AB3 system

Invariant Procedures. Journal of Chemical Physics 43 S129-S135. pie J A and G A Segal 1965. Approximate Self-Consistent Molecular Orbital Theory. II. Calculations with Complete Neglect of Differential Overlap. The Journal of Chemical Physics 43 S136-S149. iple J A and G A Segal 1966. Approximate Self-Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 systems. Journal of Chemical Physics 44 3289-3296. 

J. A. Pople and G.A. Segal, Approximate self-consistent molecular orbital theory. III. CNDO results for AB2 and AB3 systems, J. Chem. Phys. 44 3289 (1966). 

To obtain information about the geometry of molecules, e.g., about the number of AB bonds in an AB system, the spectra have to be analyzed more carefully. In a non-linear molecular compound, the total number of vibrations is 3m- 6 (m = number of atoms). In order to discuss the geometry, one must first look at the number of stretching vibrations. This number corresponds to the number of AB bonds. As a result of the symmetry, the number of observed stretching vibrations is sometimes smaller, e.g., only two vibrations are usually observed for AB3-systems, since one of them is doubly degenerate. This is true for species with D h- and with Cj -symmetry. 

Fig. 22. Changes in the size and sign of non-bonded interactions on distortion AB3 systems 2fli (a) and 3ax (b) orbitals AB4 systems 3 ax (c) and 2ax (d) orbitals AB5 systems 2ax (e) and 3 ax (f) orbitals ABg systems 2 ax (g) and 3 ax (h) orbitals.

The concept of Frey et al. [57] can be apphed to aU hb systems in order to deduce equations for the calculation of DB. In the case of AB,c monomers (x > 2), additional structural units must be considered in a structural characterization these are aligned between nonbranching L units and fuUy reacted D units, because they introduce branches but still bear nonreacted B functionalities. For the AB3 case, eight structural units can be distinguished whereby the ABb2 (Isd) and aBb2 (2sd) units are denoted as semidendritic Isd + 2sd = sD. From experimental data, the DB of an AB3 system can be calculated according to Equation 24.3 ... 

A further parameter, introduced by Erey et al., allows a comparison to be made of the density of branching of different AB polymers. This average number of branches (ANBs) deviating from the linear direction per non-terminal monomer unit, and was 0.333 for AB2 systems, 0.421 for AB3 systems, and converges to 0.582 for growing x, again for random polymerization and full conversion [57]. 

In the AB3 system, three equivalent nuclei are coupled to a fourth nucleus which lies close to them so that A /J is small. Methanol and methylmercaptan (CH3SH) serve as examples. Up to sixteen lines can be obtained in AB3 spectra, but two of these are weak combination lines and it is therefore more common to encounter up to 14 lines. 

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