Shuliang L. Zhang

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.

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.

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%.

Measurement and use of absolute infrared absorption intensities of neat liquids

Abstract This paper describes the methods used in this laboratory to measure absolute infrared absorption intensities of liquids and their applications in analytical and physical chemistry. The applications include the measurement of 43 bands of benzene, toluene, chlorobenzene and dichloromethane as secondary standards of infrared absorption for the International Union of Pure and Applied Chemistry, the use of these standards to calibrate transmission cells, measurement of the absolute intensity spectra of liquid benzene, the comparison of absorption intensities and transition moments in liquid and gaseous benzene, the separation of the integrated intensity of benzene into contributions from different transitions by curve fitting, and the determination of intensities and transition moments of the OH, OD, CH and CD stretching bands of CH 3 OH, CH 3 OD, CD 3 OH and CD 3 OD. The accuracy of the absolute intensities is impressively shown by the close similarity of the intensities of corresponding bands in the spectra of different isotopomers of methanol. One key to the measurement of accurate intensities is the determination of the baseline absorption.

Infrared Intensities of Liquids X: Accuracy of Current Methods of Obtaining Optical Constants from Multiple Attenuated Total Reflection Measurements Using the CIRCLE Cell

The literature description of the Bertie-Eysel method for obtaining the optical constants (i.e., the real and imaginary refractive indices) of liquids from multiple attenuated total reflection measurements using the CIRCLE cell is brought up to date in this paper. The accuracy of the computation methods is explored by analyzing pATR spectra which are themselves calculated from known k(ν˜) spectra that contain single Lorentzian bands, and the corresponding known n(ν˜) spectra, and also from simulated, known, n(ν˜) and k(ν˜) spectra of pure liquid methanol and glacial acetic acid. The optical constants are recovered from the pATR spectra and compared with the known originals. It is shown that k(ν˜) spectra that contain k(ν˜) values up to 0.8, 0.7, and 0.6 can be obtained accurately when the real refractive indices are near 1.3, 1.4, and 1.5, respectively. The method is, thus, reliable for spectra that can be accurately measured from the multiple reflections in the CIRCLE cell. It is likely to be troublesome for higher values of the real and the imaginary refractive indices. However, these are best measured by single-reflection methods, and more direct ways of computing the optical constants are available for such methods.

Determination and Use of Secondary Infrared Intensity Standards

The presentation of absorption intensities in infrared spectra is usually limited to relative intensities instead of absolute intensities. The measurement of absolute intensities can be facilitated by the use of secondary intensity standards. Such standards have been accepted by the Commission on Molecular Structure and Spectroscopy and the Physical Chemistry Division of the International Union of Pure and Applied Chemistry and were published recently. The secondary standards are based on the complex refractive index and molar absorption coefficient spectra of benzene, chlorobenzene, toluene, and dichloromethane. They have been used in this laboratory to calibrate the effective pathlength of a transmission cell and the effective number of reflections in a Circle® multiple attenuated total reflection cell. A computer program, IRYTRUE, has been developed to standardize the routine use of these intensity standards to calibrate the effective pathlength of a transmission cell. The program has been used to calibrate three transmission cells. The agreement between the calibrated values of the effective pathlength obtained from the use of different standard band groups was determined. The calibrated cell pathlength agrees with that calculated from the interference fringe pattern of the empty cell within 3% for very thin cells and within 1% for cells thicker than 100 μm. We propose that the effective pathlength evaluated in this manner be called the cell constant, and that this cell constant be used in place of the pathlength in quantitative infrared analysis. The calibration of multiple attenuated total reflection measurements in the Circle cell has been achieved in two ways: by the use of peak heights and by the use of areas. Programs PCCALC and CIRCLCAL and its associated program RSCALC are described for this purpose. The intensity standards allow one to measure absolute infrared absorption intensities of liquids with confidence to an estimated accuracy of 2–3% by either transmission or calibrated ATR methods.

Infrared intensities of liquids. XVII. Infrared refractive indices from 8000 to 350 cm−1, absolute integrated absorption intensities, transition moments, and dipole moment derivatives of methan‐d3‐ol and methanol‐d4 at 25 °C

This paper reports absolute infrared absorption intensities of liquids methan‐d3‐ol (CD3OH) and methanol‐d4 (CD3OD) at 25 °C between 8000 and 350 cm−1. Measurements were made by multiple attenuated total reflection spectroscopy with the CIRCLE cell, and by transmission spectroscopy with transmission cells fitted with calcium fluoride windows. In both cases, the spectra were converted to infrared real and imaginary refractive index spectra. The refractive indices obtained by these two methods agreed excellently and were combined to yield an imaginary refractive index spectrum k(ν) between 7244 and 350 cm−1 for CD3OH and between 5585 and 350 cm−1 for CD3OD. The imaginary refractive index spectrum was arbitrarily set to zero from 8000 to 7244 cm−1 (CD3OH) or 5585 cm−1 (CD3OD), where k is always less than 4×10−6, in order that the real refractive index can be calculated below 8000 cm−1 by Kramers–Kronig transformation. The results are reported as graphs and tables of the refractive indices between 8000 and 3...

Infrared Intensities of Liquids XV: Infrared Refractive Indices from 8000 to 350 cm -1 , Absolute Integrated Intensities, Transition Moments, and Dipole Moment Derivatives of Methanol- d, at 25°C

This paper reports infrared absorption intensities of liquid methanol-d, CH3OD, at 25°C, between 8000 and 350 cm−1 Measurements were made by multiple attenuated total reflection spectroscopy with the use of the CIRCLE cell, and by transmission spectroscopy with a variable-path-length cell with CaF2 windows. The results of these two methods agree excellently and were combined to yield an imaginary refractive index spectrum, k(ν˜) vs. ν˜, between 6187 and 350 cm−1. The imaginary refractive index spectrum was arbitrarily set to zero between 6187 and 8000 cm−1 where k is always less than 2 × 10−6, in order that the real refractive index can be calculated below 8000 cm−1 by Kramers-Krönig transformation. The results are reported as graphs and as tables of the real and imaginary refractive indices between 8000 and 350 cm−1, from which all other infrared properties of liquid methanol-d can be calculated. The accuracy is estimated to be ± 3% below 5900 cm−1 and ± 10% above 5900 cm−1 for the imaginary refractive index and better than ± 0.5% for the real refractive index. In order to obtain molecular information from the refractive indices, the spectrum of the imaginary polarizability multiplied by wavenumber, ν˜ vs. ν˜, was calculated under the assumption of the Lorentz local field. The area under this ν˜ spectrum was separated into the integrated intensities of different vibrations. Molecular properties were calculated from these integrated intensities—specifically, the transition moments and dipole moment derivatives of the molecules in the liquid, the latter under the harmonic approximation. The availability of the spectra of both CH3OH and CH3OD enables the integrated intensities and the molecular properties of the C-H, O-H, O-D, and C-O stretching and CH3 deformation vibrations to be determined with confidence to a few percent. Further work with isotopic molecules is needed to improve the reliability of the integrated intensities of the C-O-H(D) in-plane bending, H-C-O-H(D) torsion, and CH3 rocking vibrations.

Various absorption intensity spectra of liquids CH3OH, CH3OD, CD3OH, and CD3OD: refractive indices, transition moments, and dipole moment derivatives of these molecules

The infrared absorption intensities of liquid CH3OH, CH3OD, CD3OH and CD3OD at 25 degree(s)C have been measured by CIRCLE cell multiple attenuated total reflection spectroscopy and by transmission spectroscopy. The intensities are calculated from the spectra as the infrared real, n(v), and imaginary, k(v), refractive indices. The estimated accuracy is +/- 0.5% for n(v) and +/- 3% for k(v) in the regions of significant absorption. Other absorption intensity spectra are calculated from the refractive indices, and the wavenumbers and shapes of bands in the different spectra are compared. Molecular properties can be calculated from several different intensity quantities, under different degrees of theoretical approximation. The effect of these different approximations is shown to be unimportant for experimental spectra of CH3OH.

Absolute absorption intensities of liquids: the FFT-based Hilbert transform can be as good as the Kramers-Kronig transform, if it is done properly

A soundly based procedure is presented for the correction of the variations that occur in the baselines of spectra obtained by transmission through a thin cell containing liquid. The correction significantly improves the precision of optical constants obtained from such spectra. The method is applied to the 1036 cm-1 band of benzene.