An efficient optimization algorithm that hybridizes DFTB and DFT theories both operated within the modified basin hopping method.

The density functional tight-binding (DFTB) theory and density functional theory (DFT) are separately combined with the modified basin hopping (MBH) method into a two-stage optimization algorithm that is then applied in sequence to find the lowest-energy structures of Au clusters. In the first-stage, the DFTB/MBH is conducted mainly to provide a speedy and yet semi-quantitatively reliable searching of the lowest-energy structures so as to pave the way for the second-stage DFT/MBH for more refined and accurate sorting of them at the DFT level. To ensure high efficiency in searching the minimized energy, we pay more attention to the DFTB theory in particular the repulsive part energy and examine the quality of the DFTB parameters fitted to different sets of reference structures. This parametrization study is physically relevant since the cluster’s structure is basically determined, by and large, by the repulsive potential. To appreciate the nicety of the present method, we apply the latter and two other existing sets of DFTB parameters to perform the first-stage DFTB/MBH but, separately, we continue the second-stage optimization all by the same DFT/MBH method. We found that the lowest-energy geometries of gold clusters obtained are independent of the use of the DFTB theory to calculate the energy function in the first-stage minimization. Only the efficacy of executing the second-stage DFT/MBH which is generally time-consuming differs, however. In general, for duly-fitted DFTB parameters less computer time is required at the second-stage operation. On comparing further our calculated optimized Au structures with other theoretical calculations and existing experimental clusters, the very good agreement among them clearly explains that the present hybridized scheme has greater potential to efficiently perform with less or within affordable computing time the high-level DFT calculation for medium to larger sized clusters.