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Title: 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 re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement 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 e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the 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 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.
Authors:
 [1] ;  [1] ;  [1] ;  [1] ;  [1] ;  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-16-20827
Journal ID: ISSN 1549-9618
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 12; Journal Issue: 7; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Material Science; Quantum Molecular Dynamics, Inverse Overlap Factorization
OSTI Identifier:
1338765

Negre, Christian F. A, Mniszewski, Susan M., Cawkwell, Marc Jon, Bock, Nicolas, Wall, Michael E., and Niklasson, Anders Mauritz. Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations. United States: N. p., Web. doi:10.1021/acs.jctc.6b00154.
Negre, Christian F. A, Mniszewski, Susan M., Cawkwell, Marc Jon, Bock, Nicolas, Wall, Michael E., & Niklasson, Anders Mauritz. Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations. United States. doi:10.1021/acs.jctc.6b00154.
Negre, Christian F. A, Mniszewski, Susan M., Cawkwell, Marc Jon, Bock, Nicolas, Wall, Michael E., and Niklasson, Anders Mauritz. 2016. "Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations". United States. doi:10.1021/acs.jctc.6b00154. https://www.osti.gov/servlets/purl/1338765.
@article{osti_1338765,
title = {Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations},
author = {Negre, Christian F. A and Mniszewski, Susan M. and Cawkwell, Marc Jon and Bock, Nicolas and Wall, Michael E. and Niklasson, Anders Mauritz},
abstractNote = {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 re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement 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 e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the 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 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.},
doi = {10.1021/acs.jctc.6b00154},
journal = {Journal of Chemical Theory and Computation},
number = 7,
volume = 12,
place = {United States},
year = {2016},
month = {6}
}