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Notes: 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(ν˜), 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(ν˜) is calculated from the values of nel(ν˜) 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 ν˜+2m, m=1,2, are due to the electronic contribution and terms in ν˜−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+a2ν˜2+a4ν˜4. A similar equation, with the additional term a2ν˜−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. © 1995 American Institute of Physics.

Notes: A new and simple procedure is presented for the calculation of the infrared real, n, and imaginary, k, refractive index spectra from s-polarized attenuated total reflection (ATR) spectra by a modified Kramers–Kronig transform of the reflectance to the phase shift on reflection. The procedure consists of two parts, first a new modified Kramers–Kronig (KK) transform, and second a new, wave number-dependent, correction to the phase shift. The procedure was tested with ATR spectra which were calculated from refractive index spectra that were synthesized under the classical damped harmonic oscillator model. The procedure is far more accurate than previous procedures for the real case of a wave number-dependent refractive index of the incident medium, and yields n and k values that are accurate to ≤0.1% provided that no errors are introduced by the omission of significant reflection bands. This new procedure can be used to obtain optical constants from any ATR experiment that yields the spectrum of Rs, the reflectance polarized perpendicular to the plane of incidence. In this laboratory Rs spectra are obtained from samples held in the Spectra-Tech CIRCLE cell in a Bruker IFS 113 V spectrometer. Accordingly the ATR spectra used to test the new procedure were calculated for the optical configuration of this system, which is m reflections at 45° incidence with equal intensities of s- and p-polarized light and retention of polarization between reflections. For the previously studied [J. S. Plaskett and P. N. Schatz, J. Chem. Phys. 38, 612 (1963); J. A. Bardwell and M. J. Dignan, ibid. 83, 5468 (1985)], but unreal, case of constant refractive index of the incident medium, n0, the new transform gave better results than either of two previously studied procedures. In this case the phase shift at each wave number was corrected by a constant which ensured that the correct phase shift was obtained at the highest wave number in the transform, 7800 or 8000 cm−1. In contrast to a previous study [J. Chem. Phys. 83, 5468 (1985)] it was found that the normal KK transform is inferior for this case to a previous modified KK transform [J. Chem. Phys. 38, 612 (1963)], and it is also inferior to the new modified KK transform. Further, the new transform has only the usual singularity of a KK transform, and this makes it numerically superior to the previous modified KK transform which has an additional singularity at 0 cm−1. For the real case, in which the refractive index of the incident medium changes with wave number, the new transform was used with a new simple wave number-dependent additive correction to the phase shift. This new correction is calculated with the actual value of n0 at each wave number. For molecular liquids such as methanol and benzene the new transform is markedly superior to the previous two transforms. It yields real and imaginary refractive index values that are accurate to better than 0.1% provided the reflection spectrum is known down to 2 cm−1. The latter condition is rarely fulfilled, and the effect of the omission of low wave number bands is illustrated. A method to reduce the impact of missing low-wave number parts of the reflectance spectrum is described, and its effectiveness is illustrated. © 1996 American Institute of Physics.

Notes: This paper is concerned with the peak wave number of very strong absorption bands in infrared spectra of molecular liquids. It is well known that the peak wave number can differ depending on how the spectrum is measured. It can be different, for example, in a transmission spectrum and in an attenuated total reflection spectrum. This difference can be removed by transforming both spectra to the real, n, and imaginary, k, refractive index spectra, because both spectra yield the same k spectrum. However, the n and k spectra can be transformed to spectra of any other intensity quantity, and the peak wave numbers of strong bands may differ by up to 6 cm−1 in the spectra of the different quantities. The question which then arises is "which infrared peak wave number is the correct one to use in the comparison of infrared wave numbers of molecular liquids with wave numbers in other spectra?" For example, infrared wave numbers in the gas and liquid phase are compared to observe differences between the two phases. Of equal importance, the wave numbers of peaks in infrared and Raman spectra of liquids are compared to determine whether the infrared-active and Raman-active vibrations coincide, and thus are likely to be the same, or are distinct. This question is explored in this paper by presenting the experimental facts for different intensity quantities. The intensity quantities described are macroscopic properties of the liquid, specifically the absorbance, attenuated total reflectance, imaginary refractive index, k, imaginary dielectric constant, ε″, and molar absorption coefficient, Em, and one microscopic property of a molecule in the liquid, specifically the imaginary molar polarizability, αm″, which is calculated under the approximation of the Lorentz local field. The main experimental observations are presented for the strongest band in the infrared spectrum of each of the liquids methanol, chlorobenzene, dichloromethane, and acetone. Particular care was paid to wave number calibration of both infrared and Raman spectra. Theoretical arguments indicate that the peak wave number in the αm″ spectrum is the correct one to use, because it is the only one that reflects the properties of molecules in their local environment in the liquid free from predictable long-range resonant dielectric effects. However, it is found that the comparison with Raman wave numbers is confused when the anisotropic local intermolecular forces and configuration in the liquid are significant. In these cases, the well known noncoincidence of the isotropic and anisotropic Raman scattering is observed, and the same factors lead to noncoincidence of the infrared and Raman bands. © 1998 American Institute of Physics.