A Novel Scheme for Accurate Md Simulations of Large Systems
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ABSTRACT We present a simple and informationally efficient approach to electronic-structure-based simulations of large material science systems. The algorithm is based on a flexible embedding scheme, in which the parameters of a model potential are fitted at run time to some precise information relevant to localised portions of the system. Such information is computed separately on small subsystems by electronic-structure "black box" subprograms, e.g. based on tight-binding and/or ab initio models. The scheme allows to enforce electronic structure precision only when and where needed, and to minimise the computed information within a desired accuracy, which can be systematically controlled. Moreover, it is inherently linear scaling, and highly suitable for modern parallel platforms, including those based on non-uniform processing. The method is demonstrated by performing computations of tight-binding accuracy on solid state systems in the ten thousand atoms size scale.
INTRODUCTION Modelling materials at the atomic level via Molecular Dynamics (MD) techniques is often a computationally intensive task. In spite of the ever-increasing availability of computer power, all known MD techniques are bound to be limited. The limits concern e.g., the size of the systems studied, the physical times simulated, and the precision of the force-models used. The exact balance of the simulation parameters depends on the nature of the specific application, and is often a compromise between the competing requirements of large enough simulated sizes, sufficient accuracy, and sufficient amount of accumulated statistics. Broadly speaking, the most accurate (e.g. first principles) simulations are limited to systems of a few hundred atoms and to simulation times in the picosecond range. Simulations using classical model potentials can currently deal with several million atoms (see e.g., ref. [1]) and with the nanosecond time range. Our discussion of the current status of MD techniques starts by looking at how the computed information is normally used to determine the simulated trajectories. It turns out that for a broad range of high-accuracy applications, once a concept of a non-uniform tolerable error is specified, it is possible to speed up the computations by a non-negligible factor. This can be achieved by saving on the amount of redundant computed information. Redundancies occur if the MD algorihm used is not flexible enough to evaluate new information only wherever and whenever this is really needed. An appealing scheme to introduce such flexibility can be developed from the concept of teaching on the flight to a classical model potential about all the "difficult" situations occurring anywhere in the system during the simulation run. The "difficult" situations correspond in practice to those local atomic arrangements for which the model alone is not a priori sufficiently accurate. For them, a more precise (and "costly") technique is used to develop support information. In this way, all the necessary information is fed into the calc
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