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Journal ArticleDOI

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

01 Jul 1976-Journal of Chemical Physics (American Institute of Physics)-Vol. 65, Iss: 1, pp 455-462
TL;DR: In this paper, 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 condensed phase band contour.
Abstract: 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.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works, and cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise.
Abstract: Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works. With the aid of path integral formalism, we derive the stochastic Liouville equation for density matrices of a system. We then cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise. We elucidate the applications of the stochastic theory from the unified theoretical basis to analyze the dynamics of a system as probed by experiments. We illustrate this as a review of several experimental examples including NMR, dielectric relaxation, Mossbauer spectroscopy, neutron scattering, and linear and nonlinear laser spectroscop...

806 citations

Journal ArticleDOI
TL;DR: In this article, a hydrodynamic model is presented for the dephasing of molecular vibrations in liquids; the effects of vibrational anharmonicity are included. But the final result shows a surprising formal similarity to the isolated binary collision model developed previously.
Abstract: A hydrodynamic model is presented for the dephasing of molecular vibrations in liquids; the effects of vibrational anharmonicity are included. Agreement with coherent picosecond pulse experiments and isotropic Raman line shape data is good for lower viscosity liquids, and the qualitative temperature and density dependence of the dephasing rate is predicted correctly. The final result shows a surprising formal similarity to the isolated binary collision model developed previously.

199 citations

Journal ArticleDOI
TL;DR: In this article, the possible information content in lineshapes observed in vibrational spectroscopy of molecules adsorbed on surfaces is considered by drawing analogies with similar situations in other spectroscopic areas where the systematics are more completely understood.

166 citations

Journal ArticleDOI
TL;DR: In this article, the vibrational relaxation times of the C-H and C-D fundamentals in liquid acetonitrile were measured as a function of pressure up to 4 kbar within the temperature interval 30-120 °C.
Abstract: 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...

147 citations

Journal ArticleDOI
TL;DR: To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is transformed into an energy eigenstate representation without using the rotating wave approximation.
Abstract: Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.

111 citations

References
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Journal ArticleDOI
TL;DR: In this article, a model based on semiclassical collision theory is presented to describe the dephasing of vibrationally excited molecules in a liquid, and it is shown that fluctuations of the vibrational frequencies which are caused by the intermolecular interaction, lead to phase relaxation of a coherently excited state.

369 citations

Journal ArticleDOI
TL;DR: In this paper, a systematic investigation of orientational broadening of Raman vibrational lines is undertaken and measurements of line shapes are made for 19 liquids and a method of analysis is presented.
Abstract: A systematic investigation of orientational broadening of Raman vibrational lines is undertaken and measurements of line shapes are made for 19 liquids. The problem of separating orientational broadening from the intrinsic vibrational lineshape is discussed in detail and a method of analysis is presented. The advantages and limitations of this method are considered and compared to an earlier method proposed by Rakov [Tr. Fiz. Inst. Akad. Nauk SSSR 27, 111 (1964); Opt. Spectrosc. 7, 128 (1959)]. The intrinsic width is determined for each line studied and removed from the spectrum to give the orientational broadening. It is noted that the intrinsic line shape, measured from polarized Raman spectra, may be used to correct infrared vibrational spectra which suffer from the same problems. It is shown that neglect of intrinsic width can lead to significant errors in the interpretation of the infrared data.

319 citations

Journal ArticleDOI
TL;DR: In this article, a stochastic-type theory related to similar theories of the NMR spectra is proposed to explain the ir spectra of inert solutions of diatomic molecules, which predicts the existence of a continuous sequence of band forms comprising, among others, the profile with P and R type wings, the Lorentzian profile, the Gaussian profile, Voigt profile and several sorts of asymmetric profiles.
Abstract: A theory is proposed to explain the ir spectra of inert solutions of diatomic molecules. The theory is a stochastic‐type theory related to similar theories of the NMR spectra. The vapor‐solution band shifts are shown to depend on the difference between the solvent–solute interaction energies of the two vibrational states involved in the transition. The band profiles are basically asymmetrical; nevertheless, symmetric limiting forms exist as well. The theory predicts the existence of a continuous sequence of band forms comprising, among others, the profile with P‐ and R‐type wings, the Lorentzian profile, the Gaussian profile, the Voigt profile, and several sorts of asymmetric profiles. The relation between a given band form and the nature of the dominating relaxation process is discussed.

226 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the vibrational relaxation of a guest molecule in a host matrix and derived explicit solutions for the Wigner-Weisskopf approximation for both single phonon and multiphonon processes, which was applied for the study of the time evolution of the distribution, the cooling and heating processes of the oscillator by a thermal field and for the coupling between vibrati...
Abstract: In this paper we consider some features of vibrational relaxation of a guest molecule in a host matrix. The model system involves a harmonic molecule interacting with a harmonic medium. The molecule-medium coupling was handled by the rotating wave approximation considering linear terms in the intramolecular displacements and high terms in the medium displacements. Three specific models for the molecule-medium coupling were considered, which involve single phonon decay, vibron-phonon decay and multiphonon decay. Within the framework of the random phase approximation the Heisenberg equations of motion for the system could be expressed in terms of a unified scheme which is valid for both single phonon and multiphonon processes. Explicit solutions were derived utilizing the Wigner-Weisskopf approximation. This generalized formalism was applied for the study of the time evolution of the distribution, the cooling and the heating processes of the oscillator by a thermal field and for the coupling between vibrati...

168 citations

BookDOI
01 Jan 1974

140 citations