Structures, relative stabilities, and electronic properties of potassium clusters Kn (13 ⩽ n ⩽ 80)

We report the global minimum (GM) structures, energetic and electronic properties of Kn clusters with up to 80 atoms, obtained by combining basin hopping unbiased optimizations (based on a many-body empirical potential) with subsequent reoptimization of several candidate structures employing a density functional theory method which accounts for van der Waals dispersion interactions (vdW-DFT). A comparison with other alkali cluster systems shows that the GM structures of Kn coincide with those of Nan more often than with those of Csn clusters. Nevertheless, the inclusion of dispersion interactions produces for several clusters changes in the GM structures, which become either identical to those of Csn clusters, or completely novel (i.e. not reported for other alkali systems). Many GM structures are based on poly-icosahedral packing; some others contain Kasper polyhedral units with disclination lines. Atoms with a low coordination number (or adatoms) are avoided in the GM structures following a geometric shell closing: such additional atom is instead inserted into the outermost atomic shell of the cluster. The calculated ionization potentials, electron affinities and HOMO–LUMO gaps are found to reproduce perfectly the electron shell closings observed in photoionization measurements. The electric dipole moments of most clusters are close to zero, a distinguishing feature of metallicity previously observed for Nan clusters. However, some clusters like K26, K47 or K49 have sizable electric dipole moments. The cluster stabilities are found to explain the experimental abundances inferred from mass spectra. The enhanced stabilities (magic numbers) can be interpreted in terms of electron shell closing effects for the smaller clusters and of geometrical packing effects for the larger clusters. Although there is not a sharply defined critical size separating both regimes, it is estimated to be around 55 atoms.