Calculation of the vibrational linewidth and line shape of Raman spectra using the relaxation function. I. Method and application to nitrogen

Abstract

. (2000). Calculation of the vibrational linewidth and line shape of Raman spectra using the relaxation function : I. method and application to nitrogen. Journal of Chemical Physics, 112(3), 1395-1403. DOI: 10.1063/1.480693 General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. The spectral line shape of the fundamental vibration of nitrogen is calculated from molecular dynamics simulations by determining the Fourier transform of the relaxation function. It has been applied to the fluid phase at various pressures and temperatures, and to solid ␦-N 2 . The validity of the assumption that the spectrum at relatively high temperatures and pressures can be calculated by assuming that these systems are in the fast modulation regime (⌬ c Ӷ1), has been verified. A deviation of the vibrational line shape from the motional narrowing limit has been found for fluid nitrogen at low pressure, with a Kubo parameter, ⌬ c , equal to 0.23, and for the vibrational line of the molecules on the a sites in ␦-N 2 , with ⌬ c equal to 0.075. It is concluded that the value of the Kubo parameter is not an unambiguous criterion for the fast modulation regime. Moreover, a detailed comparison reveals a difference in the dynamical behavior of the molecules on the a and c sites. It is shown that this procedure can also be used if one does not know whether or not closely spaced lines are to be expected. The present procedure is suited to calculate line shapes in the intermediate Kubo regime, e.g., in concentrated mixtures, where no simple relations are available. Finally it is shown that in nitrogen at low density and 126 K the ratio of the correlation time of the frequency autocorrelation function and the dephasing time is smaller than in CH 3 I, where the n dependence of the vibrational overtone is subquadratic.

Isotropic Raman line shapes of N2 and O2 along their liquid–gas coexistence lines

“…Just last year the same group also calculated line shapes using the full line shape expression ͑rather than assuming motional narrowing͒ and found in some cases modest deviations from the motional narrowing result. 28 Very recently Gayathri and Bagchi 29 used the model and approach of Oxtoby et al 24 to calculate the line shape along the liquid-gas coexistence line, and in the supercritical region along the critical isochore. Their results for the line width are in reasonable agreement with experiment, especially along the coexistence line.…”

Density-Dependent Isotropic Raman Line Shapes in Compressed Room-Temperature Nitrogen

“…Recently, the same group calculated spectra using the full Kubo line-shape expression 33 (rather than assuming the extreme-narrowing limit) at several different thermodynamic state points and found in some cases modest deviations from the motional-narrowing result. 20 In a similar vein, two of us (Everitt and Skinner) developed a model for nitrogen with all of the contributions to the frequency fluctuations discussed above, including resonant intermolecular vibrational interactions and vibration-rotation coupling. 21 The and σ parameters of the two-site Lennard-Jones model were assumed to vary linearly with the vibrational coordinate, and the coefficients were adjusted to fit experimental data for the line shift along the liquid-gas coexistence curve.…”

“…There have been a number of theoretical calculations of the isotropic Raman line shape of nitrogen over the past 25 years. − The pioneering paper in the field is due to Oxtoby, who showed that one could calculate the line width from a classical molecular dynamics simulation. They considered liquid nitrogen near the normal boiling point (77 K), showed that the line shape is motionally narrowed, and found a line width in quite good agreement with experiment.…”

“…Their results for the width and shift are in good agreement with the room-temperature experiments at these higher densities. Recently, the same group calculated spectra using the full Kubo line-shape expression (rather than assuming the extreme-narrowing limit) at several different thermodynamic state points and found in some cases modest deviations from the motional-narrowing result . They did not consider densities lower than twice the critical density at room temperature.…”