Regularized Second-Order Møller–Plesset Theory: A More Accurate Alternative to Conventional MP2 for Noncovalent Interactions and Transition Metal Thermochemistry for the Same Computational Cost

Abstract

Second order Møller-Plesset theory provides a remarkably simple form for the electron correlation energy with many desirable properties, e.g. it is size-consistent, free of self-interaction error, and scales with the fifth power of system size. However, MP2 exhibits well-known shortcomings including an incomplete description of dispersion interactions and sizable failures for transition metal chemistry. Herein, we first explore multiple physically justified forms of single-parameter regularization and then demonstrate that with appropriate parameter choice, regularized MP2 with Hartree-Fock reference orbitals yields high and transferable accuracy across a wide variety of noncovalent interactions (S22, S66, XB40, A24, and L7 test sets) and (mostly closedshell) transition metal thermochemistry (metal-carbonyl dissociations and a subset of MOR41). We find that, especially for systems with interacting π systems relevant to dispersion interactions and dative bonding, regularization serves to damp overestimated pair-wise additive contributions to the first-order amplitudes that affect correlation energy and charge-density. The optimal parameter values for the noncovalent and transition metal sets are 1.1 and 0.4 for two regularizers, κ and σ 2 , respectively. These two regularizers slightly degrade the accuracy of conventional MP2 for some small-molecule test sets which are well-known to be sensitive to charge-density distribution (radical stabilization energies, barrier heights, dipole moments, and polarizabilities), most of which have relatively large gaps. Due to the relatively straightforward implementations of nuclear gradient and other properties, we recommend κ-MP2 with κ = 1.1 as a more accurate alternative to conventional MP2 and other related variants. Our results suggest that appropriately regularized MP2 models represent promising forms for the nonlocal correlation part of double hybrid density functionals, at no additional cost over conventional MP2.

Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods

“…However, it can be certainly refined for specific applications. 106 To further evidence this, Fig. 4 reports the difference between regularized (computed at η = 1.0 E h with the SRGbased regularizer) and non-regularized quasiparticle energies as functions of R H−H for each orbital.…”

“…Other choices are legitimate like the regularizers considered by Head-Gordon and coworkers within orbitaloptimized second-order Møller-Plesset theory, which have the specificity of being energy-dependent. 77,106 In this context, the real version of the simple energy-independent regularizer (21) has been shown to damage thermochemistry performance and was abandoned. 107,108 Our investigations have shown that the following energy-dependent regularizer…”

Conformational energy benchmark for longer n-alkane chains

“…With the κ regularization and orbital-optimization we only find a small improvement 0.12 kcal/mol in the MAE, as expected for closed-shell systems with large HOMO-LUMO gaps. 48,126 The MAE is reduced to 0. and a dispersion correction contribution to recover the proper long-range dispersion also significantly reduces the error of DHDFs (vide supra). However, the MAE for ACONF12 with MP2D is still 0.21 kcal/mol higher than for HF-D4 due to residual basis set incompleteness and superposition errors.…”

Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers

“…These calculations were performed using the Q-Chem 5.4 electronic structure package [99]. A value of κ = 1.1 was used for the κ-OOMP2 method, as recommended for transition metal complexes [100]. The geometry for each molecule corresponded to the B3LYP high-spin (S=5/2) optimized geometry.…”