Tetrahedra clusters

The theoretical prediction for the out-of-plane bending was crucial for the correct assignment of this band in the first INS spectra. Recently, MP2 results for a three-tetrahedra cluster were used to simulate the INS spectra for a free Br0nsted site and its change on water adsorption. Excellent agreement with INS spectra of H-ZSM-5 samples was found. ... 

In the CVM, the free energy of a given alloy is approximated in terms of probabihties for a selected set of finite clusters. The largest cluster explicitly considered in the free energy functional specifies the level of the approximation. The common practice for an fcc-based system is the tetrahedron approximation [26] in which nearest neighbor tetrahedron cluster is taken as the largest cluster. Hence, within the tetrahedron approximation, the free energy expression, F,is symbolically expressed as... 

Among cluster probabilities derived by the PPM, multibody correlations including triangle and tetrahedron cluster probabilities are not input in the simulation procedure. It is, however, worth noting that the agreements between the calculated multibody correlations and resultant ones in the simulated crystal are fairly reasonable. This is rather encouraging to go further discussions of the visualized configuration. 

The simultaneous formation of two different complexes was also observed in the reaction of copper(0) metal powder with one molar equivalent of HN(SPPh2)2 I2 in anhydrous Et20.59 They proved to be [Cu4(N(SPPh2)2)3]l3 and [Cu(HN(SPPh2)2)2]l3 MeCN the former features a tetrahedron cluster of copper(I) atoms surrounded by three bidentate (N(SPPh2)2) ligands coordinated to the metal ions through the sulfur atoms the latter is characterised by... 

Fig. 2.6 Four tetrahedron cluster models for the E and NBO point defects of SiC>2.

A competitive ordering process between six Llo ordered domains can be described by the present approach with a modification on the CVM free energy. In order to specify six Llo ordered variants, the fee lattice is divided into four simple cubic sub-lattices, and the resultant four lattice sites on a tetrahedron cluster are designated as a, j3, y and S. Then the free energy of Llo ordered phase is symbolically written as... 

For the Al-Zr binary system, we included in our truncated cluster expansion of the energy first nearest neighbor interactions up to the pair, triangle, and tetrahedron clusters and a second nearest neighbor pair interaction. Thus, using the occupation numbers pJ, the expression of the energy becomes... 

Here / is the free energy per site i Fj = T[c In c -1- (1 — c )ln(l — c )] is the mixing entropy contribution F/" = Fi(a,... Ck) is the contribution of interactions within /-site cluster of sites i,... k and m is the maximum cluster size considered. The simplest mean-field approximation (MFA) and the pair-cluster one (PCA) correspond to neglecting many-site contributions F ,>2 in (1), while in a more refined, tetrahedron cluster approximation - TCA (that should be used, in particular, to adequately describe the LI2 and Llo-type orderings [10]) Eq. (1) includes also 4-site terms [15]. 

The structure and bonding in lithium methyl have been particularly fully studied. The crystal structure consists of interconnected tetrameric units (LiMe)4 as shown in Fig. 4.17 the individual Li4C4 clusters consist of a tetrahedron... 

Figure 25.11 Metal frameworks of some high-nuclearity binary carbonyl and carbonylate clusters of osmium (a) Os5(CO)i6 (trigonal bipyramid) (b) Os6(CO)ig (bicapped tetrahedron, or capped trigonal bipyramid) (c) [Os6(CO)ig] (octahedron) (d) Os7(CO)2i (capped octahedron) (e) [Osg(CO)22] (bicapped octahedron) (f) [Osi7(CO)36] (3 shaded atoms cap an Osu trigonal bipyramid).

The thiohalides MoSX are diamagnetic (269). In Mo4S4Br4, molybdenum transfers 12 electrons to the anions, and 12 electrons remain for the cluster M04, forming a doublet for each edge of the M04 tetrahedron (269). The diamagnetism of the compounds of the type MogCligSe can be interpreted in a similar way (273) from structure considerations. These compounds have been found to be dielectric (273). 

A modification of the rf discharge method, in which the BCI3 source is held at -78°C, yields B4CI4 containing a tetrahedron of linked B atoms. Reaction of B4CI4 with diborane leads to chlorohexaborane and chlorodecaborane clusters". 

Presently it is not possible to relax the Cu lattice at the SCF level, since from a computational point of view it is composed of two different kinds of Cu atoms (those with and without the ECP). Also questions of wetting, i.e. whether the chemisorbed Be4 would prefer to remain as a tetrahedron (or distorted tetrahedron) or to spread out to a single layer are still not amenable to ab initio study. These questions have not yet been investigated using the parameterized model approach, because of the problems associated with modeling Be2 and Beg as accurately as larger Be clusters. Nonetheless, these preliminary results show that the parameterized and ab initio calculations can be used to complement each other in a multicomponent system, just as for single component systems. 

The crystal structures of many organolithium compounds have been determined.44 Phenyllithium has been crystallized as an ether solvate. The structure is tetrameric with lithium and carbon atoms at alternating corners of a highly distorted cube. The lithium atoms form a tetrahedron and the carbons are associated with the faces of the tetrahedron. Each carbon is 2.33 A from the three neighboring lithium atoms and an ether molecule is coordinated to each lithium atom. Figures 7.2a and b show, respectively, the Li-C cluster and the complete array of atoms, except for hydrogen 45 Section 6.2 of Part A provides additional information on the structure of organolithium compounds. 

B8C18 has a dodecahedral Bg c/o.vo-skclclon with 2n = 16 electrons. In this case, the Wade rule neither can be applied, nor can it be interpreted as an electron precise cluster nor as a cluster with 3c2e bonds. B4(BF2)6 has a tetrahedral B4 skeleton with a radially bonded BF2 ligand at each vertex, but it has two more BF2 groups bonded to two tetrahedron edges. In such cases the simple electron counting rules fail. 

Caesium chloride is not body-centered cubic, but cubic primitive. A structure is body centered only if for every atom in the position x, y, z there is another symmetry-equivalent atom in the position x+ j,y+ j,z+ j in the unit cell. The atoms therefore must be of the same kind. It is unfortunate to call a cluster with an interstitial atom a centered cluster because this causes a confusion of the well-defined term centered with a rather blurred term. Do not say, the 04 tetrahedron of the sulfate ion is centered by the sulfur atom. 

The field of alkyl and aryl Co complexes in low formal oxidation states has been extensively studied, and is frequently associated with cluster chemistry.92 Alkyl and aryl ligands, with or without additional functionality, are often co-ligands with tt acceptors such as carbonyls and/or phosphines, e.g., (MeOCOCH2)Co(CO)3(PPh3).93 A simple example of a cluster is (RC)Co3(CO)9, where the triangular Co(CO)3 3 moiety is capped by the 73-alkyl fragment, which occupies the apex of a distorted Co3C tetrahedron. 

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