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We develop and test methods that include second and third-order perturbationtheory (MP3) using orbitals obtained from regularized orbital-optimizedsecond-order perturbation theory, $\kappa$-OOMP2, denoted asMP3:$\kappa$-OOMP2. Testing MP3:$\kappa$-OOMP2 shows RMS errors that are 1.7 to5 times smaller than MP3 across 7 data sets. To do still better, empiricaltraining of the scaling factors for the second- and third-order correlationenergies and the regularization parameter on one of those data sets led to anunregularized scaled ($c_2=1.0$; $c_3=0.8$) denoted as MP2.8:$\kappa$-OOMP2.MP2.8:$\kappa$-OOMP2 yields significant additional improvement overMP3:$\kappa$-OOMP2 in 4 of 6 test data sets on thermochemistry, kinetics, andnoncovalent interactions. Remarkably, these two methods outperform coupledcluster with singles and doubles in 5 of the 7 data sets considered, at greatlyreduced cost (no $\mathcal{O}(N^6)$ iterations).

the journal of physical chemistry letters

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