Fixed-Point Optimization of Atoms and Density in DFT

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Density Functional Theory (DFT) is a cornerstone of modern computational materials science.
• Efficient optimization of electronic density and atomic positions is crucial for accurate DFT calculations.
• Existing methods can be computationally intensive and require significant user intervention.

Purpose of the Study:

• To introduce a novel algorithm for simultaneous fixed-point optimization of density and atomic positions in DFT.
• To enhance computational efficiency and robustness in DFT calculations.
• To reduce the need for user intervention in the optimization process.

Main Methods:

• Development of an autoadaptive hybrid of standard Broyden methods for fixed-point optimization.
• Introduction of the concept of 'algorithmic greed' to understand Broyden method behavior.
• An ansatz for algorithm structure selection based on eigenvalue analysis of the curvature condition.

Main Results:

• The new algorithm achieves approximately twice the speed of conventional DFT optimization methods.
• The algorithm demonstrates robustness and requires minimal user input.
• Analysis suggests sublinear dependence on system size, influenced by chemical environments rather than atom count.

Conclusions:

• The developed algorithm offers a significant speedup and improved usability for DFT calculations.
• The insights into algorithmic greed and phase transitions provide a deeper understanding of optimization dynamics.
• The findings are consistent with existing literature on quasi-Newton methods and system size dependence.