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 calcula ted from molecular dynamics simulations by determining the Fourier transfor m of the relaxation function. It has been applied to the fluid phase at var ious pressures and temperatures, and to solid delta-N-2. The validity of th e assumption that the spectrum at relatively high temperatures and pressure s can be calculated by assuming that these systems are in the fast modulati on regime (Delta tau(c)much less than 1), has been verified. A deviation of the vibrational line shape from the motional narrowing limit has been foun d for fluid nitrogen at low pressure, with a Kubo parameter, Delta tau(c), equal to 0.23, and for the vibrational line of the molecules on the a sites in delta-N-2, with Delta tau(c) equal to 0.075. It is concluded that the v alue of the Kubo parameter is not an unambiguous criterion for the fast mod ulation 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 closel y spaced lines are to be expected. The present procedure is suited to calcu late line shapes in the intermediate Kubo regime, e.g., in concentrated mix tures, 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 . (C) 2000 American Institute of Physics. [S0021-9606(00)51502-5].