## Investigation of molecular polarizabilities and derivatives in halomethanes

##### Abstract

The research undertaken was to obtain absolute Raman intensities for the symmetric
stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and
theory.
The intensities were experimentally measured using the Ar+ ion gas laser as excitation
source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube
as detector. These intensities arise from changes in the derivative of the polarizability (8
a'), with respect to vibration along a normal coordinate (8qi). It was intended that these
derivatives obtained with respect to normal coordinates would be converted to derivatives
with respect to internal coordinates, for a quantitative comparison with theory.
Theoretical numerical polarizability derivatives for the stretching vibrations are
obtained using the following procedure. A vibration was simulated in the molecule by
increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds
and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the
difference in the polarizability for the equilibrium geometry and the geometry when a
particular bond is changed. This difference, when divided by the amount of change in each
bond and the number of bonds present results in the derivative of the polarizability with
respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two
methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules
(AIM) analysis.
Due to errors in the experimental setup only a qualitative analysis of the results was
undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen
stretch vibrations are more intense than the respective carbon-hydrogen stretch,
but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense
than the carbon-hydrogen stretch, a fact which is attributed to the small size and high
electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a
quantitative comparison can be made.
The analysis by the theory of atoms in molecules, along with providing polarizabilities
and polarizability derivatives, gives additional information outlined below. The theory
provides a pictorial description of the main factors contributing to the molecular
polarizability and polarizability derivative. These contributions are from the charge
transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the
reorganization of atomic electronic charge distribution due to presence of an electric field.
The linear relationship between polarizability and molecular volume was also observed.