Bond profiles

If one is interested in the characterization of molecular local features, one should confine the matrix only to atoms that define the local environment of interest. When only atoms belonging to a local environment are included in the construction of the matrices, one obtains the seqnence 

Here = 2 Rk./n is the average row sum of the matrix If only atoms at the molecular periphery are included in the constrnction of the matrices, one obtains the sequence 

Moreover, when constructing the geometry-dependent matrix D one is not restricted to consider only atoms. One can introdnce any number of geometric points along chemical bond and in this way obtain sequences 

The first question to consider is to find how many points need be taken in order to reach an apparent convergence for the contour sequences. As is known, the Monte Carlo calculations, of which the above is an illustration, converge but rather slowly. In order to increase the accuracy of the results by a factor of 10, one has to increase the number of points by a factor of 100. We found for the above case that after 2000, points fluctuations between successive calculations decrease dramatically. 

The conditions for inclusion/exclusion of a randomly selected point are relatively simple. Each atom is represented by a circle  

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Moreover, an arbitrary number of points can be considered along the molecule bonds, thus deriving bond profiles ... 

Bond profiles constitute a generalization of atomic molecular profiles since they provide a characterization of molecular connectivity, which is not explicitly contained in the geometry matrix [Randic, 1996a Randic and Krilov, 1996]. 

Randic, M. (1996a). Molecular Bonding Profiles. J.Math.Chem., 19,375-392. 

Randic, M. and Krilov, G. (1996). Bond Profiles for Cuboctahedron and Twist Cuboctahedron. 

Randic, M. and Krilov, G. (1996) Bond profiles for cuboctahedron and twist cuboctahedron. Int. J. Quantum Chem. Quant. Biol. Symp., 23, 127-139. 

Figure 5 reports a comparison between the contour maps of the density difference, Ap(r), the Kullback-Leibler integrand, Ah(r), and the entropy displacement function [equation (94)], A (r), for the planes of sections shown in Fig. 4. The corresponding central bond profiles of the density and entropy difference functions are compared in Fig. 6. The optimized geometries of propellanes have been determined from the UHF calculations (GAMESS program) using the 3-21 G basis set. The contour maps have been obtained from the DFT calculations (deMon program) in DZVP basis set.

Fig. 6. The bridgehead bond profiles of the density difference function (left panel) and molecular entropy displacement (right panel) for the four propellanes of Fig. 4. For comparison the numerical values of the bond multiplicities from the difference approach (R. F. Nalewajski, J. Mrozek, G. Mazur (1996) Can. J. Chem., 74, 1121) are also reported [29].

FIGURE 11.1 (a) Target bond profile for Willstatter (1911, 1913) plan for cyclooctatetraene. (b) Target bond... 

Polymerization adhesives based on a-cyanoacrylates (see p. 30) are suitable for special bonds involving rubber, because they enable bonds of high strength to be obtained quickly and easily. Medium-viscosity types are preferred for rubber-to-rubber bonds by virtue of the minimal hardening of the joint. In the rubber industry, for example, the adhesives are used for bonding profiles to one another and also for repair work. 

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