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arXiv · 2610.22284

Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation

Florian Matz·Paul G. Graf·Markus Penz·Christian Schilling
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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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Florian Matz, Paul G. Graf, Markus Penz, Christian Schilling. 2026-10-15. Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation. https://arxiv.org/abs/2610.22284

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