Supspace Gradient-Enhanced Kriging: A Superior SCF Optimization Method, by Daniel Wessling

Since its development the dominating optimization method for the HF- and DFT-SCF procedure has been DIIS. In this work a new candidate for a superior optimization method called Subspace Gradient Enhanced Kriging (s-GEK) is presented. Being a method more closely related to machine learning, s-GEK is fundamentally different from conventional optimization procedures: S-GEK is built around a covariance function from which a surrogate model is created. This allows (1) for the exploration of the surrogate model by a restricted variance optimization (RVO) and (2) for a systematic improvement of the surrogate model with the number of SCF iterations (up to a threshold). For the model a displacement based on a second order technique, such as RS-RFO or DIIS, is needed as part of the subspace. However, it is shown that a displacement from the simple BFGS procedure is sufficient, presumably making the time spent per iteration on par with DIIS. The performance of s-GEK was tested by a benchmark consisting of small to medium sized molecules with optimized geometries and geometries close to a transition state, as well as transition metal complexes, all in closed and open shell respectively. This benchmark has proven the s-GEK method to be superior to the standard r-GDIIS in most cases. A statistical analysis of the benchmark shows that s-GEK stabilizes and accelerates the convergence especially in hard to converge cases.