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

TL;DR

LibppRPA is presented, an open-source and lightweight Python library designed for efficient and flexible ppRPA calculations of electronic excitation energy and its associated analytical gradients and (2) the ground state correlation energy, and its associated analytical gradients.

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.

Figures (5)

• Figure 1: The architecture of LibppRPA.
• Figure 2: Left: dissociation curve of H2 obtained from phRPA@HF, ppRPA@HF, ppRPA@HF (multireference DFT) and CCSD. Right: behaviors of PBE, phRPA@HF and ppRPA@HF total energies of Be as a function of the electron number. The cc-pVDZ basis set was used.
• Figure 3: Natural transition orbitals (NTOs) of the triplet ground state in $\cdot$CH2(CH2)4C(CH3)H$\cdot$ obtained from ppRPA@B3LYP. The NTO weight is 0.998. Top: NTO of adding the first nonbonding electron. Bottom: NTO of adding the second nonbonding electron. The aug-cc-pVTZ basis set was used. Geometry was taken from Ref.yangSingletTripletEnergy2015. The isosurface value is 0.04 a.u.
• Figure 4: Electron density difference between the first singlet excited state and the ground state of anthracene-TCNE obtained from ppRPA@B3LYP. Yellow and blue indicate negative and positive electron densities, respectively. The cc-pVDZ basis set was used. Geometry was taken from Ref.steinReliablePredictionCharge2009. The isosurface value is 0.003.
• Figure 5: Optimized structures for $^3\Sigma^-_g$, $^1\Delta_g$, and $^1\Sigma^+_g$ states of oxygen molecule together with the corresponding potential energy surfaces. The optimized structures are denoted as red cross. The equilibrium bond lengths are 1.1663, 1.1681, and 1.1708 Å, for $^3\Sigma^-_g$, $^1\Delta_g$, and $^1\Sigma^+_g$ states, respectively.