Time-dependent pair density from the principle of minimum Fisher information

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• The Euler equation is fundamental in describing time-dependent quantum systems.
• Pair density functional theory (PDFT) offers an alternative to traditional wavefunction methods.
• Understanding electron-electron interactions is crucial for accurate molecular modeling.

Purpose of the Study:

• To derive the Euler equation for time-dependent pair density.
• To explore the connection between minimum Fisher information and PDFT.
• To introduce a novel concept of steric effects in electron pairs.

Main Methods:

• Derivation of the Euler equation from the principle of minimum Fisher information.
• Derivation of the same Euler equation using time-dependent pair density functional theory.
• Definition of steric pair energy based on Weizsäcker kinetic energy.

Main Results:

• The Euler equation for time-dependent pair density was successfully derived via two independent methods.
• A new physical concept, the steric effect, was proposed for electron pairs.
• Steric pair energy was defined as the Weizsäcker kinetic energy of electron pairs.

Conclusions:

• The study establishes a link between Fisher information and time-dependent PDFT for pair density.
• The proposed steric effect offers a new perspective on electron correlation.
• The defined steric pair energy provides a quantifiable measure for electron pair interactions.