Development of a Minimal Auxiliary Basis for the Particle--Particle Random Phase Approximation (ppRPA): Accelerating Excited-State Calculations in Diradical Nanoparticles and Periodic Systems
Abstract
Singlet--triplet gaps set the energy scale of the two-spin manifold in molecular quantum information materials, and such systems frequently carry diradical character: metal nanoclusters, metal--organic frameworks with radical linkers, and the nitrogen--vacancy center in diamond. Time-dependent density functional theory is the standard tool at this size but describes multireference systems poorly. A closed-shell reference is inadequate for a multiconfigurational ground state, and the adiabatic kernel excludes doubly excited configurations. The particle--particle random phase approximation (\pprpa{}) changes the particle number rather than the spin. Singlet and triplet states descend from one closed-shell reference, and double excitations enter on the same footing as single ones. Computational cost has confined \pprpa{} to small systems, and the two-electron integrals that drive it are factorized through an auxiliary basis. We develop \pprpa{}--as, which reduces that basis to a minimal set of atom-centered Gaussian shells whose exponents follow from free-atom radii and one global scaling factor. The approximation enters only the excited-state step, so both calculations proceed from the same self-consistent reference. We test molecules and clusters of up to 286 atoms, including heavy elements, and seven point defects in four periodic hosts, obtaining both multiplicities and their splitting without symmetry breaking or spin projection. We optimize the scaling factor and give guidance on choosing it. An order-of-magnitude smaller auxiliary basis delivers a speed-up of up to eightfold while staying within $0.03$~eV of conventional \pprpa{}, bringing diradical nanoclusters and periodic systems within reach.
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BibTeX
@misc{wang2026development,
title = {{Development of a Minimal Auxiliary Basis for the Particle--Particle Random Phase Approximation (ppRPA): Accelerating Excited-State Calculations in Diradical Nanoparticles and Periodic Systems}},
author = {Yuchen Wang and Zhenyu Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18020},
eprint = {2610.18020},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18020},
}
RIS
TY - UNPB
TI - Development of a Minimal Auxiliary Basis for the Particle--Particle Random Phase Approximation (ppRPA): Accelerating Excited-State Calculations in Diradical Nanoparticles and Periodic Systems
AU - Yuchen Wang
AU - Zhenyu Li
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18020
UR - https://arxiv.org/abs/2610.18020
AB - Singlet--triplet gaps set the energy scale of the two-spin manifold in molecular quantum information materials, and such systems frequently carry diradical character: metal nanoclusters, metal--organic frameworks with radical linkers, and the nitrogen--vacancy center in diamond. Time-dependent density functional theory is the standard tool at this size but describes multireference systems poorly. A closed-shell reference is inadequate for a multiconfigurational ground state, and the adiabatic kernel excludes doubly excited configurations. The particle--particle random phase approximation (\pprpa{}) changes the particle number rather than the spin. Singlet and triplet states descend from one closed-shell reference, and double excitations enter on the same footing as single ones. Computational cost has confined \pprpa{} to small systems, and the two-electron integrals that drive it are factorized through an auxiliary basis. We develop \pprpa{}--as, which reduces that basis to a minimal set of atom-centered Gaussian shells whose exponents follow from free-atom radii and one global scaling factor. The approximation enters only the excited-state step, so both calculations proceed from the same self-consistent reference. We test molecules and clusters of up to 286 atoms, including heavy elements, and seven point defects in four periodic hosts, obtaining both multiplicities and their splitting without symmetry breaking or spin projection. We optimize the scaling factor and give guidance on choosing it. An order-of-magnitude smaller auxiliary basis delivers a speed-up of up to eightfold while staying within $0.03$~eV of conventional \pprpa{}, bringing diradical nanoclusters and periodic systems within reach.
ER -