QUANTUM-CLASSICAL CALCULATIONS OF THE NANOMECHANICAL PROPERTIES OF METALS

Abstract

Molecular-dynamics (MD) simulations constitute an important tool in the study of nanoscale metallic systems, especially so in the face of the difficulties plaguing their experimental analysis. Main limitations of the MD method stem from the empirical nature of the potentials employed, their functional form which is postulated ad hoc, and its classical nature. The neglect of electronic effects and the unjustified utilization of the potential for system configurations significantly different from those, for which the potential was parametrized makes the results of strictly classical calculations dubious, at least for a certain class of systems.

On the other hand, high computational complexity of quantum-based methods, where atomic interactions are described ab initio, prohibits their direct use in the study of systems larger than several tens of atoms. In the last decade, a growing popularity of so-called hybrid (or cross-scaling) methods can be observed, that is, methods which treat the most “interesting” part of the system with a quantum-based approach, while the remainder is treated classically. Physically sound handshaking between the two methodologies (quantum and classical) within a single simulation constitutes a serious challenge, the majority of difficulties concentrating around the interface between the fragments of the system treated with the two methods. The aforementioned interface is most easily constructed for covalently bonded systems, where the bonds cut by the isolation of the quantumbased region can be saturated by the introduction of specially crafted link-atoms. In metallic systems, however, due to electronic delocalization, this traditional approach cannot be employed.

This paper describes a physically sound and adequately efficient computational technique, which allows for the inclusion of results of locally employed quantum-based computations within a molecular-dynamics simulation, for systems described by the many-body Sutton-Chen (SC) potential, used in the study of fcc metals. The proposed technique was developed taking as a point of departure the Learn-on-the-Fly (LOTF) formalism, a recent development itself. The original LOTF approach is only suitable for two- or three-body potentials and is serial in nature, whereas the proposed technique can be used with many-body potentials and is parallel-ready.

An implementation of the proposed approach in the form of computer code, which allows for parallel hybrid computations for metallic systems is also described. Finally, results from a set of hybrid simulations of nanoindentation of a copper workmaterial with a hard indenter utilizing the aforementoned technique and computer code is presented, as evidence of its viability.