A study of the adiabatic connection for two-electron systems

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• The adiabatic connection method is a theoretical framework in quantum chemistry.
• It connects a non-interacting system to an interacting system via a coupling parameter.
• Understanding its behavior is crucial for accurate electronic structure calculations.

Purpose of the Study:

• To investigate the adiabatic connection method for two-particle systems.
• To explore conditions where ground-state properties may deviate from standard predictions.
• To analyze the behavior of Kohn-Sham potentials in specific interacting systems.

Main Methods:

• Constraining ground-state wave functions using moment conditions.
• Generating local one-body potentials to support these wave functions.
• Examining a two-particle system with a parameter-dependent potential and analyzing state intersections.

Main Results:

• Obtained constrained ground-state wave functions for noninteracting and partially interacting systems.
• Generated local one-body potentials supporting these wave functions.
• Observed state intersections in an interacting system where Kohn-Sham eigenvalues did not intersect, indicating potential violations of adiabatic connection assumptions.

Conclusions:

• The study demonstrates cases where occupying orbitals by energy does not guarantee the ground state.
• It highlights that assumptions of the adiabatic connection method can be violated in certain scenarios.
• This has implications for the accuracy of electronic structure calculations using this method.