body terms has been given, and some of the important physical effects embedded in the hamiltonian are discussed. A comparative analysis of the various formalisms currently in use forms the concluding section of the paper.