Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers

Abstract

We derive and assess two new classes of regularizers that cope with offending denominators in the single-reference second-order Møller-Plesset perturbation theory (MP2). In particular, we discuss the use of two types of orbital energy dependent regularizers, κ and σ, in conjunction with orbital-optimized MP2 (OOMP2). The resulting fifth-order-scaling methods, κ-OOMP2 and σ-OOMP2, have been examined for bond-breaking, thermochemistry, nonbonded interactions, and biradical problems. Both methods with strong enough regularization restore restricted to unrestricted instability (i.e., Coulson-Fischer points) that unregularized OOMP2 lacks when breaking bonds in H, CH, CH, and CH. The training of the κ and σ regularization parameters was performed with the W4-11 set. We further developed scaled correlation energy variants, κ-S-OOMP2 and σ-S-OOMP2, by training on the TAE140 subset of the W4-11 set. Those new OOMP2 methods were tested on the RSE43 set and the TA13 set where unmodified OOMP2 itself performs very well. The modifications we made were found insignificant in these data sets. Furthermore, we tested the new OOMP2 methods on singlet biradicaloids using Yamaguchi's approximate spin-projection. Unlike the unregularized OOMP2, which fails to converge these systems due to the singularity, we show that regularized OOMP2 methods successfully capture strong biradicaloid characters. While further assessment on larger data sets is desirable, κ-OOMP2 with κ = 1.45 E appears to combine favorable recovery of Coulson-Fischer points with good numerical performance.

An auxiliary-Field quantum Monte Carlo perspective on the ground state of the dense uniform electron gas: An investigation with Hartree-Fock trial wavefunctions

“…Using dynamically correlated orbitals such as those from orbital-optimized Møller-Plesset perturbation theory can be an economical way to go beyond HF trial wavefunctions. 49,94,95 Some essential symmetry breaking in the HF trial wavefunction can potentially improve the performance of ph-AFQMC greatly such as using complex, restricted HF orbitals. 127,128 Lastly, the finite-temperature extension of ph-AFQMC has been well established [129][130][131] .…”

Making many-body interactions nearly pairwise additive: The polarized many-body expansion approach

“…The ALMO-based representation of the system used in PolBE yields fragment-specific occupied and virtual orbitals. These fragment-specific virtuals, which are both fragment-sparse and smaller in number in comparison to the virtual space of the whole system, provides a compact representation of the fragment virtual space which can be exploited in the extension of PolBE to double hybrids density functionals 109 and to correlated wavefunction methods like MP2, orbital-optimized MP2, [57][58][59][60]110,111 and coupled cluster theories. 112 Extension of these ideas to correlated wavefunction methods is currently being investigated.…”

Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Møller-Plesset perturbation theory

“…Interested readers are referred to ref. 45 for more technical details. In passing we mention that Eq.…”

“…For instance, this was observed by us in the heptazethrene dimer (HZD) where broken-symmetry UHF yields Ŝ 2 = 6.3 in the cc-pVDZ basis set. 45 The subsequent correlation treatment based on these UHF solutions via second-order Møller-Plesset perturbation theory (MP2) is not effective in removing such heavy spin contamination. It is possible to employ orbital optimized MP2 (OOMP2) as an attempt to produce a reference determinant with only essential symmetry breaking (i.e., Ŝ 2 ≈ 1.0).…”