Abstract
Second-order Møller-Plesset perturbation theory (MP2) constitutes the simplest form of many-body wavefunction theory and often provides a good compromise between efficiency and accuracy. There are, however, well-known limitations to this approach. In particular, MP2 is known to fail or diverge for some prototypical condensed matter systems like the homogeneous electron gas (HEG) and to overestimate dispersion-driven interactions in strongly polarizable systems. In this paper, we explore how the issues of MP2 for metallic, polarizable, and strongly correlated periodic systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillouin-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model, and the graphene-water interaction. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for the various systems.
Highlights
Second-order Møller–Plesset perturbation theory (MP2) holds a unique place in the hierarchy of wavefunction-based electronic structure methods.1–4 Historically, it was the first correlated method in quantum chemistry that was size-extensive, invariant to unitary orbital rotations, and computationally affordable
As a first model system, we consider the homogeneous electron gas (HEG), which plays a central role in understanding the properties of simple metals and is of essential importance to the foundations of density functional theory
Κ-MP2 displays a significantly improved behavior relative to MP2, somewhat resembling the mCCD behavior though with different rates of convergence. This is quite remarkable given that the regularization parameter κ = 1.4 EH−1 was empirically optimized to small molecule thermochemistry data, which is completely unrelated to the HEG
Summary
Second-order Møller–Plesset perturbation theory (MP2) holds a unique place in the hierarchy of wavefunction-based electronic structure methods. Historically, it was the first correlated method in quantum chemistry that was size-extensive, invariant to unitary orbital rotations, and computationally affordable. MP2 still plays an important role, e.g., in its spin-component-scaled variants or as a part of double-hybrid DFT methods.6–8 Despite this popularity, the limitations of MP2-like methods are well-known. Coupled-cluster (CC) methods do not share this problem, despite being closely related to MP2.10,20 This improved behavior can be interpreted as a renormalization of the bandgap due to the inclusion of screening effects This makes CC methods highly attractive for condensed matter applications.. Different forms of regularization have been proposed as a way of empirically imitating higher-order screening effects at the MP2 level.22–25 This concept has proven very fruitful for molecular applications, but to the best of our knowledge, it has so far not been applied to extended systems. We propose a new, non-empirical regularization method based on the second-order Brillouin–Wigner (BW) perturbation theory
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