Cluster difficulties

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

Both from the experimental or theoretical point of view, clusters studies present many difficulties due to their typical size (1-10 nm), usually larger than current systems studied in chemistry, but also too small for many physical standard techniques of characterisation and manipulation. 

Abstract Molecular spectroscopy is one of the most important means to characterize the various species in solid, hquid and gaseous elemental sulfur. In this chapter the vibrational, UV-Vis and mass spectra of sulfur molecules with between 2 and 20 atoms are critically reviewed together with the spectra of liquid sulfur and of solid allotropes including polymeric and high-pressure phases. In particular, low temperature Raman spectroscopy is a suitable technique to identify single species in mixtures. In mass spectra cluster cations with up to 56 atoms have been observed but fragmentation processes cause serious difficulties. The UV-Vis spectra of S4 are reassigned. The modern XANES spectroscopy has just started to be applied to sulfur allotropes and other sulfur compounds. 

The electronic, optical, and magnetic properties of metal clusters are of great current interest, but these properties have been little studied with very mixed -metal clusters. This is to some extent a reflection of the difficulty of preparing high-nuclearity examples many of these interesting properties become important upon increasing cluster size. The limited magnetic studies to date are... 

The main difficulty in the theoretical study of clusters of heavy atoms is that the number of electrons is large and grows rapidly with cluster size. Consequently, ab initio "brute force" calculations soon meet insuperable computational problems. To simplify the approach, conserving atomic concept as far as possible, it is useful to exploit the classical separation of the electrons into "core" and "valence" electrons and to treat explicitly only the wavefunction of the latter. A convenient way of doing so, without introducing empirical parameters, is provided by the use of generalyzed product function, in which the total electronic wave function is built up as antisymmetrized product of many group functions [2-6]. 

One difficulty with many synthetic preparations of semiconductor NCs that complicates any interpretation of NMR results is the inevitable distribution of sizes (and exact shapes or surface morphologies). Therefore attempts to make semiconductors as a sort of molecular cluster having a well-defined stoichiometry are of interest to learn potentially about size-dependent NMR parameters and other properties. One approach is to confine the semiconductor inside a template, for instance the cuboctahedral cages of the sodalite framework or other zeolite structures, which have been characterized by multinuclear NMR methods [345-347], including the mesoporous channel material MCM-41 [341, 348]. 

Abundance anomalies displayed by red giants in globular clusters, and the difficulties that they raise for canonical stellar evolution theory, are discussed, e.g., by Kraft (1994). 

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