Tetrahedron complex

Four-coordinate complexes can present tetrahedron or square-planar geometries. While square-planar complexes allow cis/trans isomers, the same is not possible for tetrahedron complexes. Again, Werner was correct in his conclusions concerning the tetrahedron structure he stated that only one isomer would be produced for this composition, since, if one of the four corners is occupied than the three remaining ones are equivalent. Werner studied a series of four-coordinate complexes of palladium and platinum and two isomers had been actually iso-... 

VALENCE ELECTRON RULES FOR COMPOUNDS WITH TETRAHEDRAL STRUCTURES AND ANIONIC TETRAHEDRON COMPLEXES... 

ABSTRACT. For compounds with tetrahedral structure or anionic tetrahedron complex two valence electron concentration rules can be formulated which correlate the number of available valence electrons with particular features of the crystal structure. These two rules are known as the tetrahedral structure equation where the total valence electron concentration, VEC, is used as parameter and the generalized 8 - N rule where the parameter of interest is the partial valence electron concentration in respect to the anion, VEC. From the tetrahedral structure equation one can calculate the average number of non-bonding orbitals per atom and, in the case of non-cyclic molecular tetrahedral structures, the number of atoms In the molecule. An application of the generalized 8 - N rule allows the derivation of the average number of anion -anion bonds per anion or the number of valence electrons which remain with the cation to be used for cation - cation bonds and/or lone electron pairs. These rules have been used not only to predict probable structural features of unknown compounds but also to point out possible errors in composition or structure of known compounds. 

In the case of a ternary compound of composition CmC, n>An there may occur an anionic tetrahedron compiex formed by a central atom C, tetrahedrally surrounded by anions A (see below). Here VEC and VECa different because VEC refers to all atoms of the charged anionic tetrahedron complex, but VECa the anions. 

In the compounds of composition Cn C An the tetrahedron complex, as stated above, is formed with all the C (central atoms) and A atoms (anions). The C atoms (cations) are outside the complex and are assumed to transfer their valence electrons to the tetrahedron complex which is then negatively charged. 

A problem might exist to recognize which atoms in a ternary compound participate on an anionic tetrahedron complex and which do not. Experimental evidence has shown that the alkali elements Na, K, Rb and Cs, the alkaline earth elements Ca, Sr and Ba and the rare earth elements never have a tetrahedral coordination. They function as cations C only which transfer their valence electrons to the remaining atoms forming the anionic tetrahedron complex. There are, however, other elements such as Al which in some compounds participate on the complex but in others not. To simplify matters will shall in the following examples consider only compounds where the recognition of the elements which function as cations C causes no problems. If for a compound VEC < 4 it is evident that all atoms can not participate on a tetrahedral stoicture. But also if VEC 4, where in principle a tetrahedral structure involving all elements would be possible, the above cited elements will never participate on the anionic tetrahedron complex. 

In the most simple case the anionic tetrahedron complex consists of a simple isolated CA4 tetrahedron. However, there have to be considered four different kinds of variants of this tetrahedron, shown in Figure 6, three of them allowing for a linkage of tetrahedra and two of them involving the removal of an anion neighbour of a central atom (Parth Chabot, 1990). 

If VECa > 8 Polycationic valence compound with C C > 0 and AA = 0. A tetrahedron variant (III) and/or (IV) occurs and, depending on the composition, also variant (I). The parameter of interest is the average number of C - C bonds per tetrahedron and/or the number of electrons on the central atom per tetrahedron used for lone electron pairs. Since each tetrahedron of the anionic tetrahedron complex has only one central atom, this value is identical to C C, that is... 

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. 

Figure 7 Examples for polyanlonic valence compounds with an anionic tetrahedron complex where each tetrahedron extends one A - A bond to another tetrahedron.

Figure 8 Examples for normal valence compounds with anionic tetrahedron complexes where AA = C C =0.

Figure 10 Examples for polycaVonIc valer ce compounds with anionic tetrahedron complexes where C C = 2, characterized by a psi tetrahedron, that means an anion neighbour of the central atom has been replaced by a lone electron pair.

ANIONIC TETRAHEDRON COMPLEXES BUILT UP WITH BASE TETRAHEDRA... 

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. 

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... 

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. 

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... 

The classification codes for compounds with anionic tetrahedron complexes. For the classification code of a compound one uses the same expressions as (27). However, VECa I) calculated from the composition and the number of available... 

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. 

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. 

Figure 13 The different anionic tetrahedron complexes of four normal valence compounds with same classiticatlon code 8/3.

One has to assume that an anionic tetrahedron complex is formed and one has to make also assumptions which of the elements are the cations C, the central atoms C and the anions A. The parameters used in the Mooser - Pearson diagrams to separate compounds with adamantane structure from those having no adamantane structures are also here of some relevance, if the central atom and the anion is from the second period of the Periodic Table then a planar trianguleir anion complex is preferred to a tetrahedron complex, as for example with BOs) -, (003)2- or (NOs) -. Tetrahedral complexes are also rarely found if the central atom is from a very high period. Central atoms from periods inbetween can be expected to form tetrahedral complexes, but there are exceptions. 

The valence electron contribution is evident in most cases, but there are exceptions such as the frequently encountered cations TT + and Pb +. In the case of transition elements their valence electron contribution can only be calculated from the observed structural features of the anionic tetrahedron complex. This may in case be verified by magnetic measurements. 

Equation (23) represents a simplified expression which is correct in only 90 % of the structures. In the most general case one Is obliged to make assumptions how the electrons on the central atoms are used for C - C bonds or lone electron pairs. The reader is advised to look up the original publication of Parth Chabot (1990) to find out how the C AC values can be calculated for less common cases of anionic tetrahedron complexes. 

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. 

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 structures of silicates and related compounds contain anionic tetrahedron complexes of different configuration (single tetrahedra, pyrogroups, rings, chains, layers, frameworks etc.). Their comparative analysis considerably contributes to the sdentiiic ideas on the structures of crystalline materials in general. The interest in... 

If one takes into account the most specific features of a Si,0 tetrahedron complex, such as the number of tetrahedra in the chain period, or the types of rings which can be recognized in different layers, it is possible to estimate the total number of anionic tetrahedron complexes in the silicates as one hundred. 

In the silicate structures the Si,0 anionic tetrahedron complex will be adjusted to the cation-oxygen polyhedron fragments (Belov, 1959). In particular, this principle was confirmed with the structures having big cations (K, Na, Ca, R = rare earth elements), where the Si,0 anionic tetrahedron complex - in the form of pyrogroups [S O/] - is commensurable with the edges of the cation-oxygen polyhedra. 

Belov s concept enabled the division of the silicate structures into two groups (or chapters). However, there are several different approaches to their systematics. The common feature of these studies Is the analysis of Si,0 anionic tetrahedron complex. The first steps in this direction were made by Machatschki, Ndray-Szab6 and Bragg. 

The identical formula was derived by Parth Engel (1986) for the modified tetrahedron sharing coefficient TT, which corresponds to the average number of (central atom - bridging atom - central atom) bonds per tetrahedron in a structure with anionic tetrahedron complexes. If one restricts oneself to the case where the bridging atom forms a bridge between only two central atoms, that which is observed in all silicates, then TT = K. 

About 20 compounds with different kinds of anionic tetrahedron complexes in the same structure are considered in a special subdivision (Table 3). These structures do not obey Pauling s fifth rule. Belov s concept, emphasizing the dominating role of the cations, can be used for the interpretation of these structures with different tetrahedron complexes (Table 4). 

The structural classification of sulphates on the basis of this concept proves that the variability of mixed complexes in sulphates (Raszvetaieva Pushcharovsky, 1989) is comparable with the diversity of the anionic tetrahedron complexes in silicates (Figure 4). 

New Types of Anionic Tetrahedron Complexes in Silicates and their Analogues... 

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