Transition metal clusters cluster expansion

Solution of the Kohn-Sham equations as outlined above are done within the static limit, i.e. use of the Born-Oppenheimer approximation, which implies that the motions of the nuclei and electrons are solved separately. It should however in many cases be of interest to include the dynamics of, for example, the reaction of molecules with clusters or surfaces. A combined ab initio method for solving both the geometric and electronic problem simultaneously is the Car-Parrinello method, which is a DFT dynamics method [52]. This method uses a plane wave expansion for the density, and the inner ions are replaced by pseudo-potentials [53]. Today this method has been extensively used for studies of dynamic problems in solids, clusters, fullerenes etc [54-61]. We have recently in a co-operation project with Andreoni at IBM used this technique for studying the existence of different isomers of transition metal clusters [62,63]. 

Couple cluster methods differ from perturbation theory in that they include specific corrections to the wavefunction for a particular type to an infinite order. Couple cluster theory therefore must be truncated. The exponential series of functions that operate on the wavefunction can be written in terms of single, double and triple excited states in the determinantl " . The lowest level of truncation is usually at double excitations since the single excitations do not extend the HF solution. The addition of singles along with doubles improves the solution (CCSD). Expansion out to the quadruple excitations has been performed but only for very small systems. Couple cluster theory can improve the accuracy for thermochemical calculations to within 1 kcal/mol. They scale, however, with increases in the number of basis functions (or electrons) as N . This makes calculations on anything over 10 atoms or transition-metal clusters prohibitive. 

Mass spectra of transition metal clusters do not exhibit any abvmdance anomalies. However, if they are mixed with reactive gases prior to expansion into vacuum, the number of molecules being absorbed exhibits pronovmced size effects. Mass spectra may directly reveal the number of reactive sites on the cluster surface Coj, for example, offers six highly reactive sites towards ammonia. This number tends to increase with cluster size, but local minima are observed at certain cluster sizes, indicating closed shells or subshells in agreement with an icosahedral growth sequence. 

These heavy late- and post-transition metals in low positive oxidation states form clusters held together only by direct M—M bonds, with a relatively small number of terminal ligands. This cluster chemistry is distinctly different from that of all other aggregates (including the naked metal anions), and can be regarded as an expansion of the chemistry of Hg22+ it is most developed for... 

Supersonic expansions have been used to form small metal aggregates, (2 < n < 4). Emphasis is placed on the analysis of bound-free transitions in these small metal clusters. Discussion focuses on the characterization of variously produced sodium supersonic expansions and the analysis of laser Induced atomic fluorescence resulting from the photodissociation of triatomic sodium clusters. We will consider (1) the nature of observed "fluctuation" bands corresponding to bound-free transitions involving a repulsive excited state which dissociates to yield (Na-D line) sodium atoms and ground state,, ... 

Further studies indicate that the phenomena characterized here can be extended to the study of other bound-free transitions, furnishing a means of mapping the repulsive states which characterize small metal clusters (51). This may have significant importance for the characterization of photocatalytic processes. Further it appears that one can make use of the shallow nature of the bonding potentials characterizing many metal clusters and supersonic expansions in general to obtain "hot band" structure... 

For the more volatile (alkali) metals it has been possible since the late 1970s to create a beam of cold, naked clusters of 1 < n < 100, where n is the number of atoms per cluster 348, 349). Metal vapor is produced in an oven and then cooled by expansion. The clusters are separated in a time-of-flight mass spectrometer (TOFMS). Later it became possible to handle less volatile (transition) metals through vaporization by a laser beam 347, 350-352). For the mass analysis the neutral clusters are photoionized by a suitable UV laser. 

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