Interior Eigenvalues from Density Matrix Expansions in Quantum Mechanical Molecular Dynamics
Abstract
An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e.g., [A. M. N. Niklasson, Phys. Rev. B, 66 (2002), 155115], which are accelerated by a scale-and-fold technique [E. H. Rubensson, J. Chem. Theory Comput., 7 (2011), pp. 1233--1236]. The acceleration scheme requires interior eigenvalue estimates, which may be expensive and cumbersome to come by. Here we show how such eigenvalue estimates can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost. Our method is illustrated with density functional tight-binding Born--Oppenheimer molecular dynamics simulations, where the computational effort is dominated by the density matrix construction. In our analysis we identify two different phases of the recursive polynomial expansion, the conditioning and purification phases, and we show that the acceleration represents an improvement of the conditioning phase, which typically gives a significant reduction of the computational cost.
Keywords
- Born--Oppenheimer molecular dynamics
- density functional theory
- density matrix purification
- Fermi operator expansion
- homo-lumo gap
- interior eigenvalues
- linear scaling electronic structure theory
- matrix functions
- nonmonotonic expansion
- recursive expansion
- scale-and-fold acceleration
- trace-correcting purification
MSC codes
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: B147 - B170
DOI: 10.1137/130911585
ISSN (online): 1095-7197
Copyright
© 2014, Society for Industrial and Applied Mathematics.
History
Submitted: 1 March 2013
Accepted: 2 December 2013
Published online: 11 March 2014
Keywords
- Born--Oppenheimer molecular dynamics
- density functional theory
- density matrix purification
- Fermi operator expansion
- homo-lumo gap
- interior eigenvalues
- linear scaling electronic structure theory
- matrix functions
- nonmonotonic expansion
- recursive expansion
- scale-and-fold acceleration
- trace-correcting purification
MSC codes
Authors
Metrics & Citations
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