  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)] method. In previous
work [Phys. Rev. B 104, 054106 (2021)], 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 non-local 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 [Phys. Rev. Lett. 108, 236402 (2012)]. In this work, we
show that the MBD model can also be locally parametrized to derive a local
approximation for the highly non-local many-body effects. With this local
parametrization, we develop an atom-wise 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.
