Bonding defined

What I have done is to take a dummy centre halfway along the C3-C4 bond defined the oxygen atom by its distance from the dummy atom and work fronj there. The lengths and angles used in a Z-matrix do not have to correspond to chemical bond distances or angles, although the normal valence variables are said to be the best choice for geometry optimization. 

In the discussion of metallic radii we may make a choice between two immediate alternative procedures. The first, which I shall adopt, is to consider the dependence of the radius on the type of the bond, defined as the number (which may be fractional) of shared electron pairs involved (corresponding to the single, double, and triple bonds in ordinary covalent molecules and crystals), and then to consider separately the effect of resonance in stabilizing the crystal and decreasing the interatomic distance. This procedure is similar to that which we have used in the discussion of interatomic distances in resonating molecules.7 The alternative procedure would be to assign to each bond a number, the bond order, to represent the strength of the bond with inclusion of the resonance effect as well as of the bond type.8... 

However, this equation is valid only in the case when the dipole moment of the adsorbed XY molecule and the direction of the bond, defined by the arrangement of the... 

In this situation the two end-ring double bonds define a positive chirality. Application of the twisted diene rule gives a positive sign for the lowest-energy 1A - 1B transition, and in the case of 15-cA-(3R,3 R)-zeaxanthin this is confirmed by experiment. 

The function M(n) may then be defined as the sum of all possible products of m-bonds and y-bonds, defined in exactly the same way as R(n) except that connections are through all possible combinations of y-bonds and isolated w-bonds. (ip- and w-bonds represent the functions and m j respectively.)... 

The main parameters used to describe a polymer chain are the polymerization index N, which counts the number of repeat units or monomers along the chain, and the size of one monomer or the distance between two neighboring monomers. The monomer size ranges from a few Angstroms for synthetic polymers to a few nanometers for biopolymers. The simplest theoretical description of flexible chain conformations is achieved with the so-called freely-jointed chain (FJC) model, where a polymer consisting of N + I monomers is represented by N bonds defined by bond vectors r/ with j= Each bond vector has a fixed length r,j = a corresponding to the... 

Hirshfeld (1964) pointed out that bond bending not only occurs in ring systems, but also results from steric repulsions between two atoms two bonds apart, referred to as 1-3 interactions. The effect is illustrated in Fig. 12.3. The atoms labeled A and A are displaced from the orbital axes, indicated by the broken lines, because of 1-3 repulsion. As a result, the bonds defined by the orbital axes are bent inwards relative to the internuclear vectors. When one of the substituents is a methyl group, as in methanol [Fig. 12.3(b)], the methyl-carbon-atom hybrid reorients such as to maximize overlap in the X—C bond. This results in noncolinearity of the X—C internuclear vector and the three-fold symmetry axis of the methyl group. Structural evidence for such bond bending in acyclic molecules is abundant. Similarly, in phenols such as p-nitrophenol (Hirshfeld... 

The two a bonds define a local plane of symmetry, assumed to be the xy plane. The p orbital (pz) will always be perpendicular to the local plane of the molecule and be antisymmetric w.r.t. reflection in the plane. 

The Chemical Bond Defined.—We shall say that there is a chemical bond between two atoms or groups of atoms in case that the forces acting between them are such as to lead to the formation of an aggregate with sufficient stability to make it convenient for the chemist to consider it as an independent molecular species. 

This is an example of a Diels-Alder reaction. This is an electrocyclic reaction where no charges are involved. While no charges are involved, electron pairs do move and their movement can be illustrated using arrow pushing. The mechanism, illustrated below, involves aligning cyclopentadiene (a diene) with methyl vinyl ketone (a dienophile) such that all three double bonds define a six-membered... 

If we conceive the stationary state of these molecules in a rough first approximation as a simple superposition with equal contributions of the unexcited configurations (Kekule config.), there are produced important differences in the double-bond character of the bonds defined in this way by Pauling. ... 

Pauling s second mle is the electrostatic valence mle. It states that the charge on an ion must be balanced by an equal and opposite charge on the surrounding ions. A cation, coordinated by n anions, has an electrostatic bond strength (BBS) for each bond defined as ... 

The parameter K shown in the figure represents the reactivity of the terminal double bonds, defined by K=k lk, and k is the rate constant of TDBP. The... 

Select the strategic bond. This recommendation is especially important in those numerous cases in which the initial analysis does not identify an efficient strategic reaction and, hence, a sequential bond-by-bond dismantling of the structure becomes obligatory. The first bond in this sequence (the strategic bond) defines all subsequent steps in the retrosynthetic analysis. This approach was illustrated in the syntheses of quadrone (Section 3.2.5). 

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