Accelerating SCF Orbital Optimization with S‑GEK/RVO: Efficient Subspace Compression and Robust Convergence

We present enhancements to the S-GEK/RVO method for self-consistent
field (SCF) orbital optimization, aimed at improving computational
efficiency and robustness. Building on a gradient-enhanced Kriging
surrogate model and restricted-variance optimization, we introduce
three key modifications: (i) a cost-effective subspace expansion using
r-GDIIS or BFGS displacement predictions, (ii) a systematic undershoot
mitigation strategy in flat energy regions, and (iii) rigorous coordinate
and gradient transformations consistent with the exponential parametrization
of orbital rotations. Benchmarking across an extensive set of molecular
systemsincluding organic molecules, radicals, and transition-metal
complexesdemonstrates that the new S-GEK/RVO variants consistently
outperform the default (in OpenMolcas) r-GDIIS method in iteration
count, convergence reliability, and wall time. These improvements
make S-GEK/RVO a competitive alternative for SCF optimization and
suggest broader applicability to other orbital optimization and localization
problems.