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 quantumbased 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 longterm 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 ELLPACKR sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tightbinding 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 quantumbased simulations even for molecular structures of intermediate size. For a 4,158 atom watersolvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.
 Authors:

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 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1620827
Journal ID: ISSN 15499618
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Theory and Computation
 Additional Journal Information:
 Journal Volume: 12; Journal Issue: 7; Journal ID: ISSN 15499618
 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 quantumbased 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 longterm 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 ELLPACKR sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tightbinding 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 quantumbased simulations even for molecular structures of intermediate size. For a 4,158 atom watersolvated 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}
}