Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wavefunctions

TL;DR

This paper applies Riemannian optimization techniques to improve the convergence and robustness of Restricted-Open-shell Hartree-Fock and CASSCF wavefunction calculations by reformulating them on flag manifolds.

Contribution

It introduces a novel geometric optimization framework for ROHF and CASSCF, demonstrating advantages over traditional methods in convergence robustness without parameter fine-tuning.

Findings

Robust convergence properties without fine-tuning

Effective reformulation on flag manifolds

Potential for improved orbital optimization

Abstract

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called flag manifolds, we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests Riemannian optimization as a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.