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 differen t absorption quantities. The most important of these are the molar abs orption coefficient, E(m)(nu), the imaginary refractive index or absor ption index, k(nu), and the imaginary dielectric constant epsilon''(nu ). These are phenomenological properties of the liquid, and are not in dependent. With the assumption of a model for the local field which ac ts on the molecules in the liquid, they can be converted to a molecula r quantity. the complex molar polarizability, alpha(m)(nu). The imagin ary molar polarizability, alpha(m)''(nu), also describes the absorptio n spectrum. The lineshapes and peak positions in these different absor ption spectra differ in a way that seems not to be fully recognized. V ibrational intensities of the molecules in the liquid can be calculate d from any of these spectra as the magnitudes of the transition moment s or of the dipole moment derivatives with respect to the normal coord inates, always under an assumption about the local field but also unde r other approximations for the E(m), k and epsilon'' spectra. These in tensities 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 betwee n the lineshapes and peak positions in the different spectra. and expl ores the accuracy of the vibrational intensities calculated from them. The exploration uses the Lorentz local field, and uses both experimen tal spectra and spectra calculated from the classical damped harmonic oscillator model. The results show that the alpha(m)'' spectrum most r eliably 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, part icularly at low wavenumbers, so the alpha(m)'' or epsilon'' spectrum s hould always be used when the lineshape is relevant. Accurate calculat ion of vibrational intensities can only be done reliably from the alph a(m)'' spectrum. Sometimes high accuracy may be obtained for separated bands from the E(m), k and epsilon'' spectra, but the anomalous dispe rsion in the real dielectric constant introduces an uncertainty that i ncreases with band strength and is difficult to assess for any but wel l separated weak bands. The consequent errors in the intensities range from 0% to over 20%.