What question did this study set out to answer?

The aim is to clarify the approximations in the quantum-classical density functional theory (DFT) framework for mixed systems.

February 8, 2026

A variational formulation of the free energy of mixed quantum-classical systems: Coupling classical and electronic density functional theories.

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The aim is to clarify the approximations in the quantum-classical density functional theory (DFT) framework for mixed systems.
Developed a theoretical framework for quantum-classical systems under finite temperatures.
Introduced a variational formulation for Helmholtz free energy using QM/MM density matrix.
Employed constrained-search methods and permutational symmetry for computations.
Established connections with existing cDFT and eDFT methods.
Formulated the free energy in terms of quantum and classical one-body densities.
Generalized the cDFT and eDFT frameworks for QM/MM systems.
Introduced a new universal correlation functional for mixed systems.

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Develops a framework to clarify approximations in quantum-classical systems, suggesting a new approach for free energy calculations.

Jeanmairet et al. (2026) studied this question.

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