Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies

A simple modification of second-order Møller–Plesset perturbation theory (MP2) to improve the description of molecular ground state energies is proposed. The total MP2 correlation energy is partitioned into parallel- and antiparallel-spin components which are separately scaled. The two parameters (scaling factors), whose values can be justified by basic theoretical arguments, have been optimized on a benchmark set of 51 reaction energies composed of 74 first-row molecules. It is found, that the new method performs significantly better than standard MP2: the rms [mean absolute error (MAE)] deviation drops from 4.6 (3.3) to 2.3 (1.8) kcal/mol. The maximum error is reduced from 13.3 to 5.1 kcal/mol. Significant improvements are especially observed for cases which are usually known as MP2 pitfalls while cases already described well with MP2 remain almost unchanged. Even for 11 atomization energies not considered in the fit, uniform improvements [MAE: 8.1 kcal/mol (MP2) versus 3.2 kcal/mol (new)] are found. The results are furthermore compared with those from density functional theory (DFT/B3LYP) and quadratic configuration interaction [QCISD/QCISD(T)] calculations. Also for difficult systems including strong (nondynamical) correlation effects, the improved MP2 method clearly outperforms DFT/B3LYP and yields results of QCISD or sometimes QCISD(T) quality. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for ten diatomic molecules also show consistent enhancements. The uniformity with which the new method improves upon MP2, thereby rectifying many of its problems, indicates significant robustness and suggests it as a valuable quantum chemical method of general use.