Accelerated causal Green's function molecular dynamics

Abstract

A Green's function formalism has been applied to solve the equations of motion in classical molecular dynamics simulations. This formalism enables larger time scales to be probed for vibration processes in carbon nanomaterials. In causal Green's function molecular dynamics (CGFMD), the total interaction potential is expanded up to the quadratic terms, which enables an exact solution of the equations of motion to be obtained for problems within the harmonic approximation, reasonable energy conservation, and fast temporal convergence. Differently from conventional integration algorithms in molecular dynamics, CGFMD performs matrix multiplications and diagonalizations within its main loop, which make its computational cost high and, therefore, has limited its use. In this work, we propose a method to accelerate CGFMD simulations by treating the full system of N atoms as a collection of N smaller systems of size n. Diagonalization is performed for smaller nd×nd dynamical matrices rather than the full Nd×Nd matrix (d=1,2, or 3). The eigenvalues and eigenvectors are then used in the CGFMD equations to update the atomic positions and velocities. We applied the method for one-dimensional lattices of oscillators and have found that the method rapidly converges to the exact solution as n increases. The computational time of the proposed method scales linearly with N, providing a considerable gain with respect to the O(N3) full diagonalization. The method also exhibits better accuracy and energy conservation than the velocity-Verlet algorithm. An OpenMP parallel version has been implemented and tests indicate a speedup of 14× for N= 50000 in affordable computers. Our findings indicate that CGFMD can be an alternative, competitive integration technique for molecular dynamics simulations.