MuAPBEK: An improved analytical kinetic energy density functional for quantum chemistry

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Orbital-free density functional theory (OFDFT) offers computational efficiency by using only electron densities.
• Accurate kinetic-energy density functionals are crucial for OFDFT's success but remain a significant challenge.
• Existing functionals like APBEK have limitations in accuracy for various systems.

Purpose of the Study:

• To develop a more accurate kinetic-energy functional for OFDFT.
• To improve the computational efficiency and scalability of OFDFT simulations.
• To address limitations in current OFDFT functionals by incorporating physical constraints.

Main Methods:

• Developed the MuAPBEK functional by tuning the $\mu$ parameter of APBEK and adding corrections.
• Incorporated Kato's cusp condition and the virial theorem into the functional.
• Tested the functional on atoms and molecules, comparing results with APBEK and Thomas-Fermi-von-Weizsäcker functionals.

Main Results:

• MuAPBEK demonstrated significantly reduced energy errors compared to APBEK and Thomas-Fermi-von-Weizsäcker.
• The functional yields accurate electron densities, with minor deviations from Kohn-Sham DFT (KSDFT) results.
• Density optimization using MuAPBEK is over ten times faster than KSDFT self-consistent field (SCF) cycles, with O(N^1.96) scaling.

Conclusions:

• The MuAPBEK functional represents a significant advancement for OFDFT, offering improved accuracy and efficiency.
• Accurate and scalable OFDFT simulations are feasible beyond current practical KSDFT limits.
• This work paves the way for large-scale quantum mechanical simulations using OFDFT.