A scaled explicitly correlated F12 correction to second-order Møller–Plesset perturbation theory

T H Thompson,L Urban,C Ochsenfeld

doi:10.1063/5.0033411

T H Thompson, L Urban + Show 1 more

Open Access

https://doi.org/10.1063/5.0033411

Copy DOI

Abstract

An empirically scaled version of the explicitly correlated F12 correction to second-order Møller-Plesset perturbation theory (MP2-F12) is introduced. The scaling eliminates the need for many of the most costly terms of the F12 correction while reproducing the unscaled explicitly correlated F12 interaction energy correction to a high degree of accuracy. The method requires a single, basis set dependent scaling factor that is determined by fitting to a set of test molecules. We present factors for the cc-pVXZ-F12 (X = D, T, Q) basis set family obtained by minimizing interaction energies of the S66 set of small- to medium-sized molecular complexes and show that our new method can be applied to accurately describe a wide range of systems. Remarkably good explicitly correlated corrections to the interaction energy are obtained for the S22 and L7 test sets, with mean percentage errors for the double-zeta basis of 0.60% for the F12 correction to the interaction energy, 0.05% for the total electron correlation interaction energy, and 0.03% for the total interaction energy, respectively. Additionally, mean interaction energy errors introduced by our new approach are below 0.01 kcal mol-1 for each test set and are thus negligible for second-order perturbation theory based methods. The efficiency of the new method compared to the unscaled F12 correction is shown for all considered systems, with distinct speedups for medium- to large-sized structures.

Highlights

It is well-known that the computation and evaluation of electron correlation effects are critical for the accurate and quantitative description of chemical systems
In order to obtain reliable, well-balanced cSF12 factors for each member of the cc-pVXZ-F12 (X = D, T, Q) basis set family, which are capable of reproducing the F12 correction to the interaction energy to a high degree of accuracy, we decided to employ the S66 complexes53 for parameterization
With 23 systems representing frequently occurring hydrogen bond donor and acceptor groups, 23 structures dominated by dispersion effects, and 20 with mixed dispersion and electrostatic interactions, respectively, we consider the S66 complexes as suitable reference for fitting SF12 energies to non-covalent interactions (NCIs)

Summary

Introduction

It is well-known that the computation and evaluation of electron correlation effects are critical for the accurate and quantitative description of chemical systems. One of the simplest ab initio wave function based correlation methods is second-order Møller– Plesset perturbation theory (MP2).. 6 and 7) are able to lower the asymptotic computational scaling with the system size to as low as linear. Extrapolation and explicitly correlated R12/F12 methods have been introduced to overcome the basis set incompleteness error (BSIE). The latter incorporates explicitly coupled two-electron terms (geminals) into the wave function to better describe short-ranged correlation and satisfy electronic cusp conditions, leading to much faster convergence with respect to the size of the one-electron basis set. To improve accuracy for non-covalent interactions (NCIs), some authors have introduced a scaling of the correlation energy with an empirically determined factor..

Objectives

Results

Conclusion