Function domains and the universal matrix functional of multi-state density functional theory

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Recent advancements in Hamiltonian matrix density functionals for multiple electronic eigenstates.
• Existing Kohn-Sham density functional theory (DFT) concepts like density representability.
• Need for a rigorous theoretical framework for multistate density functional theory (MSDFT).

Purpose of the Study:

• To delve into the mathematical foundation of multistate density functional theory (MSDFT).
• To extend physical concepts of Kohn-Sham DFT to matrix density functionals.
• To establish a rigorous variational principle for MSDFT.

Main Methods:

• Generalization of the Lieb universal functional to a universal matrix functional for many states.
• Extension of density representability concepts to matrix density functionals.
• Analysis of subspace symmetry and invariance properties of the Hamiltonian matrix functional.

Main Results:

• Establishment of the existence of the universal matrix functional for many states.
• Rigorous definition of the variational principle for MSDFT within the domain of matrix densities.
• Demonstration that Hamiltonian matrix functional structure is constrained by symmetry and invariance properties.

Conclusions:

• Provides a solid theoretical framework for density functional theory of both ground and excited states.
• Ensures coherent variational optimization of all Hamiltonian matrix functional elements.
• Solidifies the theoretical foundation for treating multiple electronic states using density functional theory.