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Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients

Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients

Published on: August 22, 2018

Generalized gradient approximation model exchange holes for range-separated hybrids.

Thomas M Henderson¹, Benjamin G Janesko, Gustavo E Scuseria

¹Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005-1892, USA. th4@rice.edu

The Journal of Chemical Physics

|May 27, 2008

Summary

We developed a new model for the exchange hole in generalized gradient approximation (GGA) density functionals. This model accurately reproduces GGA energies and enables analytic calculations for hybrid density functionals.

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Last Updated: Jul 5, 2026

Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients

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Published on: August 22, 2018

Area of Science:

Computational chemistry
Quantum chemistry
Materials science

Background:

Generalized gradient approximations (GGAs) are widely used for density functional theory (DFT) calculations.
Accurate modeling of the exchange hole is crucial for improving GGA functional performance.
Existing models for the exchange hole have limitations in energy reproduction and analytic evaluation.

Purpose of the Study:

To propose a general and accurate model for the spherically averaged exchange hole corresponding to GGA exchange functionals.
To enable fully analytic evaluation of range-separated hybrid density functionals.
To improve upon existing exchange hole models for DFT calculations.

Main Methods:

Developed a general model for the spherically averaged exchange hole.
Adapted the model of Ernzerhof and Perdew.
Reported parameters for several common GGAs.
Enabled analytic evaluation of range-separated hybrid density functionals.

Main Results:

The proposed model precisely reproduces the energy of the parent GGA.
The model allows for fully analytic evaluation of range-separated hybrid density functionals.
Analytic results and thermochemical tests show improvement over the Iikura et al. model.

Conclusions:

The new exchange hole model offers improved accuracy and computational efficiency for GGA and hybrid density functionals.
This work facilitates more precise and efficient electronic structure calculations in various scientific fields.
The model provides a foundation for developing more advanced density functionals.