Trust Region Minimization of Orbital Localization Functions

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Electronic Structure Theory

Background:

• The minimization of localization functions is crucial for obtaining interpretable molecular orbitals.
• The standard trust region method can require small step sizes, hindering efficiency for large systems.
• Hartree-Fock (HF) orbitals provide a fundamental description of electronic structure.

Purpose of the Study:

• To adapt the trust region method for efficient minimization of localization functions.
• To enable the calculation of both local occupied and local virtual Hartree-Fock orbitals.
• To improve the robustness and convergence of the method for large molecular systems.

Main Methods:

• Application of the trust region method to localization function minimization.
• Modification of the trust radius update scheme for exponential parametrization.
• Integration of a line search along a conservatively estimated step direction.

Main Results:

• Successful acquisition of local occupied and local virtual Hartree-Fock orbitals.
• Demonstration that large steps can be safely taken in the modified trust region method.
• Achievement of robust and nearly monotonic convergence for large molecular systems.

Conclusions:

• The adapted trust region method provides an efficient and robust approach for orbital localization.
• The modified step size strategy overcomes limitations of the standard trust region method for large systems.
• This method facilitates the generation of localized orbitals essential for chemical interpretation.