Tetrahedron connectivity

Parthd, E. Engel, N. (1986). Relation between Tetrahedron Connections and Compositions for Structures with Anionic Tetrahedron Complexes. Acta Cryst. B42, 538 - 544. 

The core of a methane molecule CH4 is defined by a regular tetrahedron connecting the midpoints of CH bonds. The distance of a vertex from the centered carbon atom will be denoted by I, so that 21 = 1.093 A, the CH-bond length. The parameters in Eq. (45) are... 

The properties of the silicates depend on the connections between the silicate tetrahedrons. Because of the wide variety of combinations of tetrahedron connections and the many different metal ions that fit within the structure, an enormous variety of different silicate minerals exist in nature, making the silicate materials the most common structures found on Earth. 

The two coordinates defined for H4 apply also for the H3 system, and the conical intersection in both is the most symmetric structure possible by the combination of the three equivalent structures An equilateral triangle for H3 and a perfect tetrahedron for H4. These sbnctures lie on the ground-state potential surface, at the point connecting it with the excited state. This result is generalized in the Section. IV. 

A vexing puzzle m the early days of valence bond theory concerned the fact that methane is CH4 and that the four bonds to carbon are directed toward the corners of a tetrahedron Valence bond theory is based on the overlap of half filled orbitals of the connected atoms but with an electron configuration of s 2s 2p 2py carbon has only two half filled orbitals (Figure 2 8a) How can it have bonds to four hydrogens ... 

The four oxygen anions in the tetrahedron are balanced by the -i-4 oxidation state of the silicon cation, while the four oxygen anions connecting the aluminum cation are not balanced. This results in -1 net charge, which should be balanced. Metal cations such as Na", Mg ", or protons (H" ) balance the charge of the alumina tetrahedra. A two-dimensional representation of an H-zeolite tetrahedra is shown ... 

White phosphorus, P4, is so reactive that it bursts into flame in air. The four atoms in P4 form a tetrahedron in which each P atom is connected to three other P atoms, (a) Assign a hybridization scheme to the P4 molecule, (b) Is the P4 molecule polar or nonpolar ... 

Each oxygen atom is surrounded by four metal atoms, two of which are nearer than the other two. These atoms are not at the corners of a regular tetrahedron the angle between the line connecting atoms B and C and that connecting D and E is about 60°, instead of 90° as in a regular tetrahedron. 

The valence bonds of carbon have bxed directions and are equidistant in space, pointing from the center to the corners of a tetrahedron forming an angle of 109°. Thus, in propane, which we usually write as CH3-CH2 CH3, the carbon atoms are not connected in a straight line, but are actually as shown in the above three-dimensional diagram. 

Let s look at an example. In ammonia (NH3), the nitrogen atom is sp hybridized, so all four orbitals arrange in a tetrahedral structure, just as we would expect. But only three of the orbitals in this arrangement are responsible for bonds. So, if we look just at the atoms that are connected, we do not see a tetrahedron. Rather, we see a trigonal pyramidal arrangement ... 

The carbon atoms in a diamond are connected in a three-dimensional network, each atom connected to four others. Each atom is at the center of a regular tetrahedron, as shown above. We describe this geometry, which occurs in many compounds of carbon, in Chapter 9. The three-dimensional connections result in a solid that is transparent, hard, and durable. The diamond structure forms naturally only at extremely high temperature and pressure, deep within the Earth. That s why diamonds are rare and precious. 

The relations between the questions that are answered by analytical chemistry are shown in Fig. 1.4. The tetrahedron represents the basic analytical repertoire in a simplified way. It can be seen that all the analytical treatments are connected with each other. 

These microporous crystalline materials possess a framework consisting of AIO4 and SiC>4 tetrahedra linked to each other by the oxygen atoms at the comer points of each tetrahedron. The tetrahedral connections lead to the formation of a three-dimensional structure having pores, channels, and cavities of uniform size and dimensions that are similar to those of small molecules. Depending on the arrangement of the tetrahedral connections, which is influenced by the method used for their preparation, several predictable structures may be obtained. The most commonly used zeolites for synthetic transformations include large-pore zeolites, such as zeolites X, Y, Beta, or mordenite, medium-pore zeolites, such as ZSM-5, and small-pore zeolites such as zeolite A (Table I). The latter, whose pore diameters are between 0.3... 

Each atom is connected to its neighbors by four bonds pointing toward the vertices of a tetrahedron. The structure can also be considered to be made up of carbon tetrahedra, each containing a central carbon atom. Two other members of group 14, Si and Ge, as well as the allotrope of tin stable below 13.2°C, gray tin or a-Sn, also adopt the diamond structure. 

For a tetrahedron, for instance, there are 4 vertices in each of which 3 edges meet it is an example of three-connected cluster. Therefore ... 

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