INFRARED INTENSITIES OF LIQUIDS .16. ACCURATE DETERMINATION OF MOLECULAR BAND INTENSITIES FROM INFRARED REFRACTIVE-INDEX AND DIELECTRIC-CONSTANT SPECTRA

Absorption spectra of liquids in which the intensities are believed to be absolute rather than relative can be described by several different absorption quantities. The most important of these are the molar absorption coefficient, E(m)(nu), the imaginary refractive index or absorption index, k(nu), and the imaginary dielectric constant epsilon''(nu). These are phenomenological properties of the liquid, and are not independent. With the assumption of a model for the local field which acts on the molecules in the liquid, they can be converted to a molecular quantity. the complex molar polarizability, alpha(m)(nu). The imaginary molar polarizability, alpha(m)''(nu), also describes the absorption spectrum. The lineshapes and peak positions in these different absorption spectra differ in a way that seems not to be fully recognized. Vibrational intensities of the molecules in the liquid can be calculated from any of these spectra as the magnitudes of the transition moments or of the dipole moment derivatives with respect to the normal coordinates, always under an assumption about the local field but also under other approximations for the E(m), k and epsilon'' spectra. These intensities can also be calculated, under the same approximations as for the epsilon''(nu) spectra, from the peak wavenumbers in the epsilon'' and alpha(m)'' spectra. This paper illustrates the differences between the lineshapes and peak positions in the different spectra. and explores the accuracy of the vibrational intensities calculated from them. The exploration uses the Lorentz local field, and uses both experimental spectra and spectra calculated from the classical damped harmonic oscillator model. The results show that the alpha(m)'' spectrum most reliably gives the molecular properties, but it does impose the Lorentz local field model on the experimental spectrum. Symmetric alpha(m)'' and epsilon(m)'' bands correspond to asymmetric k and E(m) bands, particularly at low wavenumbers, so the alpha(m)'' or epsilon'' spectrum should always be used when the lineshape is relevant. Accurate calculation of vibrational intensities can only be done reliably from the alpha(m)'' spectrum. Sometimes high accuracy may be obtained for separated bands from the E(m), k and epsilon'' spectra, but the anomalous dispersion in the real dielectric constant introduces an uncertainty that increases with band strength and is difficult to assess for any but well separated weak bands. The consequent errors in the intensities range from 0% to over 20%.