Finite-temperature adiabatic-connection reduced density-matrix functional theory: a unified framework for i-DMFT and TAO-DFT
Abstract
Accurately describing chemical bond breaking requires capturing strong/static electron correlation, a major challenge for single-reference self-consistent-field methods such as Hartree--Fock and Kohn--Sham density-functional theory (DFT). Fractional occupations substantially improve this situation, as demonstrated by information-density-matrix-functional theory (i-DMFT) and thermally-assisted-occupation DFT (TAO-DFT). Although useful, they are formulated within rather different theoretical frameworks, are somewhat semi-empirical, and their relationship remains unclear. Here we introduce finite-temperature adiabatic-connection reduced density-matrix functional theory (FT-AC-RDMFT), in which i-DMFT and TAO-DFT emerge as different reductions of a unified framework. The effective eigenvalue equation for natural orbitals and the Fermi--Dirac occupation numbers follow directly from the variational principle, while a thermal adiabatic connection relates the empirical entropy coefficient of i-DMFT to a characteristic temperature of the auxiliary non-interacting system. Within this framework, i-DMFT is the exact-exchange-based reduction, whereas TAO-DFT results when exact exchange is replaced by a density-based exchange-correlation functional. Numerical calculations confirm that i-DMFT, apart from a constant, coincides with the exact-exchange realization of the framework, and show that the improved dissociation behavior from finite-temperature occupations extends beyond exact exchange to hybrid and semilocal density functionals. For strongly correlated V2O3, finite-temperature occupations substantially reduce the severely overestimated non-magnetic LDA bulk modulus, bringing it close to experiment. These results establish FT-AC-RDMFT as a common theoretical foundation for finite-temperature occupation-based electronic-structure methods in molecular and solid-state systems.
Related
- Adding Temperature to the Adiabatic Connection: Hybrid Functionals for Static and Dynamic Correlation
- ROSE: Deep Learning exchange-correlation functional from reduced density-matrix representations
- Uncovering Chemical Degradation Pathways in Amide-Functional Sulfur Polymers for Room-Temperature Na-S Batteries
- fix uvt and fix pimd/uvt: A Unified LAMMPS Framework for Constant-Potential Constant-Temperature Molecular Dynamics
- Fluoride-Free Siloxane Circularity at Room Temperature: Tetrabutylammonium Hydroxide as a Dual-Functional De- and Repolymerization Initiator for Silicone Oils, Elastomers, and Hybrid Coatings
BibTeX
@misc{han2026finitetemperature,
title = {{Finite-temperature adiabatic-connection reduced density-matrix functional theory: a unified framework for i-DMFT and TAO-DFT}},
author = {Jingang Han and Huanjing Gong and Kai Luo and Hongming Weng and Xinguo Ren},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14706},
eprint = {2610.14706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14706},
}
RIS
TY - UNPB
TI - Finite-temperature adiabatic-connection reduced density-matrix functional theory: a unified framework for i-DMFT and TAO-DFT
AU - Jingang Han
AU - Huanjing Gong
AU - Kai Luo
AU - Hongming Weng
AU - Xinguo Ren
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14706
UR - https://arxiv.org/abs/2610.14706
AB - Accurately describing chemical bond breaking requires capturing strong/static electron correlation, a major challenge for single-reference self-consistent-field methods such as Hartree--Fock and Kohn--Sham density-functional theory (DFT). Fractional occupations substantially improve this situation, as demonstrated by information-density-matrix-functional theory (i-DMFT) and thermally-assisted-occupation DFT (TAO-DFT). Although useful, they are formulated within rather different theoretical frameworks, are somewhat semi-empirical, and their relationship remains unclear. Here we introduce finite-temperature adiabatic-connection reduced density-matrix functional theory (FT-AC-RDMFT), in which i-DMFT and TAO-DFT emerge as different reductions of a unified framework. The effective eigenvalue equation for natural orbitals and the Fermi--Dirac occupation numbers follow directly from the variational principle, while a thermal adiabatic connection relates the empirical entropy coefficient of i-DMFT to a characteristic temperature of the auxiliary non-interacting system. Within this framework, i-DMFT is the exact-exchange-based reduction, whereas TAO-DFT results when exact exchange is replaced by a density-based exchange-correlation functional. Numerical calculations confirm that i-DMFT, apart from a constant, coincides with the exact-exchange realization of the framework, and show that the improved dissociation behavior from finite-temperature occupations extends beyond exact exchange to hybrid and semilocal density functionals. For strongly correlated V2O3, finite-temperature occupations substantially reduce the severely overestimated non-magnetic LDA bulk modulus, bringing it close to experiment. These results establish FT-AC-RDMFT as a common theoretical foundation for finite-temperature occupation-based electronic-structure methods in molecular and solid-state systems.
ER -