The Fisher-Shannon information plane, an electron correlation tool.

Area of Science:

• Quantum chemistry
• Quantum information theory

Background:

• Information theory measures like Shannon entropy and Fisher information are crucial in quantum chemistry.
• Analyzing electron density distributions provides insights into atomic and molecular properties.

Purpose of the Study:

• To introduce a novel correlation measure based on the product of Shannon entropy power and Fisher information.
• To analyze the properties of this new measure in two-electron systems.
• To investigate bounds for information measures in many-electron systems.

Main Methods:

• Analysis of the Fisher-Shannon information plane for two-electron systems (He-like ions, Hooke's atoms).
• Examination of uncertainty and scaling properties of the proposed information product.
• Derivation of bounds for Fisher and Shannon measures in finite many-electron systems.

Main Results:

• A new correlation measure, the product of Shannon entropy power and Fisher information, was successfully introduced.
• The uncertainty and scaling properties of this information product were characterized.
• Fisher and Shannon measures for many-electron systems were shown to be bounded by single-electron measures and the electron count.

Conclusions:

• The new correlation measure offers a valuable tool for analyzing electron density.
• The study provides fundamental insights into the behavior of information measures in atomic and molecular systems.
• Established bounds offer a theoretical framework for understanding electron correlation in complex systems.