John E. Bertie

Infrared Intensities of Liquids XX: The Intensity of the OH Stretching Band of Liquid Water Revisited, and the Best Current Values of the Optical Constants of H2O(l) at 25°C between 15,000 and 1 cm−1

The previously reported nonreproducibility of the intensity of the OH stretching band of liquid water has been explored. It was found that it can be eliminated in measurements with the Circle® multiple ATR cell by ensuring that the ATR rod is coaxial with the glass liquid holder. It was also found that normal laboratory temperature variations of a few degrees change the intensity by ⩽∼1% of the peak height. A new imaginary refractive index spectrum of water has been determined between 4000 and 700 cm1 as the average of spectra calculated from ATR spectra recorded by four workers in our laboratory over the past seven years. It was obtained under experimental and computational conditions superior to those used previously, but is only marginally different from the spectra reported in 1989. In particular, the integrated intensities of the fundamentals are not changed significantly from those reported in 1989. The available imaginary refractive index, k, values between 15,000 and 1 cm−1 have been compared. The values that are judged to be the most reliable have been combined into a recommended k spectrum of H2O(l) at 25 °C between 15,000 and 1 cm−1, from which the real refractive index spectrum has been calculated by Kramers–Kronig transformation. The recommended values of the real and imaginary refractive indices and molar absorption coefficients of liquid water at 25 ± 1 °C are presented in graphs and tables. The real and imaginary dielectric constants and the real and imaginary molar polarizabilities in this wavenumber range can be calculated from the tables. Conservatively estimated probable errors of the recommended k values are given. The precision with which the values can be measured in one laboratory and the relative errors between regions are, of course, far smaller than these probable errors. The recommended k values should be of considerable value as interim standard intensities of liquid water, which will facilitate the transfer of intensities between laboratories.

Absorptivity of Ice I in the Range 4000–30 cm−1

The absorbance of several samples of ice Ih has been measured in the range 4000–30 cm−1, and scaled to that of a particular film of unknown thickness. The thickness of the film has been calculated by two methods, first from the known absorptivity at 4940 cm−1, and second by equating the appropriate Kramers–Kronig integral to the known infrared contribution to the microwave refractive index. The two thicknesses agreed well and allowed the absorptivity to be obtained in the range 4000–30 cm−1. The complex refractive index and permittivity and the normal incidence reflectivity have been calculated from the absorptivity. About three‐quarters of the infrared contribution to the microwave refractive index is caused by the translational lattice vibrations and about 15% by the rotational vibrations; the O–H stretching bands which absorb very strongly contribute relatively little. The maximum of the density of states in the transverse acoustic branch is at 65 cm−1 rather than below 50 cm−1 as reported earlier. Bel...

Infrared Intensities of Liquids I: Determination of Infrared Optical and Dielectric Constants by FT-IR Using the CIRCLE ATR Cell

The CIRCLE ATR accessory has been used to measure the optical and dielectric constants of organic liquids and water. The method, based on Fresnels equations, is described in detail, and the agreement between the results obtained and literature values is shown to be adequate for chemical use. The utility of optical and dielectric constants for the calculation of traditional infrared intensities in liquids and of dipole moment derivatives is outlined.

The Raman spectra of gaseous formic acid ‐h2 and ‐d2

The Raman spectra of gaseous formic acid ‐h2 and ‐d2 at 21 °C and higher temperatures have been recorded from about 70 to 4000 cm−1. The isotope ratios of the frequencies of the intermonomer vibrations, which deform the hydrogen bonds, have allowed a convincing assignment of these vibrations. All but one of the nine low‐frequency infrared and Raman bands of (HCOOH)2, and all seven of (DCOOD)2, have been assigned. It has been thought for 40 years that the symmetric hydrogen‐bond stretching vibration is the cause of a strong Raman band of (HCOOH)2 near 230 cm−1, but the new evidence shows clearly that this is the one low‐frequency fundamental that scatters too weakly to be detected. The spectra show bands at 1381 and 1307 cm−1 due to monomeric HCOOH which are assigned to ν4 and 2ν8, respectively, as the only feasible assignment. The Raman frequencies of the intramonomer modes of the dimer show that the intermonomer coupling is large for some modes and small for others. The Raman‐active hydrogen‐bonded O–H a...

Infrared Intensities of Liquids XI: Infrared Refractive Indices from 8000 to 2 cm −1 , Absolute Integrated Intensities, and Dipole Moment Derivatives of Methanol at 25°C

This paper reports infrared absorption intensities of liquid methanol at 25°C between 8000 and 2 cm−1. Measurements were made by attenuated total reflection spectroscopy by four different workers between 1984 and 1991, with the use of CIRCLE cells of two different lengths and with several different alignments of the cell in the instrument. Steps were taken to ensure that as few parameters as possible remained unchanged throughout the series of measurements, to try to reveal systematic errors. The reproducibility was better than ±2.5% in regions of significant absorption. In order to allow comparison between different methods, results of all methods were converted to real and imaginary refractive index spectra. Measurements were also made by transmission spectroscopy in regions of weak absorption, with results that agreed excellently with those from ATR. The ATR and transmission results were combined to give a spectrum between 7500 and 350 cm−1. This spectrum agreed excellently with literature results from 350 to 2 cm−1, and the two sets of measurements were combined to yield a spectrum from 7500 to 2 cm−1. The imaginary refractive index was arbitrarily set to zero between 7500 and 8000 cm−1, where it is always less than 2 × 10−6, in order that the real refractive index can be calculated below 8000 cm−1 by Kramers-Kronig transform. The results are reported as graphs and as tables of the real and imaginary refractive indices between 8000 and 2 cm−1, from which all other infrared properties of liquid methanol can be calculated. The accuracy is estimated to be ±3% below 5000 cm−1 and ±10% above 5000 cm−1 for the imaginary refractive index and better than ±0.5% for the real refractive index. To obtain molecular information from the measurements, one calculates the imaginary molar polarizability spectrum, vs. , under the Lorentz local field assumption, and the area under bands is separated into contributions from different vibrations under several approximations. Much accuracy is lost in this process. The changes of the dipole moment during normal vibrations, and during OH, CH, and CO bond stretching and COH torsional motion, are presented.

The Raman spectrum of gaseous acetic acid at 21 °C

The Raman spectrum of gaseous acetic acid at 21 °C is presented and assigned. It is suggested that a reassignment of the in‐plane C–C–O deformation of the monomer to ∼450 cm−1 is appropriate, and that the infrared band contours between 700 and 400 cm−1 be analyzed in detail to confirm this. The Raman‐active O–H stretching mode of the dimer could not be identified. The intermonomer coupling of the other intramonomer modes in the dimer is small except for the C=O stretching and C–C–O in‐plane deformation modes. Two Raman‐active intermonomer modes were observed for the first time, at 155 and 99 cm−1. The former is ν13(Ag), the O⋅⋅⋅O stretching mode, and allows the previously [J. Chem. Phys. 76, 886 (1982)] unobserved corresponding mode of (HCOOH)2 to be placed near 180 cm−1. Frequencies are deduced of all of the intermonomer modes, and the infrared doublet at 167/187 cm−1 is reassigned to ν42(Bu) in Fermi resonance with the combination state ν21(Bg)+ν28(Au) at ∼179 cm−1, instead of the previously assigned co...

The Raman‐active O–H and O–D stretching vibrations and Raman spectra of gaseous formic acid‐d1 and ‐OD

In keeping with current theoretical activity concerning the OH and OD stretching bands of the carboxylic acids, we report the Raman spectra of gaseous formic acid‐OD and formic acid‐d1 for the first time. We emphasize the OH and OD stretching bands, which can be studied cleanly in these isotopomers but not in normal or perdeuterated formic acid. The spectra of the dimers and monomers below 2000 cm−1 are assigned, and current knowledge of the vibrations of the molecules is summarized. The Raman spectra allow the estimation of the energies of the Bu combination levels that may be in Fermi resonance with the infrared active Bu, OH or OD stretching fundamental, as well as those of the Ag overtone and combination levels that may interact with the Raman‐active stretching fundamental. We conclude that the sharp features on the Raman OH and OD stretching bands are due to overtone and combination transitions, that the stretching modes cause the underlying broad scattering, namely three broad bands, centered at 243...

Infrared intensities of liquids XXI: integrated absorption intensities of CH3OH, CH3OD, CD3OH and CD3OD and dipole moment derivatives of methanol

Abstract This paper presents the analysis of the complete set of vibrational intensities of four isotopomers of methanol. The absolute infrared absorption intensities of liquid methanol in four isotopic forms have been reported recently. In that work, spectral intensities were separated into the integrated intensities of different transitions by comparing the spectra of different isotopomers, and dipole moment derivatives with respect to valence displacements were calculated under the simplest approximations. For many bands it was not possible to determine the integrated intensity in this way because of overlap of several bands, and for others it was clear that the determination was too subjective. This paper first describes an attempt to improve this situation by using a more objective separation of the contributions to the intensity from different bands, by fitting the imaginary molar polarizability spectra with classical damped harmonic oscillator bands or Gaussian bands and calculating the entire area under each component band. The integrated intensities so obtained are compared with those reported previously, and a set of accepted integrated intensities for all vibrations is presented. These accepted intensities are then converted to transition moments and analyzed to obtain the dipole moment derivatives with respect to symmetry coordinates, ∂μ ∂S . The analysis uses the eigenvectors from a normal coordinate calculation that fits the reliably known fundamental wavenumbers of CH3OH, CH3OD, CD3OH and CD3OD, corrected for anharmonicity where possible, to better than ± 1.5 cm−1 on average, and that also fits the experimental near-identity of the wavenumbers and intensities of the CO stretching bands of CH3OH and CH3OD. These calculations were guided by literature ab initio calculations on isolated CH3OH, but an empirical normal coordinate calculation was preferred because the experimental data show clearly that some of the vibrations are not properties of isolated molecules. For lack of other evidence, the directions of the dipole moment derivatives of the A′ modes were taken from Torii and Tasumis recent ab initio calculation. Dipole moment derivatives with respect to internal coordinates, ∂μ ∂R , were calculated from the ∂μ ∂S . The resulting values for liquid methanol are compared with values for the isolated molecule calculated with an MP 2 6-31 G ext basis set by Torii and Tasumi. For the stronger fundamentals the agreement is good except for the OH and OD stretching vibrations. This suggests that the only hydrogen vibration whose intensity is strongly affected by the hydrogen bonding is the stretching vibration. This in turn implies that it is the charge flux, not the effective charge on the hydrogen atom, that is sensitive to hydrogen bonding. The results of this and other work from this laboratory suggest that most vibrational intensities may not be strongly dependent on phase.

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

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 ...

Infrared intensities of liquids XVI. Accurate determination of molecular band intensities from infrared refractive index and dielectric constant spectra

Abstract 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 ( ν ), the imaginary refractive index or absorption index, k ( ν ), and the imaginary dielectric constant ϵ″( ν ). 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, α ^ m ( ν ). The imaginary molar polarizability, α″ m ( ν ), 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 ϵ″ spectra. These intensities can also be calculated, under the same approximations as for the ϵ″( ν ) spectra, from the peak wavenumbers in the ϵ″ and α″ 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 α″ m spectrum most reliably gives the molecular properties, but it does impose the Lorentz local field model on the experimental spectrum. Symmetric α″ m and ϵ″ bands correspond to asymmetric k and E m bands, particularly at low wavenumbers, so the α″ m or ϵ″ spectrum should always be used when the lineshape is relevant. Accurate calculation of vibrational intensities can only be done reliably from the α″ m spectrum. Sometimes high accuracy may be obtained for separated bands from the E m , k and ϵ″ 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 bonds. The consequent errors in the intensities range from 0% to over 20%.