Third-Order Møller-Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy...

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, κ-OOMP2, denoted as MP3:κ-OOMP2. Testing MP3:κ-OOMP2 shows RMS errors that are 1.7-5 times smaller than those of 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 (c₂ = 1.0; c₃ = 0.8) denoted as MP2.8:κ-OOMP2. MP2.8:κ-OOMP2 yields significant additional improvement over MP3:κ-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 $$ iterations).