The refractive index of colorless liquids in the visible and infrared: Contributions from the absorption of infrared and ultraviolet radiation and the electronic molar polarizability below 20 500 cm−1

Abstract

This paper addresses the separation of the contributions to the visible refractive index of colorless liquids from electronic (ultraviolet) and vibrational (infrared) absorption. The goal is to find the most accurate infrared values of nel(ν̃), the refractive index that results solely from electronic absorption, by fitting and extrapolating currently available visible refractive index data. These values are needed, interalia, to improve the accuracy of infrared real refractive index spectra calculated by the Kramers–Kronig transform of infrared imaginary refractive-index spectra. The electronic molar polarizability αel(ν̃) is calculated from the values of nel(ν̃) at wave numbers between 20 500 and 0 cm−1. The methods are applied to ten liquids: H2O, D2O, CH3OH, CH3COOH, CH3CN (CH3)2CO, CH2Cl2, C6H6, C6H5Cl, and C6H5CH3. The visible refractive indices are expressed as power series in wave number, by expansion of the Kramers–Kronig integral. Terms in ν̃+2m, m=1,2, are due to the electronic contribution and terms in ν̃−2m are due to the vibrational contribution. The vibrational contribution to the visible refractive index is also calculated from experiment by Kramers–Kronig transformation of the known infrared imaginary refractive index spectrum of the liquid. It is shown that the vibrational absorption contributes ≥0.001 to the visible refractive index only for the four hydrogen-bonded liquids, and that, for all ten liquids, at least 25% of the vibrational contribution arises from absorption below 2000 cm−1. If the vibrational intensities are not known, the available visible refractive indices yield the most accurate infrared values of nel for all liquids except H2O if they are fitted to the equation n=a0+a2ν̃2+a4ν̃4. A similar equation, with the additional term a2ν̃−2, is theoretically superior because the latter term adequately describes the vibrational contribution to the visible refractive indices, but only for H2O are the currently available visible refractive indices sufficiently accurate and sufficiently extensive to allow the four coefficients in the equation to be determined with useful accuracy. For H2O, D2O, CH3OH, CH2Cl2, C6H6, C6H5Cl, and C6H5CH3, corrections are given to slightly improve the accuracy of the previously published infrared real refractive-index spectra.