Seniority-Zero Canonical Transformation Theory: Reducing Truncation Error with Late Truncation

TL;DR

This paper introduces a canonical transformation approach that incorporates residual electron correlation effects into a seniority-zero wavefunction, achieving high accuracy with manageable computational effort.

Contribution

It presents a novel method using BCH expansion and recursive commutator approximation to reduce truncation errors in seniority-zero electronic structure calculations.

Findings

Achieves errors around 10^{-4} Hartree in numerical tests.

Utilizes parallel computation for practicality on small- to medium-sized systems.

Exact evaluation of first three commutators enhances accuracy.

Abstract

We show how to add the effects of residual electron correlation to a reference seniority-zero wavefunction by making a unitary transformation of the true electronic Hamiltonian into seniority-zero form. The transformation is treated via the Baker Campbell Hausdorff (BCH) expansion and the seniority-zero structure of the reference is exploited to evaluate the first three commutators exactly; the remaining contributions are handled with a recursive commutator approximation, as is typical in canonical transformation methods. By choosing a seniority-zero reference and using parallel computation, this method is practical for small- to medium-sized systems. Numerical tests show high accuracy, with errors $\sim 10^{-4}$ Hartree.