Fisher Information Density Functional Theory.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Density functional theory (DFT) posits that electron density determines ground-state properties.
• Existing DFT methods rely on the electron density as the fundamental quantity.
• The inclusion of information-theoretic measures within DFT remains an active research area.

Purpose of the Study:

• To construct a novel theoretical framework based on Fisher information density.
• To explore the potential of Fisher information density as a descriptor in quantum mechanics.
• To establish the foundational principles of a Fisher information density functional theory.

Main Methods:

• Development of a theoretical formalism for Fisher information density functional theory.
• Extension of the variational principle to treat energy as a functional of Fisher information density.
• Mathematical derivation and validation of Hohenberg-Kohn-like theorems within the new framework.

Main Results:

• Demonstration that Fisher information density encapsulates all necessary information about observables.
• Successful construction of the Fisher information density functional theory.
• Proof of validity for Hohenberg-Kohn-like theorems in this information-theoretic approach.

Conclusions:

• Fisher information density functional theory offers a new perspective on electronic structure calculations.
• The established theorems suggest the potential for developing novel computational methods.
• This work opens avenues for integrating information theory into quantum mechanical descriptions.