Atomistic simulations of matter, especially those that leverage first-principles (ab initio) electronic structure theory, provide a microscopic view of the world, underpinning much of our understanding of chemistry and materials science. Over the last decade or so, machine-learned force fields have transformed atomistic modeling by enabling simulations of ab initio quality over unprecedented time and length scales. However, early machine-learning (ML) force fields have largely been limited by (i) the substantial computational and human effort required to develop and validate potentials for each particular system of interest and (ii) a general lack of transferability from one chemical system to the next. Here, we show that it is possible to create a general-purpose atomistic ML model, trained on a public dataset of moderate size, that is capable of running stable molecular dynamics for a wide range of molecules and materials. We demonstrate the power of the MACE-MP-0 model—and its qualitative and at times quantitative accuracy—on a diverse set of problems in the physical sciences, including properties of solids, liquids, gases, chemical reactions, interfaces, and even the dynamics of a small protein. The model can be applied out of the box as a starting or “foundation” model for any atomistic system of interest and, when desired, can be fine-tuned on just a handful of application-specific data points to reach ab initio accuracy. Establishing that a stable force-field model can cover almost all materials changes atomistic modeling in a fundamental way: experienced users obtain reliable results much faster, and beginners face a lower barrier to entry. Foundation models thus represent a step toward democratizing the revolution in atomic-scale modeling that has been brought about by ML force fields.

Standard Ewald sums, which calculate, e.g., the electrostatic energy or the force in periodically closed systems of charged particles, can be efficiently speeded up by the use of the fast Fourier transformation (FFT). In this article we investigate three algorithms for the FFT-accelerated Ewald sum, which have attracted widespread attention, namely, the so-called particle–particle–particle mesh ${\mathrm{(P}}^3\mathrm{M}\mathrm{),}$ particle mesh Ewald (PME), and smooth PME method. We present a unified view of the underlying techniques and the various ingredients which comprise those routines. Additionally, we offer detailed accuracy measurements, which shed some light on the influence of several tuning parameters and also show that the existing methods — although similar in spirit — exhibit remarkable differences in accuracy. We propose a set of combinations of the individual components, mostly relying on the ${\mathrm{P}}^3\mathrm{M}$ approach, that we regard to be the most flexible. The issue of estimating the errors connected with particle mesh routines is reserved to paper II.

We construct an accurate estimate for the root mean square force error of the particle–particle–particle mesh (P3M) algorithm by extending a single particle pair error measure which has been given by Hockney and Eastwood. We also derive an easy to use analytic approximation to the error formula. This allows a straightforward and precise determination of the optimal splitting parameter (as a function of system specifications and P3M parameters) and hence knowledge of the force accuracy prior to the actual simulation. The high quality of the estimate is demonstrated in several examples.