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arXiv · 2102.02989

Fast periodic Gaussian density fitting by range separation

Hong-Zhou Ye·Timothy C. Berkelbach
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Abstract

We present an efficient implementation of periodic Gaussian density fitting (GDF) using the Coulomb metric. The three-center integrals are divided into two parts by range-separating the Coulomb kernel, with the short-range part evaluated in real space and the long-range part in reciprocal space. With a few algorithmic optimizations, we show that this new method -- which we call range-separated GDF (RSGDF) -- scales sublinearly to linearly with the number of $k$-points for small to medium-sized $k$-point meshes that are commonly used in periodic calculations with electron correlation. Numerical results on a few three-dimensional solids show about $10$-fold speedups over the previously developed GDF with little precision loss. The error introduced by RSGDF is about $10^{-5}~E_{\textrm{h}}$ in the converged Hartree-Fock energy with default auxiliary basis sets and can be systematically reduced by increasing the size of the auxiliary basis with little extra work. [The article has been accepted by The Journal of Chemical Physics.]

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Hong-Zhou Ye, Timothy C. Berkelbach. 2021-03-23. Fast periodic Gaussian density fitting by range separation. https://doi.org/10.1063/5.0046617

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