Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation
Abstract
Capturing static and dynamic electron correlation simultaneously at manageable computational cost remains a key challenge in electronic structure theory. Motivated by the recurring role of effective temperature in self-consistent field methods we extend the adiabatic connection mechanism from density functional theory to include a temperature dimension. This gives rise to thermally enhanced hybrid functionals, in which static correlation is captured via fractional occupations generated by an effective "correlation temperature" within thermal Hartree-Fock, while dynamic correlation is described by established density functional approximations. The framework formally unifies information-density matrix functional theory (i-DMFT) and thermally-assisted-occupation (TAO-)DFT as special cases, clarifying their theoretical basis and the respective prescriptions for the temperature parameter. We assess the performance of several thermally enhanced hybrids for different cases where i-DMFT was previously shown to fail. Furthermore, we discuss and test different schemes for determining the correlation temperature and investigate the accuracy of different such choices for a benchmark set derived from biphenyl. The results help to clarify the achievable balance of accuracy, generality, and efficiency, establishing thermally enhanced hybrids as a systematic route toward low-cost treatment of both correlation types.
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BibTeX
@misc{matz2026adding,
title = {{Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation}},
author = {Florian Matz and Paul G. Graf and Markus Penz and Christian Schilling},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22284},
eprint = {2610.22284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22284},
}
RIS
TY - UNPB
TI - Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation
AU - Florian Matz
AU - Paul G. Graf
AU - Markus Penz
AU - Christian Schilling
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22284
UR - https://arxiv.org/abs/2610.22284
AB - Capturing static and dynamic electron correlation simultaneously at manageable computational cost remains a key challenge in electronic structure theory. Motivated by the recurring role of effective temperature in self-consistent field methods we extend the adiabatic connection mechanism from density functional theory to include a temperature dimension. This gives rise to thermally enhanced hybrid functionals, in which static correlation is captured via fractional occupations generated by an effective "correlation temperature" within thermal Hartree-Fock, while dynamic correlation is described by established density functional approximations. The framework formally unifies information-density matrix functional theory (i-DMFT) and thermally-assisted-occupation (TAO-)DFT as special cases, clarifying their theoretical basis and the respective prescriptions for the temperature parameter. We assess the performance of several thermally enhanced hybrids for different cases where i-DMFT was previously shown to fail. Furthermore, we discuss and test different schemes for determining the correlation temperature and investigate the accuracy of different such choices for a benchmark set derived from biphenyl. The results help to clarify the achievable balance of accuracy, generality, and efficiency, establishing thermally enhanced hybrids as a systematic route toward low-cost treatment of both correlation types.
ER -