Development of algebraic techniques for the atomic open-shell MBPT(3)

TL;DR

This paper develops algebraic techniques for third-order open-shell many-body perturbation theory in atoms, focusing on wave operator terms, effective Hamiltonian generation, and tensor form representation, facilitating computational implementation.

Contribution

It introduces a comprehensive algebraic framework for third-order open-shell MBPT, including generation of wave operator terms and effective Hamiltonian in tensor form, suitable for coupled-cluster methods.

Findings

Effective interaction operator terms are generated by up to eight types of n-body parts.

Operators are expressed in irreducible tensor form for computational convenience.

The reduction scheme is adaptable for coupled-cluster approach.

Abstract

The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of occupation-number representation and intermediate normalization, the third-order deviations are worked out by employing a computational software program that embodies the generalized Bloch equation. We prove that in the most general case, the terms of effective interaction operator on the proposed complete model space are generated by not more than eight types of the $n$-body ($n\geq2$) parts of the wave operator. To compose the effective Hamiltonian matrix elements handily, the operators are written in irreducible tensor form. We present the reduction scheme in a versatile disposition form, thus it is suited for the coupled-cluster approach.