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# Recent developments in symmetry‐adapted perturbation theory

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Abstract Symmetry‐adapted perturbation theory (SAPT) is a well‐established method to compute accurate intermolecular interaction energies in terms of physical effects such as electrostatics, induction (polarization), dispersion, and exchange. With many theory levels and variants, and several computer implementations available, closed‐shell SAPT has been applied to produce numerous intermolecular potential energy surfaces for complexes of experimental interest, and to elucidate the interactions in various complexes relevant to catalysis, organic synthesis, and biochemistry. In contrast, the development of SAPT for general open‐shell complexes is still a work in progress. In the last decade, new developments from several research groups, including the author's, have greatly enhanced the capabilities of SAPT. The new and emerging approaches are designed to make SAPT more widely applicable (including interactions involving multireference systems, complexes in arbitrary spin states, and intramolecular noncovalent interactions), more accurate (enhanced description of intramolecular correlation, a better account of exchange effects, relativistic SAPT, and explicitly correlated SAPT), and more efficient (enhanced density‐fitted implementations, linear‐scaling variants, empirical dispersion, and an implementation on graphics processing units). The new developments open up avenues for SAPT applications to an unprecedented variety of weakly interacting complexes. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory Molecular and Statistical Mechanics > Molecular Interactions
The groupings of available many‐body symmetry‐adapted perturbation theory corrections into the SAPT0, SAPT2, … levels of theory (concentric shaded circles) and into the overall electrostatic, exchange, induction, and dispersion contributions (pie slices of different colors), as designated in Reference
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The order‐1 F‐SAPT/6‐31G* interaction energy decomposition for the indinavir @ HIV‐II protease complex, the largest system to date studied by any variant of SAPT. All atoms in each fragment are colored according to the contribution for the full fragment. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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Convergence of the conventional and explicitly correlated and SAPT corrections for the methane dimer with the orbital basis set aug‐cc‐pVXZ≡aXZ. The algorithm with full optimization of F12 dispersion amplitudes is denoted (FULL), and the approximate optimized diagonal Ansatz (ODA), fixed‐amplitude Ansatz (FIX), and ‐F12(MP2) approaches are described in the text. The notation +(aXZ) signifies the addition of a hydrogenic aXZ set of midbond functions, with X the same as for the atom‐centered part of the basis set. The rough grouping of different approaches according to their relative complexity has been illustrated by symbols used to rate the difficulty of North American ski trails. (Reprinted with permission from Reference . Copyright 2019 American Chemical Society)
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A schematic illustration of the intramolecular SAPT (I‐SAPT) calculation of the intramolecular hydrogen bond energy in 2,4‐pentanediol. The numbers of protons and electrons in each fragment are listed as well. (Reprinted with permission from Reference . Copyright 2015 AIP Publishing LLC)
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A schematic illustration of the effects of regularization of the attractive singularities in the perturbation operator V. Without regularization (blue dashed curve), electrons from atom A tend to tunnel into the Coulomb well around the nucleus of atom B. The regularized Coulomb potential (red solid curve) has this well filled in to eliminate tunneling. As a result, regularization prevents the divergence of the polarization expansion and suppresses charge transfer in the second order
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The values of the SAPT correction for the singlet (S = 0) and septet (S = 3) states resulting from the interaction of two ground‐state nitrogen atoms as functions of the interatomic separation. The “exact” results are nonapproximated corrections from the high‐spin‐only algorithm of Reference , and the “S2” and “1‐flip” values are the spin‐flip SAPT (SF‐SAPT) arbitrary‐spin exchange energies computed using the approximations of References and , respectively. (Reprinted with permission from Reference . Copyright 2019 AIP Publishing LLC)
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Ternary diagrams illustrating the relative magnitudes of electrostatics, induction, and dispersion in the SAPT0/jun‐cc‐pVDZ energy decompositions for the S66x10 database of noncovalent complexes (the S66x8 set extended to short range in Reference ) and the SSI database of sidechain‐sidechain interactions in proteins. (Reprinted with permission from the Supporting Information to Reference . Copyright 2016 American Chemical Society)
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