Do CCSD and approximate CCSD-F12 variants converge to the same basis set limits? The case of atomization energies

TL;DR

This study compares the convergence of CCSD and approximate CCSD-F12 methods towards the basis set limit for thermochemical calculations, highlighting differences and recommending CCSD(F12*) for accuracy.

Contribution

It provides a detailed analysis of the basis set convergence behavior of CCSD and various CCSD-F12 variants, clarifying their practical equivalence and differences.

Findings

CCSD and CCSD(F12*) agree within uncertainties near the CBS limit.

CCSD-F12b shows a nontrivial difference from CCSD(F12*), related to static correlation.

CCSD(F12*) is recommended over CCSD-F12b for thermochemical accuracy.

Abstract

While the title question is a clear 'yes' from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the basis set limits of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) have been investigated on detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12*) agree to within their respective uncertainties (about \pm0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]--CCSD-F12b difference (consisting mostly of third-order terms), and a more slowly converging, repulsive, fourth-order difference between CCSD(F12*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family.