Exact Sum-Rule Approach to Polarizability and Asymptotic van der Waals Functionals─Derivation of Exact...

Area of Science:

• Theoretical Chemistry
• Quantum Mechanics
• Computational Physics

Background:

• Accurate calculation of van der Waals (vdW) forces is crucial in chemistry and physics.
• Existing density functional approximations often struggle with long-range correlation effects.
• Developing exact and efficient methods for vdW interactions remains a significant challenge.

Purpose of the Study:

• To develop an exact theoretical framework for polarizability and asymptotic vdW correlation energy functionals.
• To create functionals that depend solely on monomer ground-state properties.
• To provide a method for exact benchmarking of vdW density functionals.

Main Methods:

• Utilizing a sum-rule approach for theoretical development.
• Solving a single position-space differential equation for functional evaluation.
• Avoiding summations over excited states and frequency integrations.

Main Results:

• An exact theoretical framework for polarizability and asymptotic vdW correlation energy functionals was established.
• Explicit functional forms were derived for systems like atomic hydrogen and confined electrons.
• The method demonstrated superior performance compared to the Vydrov-van Voorhis functional when density decays at atomic scales.

Conclusions:

• The sum-rule approach offers general validity for vdW density functional theory.
• This framework enables exact benchmarking and inspection of long-range correlation effects.
• The developed functionals provide an accurate and efficient way to compute vdW interactions.