Systematic and efficient navigating potential energy surface: Data for silver doped gold clusters

Locating global minimum of certain atomistic ensemble is known to be a highly challenging and resource consuming task. This dataset represents joint usage of the semi-empirical PM7 Hamiltonian, Broyden–Fletcher–Goldfarb–Shanno algorithm and basin hopping scheme to navigate a potential energy surface. The Au20 nanocluster was used for calibration as its global minimum structure is well-known. Furthermore, Au18Ag2 and Au15Ag5 were simulated for illustration of the algorithm performance. The work shows encouraging results and, particularly, underlines proper accuracy of PM7 as applied to this type of heavy metal systems. The reported dataset motivates to use the benchmarked method for studying potential energy surfaces of manifold systems and locate their global-minimum atomistic configurations.


a b s t r a c t
Locating global minimum of certain atomistic ensemble is known to be a highly challenging and resource consuming task. This dataset represents joint usage of the semi-empirical PM7 Hamiltonian, Broyden-Fletcher-Goldfarb-Shanno algorithm and basin hopping scheme to navigate a potential energy surface. The Au 20 nanocluster was used for calibration as its global minimum structure is well-known. Furthermore, Au 18 Ag 2 and Au 15 Ag 5 were simulated for illustration of the algorithm performance. The work shows encouraging results and, particularly, underlines proper accuracy of PM7 as applied to this type of heavy metal systems. The reported dataset motivates to use the benchmarked method for studying potential energy surfaces of manifold systems and locate their global-minimum atomistic configurations. &

Value of the data
Since accuracy of PM7 was proven for gold nanoclusters, this method can be applied to other important problems in materials chemistry.
Knowledge regarding low-energy local minima of gold nanoclusters is useful to develop future synthetic methods and identify experimental structures.
The reported geometries and formation energies for unusual conformers can be elaborated using higher-level methods in computational chemistry.

Data
The paper reports possible local-minima structures of Au 20 , Au 18 Ag 2 , Au 15 Ag 5 obtained from the potential energy surface scans. Starting from an arbitrary geometry, a correct structure of the Au 20 nanocluster will be found (an experimental global-minimum conformation of Au 20 is known to be a pyramid with the T d point group symmetry) [1].

Experimental design, materials and methods
The wave functions of the GNCs at every optimization step were represented by means of the PM7 semi-empirical Hamiltonian [2]. PM7 uses the approximation of neglect of diatomic differential overlap, as applied to the Hartree-Fock (HF) method. In turn, all terms of the exact Hamiltonian in HF are expressed as a sum of one-electron operators. Unlike in HF, selected integrals in PM7 are parametrized in view of empirical data and may potentially provide more accurate results than HF. The convergence criterion of the wave function was set to 4.18 Â 10 À 4 kJ mol À 1 (Figs. 1-8).
The local optimizations were done by means of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [3]. This algorithm is essentially failure-proof at the expense of a significant number of iterations (single-point calculations) before it converges. The geometry convergence criterion was set to 1.0 kJ mol À 1 Å À 1 , which systematically corresponds to less than 0.1 kJ mol À 1 difference in total energy at two consequent BFGS steps ( Table 1).
The global optimization was propagated in the framework of the basin hopping (BH) algorithm [4]. Fifty one iterations were performed for every system and the resulting energies were compared to one another. The maximum displacement per gold atom was allowed to be 0.75 Å whereas effective temperature was set to 2000 K. The effective temperature is used to accept or decline possible translations/perturbations within the Metropolis test. For an efficient search, the temperature must be comparable to the higher barrier separating local minima on PES. Since different conformations of GNCs involve different order of bonds between the gold atoms, the bond breakage is required to go from one stable conformation towards another. The effective temperature parameter must be significantly large for the above reason.
The in-home code for navigating PES makes use of the implemented optimization routines provided by SciPy and ASE with minor technical modifications [5]. Implementation of PM7 in MOPAC2012 (openMOPAC.net), as provided by Dr. J.J.P. Stewart, was used. All structures and optimization pathways were visualized in VMD, version 1.9.1 [6]. Input structures were prepared in Gabedit [7].