A Tensor Formulation of Second-Order Brillouin-Wigner Perturbation Theory with a Size-Consistent Correlation Energy

Second-order Moller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size-consistency and extensivity, severely limiting its application to chemistry. In this work, we propose a generalized tensor formulation of second-order BWPT that recasts the energy denominator as a sum of energy-gap and regularizer tensors, where the regularizer is taken (by ansatz) to be the correlation contribution to the ionization energy of a given occupied orbital. This choice of regularizer leads to a Brillouin-Wigner correlation energy expression that is size-extensive, size-consistent, and invariant to unitary transformations among the occupied or virtual orbitals. Our size-consistent second-order Brillouin-Wigner (scBW2) approach is capable of describing the exact dissociation limit of H2 in a minimal basis set regardless of the spin-polarization of the reference orbitals. More broadly, we find that scBW2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, while rivaling coupled-cluster with single and double substitutions (CCSD) for thermochemical properties. Not only does scBW2 offer improvements in transferability relative to empirical energy-gap dependent regularizers, but the ab initio framework that we propose can be used as a guidepost for developments of future Brillouin-Wigner functionals.Comment: 12 pages, 7 figure

Optimizing the Regularization in Size-Consistent Second-Order Brillouin-Wigner Perturbation Theory

Despite its simplicity and relatively low computational cost, second-order M{\o}ller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ({\alpha}) was set to recover the exact dissociation limit of H$_2$ in a minimal basis set. Alternatively {\alpha} can be viewed as a regularization parameter, where each value of {\alpha} represents a valid variant of BW-s2, which we denote as BW-s2({\alpha}). In this work, we semi-empirically optimize {\alpha} for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal {\alpha} parameter ({\alpha} = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2({\alpha}) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2({\alpha}) is iterative $\mathcal{O}(N^5)$, this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.Comment: 7 pages main text, 7 pages supporting information, 10 figure

Software for the frontiers of quantum chemistry:An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange–correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear–electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an “open teamware” model and an increasingly modular design

Electrostatics, Charge Transfer, and the Nature of the Halide-Water Hydrogen Bond

Binary halide–water complexes X–(H2O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X–(H2O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a C2v-symmetric saddle point, with a tunneling barrier height that is –(H2O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (–(H2O) and provides a driving force for the formation of quasi-linear X...H–O hydrogen bonds. Charge-transfer energies correlate well with measured O–H vibrational redshifts for both halide–water complexes as well as OH–(H2O) and NO2–(H2O), providing some indication of a general mechanism. <br /

Reinterpreting π-Stacking

The nature of pi-pi interactions has long been debated. The term "pi-stacking" is considered by some to be a misnomer, in part because overlapping pi-electron densities are thought to incur steric repulsion, and the physical origins of the widely-encountered "slip-stacked" motif have variously been attributed to either sterics or electrostatics, in competition with dispersion. Here, we use quantum-mechanical energy decomposition analysis to investigate pi-pi interactions in supramolecular complexes of polycyclic aromatic hydrocarbons, ranging in size up to realistic models of graphene, and for comparison we perform the same analysis on stacked complexes of polycyclic saturated hydrocarbons, which are cyclohexane-based analogues of graphane. Our results help to explain the short-range structure of liquid hydrocarbons that is inferred from neutron scattering, trends in melting-point data, the interlayer separation of graphene sheets, and finally band gaps and observation of molecular plasmons in graphene nanoribbons. Analysis of intermolecular forces demonstrates that aromatic pi-pi interactions constitute a unique and fundamentally quantum-mechanical form of non-bonded interaction. Not only do stacked pi-pi architectures enhance dispersion, but quadrupolar electrostatic interactions that may be repulsive at long range are rendered attractive at the intermolecular distances that characterize pi-stacking, as a result of charge penetration effects. The planar geometries of aromatic sp2 carbon networks lead to attractive interactions that are "served up on a molecular pizza peel", and adoption of slip-stacked geometries minimizes steric (rather than electrostatic) repulsion. The slip-stacked motif therefore emerges not as a defect induced by electrostatic repulsion but rather as a natural outcome of a conformation landscape that is dominated by van der Waals interactions (dispersion plus Pauli repulsion), and is therefore fundamentally quantum-mechanical in its origins. This reinterpretation of the forces responsible for pi-stacking has important implications for the manner in which non-bonded interactions are modeled using classical force fields, and for rationalizing the prevalence of the slip-stacked pi-pi motif in protein crystal structures.<br /

Appraisal of dispersion damping functions for the effective fragment potential method

The effective fragment potential (EFP) is a polarizable force field whose physically-motivated functional form is parameterized in an automated way from ab initio calculations, and whose dispersion potential has been suggested as a correction for Hartree-Fock or density functional theory calculations. However, the parameter-free dispersion damping potentials that are currently used in EFP do not follow from a rigorous derivation and do not satisfy simple limits for the dispersion energy. We introduce several new damping expressions that correct these deficiencies, then evaluate their performance alongside existing damping functions using a new database of ionic liquid constituents. This data set, which we call IL195x8, consists of complete-basis coupled-cluster interaction energies for 195 ion pairs at each of 8 different intermolecular separations. Ultimately, we recommend a new parameter-free dispersion damping function as a replacement for the one that is currently used in EFP