Performance of a one-parameter correlation factor for transcorrelation: the Li-Ne total energies and ionization potentials

TL;DR

This paper evaluates a simple one-parameter transcorrelation approach for multi-electron systems, demonstrating its efficiency and near-chemical accuracy in calculating energies and ionization potentials compared to more complex methods.

Contribution

It introduces and tests a single-parameter correlation factor within a transcorrelation framework, showing its effectiveness for larger basis sets in quantum chemical calculations.

Findings

Single-parameter correlation factor achieves near-chemical accuracy in large basis sets.

The approach simplifies calculations of two- and three-body integrals.

Results are comparable to more elaborate correlation factors in basis set limit.

Abstract

In this work we investigate the performance of a recently proposed transcorrelated (TC) approach based on a single-parameter correlation factor [JCP, 154, 8, 2021] for systems involving more than two electrons. The benefit of such an approach relies on its simplicity as efficient numerical-analytical schemes can be set up to compute the two- and three-body integrals occuring in the effective TC Hamiltonian. To obtain accurate ground state energies within a given basis set, the present TC scheme is coupled to the recently proposed TC-full configuration interaction quantum Monte Carlo method [JCP, 151, 6, 2019]. We report ground state total energies on the Li-Ne series, together with their first cations, computed in increasing large basis sets and compare to more elaborate correlation factors involving electron-electron-nucleus coordinates. Numerical results on the Li-Ne ionization potentials show that the use of the single-parameter correlation factor brings on average only a slightly lower accuracy (1.2 mH) in a triple-zeta quality basis set with respect to a more sophisticated correlation factor. However, already using a quadruple-zeta quality basis set yields results within chemical accuracy to complete basis set limit results when using this novel single-parameter correlation factor.