Long-range interactions, polarization, and charge flow in molecular dynamics

Molecular Dynamics (MD) simulations serve as a theoretical and computational microscope, enabling researchers to zoom in on matter at the nanometer scale. This technique provides invaluable insight into microscopic processes in various disciplines, such as materials science, catalysis, solid-state physics, and mechanical engineering.

The basic principle of MD is that the equations of motion of the nuclei in a molecular system are integrated over time using classical mechanics. To do so, a model is needed to predict the forces acting on the nuclei. There are many models for interatomic forces, which differ in their tradeoff between computational cost and physical realism. In order to draw connections to experimental research, MD must often be applied to systems containing thousands of atoms, which are simulated over timescales well beyond nanoseconds. These requirements can only be met with "force fields", which do not explicitly construct an electronic wavefunction to calculate interatomic forces. Force fields were originally simple mechanical models (atoms connected by springs) but they have evolved into ever more complex formalisms. For example, reactive force fields go beyond simple spring models, and machine learning potentials strive to be both accurate and broadly applicable.

Force fields are computationally efficient because they replace expensive quantum-mechanical models with empirical approximations. The parameters of these force fields (or the weights and biases of machine learning interaction potentials) must be estimated, typically by fitting them to quantum-mechanical reference data. A fundamental limitation of this fitting procedure is the curse of dimensionality. The number of ways that atoms can be arranged within the environment of a reference atom, grows exponentially with the environment's size. Due to this exponential growth, generating all relevant environment configurations is only feasible when it is limited to a sphere with a small cutoff radius. By using a small cutoff, training data can be made exhaustive, and empirical models can be guaranteed to interpolate and not extrapolate. However, interactions between atoms at longer distances cannot be neglected. These long-range interactions play a crucial role in many situations, including the relative stability of macromolecular conformations (protein folding), the binding affinity of ligands in active sites, the adsorption of guest molecules in microporous media, or transport through interfaces.

Physically inspired models, with a solid connection to quantum-mechanical electronic structure theory, can effectively model long-range interactions and complement data-driven models that have a small cutoff radius. We have developed several new methods and models with this strategy. First, we proposed methods to partition the electronic density (and other expectation values) into atomic contributions. One example is the Minimal Basis Iterative Stockholder method. These partitioning methods provide local information from which long-range interactions can be derived. Additionally, we have proposed models that efficiently approximate polarization and charge flow. For instance, Atom-Condensed Kohn--Sham DFT approximated to 2nd order (ACKS2) overcomes the main limitations of the charge-equilibration method, such as metallic polarizability scaling and unphysical dissociation limits. Another approach we explored is the electron Machine Learning Potential (eMLP), which models polarization by condensing localized orbitals into explicit electron pair particles. eMLP is consistent with the modern theory of polarization and accurately predicts nontrivial response properties. A major challenge for the future is to make these models more robust and applicable to electronic insulators and conductors alike. Another ongoing research topic is integrating these new developments into existing models, ranging from classical biomolecular force fields to state-of-the-art machine learning interaction potentials.