Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au19 and Au20 clusters. Au20 has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap and an atomic packing similar to that of the bulk gold (J. Li et al., Science, 299 864, 2003). Our results show that the geometry of Au19 is exactly identical to that of Au20 with one missing corner atom (called as vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold cluster exhibit dramatic differences. Au20 undergoes a clear and distinct solid like to liquid like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au19 has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au19 between 650 K to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au20 is destroyed around 800 K, and the cluster is clearly in a liquid like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature which has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.

Using a combination of first principles calculations and empirical potentials we have undertaken a systematic study of the low energy structures of gold nanoclusters containing from 3 to 38 atoms. A Lennard-Jones and many-body potential have been used in the empirical calculations, while the first principles calculations employ an atomic orbital, density functional technique. For the smaller clusters (n = 3, 4 and 5) the potential energy surface has been mapped at the ab initio level, for larger clusters an empirical potential was first used to identify low energy candidates which were then optimised with full ab initio calculations. At the DFT-LDA level, planar structures persist up to 6 atoms and are considerably more stable than the cage structures by more than 0.1 eV/atom. The difference in ab initio energy between the most stable planar and cage structures for 7 atoms is only 0.04 eV/atom. For larger clusters there are generally a number of minima in the potential energy surface lying very close in energy. Furthermore our calculations do not predict ordered structures for the magic numbers n = 13 and 38. They do predict the ordered tetrahedral structure for n = 20. The results of the calculations show that gold nanoclusters in this size range are mainly disordered and will likely exist in a range of structures at room temperature.

Molecular dynamics simulations of the thermal behaviour of gold clusters containing 7, 13 and 20 atoms have been performed. Total energies and forces at each step of the simulation are calculated from first principles using density functional theory. Ion trajectories are then calculated classically from these forces. In each case the global minimum energy structure and a low-lying isomer are used as the starting structures. In most cases, the clusters do not exhibit a sharp transition from a solid-like phase to a liquid-like phase, but rather pass through a region of transformations between structural isomers that extends over a considerable temperature range. Solid-like behaviour is observed in the atomic trajectories of the simulation at temperatures up to, or above, the bulk melting point. The 20-atom tetrahedral structure is the one exception, showing a sharp transition between solid-like and liquid-like phases at about 1200 K. The starting structure used in the simulation is shown to have a considerable effect upon the subsequent thermal behaviour.

The electronic band structures of Be and BeO have been measured by transmission electron momentum spectroscopy (EMS). The low atomic number of beryllium and the use of ultrathin solid films in these experiments reduce the probability of electron multiple scattering within the sample, resulting in very clean "benchmark" measurements for the EMS technique. Experimental data are compared to tight-binding (LCAO) electronic structure calculations using Hartree-Fock (HF), and local density (LDA-VWN), gradient corrected (PBE) and hybrid (PBE0) density functional theory. Overall, DFT calculations reproduce the EMS data for metallic Be reasonably well. PBE predictions for the valence bandwidth of Be are in excellent agreement with EMS data, provided the calculations employ a large basis set augmented with diffuse functions. For BeO, PBE calculations using a moderately-sized basis set are in reasonable agreement with experiment, slightly underestimating the valence bandgap and overestimating the O(2s) and O(2p) bandwidths. The calculations also underestimate the EMS intensity of the O(2p) band around the Γ-point. Simulation of the effects of multiple scattering in the calculated oxide bandstructures do not explain these systematic differences.

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