Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Theoretical physics

Background:

• Maximum overlap methods (MOM) are crucial for optimizing wave functions in self-consistent field (SCF) models like Hartree-Fock and density functional theory.
• These methods exhibit high sensitivity to the initial guess of the target wave function, often leading to convergence issues or suboptimal solutions.

Purpose of the Study:

• To introduce a novel projection operator framework for improved non-aufbau orbital selection within MOM.
• To develop new algorithms, Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), addressing the initial guess sensitivity.
• To present a new metric for quantifying the agreement between target and SCF results during MOM calculations.

Main Methods:

• Definition of a projection operator framework to establish a metric for orbital selection.
• Development and implementation of the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM).
• Utilizing simple user-defined target solutions based on molecular orbital permutations.

Main Results:

• PMOM and PIMOM demonstrate exceptional performance in optimizing wave functions.
• The proposed methods effectively address the sensitivity to initial guesses in MOM.
• A new, conceptually simple metric is introduced to measure SCF result agreement with the target.

Conclusions:

• The developed projection operator framework and associated algorithms (PMOM/PIMOM) offer a robust solution for wave function optimization.
• The new metric provides a valuable tool for monitoring and assessing the convergence and accuracy of MOM calculations.
• This work enhances the reliability and efficiency of computational chemistry methods for ground and excited states.