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Accelerated Green's function molecular dynamics



Vitor R. Coluci, Socrates de Oliveira Dantas Dantas, Vinod Tewary


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 Green's function molecular dynamics (GFMD), the total interaction potential is ex- panded up to the quadratic terms which, which enables an exact solution of the equations of motion to be obtained for problems within the harmonic approxima- tion, reasonable energy conservation, and fast temporal convergence. Differently from conventional integration algorithms in molecular dynamics, GFMD per- forms 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 GFMD simulations by treating the full system of N atoms as a collection of N smaller systems of size n. Diago- nalization is performed for smaller nd X nd dynamical matrices rather than the full Nd X Nd matrix (d = 1; 2; or 3). The eigenvalues and eigenvectors are then used in the GFMD 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 indi- cate a speed up of 14x for N = 50000 in affordable computers. Our findings indicate that GFMD can be an alternative, competitive integration technique for molecular dynamics simulations.
Computer Physics Communications


Green's functions, lattice vibrations, Laplace transform, materials modeling, molecular dynamics, parallel processing


Coluci, V. , Dantas, S. and Tewary, V. (2022), Accelerated Green's function molecular dynamics, Computer Physics Communications, [online], , (Accessed June 23, 2024)


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Created April 16, 2022, Updated March 2, 2023