A deep potential model with long-range electrostatic interactions

Abstract

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

Towards predictive design of electrolyte solutions by accelerating ab initio simulation with neural networks

“…A lot of sophisticated work is focused on addressing this problem for complex systems. [102][103][104][105][106] But for electrolyte solutions these interactions are already known analytically, i.e., a dielectric screened Coulomb interaction. It is therefore not clear that it is essential to capture them with a NNP.…”

Ab initio multi-scale modeling of ferroelectrics: The case of PbTiO3

“…Our definition of Wannier centroid is consistent with [32]. For PbTiO 3 we also assign a local dipole moment to each Ti atom, echoing the definition of Ti-centered local polarization for elementary unit cells [69].…”

“…1 we display a schematic representation of the ground-state P4mm tetragonal structure of PbTiO 3 , including the location of the centers of the maximally localized Wannier functions (MLWCs) [2]. We further define the Wannier centroid [32] associated to an atom as the average position of the MLWCs closer to that atom.…”

Towards predictive design of electrolyte solutions by accelerating ab initio simulation with neural networks.

“…A lot of sophisticated work is focused on addressing this problem for complex systems. [103][104][105][106][107] But for electrolyte solutions these interactions are already known analytically, i.e., a dielectric screened Coulomb interaction. It is therefore not clear that it is essential to capture them with a NNP.…”