Energy Landscape Exploration of Sub‐Nanometre Copper–Silver Clusters

Abstract

The energy landscapes of sub-nanometre bimetallic coinage metal clusters are explored with the Threshold Algorithm coupled with the Birmingham Cluster Genetic Algorithm. Global and energetically low-lying minima along with their permutational isomers are located for the Cu(4)Ag(4) cluster with the Gupta potential and density functional theory (DFT). Statistical tools are employed to map the connectivity of the energy landscape and the growth of structural basins, while the thermodynamics of interconversion are probed, based on probability flows between minima. Asymmetric statistical weights are found for pathways across dividing states between stable geometries, while basin volumes are observed to grow independently of the depth of the minimum. The DFT landscape is found to exhibit significantly more frustration than that of the Gupta potential, including several open, pseudo-planar geometries which are energetically competitive with the global minimum. The differences in local minima and their transition barriers between the two levels of theory indicate the importance of explicit electronic structure for even simple, closed shell clusters.

Computational studies of stable hexanuclear CulAgmAun(l + m + n = 6;l,m,n > 0) clusters

“…As for the Quantum Chemistry (QC) methods and combined schemes (EP and QC in tandem), they allow limited PES searches for small clusters mainly because of the demanding convergence process involved in the quantum mechanical solution of the multi‐electron problem. Nevertheless QC approaches have revealed the existence of unexpected structures in pure or bimetallic clusters …”

“…Nevertheless QC approaches have revealed the existence of unexpected structures in pure or bimetallic clusters. [28][29][30] Earlier studies on coinage metal (Cu, Ag, and Au) clusters were performed using EP to analyze a variety of properties, for example, thermodynamic properties of small clusters, [21,31,32] and more recently, larger noble metal nanoparticles have been the subject of extensive computations regarding their thermal stability and structural changes. [33] Despite the relatively good description of atomic bonding provided by empirical potentials, the electronic contribution is taken into account only implicitly in the parameter set of each EP.…”

Prediction and clarification of structures of (bio)molecules on surfaces

“…For the exploration of the connectivity and barrier structure of the energy landscape of molecules, various search methods such as standard saddle-point search procedures [16], the threshold algorithm [157] where random walkers explore the landscape below a given set of energy lids [81,158], and metadynamics [140] where MD or MC simulations are combined with elements of taboo-searches [159] that prevent a return to previously explored parts of the energy landscape [53], are available and have been employed to study molecular systems. Besides these global search methods, there…”

“…For small systems like e.g. inorganic [81] or intermetallic [158] clusters in vacuum, such searches could be performed on the ab initio energy level [156], but for larger ones, empirical potentials were employed, often combined with ab initio local optimizations [189]. Nevertheless, there are some studies following the procedure type F, which could be considered global searches.…”

First principles global optimization of metal clusters and nanoalloys

“…New regions of the landscape become available by increasing the threshold and repeating the stochastic exploration of the PES. For example, DFT has been used in a combined threshold algorithm and GA study to investigate the structures and interconversions of low-lying isomers of Cu 4 Ag 4 [156].…”