LibRPA: A software package for low-scaling first-principles calculations of random phase approximation electron correlation energy based on numerical atomic orbitals

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 $O\left(N^2\right)$ 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

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.

Program summary

Program title: LibRPA

CPC Library link to program files: https://doi.org/10.17632/kdwm5vzgk6.1

Developer's repository link: https://github.com/Srlive1201/LibRPA

Licensing provisions: LGPL

Programming language: C++, Fortran, Python

Nature of problem: Calculating RPA electron correlation energies is computationally expensive, typically scaling as $O\left(N^4\right)$ with system size, hindering its application to large-scale materials science problems.

Solution method: LibRPA utilizes the Localized Resolution of Identity (LRI) technique, reducing computational scaling to $O\left(N^2\right)$ or better. Implemented in C++ and Python with MPI/OpenMP parallelization, it integrates with NAO-based DFT packages, facilitating efficient and accurate RPA calculations for large-scale periodic systems.