The Source of Some Empirical Density Functionals van der Waals Forces

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density functional approximations (DFAs) are essential in chemistry for their balance of accuracy and computational cost.
• Minnesota functionals are highly parameterized DFAs known for exceptional accuracy in thermochemistry and weak interactions.
• However, their underlying physical mechanisms and potential limitations require further investigation.

Purpose of the Study:

• To investigate the origin of the high accuracy of Minnesota functionals, particularly in describing weak medium-range interactions.
• To determine if the performance of these functionals is linked to artifacts or physical principles.
• To provide guidance for the development of future density functional approximations.

Main Methods:

• Analysis of the performance of various Minnesota functionals.
• Investigation of the role of basis set incompleteness in the functionals' accuracy.
• Evaluation of the electron density distortion and adherence to fundamental theorems like the Hellmann-Feynman theorem.

Main Results:

• The remarkable accuracy of many Minnesota functionals in reproducing weak interactions stems from exploiting basis set incompleteness.
• This exploitation leads to a physics-defying behavior and can cause distortions in calculated electron densities.
• The Hellmann-Feynman theorem is often violated, indicating a potential artifact rather than true physical accuracy.

Conclusions:

• The accuracy of Minnesota functionals in certain areas is an artifact of basis set incompleteness, not necessarily robust physical modeling.
• Future development of highly parameterized density functionals, including neural network-based approaches, should prioritize adherence to fundamental theorems like the Hellmann-Feynman theorem.
• Satisfying the Hellmann-Feynman theorem should be a key criterion for parameterization to ensure physically meaningful results.