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arXiv · 2311.18161

Random Green's function method for large-scale electronic structure calculation

Mingfa Tang·Chang Liu·Aixia Zhang·Qingyun Zhang·Shengjun Yuan·Youqi Ke
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Abstract

We report a linear-scaling random Green's function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states to stochastically express the density matrix, and rGF is calculated with the linear-scaling computational cost. We show the rGF method is generally applicable to the nonorthogonal localized basis, and circumvent the large Chebyshev expansion for the density matrix. As a demonstration, we implement rGF with density-functional Tight-Binding method and apply it to self-consistently calculate water clusters up 9984 H2Os. We find the rGF method combining with a simple fragment correction can reach an error of ~1meV per H2O in total energy, compared to the deterministic calculations, due to the self-average. The development of rGF method advances the stochastic electronic structure theory to a new stage of the efficiency and applicability.

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Mingfa Tang, Chang Liu, Aixia Zhang, Qingyun Zhang, Shengjun Yuan, Youqi Ke. 2023-11-30. Random Green's function method for large-scale electronic structure calculation. https://arxiv.org/abs/2311.18161

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