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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Exactly Factorized Molecular Kohn-Sham Density Functional Theory.

Lucien Dupuy^1,2, Benjamin Lasorne³, Emmanuel Fromager^1,2

¹Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France.

Journal of Computational Chemistry

|July 13, 2026

Summary

This study extends Kohn-Sham density functional theory (KS-DFT) to include both electrons and nuclei. New equations disentangle nuclear and electronic densities, enabling extensions beyond the Born-Oppenheimer approximation.

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Area of Science:

Quantum Chemistry
Computational Physics
Electronic Structure Theory

Background:

Recent work established an exact Kohn-Sham density functional theory (KS-DFT) for electrons and nuclei.
This theory maps nuclear and electronic densities to a fictitious non-interacting system.

Purpose of the Study:

To apply the exact factorization formalism to the molecular KS wavefunction.
To derive disentangled, coupled marginal and conditional KS equations.
To explore extensions of KS-DFT beyond the Born-Oppenheimer approximation.

Main Methods:

Application of the exact factorization formalism.
Derivation of marginal and conditional KS equations.
Analysis of second-order geometrical derivatives.

Main Results:

The derived equations are equivalent to the original exact KS-DFT.
These equations offer new avenues for extending KS-DFT beyond the Born-Oppenheimer approximation.
The role of correlations from second-order geometrical derivatives is investigated.

Conclusions:

The new formalism provides a pathway to incorporate nuclear quantum effects within KS-DFT.
This work facilitates practical extensions of KS-DFT beyond the Born-Oppenheimer approximation.
Understanding correlations is crucial for accurate electronic structure calculations.