An exploratory analysis of experimental polar tensor data

Abstract

An exploratory sratistical study of 157 atomic polar tensors (APT's) taken from 50 molecules is reported. Correlations for all five APT invariants show that comparisons of APT's for different molecules can be made by using mean dipole moment derivative and anisotropy values with only a small loss of statistical information. The use of these values for comparisons with molecular structural parameter values is illustrated. The mean dipole moment derivative values correlate well with electronegativity values for various subgroups of the APT'S studied. Anisotropy values can be related to the electronic environment of atoms and bonds adjacent to the atom being studied. Atoms with a polarizable lone pair or an unsaturated bond provoke larger anisotropy values for their neighboring atoms than do completely saturated atoms or bonds. The mean dipole derivative and anisotropy values provide some class discrimination that can be useful for polar tensor transference procedures. I. Introduction In the 12 years or so that have elapsed since the publication of the polar tensor formalism in conventional spectroscopic notation,' a fairly large number of atomic polar tensors have been obtained from experimental vibrational intensities. Other parametric schemes have been forwarded, based on electrooptical parameters2 or charges and charge fl~xes,~ but they are ultimately related to the polar tensor formalism and usually require a larger number of parameters. By contrast, the relatively small number of parameters involved in the polar tensor formalism, together with its comparative simplicity, makes it a choice method for the analysis of infrared intensity data. Much effort has been devoted, within each formalism, to find relations between parameters derived from vibrational intensities and other, more traditional, chemical parameters. Good correlations have been obtained with electr~negativities,~ force constant~,~ bond length^,^ degrees of acidity,6 percent of ionic character,' and the ability to form molecular complexes.6 In all such studies, however, only relatively small groups of molecules were considered, and the conclusions reached were therefore somewhat limited in scope. In this paper we report a study of a much larger group of molecules. A very extensive set of experimental atomic polar tensors (APT's) is subjected to an exploratory analysis, with a 2-fold objective. In the first place we wish to investigate the possible existence, in this large collection of data, of statistical relations involving the rotationally invariant quantities of the atomic polar tensors. We have chosen the invariants because, unlike the APT elements, they are independent of the orientation of the Cartesian coordinate system for a given molecule and are therefore appropriate for comparisons of data taken from many different sources. Our second objective is to identify general patterns that will help to define classes or groups of molecules that may act as a guide to the direct transference of atomic polar tensors from one molecule to another. These patterns should also be useful in the construction of similarity models for a more accurate transference of vibrational parameters.8 We also expect that a systematic study involving such a large number of APT invariants will lead to a clearer understanding of the relationships between intensity data and molecular structural parameters. 11. The Atomic Polar Tensor Data Set