Clusters closed shell

Another series of cubic clusters of general composition M9(/.i4-E)6Lg (M = Ni or Pd E = Ge, P, As, Te) incorporates a metal atom in the center of the cube. The bonding in these cluster compounds is also analyzed by means of EH and SCF-MS-Xa calculations. The number of MVE ranges from 130 to 121. Examination of the electronic structures has shown that the cluster compounds are at the interface between molecular and solid state materials. In the cubic clusters, closed-shell electron configurations of stable molecular systems with a significant HOMO-LUMO gap coexist with open-shell electron configurations of solid-state systems with no significant gap between the skeletal frontier orbitals. 

Figure Cl. 1.2. (a) Mass spectmm of sodium clusters (Na ), N= 4-75. The inset corresponds to A = 75-100. Note tire more abundant clusters at A = 8, 20, 40, 58, and 92. (b) Calculated relative electronic stability, A(A + 1) - A(A0 versus N using tire spherical electron shell model. The closed shell orbitals are labelled, which correspond to tire more abundant clusters observed in tire mass spectmm. Knight W D, Clemenger K, de Heer W A, Saunders W A, Chou M Y and Cohen ML 1984 Phys. Rev. Lett. 52 2141, figure 1.

Besides these many cluster studies, it is currently not knovm at what approximate cluster size the metallic state is reached, or when the transition occurs to solid-statelike properties. As an example. Figure 4.17 shows the dependence of the ionization potential and electron affinity on the cluster size for the Group 11 metals. We see a typical odd-even oscillation for the open/closed shell cases. Note that the work-function for Au is still 2 eV below the ionization potential of AU24. Another interesting fact is that the Au ionization potentials are about 2 eV higher than the corresponding CUn and Ag values up to the bulk, which has been shown to be a relativistic effect [334]. A similar situation is found for the Group 11 cluster electron affinities [334]. 

More often, polyhedral clusters with strong metal-metal (or metalloid-metalloid) bonding are the major structural motifs of classic Zintl phases. These are nominally salts composed of reduced p- (i.e., post-transition) elements that are usually inter-bonded into closed shell polyanions plus active metal cations, originally the alkali... 

These and many similar examples resulted in a highly successful general picture of transition-metal ions M coordinated by closed-shell ligands L (anionic or neutral) to form complex cluster ions [ML ]9 in solution. The characteristic coordination shell of each M corresponds to a specific number of sites, with idealized geometry that dictates the possible number of distinct [M(Li) (L2)m. .. ]q structural isomers. Each cluster ion is subject to equilibria with other cluster ions or dissociated ligands in solution,... 

Uneven open shell Pn clusters are easier to ionize than even closed shell ones and the stability of the closed shell uneven P cluster cations is higher. For very large Pn+ cations with n = 25 + 8x (x — 0.1.2. 8) islands of stability were observed in the time of flight mass spectrum (TOF-MS) obtained by laser ablation of red phosphorus, suggesting that the more stable P clusters have connections with units of eight P atoms [71d]. A lot of effort has been put into the calculation of the most stable Pn+ cation structures. The respective global minimum structures of the more stable uneven P3+, Ps+, P71 and P<)h cluster cations are shown in Figure 2.6-10 [73, 74],... 

Another approach of this kind uses the approximate Brueckner orbitals from a so-called Brueckner doubles, coupled-cluster calculation [39, 40]. Methods of this kind are distinguished by their versatility and have been applied to valence ionization energies of closed-shell molecules, electron detachment energies of highly correlated anions, core ionization... 

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