Automated fit of high-dimensional potential energy surfaces using cluster analysis and interpolation over descriptors of chemical environment

We present a method for fitting high-dimensional potential energy surfaces that is almost fully automated, can be applied to systems with various chemical compositions, and involves no particular choice of function form. We tested it on four systems: Ag20, Sn6Pb6, Si10, and Li8. The cost for energy evaluation is smaller than the cost of a density functional theory (DFT) energy evaluation by a factor of 1500 for Li8, and 60,000 for Ag20. We achieved intermediate accuracy (errors of 0.4 to 0.8 eV on atomization energies, or, 1% to 3% on cohesive energies) with rather small datasets (between 240 and 1400 configurations). We demonstrate that this accuracy is sufficient to correctly screen the configurations with lowest DFT energy, making this function potentially very useful in a hybrid global optimization strategy. We show that, as expected, the accuracy of the function improves with an increase in the size of the fitting dataset.