Atom-wise formulation of the many-body dispersion problem for linear-scaling van der Waals corrections

A common approach to modeling dispersion interactions and overcoming the inaccurate description of long-range correlation effects in electronic structure calculations is the use of pairwise-additive potentials, as in the Tkatchenko-Scheffler [Phys. Rev. Lett. 102, 073005 (2009)10.1103/PhysRevLett.102.073005] method. In previous work [H. Muhli, Phys. Rev. B 104, 054106 (2021)10.1103/PhysRevB.104.054106], we have shown how these are amenable to highly efficient atomistic simulation by machine learning their local parametrization. However, the atomic polarizability and the electron correlation energy have a complex and nonlocal many-body character and some of the dispersion effects in complex systems are not sufficiently described by these types of pairwise-additive potentials. Currently, one of the most widely used rigorous descriptions of the many-body effects is based on the many-body dispersion (MBD) model [A. Tkatchenko, Phys. Rev. Lett. 108, 236402 (2012)10.1103/PhysRevLett.108.236402]. In this work, we show that the MBD model can also be locally parametrized to derive a local approximation for the highly nonlocal many-body effects. With this local parametrization, we develop an atomwise formulation of MBD that we refer to as linear MBD (lMBD), as this decomposition enables linear scaling with system size. This model provides a transparent and controllable approximation to the full MBD model with tunable convergence parameters for a fraction of the computational cost observed in electronic structure calculations with popular density-functional theory codes. We show that our model scales linearly with the number of atoms in the system and is easily parallelizable. Furthermore, we show how using the same machinery already established in previous work for predicting Hirshfeld volumes with machine learning enables access to large-scale simulations with MBD-level corrections.