Hydrogen Molecule Dissociation Curve with Functionals Based on the Strictly Correlated Regime

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Density Functional Theory (DFT) approximations limit accuracy in strong electron correlation regimes.
• The exact strong-interaction limit of DFT, represented by strictly correlated electrons (SCE), is crucial for accurate electronic structure calculations.
• Understanding electron-electron interactions is fundamental to predicting molecular properties.

Purpose of the Study:

• To compute the strictly correlated electrons (SCE) functional for a hydrogen molecule using the dual Kantorovich formulation.
• To explore the comotion function and its corrections derived from an exact relation between the Kantorovich potential and the optimal map.
• To investigate the transformation of electron-electron distance into a one-body quantity by the SCE functional and its implications for new functional development.

Main Methods:

• Utilizing the dual Kantorovich formulation to calculate the SCE functional.
• Employing an exact relation between the Kantorovich potential and the optimal map to derive the comotion function.
• Analyzing the behavior of the SCE functional for a hydrogen molecule along its dissociation curve.

Main Results:

• The SCE functional was computed for the hydrogen molecule, providing insights into the strong-interaction limit of DFT.
• The study demonstrated that the SCE functional exactly converts the electron-electron distance into a one-body quantity.
• The dual Kantorovich formulation naturally yields the constant in the Kohn-Sham potential for finite systems, as proposed by Levy and Zahariev.

Conclusions:

• The dual Kantorovich formulation is a powerful tool for computing SCE functionals and understanding electron correlation.
• The exact transformation of electron-electron distance into a one-body quantity offers a pathway for developing improved approximate DFT functionals.
• This work validates and extends the application of the dual Kantorovich method in electronic structure theory.