A theory for the effects of repulsive and spatially slowly varying attractive forces on the vibrational frequency and dephasing of polyatomic molecular liquids is developed. Thermodynamic state dependence of these features is of particular interest because of the competition between the two types of forces. Solvent shifts of vibrational lines are computed. Proper separation of the rapidly and slowly varying branches of the intermolecular potentials leads to a separation of time scales that allows the dephasing relaxation to be computed using a combination of binary collision and mean field ideas. The question of homogeneous vs inhomogeneous broadening of the isotropic Raman line is addressed. The theory is applied to several polyatomic fluids with special emphasis on the isothermal density dependence of the spectral features. Agreement with experiment is good. The slowly varying attractive forces are found to play a significant role in determining the Raman linewidth for all the systems studied. Comparison with previous theories is made.

Vibrational dephasing and frequency shifts of polyatomic molecules in solution

A simple application of Kubo’s line shape theory to the domain of vibrational frequencies is presented, compared with the experiment, and used for predictions. In vibrational modes where vibrational dephasing processes are predominant in determining the shape of the condensed phase band contour, the formalism shows that the vibrational correlation obeys a fast modulation mechanism (’’motional narrowing’’), e.g., in quinoline, tetravinyl tin, and isopropyl alcohol. However, even smaller molecules such as chloroform and methyl iodide show similar characteristics and only in exceptional cases (the uncoupled O–D stretch of D2O in H2O) is the modulation slow. This behavior is a consequence of the short modulation times (order of fractions of a picosecond) in the liquid which determine the phase loss of the vibrational amplitude after a brief period of a quasistatic distribution of molecular environments (’’rigid lattice’’) —times which can be approximately identified with the inverse average collision frequency. In order to compare theory and experiment quantitatively, the model requires that the vibrational second spectral moment must be measured in addition to the vibrational correlation function. Comparisons with vibrational memory functions, obtained from the correlation functions via the modified Langevin equation, corroborate the usefulness of the model.

Motional characteristics of large molecules from their Raman and infrared band contours: Vibrational dephasing

We relate the dephasing of molecular vibrations in liquids to certain correlation functions involving only the translational and rotational degrees of freedom; these correlation functions are then determined through a classical molecular dynamics simulation of rigid, nonvibrating molecules. Using a Lennard‐Jones atom–atom potential for N2 (liq) near its boiling point, we calculate a dephasing time of 62 psec, in good agreement with picosecond pulse and isotropic Raman linewidth measurements. The importance and characterisic time scales of different dephasing mechanisms are studied, and the significant effect of vibrational anharmonicity is demonstrated.

A molecular dynamics simulation of dephasing in liquid nitrogen

The vibrational dephasing of polyatomic molecules in condensed phases by intermolecular vibrational energy exchange is treated theoretically In the exchange model, dephasing arises from random modulation of the vibrational frequency caused by intramolecular anharmonic coupling to low frequency modes which are undergoing intermolecular energy exchange with the bath The exchange rates are temperature dependent and as a consequence manifest themselves experimentally as a temperature dependent broadening and shift of the Raman spectral line shape Using a reduced density matrix technique within the constraints of a Markoff approximation, the theory allows the time dependence introduced by the exchange process to be properly accounted for, and allows explicit expressions for the vibrational correlation function and corresponding spectral line shape functions to be derived and related to molecular parameters Application of the theory can have important consequences experimentally, since an analysis of the te

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The origin of vibrational dephasing of polyatomic molecules in condensed phases

The Raman line shapes of the ν1(a1) C–H and C–D fundamentals in liquid acetonitrile and acetonitrile‐d3 have been measured as a function of pressure up to 4 kbar within the temperature interval 30–120 °C. Densities have also been determined. From the isotropic component of the vibrational Raman band shape the vibrational relaxation times have been obtained as a function of temperature and pressure (density). The experimental results can be summarized as follows: (i) as T increases at constant density ρ, the vibrational relaxation rate (τvib)−1 increases; (ii) at constant T as density is raised τvib−1 increases; (iii) at constant pressure the T increase produces higher τvib−1, however, the change is more pronounced for the CD3CN liquid. Isotopic dilution studies of the CH3CN/CD3CN mixtures shows no significant effect on (τvib−1). The experimental data are interpreted in terms of the Kubo stochastic line shape theory and the dephasing model of Fischer and Laubereau. The results based on Kubo formalism indic...

M. De Zwart

Papers

Intermolecular vibrational relaxation in liquids