Generalizing Density Functional Theory with a Particle-Hole Expansion
Abstract
Strong electron correlation remains difficult to describe within conventional density functional approximations, particularly when natural-orbital occupations become strongly fractional. We introduce a systematic particle-hole expansion that generalizes density functional theory (DFT) through an explicit functional of the one-electron reduced density matrix. The previously derived cumulant-based correction emerges as the leading term and the thermal (entropic) correction as an infinite-order member whose coefficients are fixed by a single parameter. The expansion can be formulated as a moment problem solved by semidefinite programming with computational scaling comparable to DFT. We show that both the first- and second-order corrections yield closed-form natural-orbital occupations. Applications to periacenes and Fe-porphyrin demonstrate that the second-order correction substantially reduces excessive orbital fractionalization, yielding natural-orbital occupations and fundamental gaps in improved agreement with correlated calculations.
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BibTeX
@misc{zhao2026generalizing,
title = {{Generalizing Density Functional Theory with a Particle-Hole Expansion}},
author = {Shurui Zhao and Madhubani Mukherjee and David A. Mazziotti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40621},
eprint = {2610.40621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40621},
}
RIS
TY - UNPB
TI - Generalizing Density Functional Theory with a Particle-Hole Expansion
AU - Shurui Zhao
AU - Madhubani Mukherjee
AU - David A. Mazziotti
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40621
UR - https://arxiv.org/abs/2610.40621
AB - Strong electron correlation remains difficult to describe within conventional density functional approximations, particularly when natural-orbital occupations become strongly fractional. We introduce a systematic particle-hole expansion that generalizes density functional theory (DFT) through an explicit functional of the one-electron reduced density matrix. The previously derived cumulant-based correction emerges as the leading term and the thermal (entropic) correction as an infinite-order member whose coefficients are fixed by a single parameter. The expansion can be formulated as a moment problem solved by semidefinite programming with computational scaling comparable to DFT. We show that both the first- and second-order corrections yield closed-form natural-orbital occupations. Applications to periacenes and Fe-porphyrin demonstrate that the second-order correction substantially reduces excessive orbital fractionalization, yielding natural-orbital occupations and fundamental gaps in improved agreement with correlated calculations.
ER -