Estimation of fundamental frequencies of perhalogenated ethylenes in terms of molecular fragment contributions

Abstract

A model, in which a molecule is subdivided into a number of subunits, is used to calculate approximately fundamental frequencies of perhalogenated ethylenes in terms of contributions of subunits and clusters of subunits. Different levels of approximation are defined by a subunit additivity scheme, a linear subunit pair and subunit triple scheme as well as by a nonlinear coupled subunit pair scheme. Algebraic dependencies of the approximate formulas for distinct ethylene derivatives are used as criteria for testing the different schemes. The method is applied to the fundamental frequencies of normal vibrations which, with respect to symmetry, correlate uniquely in the series of substituted ethylenes considered, otherwise the method is applied to corresponding sums of frequencies. For the fundamental frequencies of the 27 ethylene derivatives C2FnClmBr4−n−m, n+m≤4, completely known from a normal coordinate analysis, the main results are: (a) The out-of-plane frequencies correlate uniquely in these molecules, three of the in-plane frequencies and two sums formed from the remaining ones correlate as well. (b) The simple additivity scheme with three parameters for each set of correlating frequencies yields a sufficiently exact fit of the out-of-plane frequencies; their mean absolute deviation is about 5 cm−1. (c) The linear subunit pair approximation with twelve parameters for each set is sufficiently exact for all the correlating frequencies and sums of frequencies, respectively; their mean absolute deviation is about 1 cm−1.