The FADE mass-stat: a technique for inserting or deleting particles in molecular dynamics simulations

The emergence of new applications of molecular dynamics (MD) simulation calls for the development of mass-statting procedures that insert or delete particles on-the-fly. In this paper we present a new mass-stat which we term FADE, because it gradually "fades-in" (inserts) or "fades-out" (deletes) molecules over a short relaxation period within a MD simulation. FADE applies a time-weighted relaxation to the intermolecular pair forces between the inserting/deleting molecule and any neighbouring molecules. The weighting function we propose in this paper is a piece-wise polynomial that can be described entirely by two parameters: the relaxation time scale and the order of the polynomial. FADE inherently conserves overall system momentum independent of the form of the weighting function. We demonstrate various simulations of insertions of atomic argon, polyatomic TIP4P water, polymer strands, and C60 Buckminsterfullerene molecules. We propose FADE parameters and a maximum density variation per insertion-instance that restricts spurious potential energy changes entering the system within desired tolerances. We also demonstrate in this paper that FADE compares very well to an existing insertion algorithm called USHER, in terms of accuracy, insertion rate (in dense fluids), and computational efficiency. The USHER algorithm is applicable to monatomic and water molecules only, but we demonstrate that FADE can be generally applied to various forms and sizes of molecules, such as polymeric molecules of long aspect ratio, and spherical carbon fullerenes with hollow interiors.