  Global Optimization with First-principles Energy Expressions (GOFEE) is an
efficient method for identifying low energy structures in computationally
expensive energy landscapes such as the ones described by density functional
theory (DFT), van der Waals-enabled DFT, or even methods beyond DFT. GOFEE
relies on a machine learned surrogate model of energies and forces, trained
on-the-fly, to explore configuration space, eliminating the need for expensive
relaxations of all candidate structures using first-principles methods. In this
paper we elaborate on the importance of the use of a Gaussian kernel with two
length scales in the Gaussian Process Regression (GPR) surrogate model. We
further explore the role of the use in GOFEE of the lower confidence bound for
relaxation and selection of candidate structures. In addition, we present two
improvements to the method: 1) the population generation now relies on a
clustering of all low-energy structures evaluated with DFT, with the lowest
energy member of each cluster making up the population. 2) the very final
relaxations in well-sampled basins of the energy landscape, the final
exploitation steps, are now performed as continued relaxation paths within the
first-principles method, to allow for arbitrarily fine relaxations of the best
structures, independently of the predictive resolution of the surrogate model.
The versatility of the GOFEE method is demonstrated by applying it to identify
the low-energy structures of gas-phase fullerene-type 24-atom carbon clusters
and of dome-shaped 18-atom carbon clusters supported on Ir(111).
