Density-functional expansion methods: evaluation of LDA, GGA, and meta-GGA functionals and different integral...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density Functional Theory (DFT) is a powerful tool for electronic structure calculations.
• The Kohn-Sham (KS) framework is a cornerstone of modern DFT.
• Approximations in DFT functionals and integral calculations can impact accuracy.

Purpose of the Study:

• To extend the Kohn-Sham potential energy expansion (VE) to include kinetic energy density variations.
• To perform a systematic comparison of local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA density functionals.
• To investigate the impact of integral approximations on self-consistent charge density-functional tight-binding (SCC-DFTB) methods.

Main Methods:

• Utilized the VE formulation with a 6-31G* basis set.
• Employed a
• Jacob's ladder
• approach to compare different functional types.
• Examined the effect of integral approximations on energy and matrix elements.

Main Results:

• The VE formulation accurately reproduces standard KS-DFT results without integral approximations.
• Meta-GGA functionals offer no substantial improvement over GGA functionals for the studied properties.
• GGA functionals demonstrate clear advantages over LDA functionals in modeling hydrogen bonds.
• Integral approximations, particularly to first-order matrix elements, are identified as the primary source of short-range repulsion in SCC-DFTB.

Conclusions:

• The VE formulation is a reliable extension of KS-DFT.
• The choice of functional (GGA vs. LDA) is crucial for accurately describing hydrogen bonds.
• Approximations in integral calculations significantly influence the accuracy of SCC-DFTB methods, especially concerning short-range interactions.