Stochastic density functional and GW theories scaling linearly with system size

Roi Baer, Fritz Haber Center for Molecular Dynamics,Institute of Chemistry, The Hebrew University, Jerusalem, Israel
Daniel Neuhauser, Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, United States
Eran Rabani, Department of Chemistry, University of California, Berkelet, Berkeley, United States

Abstract

Kohn-Sham density functional theory (KS-DFT) is formulated as a statistical theory in which the electron density is determined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the forces on nuclei, the density and its moments, etc. "Self-averaging" leads to sublinear scaling KS-DFT electronic structure. The approach sidesteps calculation of the density matrix and thus is insensitive to its evasive sparseness. An embedded fragment stochastic DFT is then developed which greatly decreases the statistical fluctuations and allows improving the description of localized sites of interest. Based on the stochastic DFT a GW method is developed which scales linearly with system size. We demonstrate the results on silicon nanocrystals and large water clusters.

References

1. R. Baer, D. Neuhauser, E. Rabani "Self-averaging stochastic Kohn-Sham density functional theory", Phys. Rev. Lett. 111, 106402 (2013).

2. D. Neuhauser, Y. Gao, C. Arntsen, C. Karshenas, E. Rabani and R. Baer, "Breaking the theoretical scaling limit for predicting quasi-particle energies: The stochastic GW approach", Phys. Rev. Lett. 113, 076402 (2014).

3. D. Neuhauser, R. Baer and E. Rabani, "Embedded fragment stochastic density functional theory", J. Chem. Phys. 141, 041102 (2014).


Stochastic density functional and GW theories scaling linearly with system size Roi Baer, Fritz Haber Center for Molecular Dynamics,Institute of Chemistry, The Hebrew University, Jerusalem, Israel Daniel Neuhauser, Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, United States Eran Rabani, Department of Chemistry, University of California, Berkelet, Berkeley, United States Abstract Kohn-Sham density functional theory (KS-DFT) is formulated as a statistical theory in which the electron density is determined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the forces on nuclei, the density and its moments, etc. "Self-averaging" leads to sublinear scaling KS-DFT electronic structure. The approach sidesteps calculation of the density matrix and thus is insensitive to its evasive sparseness. An embedded fragment stochastic DFT is then developed which greatly decreases the statistical fluctuations and allows improving the description of localized sites of interest. Based on the stochastic DFT a GW method is developed which scales linearly with system size. We demonstrate the results on silicon nanocrystals and large water clusters. References 1. R. Baer, D. Neuhauser, E. Rabani "Self-averaging stochastic Kohn-Sham density functional theory", Phys. Rev. Lett. 111, 106402 (2013). 2. D. Neuhauser, Y. Gao, C. Arntsen, C. Karshenas, E. Rabani and R. Baer, "Breaking the theoretical scaling limit for predicting quasi-particle energies: The stochastic GW approach", Phys. Rev. Lett. 113, 076402 (2014). 3. D. Neuhauser, R. Baer and E. Rabani, "Embedded fragment stochastic density functional theory", J. Chem. Phys. 141, 041102 (2014).

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