Practical auxiliary basis implementation of Rung 3.5 functionals.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Kohn-Sham density functional theory (DFT) often uses approximate exchange-correlation functionals.
• Incorporating exact exchange improves accuracy but is computationally demanding.
• Existing methods struggle to balance accuracy and computational cost.

Purpose of the Study:

• To implement and test Rung 3.5 functionals, a novel approach to approximate DFT.
• To evaluate the performance of Rung 3.5 functionals for diverse chemical and physical properties.
• To explore the potential of Rung 3.5 functionals in advancing electronic structure calculations.

Main Methods:

• Developed a practical implementation of Rung 3.5 functionals.
• Expanded the dependence of the semilocal model density matrix (γSL) using an auxiliary basis set.
• Calculated energies and energy derivatives via 3D numerical integration.

Main Results:

• Rung 3.5 functionals demonstrated accuracy intermediate between semilocal and hybrid DFT approximations.
• Tested properties included molecular thermochemistry, kinetics, geometries, vibrational frequencies, bandgaps, and excitation energies.
• Nonlocal potential contributions from γSL showed both successes and limitations in predicting band structures and excitation energies.

Conclusions:

• Rung 3.5 functionals represent a promising advancement in DFT, offering a balance between accuracy and computational feasibility.
• The implementation and testing provide a foundation for further development and refinement of Rung 3.5 functional forms.
• Continued exploration of Rung 3.5 functionals is warranted to optimize their performance for electronic structure predictions.