The description of electron correlation in quantum chemistry often relies on multi-index quantities. Here, we examine a compressed representation of the long-range part of electron correlation that is associated with dispersion interactions. For this purpose, we perform coupled-cluster singles and doubles (CCSD) computations on localized orbitals, and then extract the portion of CCSD amplitudes corresponding to dispersion energies. Using singular value decomposition, we uncover that a very compressed representation of the amplitudes is possible in terms of occupied-virtual geminal pairs located on each monomer. These geminals provide an accurate description of dispersion energies at medium and long distances. The corresponding virtual orbitals are examined by further singular value decompositions of the geminals. We connect each component of the virtual space to the multipole expansion of dispersion energies. Our results are robust with respect to basis set change and hold for systems as large as the benzene-methane dimer. This compressed representation of dispersion energies paves the way to practical and accurate approximations for dispersion, for example, in local correlation methods.

Three-body dispersion interactions are much weaker than their two-body counterpart. However, their importance grows quickly as the number of interacting monomers rises. To explore the numerical performance of correlation methods for long-range three-body dispersion, we performed calculations on eight very simple dispersion-dominated model metal trimers: Na₃, Mg₃, Zn₃, Cd₃, Hg₃, Cu₃, Ag₃, and Au₃. One encouraging aspect is that relatively small basis sets of augmented triple-ζ size appear to be adequate for three-body dispersion in the long-range. Coupled cluster calculations were performed at high levels to assess MP3, CCSD, CCSD(T), empirical density functional theory dispersion (D3), and the many-body dispersion (MBD) approach. We found that the accuracy of CCSD(T) was generally significantly lower than for two-body interactions, with errors sometimes reaching 20% in the investigated systems, while CCSD and particularly MP3 were generally more erratic. MBD is found to perform better than D3 at large distances, whereas the opposite is true at shorter distances. When computing reference numbers for three-body dispersion, care should be taken to appropriately represent the effect of the connected triple excitations, which are significant in most cases and incompletely approximated by CCSD(T).

The feasibility of the compression of localized virtual orbitals is explored in the context of intramolecular long-range dispersion interactions. Singular value decomposition (SVD) of coupled cluster doubles amplitudes associated with the dispersion interactions is analyzed for a number of long-chain systems, including saturated and unsaturated hydrocarbons and a silane chain. Further decomposition of the most important amplitudes obtained from these SVDs allows for the analysis of the dispersion-specific virtual orbitals that are naturally localized. Consistent with previous work on intermolecular dispersion interactions in dimers, it is found that three important geminals arise and account for the majority of dispersion interactions at the long range, even in the many body intramolecular case. Furthermore, it is shown that as few as three localized virtual orbitals per occupied orbital can be enough to capture all pairwise long-range dispersion interactions within a molecule.

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.

Simulating solids with quantum chemistry methods and Gaussian-type orbitals (GTOs) has been gaining popularity. Nonetheless, there are few systematic studies that assess the basis set incompleteness error (BSIE) in these GTO-based simulations over a variety of solids. In this work, we report a GTO-based implementation for solids and apply it to address the basis set convergence issue. We employ a simple strategy to generate large uncontracted (unc) GTO basis sets that we call the unc-def2-GTH sets. These basis sets exhibit systematic improvement toward the basis set limit as well as good transferability based on application to a total of 43 simple semiconductors. Most notably, we found the BSIE of unc-def2-QZVP-GTH to be smaller than 0.7 mE_h per atom in total energies and 20 meV in bandgaps for all systems considered here. Using unc-def2-QZVP-GTH, we report bandgap benchmarks of a combinatorially designed meta-generalized gradient approximation (mGGA) functional, B97M-rV, and show that B97M-rV performs similarly (a root-mean-square-deviation of 1.18 eV) to other modern mGGA functionals, M06-L (1.26 eV), MN15-L (1.29 eV), and Strongly Constrained and Appropriately Normed (SCAN) (1.20 eV). This represents a clear improvement over older pure functionals such as local density approximation (1.71 eV) and Perdew-Burke-Ernzerhof (PBE) (1.49 eV), although all these mGGAs are still far from being quantitatively accurate. We also provide several cautionary notes on the use of our uncontracted bases and on future research on GTO basis set development for solids.