Efficient Treatment of Local Meta-generalized Gradient Density Functionals via Auxiliary Density Expansion: The...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Meta-generalized gradient approximation (mGGA) functionals are crucial for accurate electronic structure calculations.
• Density fitting (DF) techniques, including DF-J and DF-X, accelerate computations by approximating integrals.
• Integrating mGGAs with DF methods presents challenges, particularly in computing the kinetic energy density (τ).

Purpose of the Study:

• To develop an efficient method for treating mGGA functionals with density fitting (DF-JX).
• To enable the use of υ-form mGGAs within the DF-JX framework.
• To assess the computational cost and potential of this new approach for molecular property calculations.

Main Methods:

• Developed a technique to compute the Laplacian of the density (υ) in DF-JX calculations, bypassing the need for kinetic energy density (τ).
• Compared the computational cost of υ-form mGGAs with standard GGAs and τ-based mGGAs.
• Investigated the translation of υ-form mGGAs to τ-form mGGAs using kinetic energy functionals.

Main Results:

• The υ-form mGGA calculations with DF-JX are only 10%-20% more expensive than GGAs.
• These calculations are several times faster than traditional τ-based mGGA calculations.
• Direct translation of υ-form to τ-form mGGAs was found to be unreliable currently.

Conclusions:

• The developed technique offers a computationally efficient way to implement mGGAs with density fitting.
• While direct translation to τ-form is not yet reliable, reparametrization of mGGAs into the υ-form is feasible.
• This method is expected to significantly aid in computing reaction pathways and transition states for medium-sized molecules.