Perturbation-Adapted Perturbation Theory

TL;DR

This paper introduces a novel perturbation theory approach that constructs an optimal zero-order Hamiltonian tailored to the problem, significantly improving convergence in many-electron systems compared to traditional methods.

Contribution

It presents a general method for defining an optimal zero-order Hamiltonian that enhances convergence in perturbation theory, especially for many-electron problems.

Findings

Enhanced convergence in many-electron perturbation calculations.

Significant improvements over conventional Fock Hamiltonian methods.

Applicable to a broad class of Hamiltonians.

Abstract

A new general approach is introduced for definining an optimum zero-order Hamiltonian for Rayleigh-Schr\"odinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the exact Hamiltonian within any desired functional form. When applied to many-body perturbation theory for electrons, strongly improved convergence is observed in cases where the conventional Fock hamiltonian leads to divergence or slow convergence.