CECAM workshop on:
Upscaling from ab initio to Molecular Dynamics:
Interatomic Potentials and Hybrid Methods

Scientific background

The so-called ``up-scaling'' of materials simulations, from ab initio Quantum Mechanics, to classical molecular dynamics, to mesoscopic approaches such as phase field or discrete dislocation dynamics, to continuum-level simulations, presents a number of challenging problems which bring together a variety of fields in science and engineering. Such Multiscale Modeling approaches are currently being developed for a wide variety of materials, including soft matter (biomaterials, polymers, etc.), molecular crystals (such as high explosives), ceramics, and metals.   A key step in ''bridging the scales'' from electrons to devices is the ability to perform large scale atomistic simulations (Molecular Dynamics or Monte Carlo) of the fundamental processes that govern the behavior of the material with an accurate and computationally efficient description of the atomic interactions.  Despite the enormous advances in ab initio methods such calculations are too computationally demanding to study directly most of the processes relevant for the modeling of mechanical or electrical properties, chemistry, etc. Thus, the need for accurate interatomic potentials is evident.

The most common approach to obtain accurate atomic interactions is fitting a classical potential to a variety of data coming from
experiments and/or ab initio simulations. In order to increase the accuracy and range of validity of the potentials, this data should sample a wide variety of atomic conformations (equations of state in a wide pressure range for different structures, defect energies, etc.). Ab initio methods are the most appropriate means of obtaining such fundamental information.  This ``global'' procedure allows the design of a unique potential, which can reproduce the properties of a material (plasticity, phase transitions, etc.) with good accuracy under various conditions [1].

An alternative approach considers, instead, the classical potential as valid only in a particular localized region of the (P,T) phase
diagram.  Using a set of configurations that sample the phase space region of interest, the parameters of a classical potential are fitted to reproduce the force on each atom, evaluated from high-quality ab initio simulations. Although this potential is in general non-transferable to other thermodynamic conditions, there is a gain in the accuracy of the classical simulations results near the specified thermodynamical state.  This ``optimal potential'' method has been successively employed to investigate the melting curve and shock Hugoniot of iron [2], and the shock Hugoniot of tin [3]. An important, but largely unaddressed, question regarding this approach is how the parameters entering the potential function vary across the phase diagram, particulary phase boundaries.

Both of these approaches have been successfully applied to the study of metals, including phase transitions and high pressure
properties, such as those found under shock loading conditions. On the other hand, additional complications arise when covalent species, such as the organic compounds prevalent in chemical and biochemical systems, are considered.
A purely classical description for chemical reactions, the reactive empirical bond order (REBO) potential, has been developed and greatly extended by White, Brenner, and their collaborators for model explosives [4] and hydrocarbons [5,6]. The effect of the bond order term is included is to make the strength of chemical bonds depend on their local environments, thus allowing bond breaking and forming. A classical potential has been developed for explosives based on ab initio calculations [7]. Recently, even more complex potentials (including long-range electrostatic interactions with environment-dependent charges and bond order dependent valence terms) were developed and applied for hydrocarbons, energetic materials such and RDX and HMX (containing N and O in addition to C and H), metal oxides and metals [8].

However, as these empirical potentials become progressively more complex, it becomes apparent that more computational effort than necessary is being applied to ``uninteresting'' regions which are merely spectators, while still leaving questions about the accuracy in the chemically reactive regions undergoing bond breaking and forming or large strains. It seems worthwhile to explore hybrid methods which couple ab initio and classical molecular dynamics techniques; applying high-level treatments in chemically active regions while using simpler classical potentials for the less important spectator atoms [9,10].  If desired, the classical potential may even be modified on-the-fly during the simulation, as in the optimal potential technique. Although very accurate, these methods are still expensive as far as CPU time is concerned (dominated by the ab initio computation, even for small reactive regions).

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