Physics-Guided Solutions to Dispersion in Density-Functional Theory

Abstract

Density-functional theory (DFT) has become the workhorse of modern computational chemistry, enabling first-principles modelling of large-scale systems with remarkable accuracy and efficiency. Its success is partly due to the development of numerous corrections to model London dispersion, which is the weakest of the intermolecular van der Waals forces. One such dispersion correction is the exchange-hole dipole moment (XDM) model. XDM calculates the dispersion energy by summing the contributions from all atom pairs, prompting recent questions about its treatment of many-body effects. To investigate this, variational model systems of interacting Drude oscillators were studied from first principles. XDM's dispersion coefficients were then compared to those computed by the many-body dispersion (MBD) model, which is known to capture these many-body effects. Explicit three-body contributions were calculated using the Axilrod--Teller--Muto (ATM) and random-phase approximation (RPA) methods, but neither contributed meaningfully to the dispersion energy. We further showed that the dominant many-body effect is electronic, reflected in the dynamic response of the dispersion coefficients to changes in the surrounding chemical environment. A subsequent study compared XDM to other leading post-SCF dispersion corrections, where it showed best-in-class performance on the DES15K benchmark, which spans almost 15,000 noncovalent interactions across compressed to expanded geometries.

Building on this solid foundation of both physical rigour and numerical accuracy, we pursue physics-guided improvements to further refine dispersion modelling and reduce empiricism. Here, we introduce two new XDM variants. The first, XCDM, supplements the exchange hole with same- and opposite-spin dynamical correlation holes when calculating multipole moments. The second, XDM(Z), implements Z-damping, a novel one-parameter damping function based on atomic numbers. This reduces the number of fitted empirical parameters in XDM from two to one. These variants were tested comprehensively across both molecular systems and the solid state. XCDM proves to be exceptionally accurate for molecular systems, and the data suggests a possible use case for crystal structure prediction. Z-damping displays impressive performance considering the reduction in empirical parameters. XDM(Z) may represent a Pauling point for the XDM methods, rarely the best but consistently reliable across the widest range of systems.