Bond Length Effects

A basic tenet of organic conformational analysis is that the lessons learned from the extensively studied hydrocarbon systems will carry over more or less unperturbed to systems with heteroatoms. The conformational analysis of methyl ethyl ether should not be too different from that of n-butane. However, in certain cases, when multiple heteroatoms are superimposed on a hydrocarbon framework in close proximity, a number of novel effects arise, which often stabilize otherwise unstable conformations. These effects, such as the anomeric effect and the gauche effect, all have similar origins that can be easily understood using the bonding models of Chapter 1. Let s start by analyzing bond length effects. 

One simple difference in the conformations of pure hydrocarbons and heterocyclic rings results from the fact that C-heteroatom bonds are of different lengths than C-C bonds. Bonds to O and N are shorter, often causing increased steric strain. Bonds to S are significantly longer. 

These differences are reflected in the A values for groups attached to cyclohexane analogues. Table 2.16 shows a number of A values for groups attached to various positions on heterocycles relative to cyclohexane. Note the dramatic difference between the 2- and 5-positions on 1,3-dioxane. This difference reflects the shorter C-Obond lengths, making the 1,3-diaxial interactions more repulsive. 

A Values (AG° in kcal/mol) for Three Groups in Particular Positions in Heterocyclic Systems 

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In a continuous model, the conformation is primarily determined by the hydrophobic contact pattern and the dihedral angles of the molecule. We ignore the bond-angle and bond-length effects as these are nearly fixed with respect the torsion angles and contacts. To apply the overlap function methodology to the continuous case, we must discretize the continuous space and capture information about both the torsion angles and contacts. 

The following tables contain experimentally-determined commensurate structure parameters for alkali metal adsorption systems (only simple structures are listed). The temperatures quoted are the measurement temperature. The bond length quoted is the chemisorption bond length. Effective r (Eff r) is the chemisorption bond length minus the metalHc radius of the substrate atom. Excess r (Exc. r) is the Effective r minus the ionic radius of the alkali metal atom N is the coordination number of the alkali adatom. A coordination number denoted as indicates that due to surface reconstruction, an unambiguous assigmnent carmot be made. 

Hosseinzadeh et al. (2006) provided a simple equation for establishing the effective bond length. Effective bond length is defined as the bond... 

It is not possible to apply (C2.1.1) down to the level of monomers and replace by the degree of polymerization N and f by the sum of the squares of the bond lengths in the monomer because the chemical constitution imposes some stiffness to the chain on the length scale of a few monomer units. This effect is accounted for by introducing the characteristic ratio defined as C- — The characteristic ratio can be detennined... 

MM2 was, according the web site of the authors, released as MM2 87). The various MM2 flavors are superseded by MM3, with significant improvements in the functional form [10]. It was also extended to handle amides, polypeptides, and proteins [11]. The last release of this series was MM3(%). Further improvements followed by starting the MM4 series, which focuses on hydrocarbons [12], on the description of hyperconjugative effects on carbon-carbon bond lengths [13], and on conjugated hydrocarbons [14] with special emphasis on vibrational frequencies [15]. For applications of MM2 and MM3 in inorganic systems, readers are referred to the literature [16-19]. 

If one is interested in the probability that mh be observed when is measured regardless of what bond length r is involved, then it is appropriate to integrate this expression over the r-variable about which one does not care. This, in effect, sums contributions from all r-values to obtain a result that is independent of the r variable. As a result, the probability reduces to ... 

The amount of computation necessary to try many conformers can be greatly reduced if a portion of the structure is known. One way to determine a portion of the structure experimentally is to obtain some of the internuclear distances from two-dimensional NMR experiments, as predicted by the nuclear Over-hauser effect (NOE). Once a set of distances are determined, they can be used as constraints within a conformation search. This has been particularly effective for predicting protein structure since it is very difficult to obtain crystallographic structures of proteins. It is also possible to define distance constraints based on the average bond lengths and angles, if we assume these are fairly rigid while all conformations are accessible. 

In Section 4 the data on bond lengths and strengths have been vastly increased so as to include not only the atomic and effective ionic radii of elements and the covalent radii for atoms, but also the bond lengths between carbon and other elements and between elements other than carbon. All... 

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