Evolution of the Structural and Electronic Properties of Medium-Sized Sodium Clusters: A Honeycomb-Like Na₂₀ Cluster

Abstract

Sodium is one of the best examples of a free-electron-like metal and of a certain technological interest. However, an unambiguous determination of the structural evolution of sodium clusters is challenging. Here, we performed an unbiased structure search among neutral and anionic sodium clusters in the medium size range of 10-25 atoms, using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method. Geometries are determined by CALYPSO structure searches, followed by reoptimization of a large number of candidate structures. For most cluster sizes the simulated photoelectron spectra of the lowest-energy structures are in excellent agreement with the experimental data, indicating that the current ground-state structures are the true minima. The equilibrium geometries show that, for both neutral and anionic species, the structural evolution from bilayer structures to layered outsides with interior atoms occurs at n = 16. A novel unprecedented honeycomb-like structure of Na cluster with C symmetry is uncovered, which is more stable than the prior suggested structure based on pentagonal structural motifs.

Generation of ground‐state structures and electronic properties of ternary AlxTiyNiz clusters (x + y + z = 6) with a two‐stage density functional theory global search approach

“…Binding energy per atom ( E b ) is employed to measure the total thermodynamic stability of a cluster . E b of a cluster is calculated by using the equation: …”

Photoabsorption spectra of small Na clusters: TDHF and BSE versus CI and experiment

“…Studies of the structure of Na 20 using DFT molecular dynamics 64,83 or an empirical potential 84 followed by DFT optimization found a ground state structure with C s point symmetry. However, a recent study 63 using a particle swarm optimization method found a Na 20 structure with C 3 point symmetry which was lower in energy than the C s structure by 60 meV (Møller-Plesset MP2 theory) or 150 meV using a CCSD method.…”

“…Guet and Johnson 30 using a similar approach found similar optical absorption at 2. with C s or C 3 symmetry using coordinates from Ref. [63]. The shell structure of occupied and virtual levels in a spherical jellium structure is 1s 2 1p 6 1d 10 2s 2 1f 0 2p 0 2d 0 .…”

“…Various many-body potential approaches have also been applied to structure determination, especially of larger clusters 62 . More recently, a particle swarm optimization technique combined with a hybrid density functional was used to obtain structures of Na n clusters with 10 to 25 atoms 63 . An ab initio molecular dynamics approach has been used to study melting of Na clusters 64 .…”

Re‐weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster

“…Clusters are gas phase nano‐sized aggregates of matter, they are vitally important for technological advances, and can serve as model systems to untangle and simplify the investigation of otherwise intractable problems at the fundamental level using a combination of theoretical and experimental methods. The contributions along these two lines are so numerous that it would be impossible to provide a meaningful comprehensive review of the literature within the confines of a research article. One fundamental issue that can be addressed theoretically and experimentally using clusters is the determination of the nuclear quantum effects on the dynamics and thermodynamics of microsolvation.…”