Improved CPS and CBS Extrapolation of PNO-CCSD(T) Energies: The MOBH35 and ISOL24 Data Sets

TL;DR

This paper introduces a simple two-point CPS extrapolation method to eliminate PNO truncation errors in PNO-CCSD(T) energies, enabling accurate CBS limit calculations for large molecules with reduced computational cost.

Contribution

The study develops a practical extrapolation scheme that combines small basis set information to estimate PNO truncation errors, improving the accuracy of large molecule energy calculations.

Findings

PNO truncation errors follow a $T^{1/2}$ convergence model.

Very tight thresholds ($T=10^{-8}$) are needed for chemical accuracy.

The method reliably estimates CBS limit energies for large molecules.

Abstract

Computation of heats of reaction of large molecules is now feasible using domain-based PNO-CCSD(T) theory. However, to obtain agreement within 1~kcal/mol of experiment, it is necessary to eliminate basis set incompleteness error, which comprises of both the AO basis set error and the PNO truncation error. Our investigation into the convergence to the canonical limit of PNO-CCSD(T) energies with PNO truncation threshold $T$ shows that errors follow the model $E(T) = E + A T^{1/2}$. Therefore, PNO truncation errors can be eliminated using a simple two-point CPS extrapolation to the canonical limit, so that subsequent CBS extrapolation is not limited by residual PNO truncation error. Using the ISOL24 and MOBH35 data sets, we find that PNO truncation errors are larger for molecules with significant static correlation, and that it is necessary to use very tight thresholds of $T=10^{-8}$ to ensure errors do not exceed 1~kcal/mol. We present a lower-cost extrapolation scheme that uses information from small basis sets to estimate PNO truncation errors for larger basis sets. In this way the canonical limit of CCSD(T) calculations on large molecules with large basis sets can be reliably estimated in a practical way. Using this approach, we report complete basis set limit CCSD(T) reaction energies for the full ISOL24 and MOBH35 data sets.