Normal Coordinate Analysis of Halogenated Ethylenes. I. General Methods

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Abstract
Methods and detailed algebraic expressions are given for the normal‐coordinate analysis of ethylenic molecules. In the following paper they are applied to the calculation of potential constants, normal modes, and vibrational frequencies for a series of perhalogenated ethylenes. A force field of the Urey‐Bradley type is used for the planar vibrations, and a simple valence‐type potential function is applied to the nonplanar motions. The force constants established for the molecules with Vh symmetry are to be used with only linear interpolation and no further adjustment to calculate the fundamental frequencies and modes of all the remaining, less symmetrical ethylenes. For the Vh molecules the vibrational secular equations are set up in the customary GF matrix fashion. The other ethylenes require a somewhat different form which is more readily adapted to calculation by an electronic digital computer. In order that the force constants determined for the Vh molecules be as good as possible a method is given for their adjustment by a least‐squaring process.