Focal-point approach with pair-specific cusp correction for coupled-cluster theory

TL;DR

This paper introduces a basis set correction scheme for CCSD that uses FNOs and a pair-specific cusp correction to efficiently reduce basis set incompleteness errors, improving accuracy for molecules and the uniform electron gas.

Contribution

The authors develop a simple, implementable correction method for CCSD that effectively addresses basis set errors using a pair-specific MP2 scaling approach with FNOs.

Findings

Significant reduction in basis set errors for atoms and molecules.

Rapid convergence of reaction and atomization energies with FNOs.

Effective correction of triples contribution in CCSD(T) with FNOs.

Abstract

We present a basis set correction scheme for the coupled-cluster singles and doubles (CCSD) method. The scheme is based on employing frozen natural orbitals (FNOs) and diagrammatically decomposed contributions to the electronic correlation energy that dominate the basis set incompleteness error (BSIE). As recently discussed in [https://doi.org/10.1103/PhysRevLett.123.156401], the BSIE of the CCSD correlation energy is dominated by the second-order M{\o}ller-Plesset (MP2) perturbation energy and the particle-particle ladder term. Here, we derive a simple approximation to the BSIE of the particle-particle ladder term that effectively corresponds to a rescaled pair-specific MP2 BSIE, where the scaling factor depends on the spatially averaged correlation hole depth of the coupled-cluster and first-order pair wavefunctions. The evaluation of the derived expressions is simple to implement in any existing code. We demonstrate the effectiveness of the method for the uniform electron gas. Furthermore, we apply the method to coupled-cluster theory calculations of atoms and molecules using FNOs. Employing the proposed correction and an increasing number of FNOs per occupied orbital, we demonstrate for a test set that rapidly convergent closed and open-shell reaction energies, atomization energies, electron affinities, and ionization potentials can be obtained. Moreover, we show that a similarly excellent trade-off between required virtual orbital basis set size and remaining BSIEs can be achieved for the perturbative triples contribution to the CCSD(T) energy employing FNOs and the (T*) approximation.