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arXiv · 2005.12338

Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory

Wenjie Dou·Ming Chen·Tyler Y. Takeshita·Roi Baer·Daniel Neuhauser·Eran Rabani
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Abstract

We develop a range-separated stochastic resolution of identity approach for the $4$-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic resolution of identity and the remaining terms are treated using a stochastic resolution of identity. The approach is implemented within a second-order Greens function formalism with an improved $O(N^3)$ scaling with the size of the basis set, $N$. Moreover, the range-separated approach greatly reduces the statistical error compared to the full stochastic version ({\it J. Chem. Phys.} {\bf 151}, 044144 (2019)), resulting in computational speedups of ground and excited state energies of nearly two orders of magnitude, as demonstrated for hydrogen dimer chains.

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Wenjie Dou, Ming Chen, Tyler Y. Takeshita, Roi Baer, Daniel Neuhauser, Eran Rabani. 2020-05-25. Range-Separated Stochastic Resolution of Identity: Formulation and Application to Second Order Green's Function Theory. https://arxiv.org/abs/2005.12338

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