931.00 Chemical Bonds

931.10 Omnicongruence: When two or more systems are joined vertex to vertex, edge to edge, or in omnicongruencein single, double, triple, or quadruple bonding, then the topological accounting must take cognizance of the congruent vectorial build in growth. (See Illus. 931.10.)

931.20 Single Bond: In a single-bonded or univalent aggregate, all the tetrahedra are joined to one another by only one vertex. The connection is like an electromagnetic universal joint or like a structural engineering pin joint; it can rotate in any direction around the joint. The mutability of behavior of single bonds elucidates the compressible and load-distributing behavior of gases.

931.30 Double Bond: If two vertexes of the tetrahedra touch one another, it is called double-bonding. The systems are joined like an engineering hinge; it can rotate only perpendicularly about an axis. Double-bonding characterizes the load-distributing but noncompressible behavior of liquids. This is edge-bonding.

931.40 Triple Bond: When three vertexes come together, it is called a fixed bond, a three-point landing. It is like an engineering fixed joint; it is rigid. Triple-bonding elucidates both the formational and continuing behaviors of crystalline substances. This also is face-bonding.

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Fig. 931.10 Tetrahedral Characteristics of Chemical Bonding: Tetrahelix: Chemical bonds as demonstrated by arrangements of tetrahedra:

1. The single-bonded tetrahedron system is like an engineering pin joint: it can move in any direction. It characterizes the behavior of gases.

2. The double-bonded tetrahedron system is like an engineering hinge joint: it can rotate about an axis. It characterizes the behavior of liquids.

3. The triple-bonded tetrahedron system is like an engineering fixed joint: it is rigid. It demonstrates the behavior of crystalline substances.

D & E. The quadri-bond and mid-edge-coordinate tetrahedron systems demonstrate the super strength of substances such as diamond and the metals.

F. The tetrahelix: a helical array of triple-bonded tetrahedra.

931.50 Quadruple Bond: When four vertexes are congruent, we have quadruple-bonded densification. The relationship is quadrivalent. Quadri-bond and mid-edge coordinate tetrahedron systems demonstrate the super-strengths of substances such as diamonds and metals. This is the way carbon suddenly becomes very dense, as in a diamond. This is multiple self-congruence.

931.51 The behavioral hierarchy of bondings is integrated four-dimensionally with the synergies of mass-interattractions and precession.

931.60 Quadrivalence of Energy Structures Closer-Than-Sphere Packing: In 1885, van’t Hoff showed that all organic chemical structuring is tetrahedrally configured and interaccounted in vertexial linkage. A constellation of tetrahedra linked together entirely by such single-bonded universal jointing uses lots of space, which is the openmost condition of flexibility and mutability characterizing the behavior of gases. The medium-packed condition of a double-bonded, hinged arrangement is still flexible, but sum-totally as an aggregate, allspace-filling complex is noncompressibleas are liquids. The closest-packing, triple-bonded, fixed-end arrangement corresponds with rigid-structure molecular compounds.

931.61 The closest-packing concept was developed in respect to spherical aggregates with the convex and concave octahedra and vector equilibria spaces between the spheres. Spherical closest packing overlooks a much closer packed condition of energy structures, which, however, had been comprehended by organic chemistry extemdash that of quadrivalent and fourfold bonding, which corresponds to outright congruence of the octahedra or tetrahedra themselves. When carbon transforms from its soft, pressed-cake, carbon black powder (or charcoal) arrangement to its diamond arrangement, it converts from the so-called closest arrangement of triple bonding to quadrivalence. We call this self-congruence packing, as a single tetrahedron arrangement in contradistinction to closest packing as a neighboring-group arrangement of spheres.

931.62 Linus Pauling’s X-ray diffraction analyses revealed that all metals are tetrahedrally organized in configurations interlinking the gravitational centers of the compounded atoms. It is characteristic of metals that an alloy is stronger when the different metals’ unique, atomic, constellation symmetries have congruent centers of gravity, providing mid-edge, mid-face, and other coordinate, interspatial accommodation of the elements’ various symmetric systems.

931.63 In omnitetrahedral structuring, a triple-bonded linear, tetrahedral array may coincide, probably significantly, with the DNA helix. The four unique quanta corners of the tetrahedron may explain DNA’s unzipping dichotomy as well as T-A; G-Cpatterning control of all reproductions of all biological species.