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Title: Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

Journal Article · · Journal of Chemical Theory and Computation
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  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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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.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-06NA25396
OSTI ID:
1338765
Report Number(s):
LA-UR-16-20827
Journal Information:
Journal of Chemical Theory and Computation, Vol. 12, Issue 7; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science

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Cited By (6)

The basic matrix library (BML) for quantum chemistry journal August 2018
Next generation extended Lagrangian first principles molecular dynamics journal August 2017
Canonical-ensemble extended Lagrangian Born–Oppenheimer molecular dynamics for the linear scaling density functional theory journal September 2017
Three-body expansion of the fragment molecular orbital method combined with density-functional tight-binding journal January 2017
Machine Learning Meliorates Computing and Robustness in Discrete Combinatorial Optimization Problems journal November 2016
Adaptive frozen orbital treatment for the fragment molecular orbital method combined with density-functional tight-binding journal February 2018

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Related Subjects

36 MATERIALS SCIENCE
Material Science
Quantum Molecular Dynamics
Inverse Overlap Factorization