A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures

In this work, three
versions of self-consistent field/Kohn–Sham
density functional theory (SCF/KS-DFT) orbital optimization are described
and benchmarked. The methods are a modified version of the geometry
version of the direct inversion in the iterative subspace approach
(which we call r-GDIIS), the modified restricted step rational function
optimization method (RS-RFO), and the novel subspace gradient-enhanced
Kriging method combined with restricted variance optimization (S-GEK/RVO).
The modifications introduced are aimed at improving the robustness
and computational scaling of the procedures. In particular, the subspace
approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization
of a machine learning technique that has proven to be successful in
geometry optimizations. The performance of the three methods is benchmarked
for a large number of small- to medium-sized organic molecules, at
equilibrium structures and close to a transition state, and a second
set of molecules containing closed- and open-shell transition metals.
The results indicate the importance of the resetting technique in
boosting the performance of the r-GDIIS procedure. Moreover, it is
demonstrated that already at the inception of the subspace version
of GEK to optimize SCF wave functions, it displays superior and robust
convergence properties as compared to those of the standard state-of-the-art
SCF/KS-DFT optimization methods.