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

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.