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Issue 47, 2015
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A real-space stochastic density matrix approach for density functional electronic structure

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Abstract

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn–Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman–Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

Graphical abstract: A real-space stochastic density matrix approach for density functional electronic structure

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Publication details

The article was received on 01 Mar 2015, accepted on 07 May 2015 and first published on 08 May 2015


Article type: Paper
DOI: 10.1039/C5CP01222H
Citation: Phys. Chem. Chem. Phys., 2015,17, 31472-31479
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    A real-space stochastic density matrix approach for density functional electronic structure

    T. L. Beck, Phys. Chem. Chem. Phys., 2015, 17, 31472
    DOI: 10.1039/C5CP01222H

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