TY - JOUR

T1 - Expeditious stochastic calculation of random-phase approximation energies for thousands of electrons in three dimensions

AU - Neuhauser, Daniel

AU - Rabani, Eran

AU - Baer, Roi

PY - 2013/4/4

Y1 - 2013/4/4

N2 - A fast method is developed for calculating the random phase approximation (RPA) correlation energy for density functional theory. The correlation energy is given by a trace over a projected RPA response matrix, and the trace is taken by a stochastic approach using random perturbation vectors. For a fixed statistical error in the total energy per electron, the method scales, at most, quadratically with the system size; however, in practice, due to self-averaging, it requires less statistical sampling as the system grows, and the performance is close to linear scaling. We demonstrate the method by calculating the RPA correlation energy for cadmium selenide and silicon nanocrystals with over 1500 electrons. We find that the RPA correlation energies per electron are largely independent of the nanocrystal size. In addition, we show that a correlated sampling technique enables calculation of the energy difference between two slightly distorted configurations with scaling and a statistical error similar to that of the total energy per electron.

AB - A fast method is developed for calculating the random phase approximation (RPA) correlation energy for density functional theory. The correlation energy is given by a trace over a projected RPA response matrix, and the trace is taken by a stochastic approach using random perturbation vectors. For a fixed statistical error in the total energy per electron, the method scales, at most, quadratically with the system size; however, in practice, due to self-averaging, it requires less statistical sampling as the system grows, and the performance is close to linear scaling. We demonstrate the method by calculating the RPA correlation energy for cadmium selenide and silicon nanocrystals with over 1500 electrons. We find that the RPA correlation energies per electron are largely independent of the nanocrystal size. In addition, we show that a correlated sampling technique enables calculation of the energy difference between two slightly distorted configurations with scaling and a statistical error similar to that of the total energy per electron.

KW - correlation energy

KW - density functional theory

KW - random phase approximation

KW - stochastic iterations

UR - http://www.scopus.com/inward/record.url?scp=84875786795&partnerID=8YFLogxK

U2 - 10.1021/jz3021606

DO - 10.1021/jz3021606

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AN - SCOPUS:84875786795

SN - 1948-7185

VL - 4

SP - 1172

EP - 1176

JO - Journal of Physical Chemistry Letters

JF - Journal of Physical Chemistry Letters

IS - 7

ER -