Enhancing Reduced Density Matrix Functional Theory Calculations by Coupling Orbital and Occupation Optimizations.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Reduced density matrix functional theory (RDMFT) calculations typically use decoupled optimization methods for orbitals and occupations.
• Existing methods like unitary optimization for orbitals and explicit-by-implicit (EBI) for occupations, while robust individually, lead to slow convergence.
• Decoupled RDMFT optimizations often require numerous alternations, hindering computational efficiency and broader applicability.

Purpose of the Study:

• To develop a novel coupled optimization method for RDMFT calculations.
• To enhance the convergence speed, stability, and practicality of RDMFT.
• To enable simultaneous updates of orbitals and occupations within a single optimization step.

Main Methods:

• A coupled optimization strategy combining unitary and EBI methods for simultaneous orbital and occupation updates.
• Introduction of an effective preconditioner and line search to ensure favorable convergence with a first-order algorithm.
• Extensive testing on various molecules, basis sets, functionals, and initial guesses to validate the method's performance.

Main Results:

• The coupled optimization method demonstrates superior convergence speed, accuracy, and stability compared to all tested decoupled methods.
• Significant reduction in the number of iterations required for convergence, even for large systems like C60.
• Achieved high precision (10^-8 au) for a C60 molecule in a practical number of iterations (154).

Conclusions:

• The proposed coupled optimization method offers a substantial improvement over traditional decoupled approaches in RDMFT.
• This advancement makes RDMFT calculations more efficient and practical for a wider range of scientific applications.
• The coupled method facilitates further development and broader adoption of RDMFT in computational chemistry and related fields.