PIGLE — Particles Interacting in Generalized Langevin Equation simulator

Abstract

We present a package using Simulink and MATLAB to perform molecular dynamics simulations of interacting particles obeying a Generalized Langevin Equation. The package, which accounts for three spatial dimensions and rigid-body like rotation, is tuned to explore surface diffusion of co-adsorbed species. The physical parameters are species specific, and include userdefined colored noise spectra and memory friction kernels acting independently on translational and rotational degrees of freedom. We benchmark the simulations using established analytical results for dynamical correlation functions, and we use the package to numerically verify novel analytical results concerning dissipative rotational motion and mutli-exponential friction kernels. The package provides a straightforward way to expand the modeling of ultra-fast surface diffusion problems at the atomic scale.

Alkali metal adsorption on metal surfaces: new insights from new tools

“…The simulations are carried out on the Cambridge High Performance Computing cluster using the PIGLE MD Simulator. 43 PIGLE MD simulations used in this work follow the Langevin equation, in which a static Potential Energy Surface (PES), a drag term proportional to particle velocity, Gaussian distributed stochastic forces satisfying the fluctuation dissipation theorem, and pairwise, radial interadsorbate interactions, are applied. Since the decay of the ISFs tends to zero as DK approaches zero, we have concluded that perpendicular motion is insignificant in the measured ISFs, and hence carried out 2D simulations.…”

“…For each simulation, the PES was generated using Fourier interpolation between the DFT values for the principal adsorption sites (top, bridge and hollow), and assuming the potential at half way between the top and hollow sites, is an average of the two. 43 In both cases the coverage is y = 0.028 ML, as determined above, and the repulsive forces are calculated from the dipole interactions and the known changes in the workfunction. The simulations are performed for a range of friction values from 0 to 4 ps À1 .…”

Inter-adsorbate forces and coherent scattering in helium spin-echo experiments

“…In the present work we are concerned with the calculation of scattering from the adsorbates and, for that purpose, the Langevin, or Generalised-Langevin framework provides a convenient and well established method to understand the motion. [25][26][27][28][29] Here, the dynamical coordinates of the adsorbates are treated explicitly while the substrate interactions are represented by an adiabatic potential-energy surface. Thermal excitation is represented by a combination of random forces and an appropriate frictional force and it is possible to include an explicit description of inter-adsorbate interactions.…”

Atomic Scattering For Chemical Analysis Of Surfaces

“…To simulate the adsorbate dynamics, we use PIGLE, a molecular dynamics simulator which solves the Langevin equation ( 1) for the particles. 9 The Langevin equation is written as…”

“…where the r i denotes the trajectory of the i th particle, µ denoting the species of particles, V the surface potential, γ the drag coefficient, ξ(t) the stochastic noise and F ij the interactions between the particles. 9 Once the dynamics are solved for, the scattered amplitude from the i th adsorbate of the µ's species can be calculated assuming the kinematic approximation:…”