Explicit-by-Implicit Treatment of Natural Orbital Occupations Using First- and Second-Order Optimization Algorithms:...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Reduced Density Matrix Functional Theory (RDMFT) is crucial for accurate electronic structure calculations.
• Convergence issues in RDMFT optimization affect the reliability of theoretical models.
• The ensemble N-representability constraint poses a significant challenge.

Purpose of the Study:

• To investigate and improve convergence in RDMFT natural occupation optimization.
• To evaluate the performance of the explicit-by-implicit (EBI) method combined with various optimization algorithms.
• To assess the reliability of RDMFT for strongly correlated systems and large molecules.

Main Methods:

• Exploration of EBI combined with Lagrangian Multipliers (LM), Augmented Lagrangian Methods (ALM), and Gradient Descent (GD).
• Comparison of first- and second-order numerical optimization algorithms.
• Performance evaluation on various systems, including strongly correlated and large molecules.

Main Results:

• LM and ALM exhibit convergence issues across different system sizes.
• EBI optimizations converge to better energies with fewer iterations than LM/ALM.
• EBI combined with Gradient Descent (EBI@GD) consistently yields the lowest energies with favorable computational scaling.
• EBI@NM struggles with local minima in strongly correlated systems and large molecules.

Conclusions:

• The EBI method offers significant advantages for RDMFT calculations, particularly for transition states, strongly correlated systems, and large molecules.
• EBI@GD emerges as a robust and efficient approach for RDMFT optimization.
• This study provides valuable insights for developing more efficient RDMFT algorithms.