Bond directional principle

Obviously, graphical techniques are equally important in the study of electron momentum densities. Coulson [2,4] made the pioneering effort in this direction. Other early work was published by Henneker and Cade [305] Epstein and Lipscomb [306-308] Kaijser, Lindner, and coworkers [309-311] Tanner and Epstein [312] and Tawil and Langhoff [313,314]. A synthesis of these studies was made by Epstein and Tanner [13], who abstracted some principles that they hoped would be generally applicable to chemical bonding. One of their abstractions pinned down an observation about the anisotropy of n(p) that had been made in several of the earlier studies. Epstein and Tanner called it the bond directional principle, and they stated it as follows [13] ... 

In view of the many exceptions to the bond directional principle [13] found in the work cited in the last three paragraphs, Tanner carefully reassessed it in a thoughtful paper [315]. He then formulated a new version as follows... 

Tanner pointed out that a few exceptions to the revised bond directional principle were already known. He emphasized that the principle is a qualitative one, and attempts to makes it more precise would defeat the purpose of giving a feel for what n(p) is like. 

A.C. Tanner. The Bond Directional Principle for Momentum Space Wavefunc-tions Comments and Cautions. Chemical Phy.sic.s, 123 (1988). 241-247. 

The structure of a molecule depends essentially on the covalent bond forces acting between its atoms. In the first place, they determine the constitution of the molecule, that is, the sequence of the linkage of the atoms. The constitution can be expressed in a simple way by means of the valence bond formula. For a given constitution the atoms arrange themselves in space according to certain principles. These include atoms not bonded directly with one another may not come too close (repulsion of interpenetrating electron shells) and the valence electron pairs of an atom keep as far apart as possible from each other. 

The same "heuristic principles" which are applied to carbocyclic compounds also hold true for simple heterocyclic compounds containing one heteroatom. However, in the case of bridged heterocyclic molecules a modified strategic bond selection must be applied. Besides the strategic bonds which meet Corey s six rules, the bonds directly attached to nucleophilic heteroatoms -such as O, S and N-are also strategic Cf. heuristic principle HP-7), provided that they satisfy rules 2B, 4, 5 and 6. For instance, in compound 31a besides the five strategic bonds determined by rules 1-6 (cf. compound 26), the sixth darkened C-N bond in 31b is also a strategic bond. 

Notice that the lowest energy state j = 0 has E = 0, but it does not correspond to a bond which is merely pointing in one direction in space just like an s orbital, it is simultaneously pointing in all directions. This is yet another manifestation of the Uncertainty Principle. If a bond is known to point in one direction, the positional uncertainty perpendicular to the bond direction is zero, and the momentum uncertainty is infinite ... 

In the first three solid types (metals, ionic crystals, van der Waals crystals), the forces of interaction that hold the particles together do not act in any preferred direction in covalent crystals, the bonds are formed only in special directions because of the directional character of the covalent bond. The principles governing the direction of bond formation in covalent crystals are the same as those governing the covalent bond in molecules. 

Bond orbitals and stereochemistry. The number and direction of the valence bonds in compounds depends on the particular electron orbitals which form the bonds. The principles may be seen by referring to 6-coordinated cobalt, planar 4-coordinated nickel, and, tetrahedral 4-coordinated... 

Two of the major goals of alkane functionalization have been the selective conversion of methane to methanol and the replacement of strong terminal alkyl C-H bonds with a functional group. These goals have also included the selective functionalization of a single aliphatic or aromatic C-H bond, directed by either a substituent attached to the arene or controlled by the particular steric or electronic properties of the substrate. Thus, many of the principles that have been developed for the functionalization of small molecules with the goal of producing chemical feedstocks have now been adopted for more intricate synthetic applications. 

The appreciable adsorption of water molecules linked with gallium through their oxygen atoms must, in principle, result in a higher overpotential. This increase may be caused both by the surface being partially blocked by molecules oriented in such a way that they cannot transform to hydroxonium ions with the O-H bond directed toward the metal, and by the fact that the chemisorption of water will weaken, just as adsorption of other donor particles, the adsorption bond of hydrogen. 

The principles used to describe the bonding for methane can be extended to larger molecules that have additional carbon atoms and carbon-carbon bonds rather than only the C-H bonds found in methane. Ethane (5) has a covalent bond between two carbon atoms, for example, and both carbons have four bonds directed to the corners of a tetrahedron. The structure of ethane is shown in Figure 3.12, first with the Lewis dot formula for ethane (5a) and then as a structure made by overlapping two tetrahedrons of carbon (5b), each carbon with three hydrogen atoms and the fourth bond between carbon and carbon. The carbon-carbon bond is represented by overlap of the tetrahedrons in 5b. 

Adhesive strips are constructed so, that in spite of their high adhesion, they can be removed easily from all surfaces just by stretching them in the bond direction. This principle first was used fi)r medical applications [277]. More recent developments allow objects weighing up to a few kilograms reversibly to be fastened to various surfaces [2781. 

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