Robust All-Electron Optimization in Orbital-Free Density-Functional Theory Using the Trust-Region Image Method.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Orbital-free density-functional theory (OF-DFT) offers a computationally efficient alternative to Kohn-Sham DFT.
• Accurate optimization of the electron density and chemical potential is crucial for OF-DFT.
• Existing optimization methods can be computationally intensive, limiting OF-DFT applications.

Purpose of the Study:

• To present a novel Gaussian-basis implementation of OF-DFT utilizing the trust-region image method (TRIM).
• To achieve highly accurate, benchmark all-electron results with stringent convergence criteria.
• To enable self-consistent handling of semilocal kinetic-energy and exchange-correlation functionals.

Main Methods:

• Implementation of OF-DFT using Gaussian basis sets.
• Application of the trust-region image method (TRIM) for second-order optimization.
• Simultaneous optimization of electron density and chemical potential, preserving saddle-point nature.

Main Results:

• Achieved an order of magnitude reduction in required iterations for convergence.
• Demonstrated benchmark all-electron results with very tight convergence.
• Successfully handled semilocal kinetic-energy and exchange-correlation functionals self-consistently.

Conclusions:

• The TRIM-based OF-DFT implementation provides a significant speedup in convergence.
• This method allows for direct comparison with established quantum-chemical and Kohn-Sham DFT methods.
• The developed tool is valuable for analyzing approximate kinetic-energy functionals in finite systems.