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

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 δ-N2. 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 (Δτc≪1), 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, Δτc, equal to 0.23, and for the vibrational line of the molecules on the a sites in δ-N2, with Δτc 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 CH3I, where the n dependence of the vibrational overtone is subquadratic.