Energy decomposition analysis (EDA) is a widely used tool for extracting physical and chemical insights from electronic structure calculations of intermolecular interactions, as well as for the development of advanced force fields for describing those interactions. Recently, the absolutely localized molecular orbital (ALMO) EDA has been extended from the self-consistent field level to the second-order Møller-Plesset (MP2) theory level. This paper reports an efficient implementation of the MP2 ALMO-EDA that scales optimally, employs the resolution of the identity (RI) approximation for post-SCF matrix elements, and is shared-memory parallel. The algorithms necessary to achieve this implementation are described in detail. Performance tests using the aug-cc-pVTZ basis set for water clusters of up to 10 molecules are reported. The timings suggest that the MP2 ALMO-EDA is computationally feasible whenever MP2 energy calculations themselves are feasible, and the cost is dominated by the SCF itself in this size regime. The MP2 ALMO-EDA is applied to study the origin of substituent effects in anion-π interactions between chloride and benzene and mono- through hexafluorobenzene. The effect of fluoro substituents was primarily to change the frozen interaction. Detailed analysis supports the interpretation that anion-π interactions are favorable because of electrostatic interaction with the substituents.

The electron-electron correlation energy is negative, and attractive dispersion interactions are entirely a correlation effect; therefore, the contribution of correlation to intermolecular binding is commonly assumed to be negative, or binding in nature. However, there are many cases where the long-range correlation binding energy is positive, with certain geometries of the water dimer as a prominent example. Geometries with dipoles misaligned can also have an electrostatically dominated, though negative, long-range correlation binding. In either case, the interaction decays as R(-3). This has its origin in the systematic overestimation of dipole moments by Hartree-Fock theory, leading to a reduction in the calculated electrostatic attraction upon inclusion of correlation. Thus, energy decomposition analyses that include correlation but do not correct mean field electrostatic terms are suboptimal. Attenuated second-order Møller-Plesset theory, which smoothly truncates long-range electron correlation effects to zero, can, paradoxically, have the correct long-range behavior for many intermolecular interactions.

An energy decomposition analysis (EDA) of intermolecular interactions is proposed for second-order Møller-Plesset perturbation theory (MP2) based on absolutely localized molecular orbitals (ALMOs), as an extension to a previous ALMO-based EDA for self-consistent field methods. It decomposes the canonical MP2 binding energy by dividing the double excitations that contribute to the MP2 wave function into classes based on how the excitations involve different molecules. The MP2 contribution to the binding energy is decomposed into four components: frozen interaction, polarization, charge transfer, and dispersion. Charge transfer is defined by excitations that change the number of electrons on a molecule, dispersion by intermolecular excitations that do not transfer charge, and polarization and frozen interactions by intra-molecular excitations. The final two are separated by evaluations of the frozen, isolated wave functions in the presence of the other molecules, with adjustments for orbital response. Unlike previous EDAs for electron correlation methods, this one includes components for the electrostatics, which is vital as adjustment to the electrostatic behavior of the system is in some cases the dominant effect of the treatment of electron correlation. The proposed EDA is then applied to a variety of different systems to demonstrate that all proposed components behave correctly. This includes systems with one molecule and an external electric perturbation to test the separation between polarization and frozen interactions and various bimolecular systems in the equilibrium range and beyond to test the rest of the EDA. We find that it performs well on these tests. We then apply the EDA to a halogen bonded system to investigate the nature of the halogen bond.

Non-covalent interactions play a primordial role in chemistry. Beyond their quantification, the detailed understanding of their physical processes is necessary to rationalize chemical trends and improve designs of chemical systems. Energy decomposition analyses allow detailed insight into non-covalent interactions by extracting electrostatics, Pauli repulsion, polarization, dispersion and charge transfer components from interaction energies. Recent work has demonstrated that electronic correlation influenced significantly all of these energy components, whereas previous decompositions only partitioned correlation between dispersion and charge transfer. The MP2 energy decomposition analysis with Absolutely Localized Molecular Orbitals (MP2 ALMO-EDA) takes these results fully into account and offers a correlation correction for each extracted component. A recent detailed investigation of the CCSD dispersion energy showed that a small number of virtual orbitals is sufficient to describe dispersion interactions accurately in the long-range, which potentially offers a basis-set independent definition of dispersion. Finally, we present an application of MP2 ALMO-EDA to a series of unusual halogen bonding complexes where charge transfer dominates over the electrostatic σ-hole interaction.

The halogen bond is a class of non-covalent interaction that has attracted considerable attention recently. A widespread theory for describing them is the σ-hole concept, which predicts that the strength of the interaction is proportional to the size of the σ-hole, a region of positive electrostatic potential opposite a σ bond. Previous work shows that in the case of CX3I, with X equal to F, Cl, Br, and I, the σ-hole trend is exactly opposite to the trend in binding energy with common electron pair donors. Using energy decomposition analysis (EDA) applied to a potential energy scan as well as the recent adiabatic EDA technique, we show that the observed trend is a result of charge transfer. Therefore a picture of the halogen bond that excludes charge transfer cannot be complete, and permanent and induced electrostatics do not always provide the dominant stabilizing contributions to halogen bonds. Overall, three universally attractive factors, polarization, dispersion and charge transfer, together with permanent electrostatics, which is usually attractive, drive halogen bonding, against Pauli repulsion.

To study intermolecular interactions involving radicals at the correlated level, the energy decomposition analysis scheme for second-order Mo̷ller-Plesset perturbation theory based on absolutely localized molecular orbitals (ALMO-MP2-EDA) is generalized to unrestricted and restricted open-shell MP2. The benefit of restricted open-shell MP2 is that it can provide accurate binding energies for radical complexes where density functional theory can be error-prone due to delocalization errors. As a model application, the open-shell ALMO-MP2-EDA is applied to study the first solvation step of halogenated benzene radical cations, where both halogen- and hydrogen-bonded isomers are possible. We determine that the lighter halogens favor the hydrogen-bonded form, while the iodine-substituted species prefers halogen bonding due to larger polarizability and charge transfer at the halogen. As a second application, relevant to the activation of CO₂ in photoelectrocatalysis, complexes of CO₂^-· interacting with both pyridine and imidazole are analyzed with ALMO-MP2-EDA. The results reveal the importance of charge transfer into the π* orbital of the heterocycle in controlling the stability of the carbamate binding mode, which is favored for pyridine but not for imidazole.

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.