Base tetrahedron

ANIONIC TETRAHEDRON COMPLEXES BUILT UP WITH BASE TETRAHEDRA... 

In Figure 11 are presented the 32 possible base tetrahedra where each central atom has at least two anion neighbours and where each anion is either unshared or shared with only one other tetrahedron. The shared anions are shown as half circles and the tangling A - A and C - C bonds by short heavy lines extending from the open or filled circles, respectively. A lone electron pair is indicated by a heavy bar on a filled circle. 

Figure 11 Graphs of 32 base tetrahedra with unshared anions or shared between two tetrahedra oniy.

For the base tetrahedra in Figure 11 with tangling A - A bonds one calculates VECa < 8. These base tetrahedra can be used for the construction of the anionic tetrahedron complexes in polyanionic valence compounds. For all base tetrahedra where AA = C C = 0 one finds that VECa = 8- These are the base tetrahedra which are important for the anionic tetrahedron complexes in normal valence compounds. Finally, all base tetrahedra with C C>0 have VECa >8. These are the base tetrahedra which build up the anionic tetrahedron complexes in polycationic valence compounds. 

Note, that AA-(n/m ) and C C (for our case also 2-n/m ) can have int ral values only. The number of possible base tetrahedra is therefore limited. Equeilly limited is the list of specific VECa values which compounds must have for them to be built up of one kind of base tetrahedron only. 

The classification codes for base tetrahedra. It was found desirable to design for the base tetrahedra a classification code which contains all the information necessary to draw a graph and includes also the VECa value which a compound must have for its anionic tetrahedron complex to be built up of this base tetrahedron (Partlfo Chabot, 1990). We shall use for the classification code the values of AA-(n/m ) or CC, VECa and CAC, which, except for VECa, cari be obtained directly from a study of the drawing of the base tetrahedron. Depending on the VECa value the classification code of a base tetrahedron will be written as... 

In Figures 7 to 10 the classification codes had been listed in the last rows of the text blocks. As seen in Figure 11, where the classification code is written below each base tetrahedron graph, all 32 different base tetrahedra have different codes and are thus unambiguously identified. 

The classification code of the compound is not identical with the classification code of a base tetrahedron. Whenever the C AC or the C C or AA-(n/m ) values of the classification code of a compound are not integers, the tetrahedron complex is built up of more than one kind of base tetrahedron. As simple solution one selects from Figure 11a pair of base tetrahedra with similar classification codes. As a guide to find their proper porpoit ons one may use the following equations which relate the classification code and the n/m ratio of a tetrahedron complex built up of different base tetrahedra to the classification codes and n/m ratios of the base tetrahedra involved. 

Examples for anionic tetrahedron complexes constructed of two Mnds of base tetrahedra. As a simple example for a compound where the anionic tetrahedron complex is built up of two kinds of base tetrahedra one may consider the amphiboles, listed in Table 2. Based on their classification code 8/2.5 one can conclude, considering (28d), that the anionic tetrahedron compiex is constructed of equal amounts of °8/2 and °8/3 base tetrahedra. From (28e) one finds that in this case n/m = 11/4, which agrees with the compositions of the amphiboles. 

Two more examples of normal valence compounds with two different kinds of base tetrahedra are presented in Figure 12. In the case of the ultraphosphate NdPsO A with ciassification code °8/2.4 one expects, in agreement with (28d), that for every three °8/2 base tetrahedra there are two °8/3 base tetrahedra. This agrees with the experimentaliy determined anionic tetrahedron complex of NdPsO A, shown in schematic form on the left hand side. 

Figure 12 The observed anionic tetrahedron complexes of two normal valence compounds where the anionic tetrahedron complexes are built up of two kinds of base tetrahedra. In the second last row of the text columns are listed the classification codes of the compounds and in the last row the classification codes of the base tetrahedia involved and their proportions.

Structural features which can not be predicted with valence ekstron rules. The valence elctron rules allow the prediction of a probable base tetrahedron for a compound with an anionic tetrahedron complex, however not the details how this base tetrahedron is linked with itself. In addition, instead of an expected single base tetrahedron there may occur two different base tetrahedra but with the restriction that the average of their codes, calculated with (28), corresponds to the classification code of the compound. 

As example one may consider the observed anionic tetrahedron complexes of the four normal valence compounds with the same classification code °8/3, shown in Figure 13. The first three tetrahedron complexes are constructed alone of < 8/3 base tetrahedra. In Na2Ge2Se5 and Na2Ge2S5 the base tetrahedra are only comer linked, however in Rb4ln2Sg comer and edge linked. Even if there are only comer linked base tetrahedra the anionic tetrahedron complex may have the shape of a two-dimensional layer or a cyclic molecule. Rnally, the anionic tetrahedron complex in Cs4Ge Se5, a multicyclic molecule, is constructed, instead of 8/3 base tetrahedra, of °8/2 and 8/4 base tetrahedra in equal proportions. 

The anionic tetrahedron compiex in Na3Mg2P50i6 shouid consist of a molecule with 21 atoms which, in the most simple case, is constructed of two °8/1 and three 8/2 base tetrahedra. This corresponds to a finite chain of five comer linked tetrahedra which is actuaily observed. 

The actuai anionic tetrahedron complex of LiQeTeg is built up not of the expected 18.5/2 base tetrahedra, but of equal amounts of 18.4/1 ind 18.667/3 base tetrahedra. Using (28b), (28c) and (28e) one can verify that the average corresponds to 18.5/2, the ciassification code of the compound. 

The peculiar properties that characterize these glasses can be mainly ascribed to the typical phosphate network. Therefore, detailed structural characterization becomes fundamental to investigate the structure evolution associated to compositional changes that directly results in the macroscopic behaviour of the materials [32-34]. The basic structural units of the amorphous phosphate systems are the P-based tetrahedra. Different polymerizations of the phosphate chains can be identified and codified by the Q" where n represents the number of bridging oxygens (BOs) per tetrahedron (shown schematically in Fig. 8.1) [35]. 

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Talc is hydrated magnesium silicate, a nonmetallic mineral, white-colored, chemically inert. Unlike many other minerals, its particles have a distinct platy shape. It has a natural affinity to oil and, therefore, serves as a good filler for hydrophobic plastics, such as polyethylenes and polypropylene. Platy particles of talc are structurally not uniform they have a layered composition, in which a brucite (magnesium-based, tetrahedron-cell atomic structure) sheet is sandwiched between two silica (octahedron-cell atomic structure) sheets. The elementary sheet is of ik (0.7 nm) thick. 

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Pahadi, N.K., Ube, H. and Terada, M. (2007) Aza-Henry reaction of ketimines catalysed by guanidine and phosphazene bases. Tetrahedron Letters, 48, 8700-8703. 

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Palacios, R, Aparicio, D., de los Santos, J.M. et al. (2000) Easy and efficient generation of reactive anions with free and supported ylides as neutral Brpnsted bases. Tetrahedron, 56, 663-669. 

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Talas, E. Margitfalvi, J. Machytka. D. Czugler. M. Synthesis and resolution of naphthyl-Troger s base. Tetrahedron Asymmetry 1998, 9, 4151-4156. 

In these base tetrahedron drawings the central atoms are shown by filled small circles and the anions by larger open circles. Anions shared with an other tetrahedron are presented by half circles. A bond between anions or between central atoms is indicated by a short heavy line extending from the open or filled circle, respectively. In the case of a psi tetrahedron the lone electron pair on the central atom Is shown by a heavy bar alongside the filled circle. 

The drawings are complemented with text blocks detailing the numerical values of the different parameters which can be calculated from the valence electron equations discussed above. On top is given the total valence electron concentration, VEC. If VEC < 4 a tetrahedral structure involving all atoms is impossible. The parameters listed below VEC are derived from the valence electron concentration of the charged anion partial structure, VEC, and the next one from the partial valence electron concentration in respect to the anion, VECa- parameter C AC, to be discussed in the next paragraph, refers to the sharing of the anions and can be calculated from the composition of the compound. Finally, on the last row one finds a classification code for the base tetrahedron, also to be discussed later on. 

For all the compounds discussed in Figures 7 to 10 the observed structural features, in particular the features of the base tetrahedron which can be used to construct the complete anionic tetrahedron complex, are in perfect agreement with the predictions based on the valence electron rules. 

Definition of a base tetrahedron. In the examples given above we have demonstrated how one can use the two valence electron rules to predict certain structural features of a compound assuming that an anionic tetrahedron complex is formed. In particular, for each compound we had given a list of calculated parameters and had presented a corresponding graph of a base tetrahedron with which the anionic tetrahedron complex of the compound can be constructed. 

One denotes as base tetrahedron the isolated CA4 tetrahedron and all other single tetrahedra which differ by having eui unshared anion (or more) replaced by a shared anion or by a C - C bond or a lone electron pair or where the anion extends a bond to another anion of a different tetrahedron. Since reference is made to a single tetrahedron the C - C and A - A bonds are considered as tangling bonds and the anions shared with another tetrahedron are counted only as half an anion. 

For each base tetrahedron can be specified a particular VEC and corresponding VEC value which a compound must have if its anionic tetrahedron complex is to be constructed with this particular base tetrahedron. The VEC/v value of a base tetrahedron, based alone on information which can be found in the graph, can be calculated by means of the generalized 8-Nmle, that is... 

Depending on the classification code of a compound two cases have to be distinguished to find the most probable base tetrahedron(a) ... 

The classification code of the compound is identical with the classification code of a base tetrahedron. Here, one expects as most simple solution that the anionic tetrahedron complex is constructed alone with this base tetrahedron. This is the case for all the examples treated in Figures 7 to 10. 

Problem 3 The compounds listed below are characterized by an anionic tetrahedron complex. Write down the classification codes of the compounds and make graph drawings of the probable base tetrahedron(a) involved in the construction of the anionic tetrahedron complexes. 

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Nakanishi K, Kotani S, Sugiura M, Nakajima M (2008) First asymmetric Abramov-type phosphonylation of aldehydes with trialkyl phosphites catalyzed by chiral lewis bases. Tetrahedron 64 6415-6419... 

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