# Third-Order M{\o}ller-Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics and Intermolecular Interactions

## TL;DR

This paper introduces improved third-order perturbation methods using optimized orbitals, significantly enhancing accuracy in thermochemistry, kinetics, and intermolecular interactions, often surpassing coupled cluster methods at lower computational cost.

## Contribution

The authors develop and empirically optimize a new third-order perturbation method with regularized orbitals, achieving substantial accuracy improvements over existing methods.

## Key findings

- MP3:$7$-OOMP2 reduces RMS errors 1.7 to 5 times compared to MP3.
- Empirical scaling yields MP2.8:$7$-OOMP2, further improving accuracy.
- Proposed methods outperform coupled cluster in 5 of 7 data sets at lower cost.

## Abstract

We develop and test methods that include second and third-order perturbation theory (MP3) using orbitals obtained from regularized orbital-optimized second-order perturbation theory, $\kappa$-OOMP2, denoted as MP3:$\kappa$-OOMP2. Testing MP3:$\kappa$-OOMP2 shows RMS errors that are 1.7 to 5 times smaller than MP3 across 7 data sets. To do still better, empirical training of the scaling factors for the second- and third-order correlation energies and the regularization parameter on one of those data sets led to an unregularized scaled ($c_2=1.0$; $c_3=0.8$) denoted as MP2.8:$\kappa$-OOMP2. MP2.8:$\kappa$-OOMP2 yields significant additional improvement over MP3:$\kappa$-OOMP2 in 4 of 6 test data sets on thermochemistry, kinetics, and noncovalent interactions. Remarkably, these two methods outperform coupled cluster with singles and doubles in 5 of the 7 data sets considered, at greatly reduced cost (no $\mathcal{O}(N^6)$ iterations).