LibppRPA: An Open-Source Library for Particle-Particle Random Phase Approximation

Abstract

The accurate description of electron correlation and excitation energies remains a fundamental challenge in quantum chemistry. The particle-particle random phase approximation (ppRPA) has emerged as a promising method for capturing a broad range of excited-state properties. However, the implementation of ppRPA has been largely limited to in-house software, restricting its accessibility and usability. In this work, we present LibppRPA, an open-source and lightweight Python library designed for efficient and flexible ppRPA calculations of (1) electronic excitation energy and its associated analytical gradients and (2) the ground state correlation energy, and its associated analytical gradients. LibppRPA enables seamless integration with existing quantum chemistry packages, such as PySCF, by utilizing occupation numbers, molecular orbital coefficients, and three-center electron repulsion integrals. We implement both direct diagonalization and the iterative Davidson algorithm for solving the ppRPA equations, as well as active-space approximations, allowing users to balance accuracy and computational efficiency. We demonstrate the performance of LibppRPA through benchmark calculations on singlet-triplet gaps, double excitations, charge-transfer excitations, and valence/Rydberg excitations, showcasing its reliability across diverse molecular systems. The library provides a robust platform for studying electronic excitations and offers new opportunities for future developments in electronic structure theory.