Using electronegativity and hardness to test density functionals | JoVE Visualize

Area of Science:

Computational Chemistry
Quantum Chemistry
Materials Science

Background:

Density functional theory (DFT) is widely used but suffers from a lack of universality, limiting its predictive power.
Energy-density imbalances and errors in functionals can arise, particularly concerning the chemical potential.
Absolute electronegativity (χ) and hardness (η) are proposed as key indicators of the energy-density relationship and DFT universality.

Purpose of the Study:

To investigate the universality of 50 diverse DFT functionals by evaluating their performance in describing absolute electronegativity (χ) and hardness (η) for atoms Z = 1-36.
To identify which functionals best capture the chemical potential (∂E/∂N) and its second derivative (∂²E/∂N²), crucial aspects of DFT universality.
To establish performance metrics for χ and η as a simple probe of functional universality.

Main Methods:

Calculated absolute electronegativity (χ) and hardness (η) for atoms Z = 1-36 using 50 different DFT functionals.
Analyzed the mean absolute errors (MAE) for χ and η across various functional classes (GGA, hybrid, etc.).
Performed density sensitivity calculations to understand errors related to orbital occupations and exact exchange.

Main Results:

Few functionals accurately describe both χ and η; η shows error cancellation, while χ is sensitive to error propagation.
Standard GGA and hybrid functionals exhibit limited accuracy for χ, indicating issues with describing the chemical potential in DFT.
Popular functionals like B3LYP, PBE, and revPBE perform poorly for both χ and η.
Density-derived errors, especially from degenerate p- and d-orbitals, contribute to non-universality and dependence on exact exchange.
Functionals B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD show the best performance for χ, indicating higher universality.
B98 and B97-1 demonstrate accuracy for diverse metal-ligand bonds, supporting χ and η as probes of universality.

Conclusions:

Performance in describing absolute electronegativity (χ) serves as a critical metric for assessing DFT functional universality, probing the chemical potential.
A balanced description of both χ and η is essential for a universal functional, with B98 and B97-1 showing promising results.
The study provides a framework for evaluating and developing more universal DFT functionals.