A generalized Poisson equation and short-range self-interaction energies.

Area of Science:

• Physics
• Quantum Chemistry
• Computational Chemistry

Background:

• The Poisson equation is fundamental in describing potentials generated by charge distributions.
• Understanding self-interaction energy is crucial for accurate electronic structure calculations.
• Existing methods often struggle with short-range interactions and attenuation effects.

Purpose of the Study:

• To generalize the Poisson equation for attenuated Newtonian potentials.
• To establish a local mapping between density and potential under exponential attenuation.
• To derive novel density functionals for short-range self-interaction energy.

Main Methods:

• Generalization of the Poisson equation.
• Mathematical derivation of the local density-potential mapping.
• Application to derive density functionals.

Main Results:

• A generalized Poisson equation for attenuated potentials was formulated.
• A local mapping between density and potential was proven for exponential attenuation.
• Several density functionals for short-range self-interaction were derived.

Conclusions:

• The generalized Poisson equation offers a powerful tool for systems with attenuated potentials.
• The derived density functionals can improve the accuracy of electronic structure calculations.
• This work provides a new theoretical framework for addressing self-interaction errors.