Normal Vibrations of the Polymer Molecules of Helical Configuration

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Abstract
A method suitable for numerical calculations of the normal vibrations of helical molecules is derived by the use of GF‐matrix method. The method is described for the case of the isolated infinite helical molecule in which the one‐dimensional crystallographic repeat unit contains n chemical units and m turns (one chemical unit contains p atoms). It is shown that the optically active fundamental frequencies of such molecules can be obtained by solving the secular equations for A, B, E 1, and E 2 species, the maximum orders of which are 3p—2, 3p, 3p—1, and 3p, respectively. This method can be also applied to the cases of infinitely extended planar zigzag chains such as polyethylene and cyclic molecules such as trioxane, etc., as special cases. As examples of application of this method, calculations of the skeletal vibrations of a simple model of polyoxymethylene molecule under the group D(10π/9) and of the planar zigzag chain of carbon atoms are given.

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