Efficient CPU and GPU implementations of multicenter integrals over long-range operators using Cartesian Gaussian functions

19 January 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

We present a library for evaluating multicenter integrals over polarization operators of the form $x^{m_x} y^{m_y} z^{m_z} r^{-k} C(r)$ using Cartesian Gaussian basis functions. $m_x, m_y, m_z \geq 0$, $k > 2$ are integers, while the cutoff function, $C(r)=(1 - e^{-\alpha r^2})^q$, with $\alpha \in \mathbb{R}_{+}$ and certain integer values of $q$ ensures the existence of the integrals. The formulation developed by P. Schwerdtfeger and H. Silberbach [Phys. Rev. A 37, 2834 (1988)] is implemented in an efficient and stable way taking into account a recent fix in one of the equations. A cheap upper bound is presented that allows negligible integrals to be prescreened. The correctness of the analytical integrals was verified by numerical integration. The library provides separate codes for serial CPU and parallel GPU architectures and can be wrapped into a python module.

Keywords

polarization integrals
polarizable embedding
Gaussian basis sets
core polarization potentials
one-electron integrals
long-range interaction
multipole expansion

Supplementary materials

Title
Description
Actions
Title
source code of library for polarization integrals
Description
C++/CUDA/python implementation of the polarization integrals according to Schwerdtfeger et al. Phys. Rev. A 37, 2834-2842 (1988)
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