We explore the role of long-range interactions in atomistic machine-learning models by analyzing the effects on fitting accuracy, isolated cluster properties, and bulk thermodynamic properties. Such models have become increasingly popular in molecular simulations given their ability to learn highly complex and multi-dimensional interactions within a local environment; however, many of them fundamentally lack a description of explicit long-range interactions. In order to provide a well-defined benchmark system with precisely known pairwise interactions, we chose as the reference model a flexible version of the Extended Simple Point Charge (SPC/E) water model. Our analysis shows that while local representations are sufficient for predictions of the condensed liquid phase, the short-range nature of machine-learning models falls short in representing cluster and vapor phase properties. These findings provide an improved understanding of the role of long-range interactions in machine learning models and the regimes where they are necessary.

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.

Among the many existing molecular models of water, the MB-pol many-body potential has emerged as a remarkably accurate model, capable of reproducing thermodynamic, structural, and dynamic properties across water’s solid, liquid, and vapor phases. In this work, we assessed the performance of MB-pol with respect to an important set of properties related to vapor–liquid coexistence and interfacial behavior. Through direct coexistence classical molecular dynamics simulations at temperatures of 400 K < T < 600 K, we calculated properties such as equilibrium coexistence densities, vapor–liquid interfacial tension, vapor pressure, and enthalpy of vaporization and compared the MB-pol results to experimental data. We also compared rigid vs fully flexible variants of the MB-pol model and evaluated system size effects for the properties studied. We found that the MB-pol model predictions are in good agreement with experimental data, even for temperatures approaching the vapor–liquid critical point; this agreement was largely insensitive to system sizes or the rigid vs flexible treatment of the intramolecular degrees of freedom. These results attest to the chemical accuracy of MB-pol and its high degree of transferability, thus enabling MB-pol’s application across a large swath of water’s phase diagram.

Gas phase unimolecular fragmentation of the two model doubly protonated tripeptides threonine-isoleucine-lysine (TIK) and threonine-leucine-lysine (TLK) is studied using chemical dynamics simulations. Attention is focused on different aspects of collision induced dissociation (CID): fragmentation pathways, energy transfer, theoretical mass spectra, fragmentation mechanisms, and the possibility of distinguishing isoleucine (I) and leucine (L). Furthermore, discussion is given regarding the differences between single collision CID activation, which results from a localized impact between the ions and a colliding molecule N, and previous thermal activation simulation results; Z. Homayoon, S. Pratihar, E. Dratz, R. Snider, R. Spezia, G. L. Barnes, V. Macaluso, A. Martin-Somer and W. L. Hase, J. Phys. Chem. A, 2016, 120, 8211-8227. Upon thermal activation unimolecular fragmentation is statistical and in accord with RRKM unimolecular rate theory. Simulations show that in collisional activation some non-statistical fragmentation occurs, including shattering, which is not present when the ions dissociate statistically. Products formed by non-statistical shattering mechanisms may be related to characteristic mass spectrometry peaks which distinguish the two isomers I and L.

A sudden change from indirect to direct mechanism for Cl− + CH3I at Erel of 0.27–0.28 eV in a relatively small collision energy range of 0.15–0.40 eV is revealed and many indirect mechanisms are identified.