A Continuum-Mechanically Oriented Revisitation of Andersen-Parrinello-Rahman Molecular Dynamics

A study of structural phase transitions in solids may have disparate goals and, con-sequently, be conducted within different conceptual frameworks: for example, energy-driven pattern formation is studied by variational methods, once an energy landscape has been specified qualitatively and quantitatively; but oftentimes such specifications are missing or insufficient, and more information is sought about the set of local min-ima and about the shape and height of the energy barriers around them, a task that molecular dynamics can handle [1, 2, 3, 4]. Or, one may ask whether or not there is an evolution process that connects two given local minima, a question whose answer is ultimately for continuum mechanics to give but may be hinted at by concocting a suitable metadynamics [5, 6, 7, 8, 9]. Or even, given an intermolecular potential of the type used by computational physicists for crystalline matter, one may try and arrive by a rigorous mathematical limit procedure at a consistent form of an energy functional to be scrutinized for possible pattern formation [10, 11, 12, 13]. Current Molecular Dynamics simulations concern a basic cell X including some 105 molecules – that is, matter chunks of attomole size – and have a duration T between 0.