Valency angles

A considerable number of experiments have shown that symmetrical PMDs in the ground state have an aH-trans configuration and are nearly planar with practically equalized carbon—carbon bonds and slightly alternating valence angles within the polymethine chain (1,3,5,22,23). This is caused by some significant features of the PMD electron stmcture. 

Here and below, T , 1, , and e, i, j = 1,. . . , 5, denote atomic position vectors, atom-atom distances, and the corresponding unit vectors, respectively. In order to construct a correctly closed conformation, variables qi,. . . , q4 are considered independent, and the last valence angle q is computed from Eq. (7) as follows. Variables qi,.. ., q4 determine the orientation of the plane of q specified by vector 634 and an in-plane unit vector 6345 orthogonal to it. In the basis of these two vectors, condition (7) results in... 

Figure 4 Time step dependence of the average total energy for two models of a partially hydrated dodecamer DNA duplex. Thinner traces show results for virtually harmonic conditions when temperature was lowered to 1 K. The DNA molecule has fixed bond lengths, rigid bases, and fixed valence angles except for the mtra- and extracyclic bond angles m sugars, (a) No modifications of inertia (b) inertia modified as explained m the text. (From Ref. 54.)...

The structure of 91 was studied by X-ray (94MI1). The five-member heterocycle is planar. The valence angle (79.4°) has the lowest value for all known five-member tellurium-containing heterocycles. 

As the most notable contribution of ab initio studies, it was revealed that the different modes of molecular deformation (i.e. bond stretching, valence angle bending and internal rotation) are excited simultaneously and not sequentially at different levels of stress. Intuitive arguments, implied by molecular mechanics and other semi-empirical procedures, lead to the erroneous assumption that the relative extent of deformation under stress of covalent bonds, valence angles and internal rotation angles (Ar A0 AO) should be inversely proportional to the relative stiffness of the deformation modes which, for a typical polyolefin, are 100 10 1 [15]. A completly different picture emerged from the Hartree-Fock calculations where the determined values of Ar A0 AO actually vary in the ratio of 1 2.4 9 [91]. 

B. Molecular Geometry Bond Lengths and Valence Angles.345... 

Equilibrium valence angles calculated by unrestricted CNDO/2 (66) and INDO (85) methods for several AB2 and AB3 radicals are listed in Table III. We recalculated (68) this series of radicals by the restricted CNDO/2 method (Longuet-Higgins and Pople) and obtained results which are practically identical with those in Table III. The MINDO method also appears to give reasonable results (82, 83). 

Thus the fully extended length of the equivalent chain will be set equal to that of the real chain with all valence angle B and ) restrictions removed. Then n and V (and therefore m) for the equivalent chain are completely defined by... 

Valence angle between successive bonds in the polymer chain (Chaps. X and XIV). 

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