Towards a Holomorphic Density Functional Theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Self-consistent-field (SCF) approximations in Hartree-Fock (HF) and Kohn-Sham density-functional theory (KS-DFT) can lead to multiple solutions.
• The relationship between these multiple SCF solutions across HF and KS-DFT remains poorly understood.

Purpose of the Study:

• To investigate the formal relationship between multiple SCF solutions in HF and KS-DFT.
• To develop a method for continuously mapping these solutions between the two theoretical frameworks.

Main Methods:

• Introduction of a parameterized functional to scale between HF and KS-DFT representations.
• Continuous mapping of multiple SCF solutions using the hydrogen molecule and an electron transfer model.
• Development of a complex-analytic extension of DFT, termed "holomorphic DFT".

Main Results:

• Multiple SCF solutions were observed to coalesce and disappear as the functional was varied.
• This behavior was found to be analogous to the vanishing of real HF solutions during structural changes.
• The holomorphic DFT approach enables analytical continuation of SCF stationary states across molecular structures and functionals.

Conclusions:

• A direct connection between multiple SCF solutions in HF and KS-DFT has been established.
• Holomorphic DFT provides a robust framework for tracking SCF solutions, overcoming their disappearance under varying conditions.
• This work offers a deeper understanding of SCF solution landscapes in quantum chemical calculations.