LibRPA: A Software Package for Low-scaling First-principles Calculations of Random Phase Approximation Electron Correlation Energy Based on Numerical Atomic Orbitals

Abstract: LibRPA is a software package designed for efficient calculations of random phase approximation (RPA) electron correlation energies from first principles using numerical atomic orbital (NAOs). Leveraging a localized resolution of identity (LRI) technique, LibRPA achieves $O(N^2)$ or better scaling behavior, making it suitable for large-scale calculation of periodic systems. Implemented in C++ and Python with MPI/OpenMP parallelism, LibRPA integrates seamlessly with NAO-based density functional theory (DFT) packages through flexible file-based and API-based interfaces. In this work, we present the theoretical framework, algorithm, software architecture, and installation and usage guide of LibRPA. Performance benchmarks, including the parallel efficiency with respect to the computational resources and the adsorption energy calculations for H$_2$O molecules on graphene, demonstrate its nearly ideal scalability and numerical reliability. LibRPA offers a useful tool for RPA-based calculations for large-scale extended systems.