A Simple 'Range Extender' for Basis Set Extrapolation Methods for MP2 and Coupled Cluster Correlation Energies

TL;DR

This paper introduces a simple extension to basis set extrapolation formulas for MP2 and coupled cluster energies, demonstrating their effectiveness and equivalence to existing methods for large basis sets.

Contribution

The authors propose a straightforward 'range extender' for basis set extrapolation formulas, enabling accurate extrapolation to larger basis sets like n=7 and beyond.

Findings

Extrapolation formulas closely resemble Petersson (L+a)^{-3} with basis-specific shift.

Validated the extended formulas against optimized factors for AV6/7Z and literature data.

Demonstrated equivalence of CCSD extrapolations to a simple power law for large basis sets.

Abstract

We discuss the interrelations between various basis set extrapolation formulas and show that for the nZaPa and aug-cc-pVnZ basis set formulas, for n=4--6 their behavior closely resembles the Petersson (L+a)^{-3} formula with a shift a specific to the basis set family and level of theory. This is functionally equivalent to the Pansini-Varandas extrapolation for large L. This naturally leads to a simple way to extend these extrapolations to n=7 and higher. The formula is validated by comparison with newly optimized extrapolation factors for the AV{6,7}Z basis set pairs and literature values for {6,7}ZaPa. For L\geq5, the CCSD extrapolations of both the Schwenke and Varandas type are functionally equivalent to E(L)=E_\infty+A.(L-0.30)^{-3}, i.e., E(\infty)=E(L)+[E(L)-E(L-1)]/([(L-0.30)/(L-1.30)]^3-1)