Sodium clusters structures

Knight W D, Clemenger K, de Heer W A, Saunders W A, Chou M Y and Cohen M L 1984 Electron shell structure and abundances of sodium clusters Phys. Rev. Lett. 52 2141... 

The most stable cluster consists of an aggregation of four cation vacancies in a tetrahedral geometry surrounding an Fe3+ ion, called a 4 1 cluster. Cations in the sodium chloride structure normally occupy octahedral sites in which each metal is coordinated to six nonmetal atoms. The central Fe3+ ion in the 4 1 cluster is displaced into a normally unoccupied tetrahedral site in which the cation is coordinated to four oxygen ions. Because tetrahedral sites in the sodium chloride structure are normally empty, the Fe3+ is in an interstitial site. Equation (4.1) can now be written correctly as... 

Defect clusters can move by a variety of mechanisms. As an example, the idealized diffusion of a cation-anion divacancy within the (100) face of a sodium chloride structure crystal by way of individual cation and anion jumps is shown in Figure 5.13. 

Doi, M., Asano, A., Ishida, T., Katsuya, Y., Mezaki, Y., et al. (2001) Caged and clustered structures of endothelin inhibitor BQ123, cyclo(-D-Trp-D-Asp-Pro-D-Val-Leu-)-Na", forming five and six coordination bonds between sodium ions and peptides. Acta Crystal-logr. D Biol. Crystallogr. 57 628-634. 

The strong fluctuation of IP or of the mass abundance is an electronic-structure effect, reflecting the global shape of the cluster, but not necessarily its detailed ionic structure. This is demonstrated in Fig. 6, where the ionization potentials of sodium clusters obtained by the spheroidal jellium model [32] are compared with their experimental values [46]. The odd-even oscillation of IP for low N is reproduced well. The amplitude of these oscillations is exaggerated, but this is corrected by using the spin-dependent LSDA, instead of the simple LDA [47]. The same occurs for the staggering of d2 N) [48]. 

Within the shell-model of the electronic structure of clusters of monovalent metals, the ionization potential drops to a low value between sizes and N(, -I-1, where N. indicates a closed-shells cluster. The electron affinity, on the other hand, drops between Nj — 1 and Nc, since the cluster with size N — 1 easily accepts an extra electron to close its nearly-filled external shell. Consequently, the cluster of size N has a large ionization potential and a low electron affinity and will be inert towards reaction. One then expects peaks in a plot of 1 — A versus N for closed shell clusters. The shell effects arc clearly displayed in a Kohn-Sham density functional calculation. Figure 10 shows the results of such a calculation for jellium-like Sodium clusters using the non-local WDA description of exchange and correlation. This calculation employed the Przybylski-Borstel version of the WDA see reference 30 for details). The peaks in I — A occur at the familiar magic clusters with N = 2, 8,18, 20,34,40 and 58. It is well... 

The nature of the association maintains a locally effective shielding of the sulfonate anions within the aggregate and preservation of the clustered structure. This suggests that for these block polymer structures, the energetics of maintaining hydrophobic association are more favorable than monomer dispersion due to ionic repulsion. This was further demonstrasted by the extreme salt sensitivity of these polymers to solution ionic strength. Small amounts of sodium chloride resulted in polymer precipitation and of course loss of viscosification. This precludes the use of these particular polymers for chemically enhanced oil recovery and indicates the need for nonionic functionality to provide water solubility. To further pursue this approach acrylamide based polymers were studied. 

Early LSDA static pseudopotential approaches to sodium microclusters date back approximately 20 years [122], see Appendix C. It would be misleading to consider LDA calculations as the natural extension of jellium models. However, the global validity of the latter cannot but anticipate the success of the former. Clearly, these should also clarify the role of the atomic structure in determining the electronic behavior of the clusters and the extent to which the inhomogeneity of the electron distribution is reflected in the measurable properties. Many structural determinations are by now available for the smaller aggregates, made at different levels of approximation and of accuracy (e.g. [110, 111], see Appendix C). The most extensive investigation of sodium clusters so far is the LDA-CP study of Ref. [123] (see Appendix C), which makes use of all the features of the CP method. Namely, it uses dynamical SA to explore the potential-energy surface, MD to simulate clusters at different temperatures, and detailed analysis of the one-electron properties, which can be compared to the predictions of jellium-based models. 

Early interest in heteroatom clusters having alkali metals as the host was academic rather than dictated by precise observations. The main question regarded the extent to which the jellium-derived shell model retained its validity. However, this question was approached on the basis of oversimplified structural models in which the heteroatom (typically a closed-shell alkali-earth such as Mg) was located at the center of the cluster [235, 236]. In this hypothetical scheme, the perturbation of the electronic structure relative to that of the isoelectronic alkali cluster is somewhat trivial for instance, in the Na Mg system the presence of Mg would only alter the sequence of levels of the shell jellium model from Is, Ip, Is, 2s,. .. (appropriate to sodium clusters) to Is, Ip, 2s, Id,. .. (see also [236]). This would lead to the prediction that Na6Mg and NasMg are MNs. 

The data for the larger clusters (10 to 10" atoms) have been obtained by the T. P. Martin group [18]. From the structure in their mass spectra it is deduced that these large clusters have either icosahedral or fee symmetry. Bulk sodium is bcc, on the other hand, so that a structural phase transition must occur between n = and the bulk. An alternative interpretation would be large sodium clusters near their melting point show the same icosahedral precursor as calculated in Ref. [73] for gold clusters. In this case the ground state could already be bcc-like. 

The existence of discrete electronic states of electrons confined in a small metal cluster has been observed to influence the thermodynamic stability of the system, in particular during the production of sodium clusters in supersonic beams composed of the metal vapor and an inert gas. The statistics of the relative abundances of different particle sizes reveal the existence of magic numbers for the number of atoms in the cluster, A = 8, 20,40,58, 92,... [3.9]. This has been interpreted in terms of the existence of degenerate energy levels in a spherical well with infinite-potential walls. Particularly stable structures are obtained when the number of valence electrons is such that it leads to a closed-shell electronic structure, i. e. a structure with a completely filled energy level and an empty up-... 

Individual molecular structures besides these two are not resolved in the calculated finite temperature sodium cluster polarizabilities. 

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