Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.
We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.
Theoretical Division and ‡Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States.
Christian F A
CF
Negre
Theoretical Division and ‡Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States.
Susan M
SM
Mniszewski
Theoretical Division and ‡Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States.
Marc J
MJ
Cawkwell
Theoretical Division and ‡Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States.
Nicolas
N
Bock
Theoretical Division and ‡Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States.
Michael E
ME
Wall
Theoretical Division and ‡Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory , Los Alamos, New Mexico 87545, United States.
Anders M N
AM
Niklasson