The limitations of Slater's element-dependent exchange functional from analytic density-functional theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Density-Functional Theory

Background:

• The Slater-Roothaan (SR) method utilizes Gaussian basis sets for expressing molecular orbitals and electron density within density-functional theory (DFT).
• Variational fitting techniques can be extended to the resolution of identity method, impacting the accuracy of two-electron integrals.

Purpose of the Study:

• To review the analytic and variational Slater-Roothaan (SR) method formulation.
• To examine the performance of the SR method using different alpha parameters for predicting atomization energies, bond distances, and ionization potentials.
• To propose improvements for the SR method to achieve chemical accuracy in energy calculations.

Main Methods:

• The study reviews the analytic and variational Slater-Roothaan (SR) method, which allows arbitrary scaling of the exchange-correlation potential via Slater's exchange parameters (alpha).
• Performance evaluation involved calculating atomization energies for 148 molecules using Hartree-Fock (HF) alpha(HF) and exact atomic (EA) alpha(EA) parameters.
• A new set of alpha values was determined by minimizing the mean absolute error (MAE) in atomization energies.

Main Results:

• The SR method with alpha(EA) parameters yielded a mean absolute error (MAE) of approximately 33 kcal/mol for atomization energies.
• Using alpha(HF) parameters improved performance with an MAE of about 26 kcal/mol.
• Optimizing alpha values by minimizing MAE resulted in an MAE of approximately 14.5 kcal/mol, outperforming widely used generalized-gradient approximations.

Conclusions:

• The Slater-Roothaan (SR) method demonstrates good performance for predicting atomization energies, bond distances, and ionization potentials, outperforming local-density approximation and Hartree-Fock theory.
• Optimized alpha parameters significantly enhance the accuracy of atomization energy predictions.
• The computationally efficient SR method is a promising tool for studying large molecular systems.