An Analysis of Regularized Second-Order Energy Expressions in the Context of Post-HF and KS-DFT Calculations: What Do We Gain and What Do We Lose?

Møller-Plesset second-order (MP2) perturbation energy expression has been a workhorse for quantum chemistry methods for many years due to its very appealing accuracy/cost ratio compared to more advanced methods. It has been widely utilized in the post-Hartree-Fock (post-HF) calculations and Kohn-Sham density functional theory (KS-DFT) to define, e.g., the double-hybrid class of density functional approximations. Although the list of successful applications of the MP2 method is quite long, it suffers from various limitations, e.g., in strongly correlated systems, divergence in small energy gap systems, or overestimation of binding energies for large noncovalently bonded species. In this work, we analyze a few of the most commonly utilized forms of regularized MP2 correlation energy expression in the context of post-HF and KS-DFT calculations. To this end, we perform various tests for model systems, e.g., homogeneous electron gas, one-dimensional Hubbard model, Harmonium atoms, and some real-life examples, to trace back the advantages and disadvantages of these formulas, providing practical guidelines for their utilization in everyday quantum chemical calculations.