In this paper we address some of the unique, novel and basic features of clusters, which involve the physical and chemical consequences of their large surface/volume ratio and the size dependence of the properties of large finite systems Energetic, quantum, electronic, spectroscopic, and electrodynamic size effects in clusters were quantified by cluster size equations (CSEs), which describe the gradual “transition” from the large finite cluster to the infinite bulk system, with increasing the cluster size Some progress was also accomplished in the description of the “transition” from cluster microsurfaces to macrosurfaces, which can be described in terms of surface CSEs The analysis implies a nonuniversality principle for cluster size effects, with different physical properties being described in terms of distinct CSEs The CSEs provide a quantitative answer to a central question in the area of cluster chemical physics: What is the minimal cluster size for which its properties become size invariant and do not differ in any significant way from those of the macroscopic sample of the same material? A unified (but not universal) description is advanced for the merging between the properties of microscopic large finite systems and those of a macroscopic bulk material

Cluster size effects

We describe a new experimental setup for photoluminescence spectroscopy on van der Waals clusters. It consists of a molecular beam apparatus with a cluster beam installed behind a high intensity vacuum ultraviolet synchrotron radiation beamline. Special emphasis was given to the design of a very intense cluster source which can also be used for the preparation of quantum clusters (He,H2). For the determination of the cluster size a time‐of‐flight mass spectrometer can be attached to the setup. In addition, an atomic cross jet is installed in the experimental chamber which can be used for mass separation or for doping of the clusters. The luminescence light can be recorded with several different detectors or spectrally analyzed with a secondary monochromator which is equipped with a position sensitive detector. The pulsed nature of synchrotron radiation provides the basis for time‐resolved measurements in the regime 100 ps–3 μs.

CLULU: An experimental setup for luminescence measurements on van der Waals clusters with synchrotron radiation

We have measured the photoabsorption spectra of mass selected Ar+n clusters, n=3–40, from 355–1064 nm. The smaller clusters, n<15, display a visible photoabsorption spectrum similar to Ar+3, i.e., a broad, intense band peaking near 520 nm. From n=15–20 this photoabsorption band shifts smoothly to a longer wavelength, peaking near 600 nm for Ar+20. This band does not change appreciably as n increases from 20 to 40. These results clearly demonstrate that the Ar+n clusters have photophysical properties quite different from those of Ar+2. We have also studied the photoabsorption and subsequent photofragmentation of Ar+n cluster ions, n=3–60, at selected visible wavelengths. The ionic photofragment distributions both indicate that photofragmentation proceeds through the loss of individual Ar atoms and place an upper bound of 90 meV on the cluster ion binding energy in the large cluster limit.

Photoabsorption and photofragmentation studies of (Ar+)n cluster ions

Clusters of argon, krypton, and xenon are grown in a free jet and ionized by electron impact. The size of these clusters, (Rg)+n, extends up to n≂1000. Individual cluster sizes are mass resolved up to n≂570 in the case of Ar+n. The well known, but puzzling differences in the size distributions of Kr and Xe clusters disappear beyond n≂130, while those between Ar and Xe disappear beyond n≂220. The most pronounced ‘‘magic numbers’’ in the distributions of large cluster ions occur at n=147 (148 for Ar), 309, and 561, in striking agreement with the number of atoms required to build icosahedral clusters with 3, 4, and 5 complete coordination shells, respectively. Closure of the 6th icosahedral coordination shell is indicated by another strong intensity drop at n≂923 in the unresolved part of the spectra. Several additional intensity extrema are observed between major shell closures. A simple structural model, assuming an icosahedral core decorated by the additional atoms, accounts for these anomalies reasonably well up to n=561.

Mass spectrometric evidence for icosahedral structure in large rare gas clusters: Ar, Kr, Xe

We have simulated the cluster dissociation reaction Arn→Arn−1+Ar (12≤n≤14) using molecular dynamics (MD) with well defined internal energy and total angular momentum. Reaction rates and kinetic energy release distributions are compared to the predictions of several statistical theories: Rice, Ramsperger, and Kassel (RRK), Engelking, and phase space theory (PST). We employ the Nose prescription for constant temperature dynamics coupled with the multiple histogram method of Labastie and Whetten to obtain highly accurate vibrational densities of states for the clusters. The absolute densities are determined by the adiabatic switching method of Reinhardt. Incorporation of these accurate anharmonic vibrational densities of states into classical PST allows us to make a direct comparison with the simulation results and eliminates any parameters from the theory. Then PST predictions for the kinetics of evaporation are given for the low energy (long time scale) regime where MD simulations are prohibitively expensive. A critical evaluation of the approximate statistical theories is presented.

Absolute classical densities of states for very anharmonic systems and applications to the evaporation of rare gas clusters

The method of diatomics-in-molecules (DIM) is applied to the calculation of the energy of the homogeneous noble-gas ionic clusters Ar
 +
 and Xe
 +
 forn=3, 4, ..., 22. The trimers are stable symmetric linear molecules exhibiting chemical binding, a result in agreement both with ab initio calculations and with previous DIM work. The clusters up ton=13 are best described as a trimer ion surrounded by neutrals, whereby the charge distribution changes slightly with increasingn. Both noble gases exhibit a special stability associated with the completion of the first shell of neutral atoms atn=13. Asn increases from 13 to 22, there is a greater delocalization of the positive charge, the central ion tending to become a linear tetramer, symmetric for Xe and unsymmetric for Ar. Energies of the excited electronic states are reported and the possibility of developing simpler DIM models for the clusters and for mixed noble gases is discussed.

P. J. Kuntz

Papers

A DIM model for homogeneous noble gas ionic clusters