Exploring energy landscapes at the DFTB quantum level using the threshold algorithm: the case of the anionic metal cluster Au$$_{20}^{-}$$

Abstract

We report the combination of the threshold algorithm with the Density Functional-based Tight Binding method allowing for the exploration of complex potential energy surfaces and the evaluation of probability flows between their regions, at the quantum level. This original scheme is used to explore the energy landscape of an anionic 20-atom gold cluster, Au $$_{20}^{-}$$ . On the basis of the relevant structures, 19 structural groups are highlighted, all of them being variations about the pyramidal shape: (1) distorted pyramids, (2) pyramids in which the atom of one of the facets has been removed, leaving a hole, and placed at different positions on the cluster and (3) pyramids on which an atom located at a vertex has been removed and placed on an edge or on a facet. Upper limits of the energies required to connect the basins of the 19 groups on the potential energy surface are evaluated. Moreover, the attractive basins are identified on the basis of the analysis of the probability flows on the landscape. The comparison of the disconnectivity tree with the results of the flux analysis provides a consistent representation of the Au $$_{20}^{-}$$ basins’ proximity. Finally, we show how the new scheme allowed for the identification of counter-intuitive transition pathways.