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

In this report, three versions of SCF/KS-DFT orbital optimization are described and benchmarked. The methods are a modified version of the gradient type of the direct inversion in the iterative subspace approach (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 to improve 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 technique that has proved 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 standard state-of-the-art SCF/KS-DFT optimization methods.