Vibrational Relaxation In Polyatomic Molecules Research Articles

Sequential vibrational relaxation of polyatomic molecules at surfaces: C2HD and C2H2 scattered from LiF(001)

Reported here is a detailed study of the vibrational relaxation of C2H2 and C2HD upon scattering from LiF(001). While direct (specular) scattering shows no vibrational quenching for either molecule, the residence times associated with trapping–desorption are long enough to give significant quenching. By studying this quenching as a function of surface temperature, thereby varying the residence times, we show that vibrational relaxation proceeds via multiple steps. The differences between C2H2 and C2HD quenching can be understood in terms of the presence of a Fermi resonance in the former, which enhances the relaxation rates associated with the early steps. A simple kinetic model is used to fit the data, confirming that vibrational quenching proceeds via a cascading mechanism, which is likely to be quite general for polyatomic molecules.

A semiclassical surface-hopping procedure for vibrational relaxation in polyatomic molecules: model calculations

In this paper, the application to polyatomic systems of a semiclassical surface-hopping theory for the calculation of vibrational transition probabilities and rates is explored through the use of simple model systems. The theory has previously been applied to relaxation of vibrational excitation energy in diatomics. The non-adiabatic coupling is analyzed for the polyatomic case. Two systems are considered. One of these, which qualitatively mimics CO2 in Ar, has a strongly bonded triatomic. In the other system, which roughly models KrF2 in Ar, the triatomic is a comparatively weakly bonded molecule, and the solvent interactions are relatively more significant. Results of calculations using this theory are compared with calculations based on approximations to the full theory. These approximations have previously been found to provide a very computationally facile procedure for the calculation vibrational relaxation rates of diatomic molecules in condensed-phase systems.

Theory of vibrational relaxation of polyatomic molecules in liquids

A simple tractable theory of vibrational relaxation of polyatomic molecules in polyatomic solvents, which is also applicable to solid solutions, is presented. The theory takes as its starting point Fermi’s golden rule, avoids additional assumptions such as the rotating wave or random phase approximations, and treats both the internal degrees of freedom of the relaxing molecule and the bath degrees of freedom in a fully quantum mechanical manner. The results yield intuitively understandable expressions for the relaxation rates. The treatment of the annihilation as well as the creation of all participating bosons allows the theory to go beyond earlier analyses which treated only cascade processes. New predicted features include temperature effects and asymmetry effects in the frequency dependence. The theory is constructed in a manner which facilitates the use of recent developments in the analysis of instantaneous normal modes of liquids.

Perturbation theory approach to dynamical tunneling splitting of local mode vibrational states in ABA molecules

We introduce a point of view for treating the dynamical tunneling splitting of symmetric local mode vibrational states in ABA molecules (A=H typically) which is the one we have employed in treating the vibrational spectroscopy of CH overtones in molecules such as (CX3)3YCCH. Namely, the vibrational coupling corresponding to the dynamical tunneling in semiclassical mechanics via many intermediate off-resonance weak transitions between initial and final states can be treated by a standard high-order perturbation theory. We apply that method to the present simpler problem of tunneling splittings in ABA molecules, and compare the results with those of exact diagonalization, the semiclassical method, and the periodic orbit quantization. Of all the approximate methods, the perturbation theory was found to provide the best approximation to the results of exact diagonalization for the system treated. The relationship between these three methods and application to the problem of vibrational relaxation in polyatomic molecules with tunneling mechanism of intramolecular vibrational relaxation is discussed.

Effects of collision-induced perturbation of atomic motions on the vibrational relaxation of polyatomic molecules

We have performed model calculations on the vibrational relaxation (including population relaxation and dephasing) induced by intermolecular interactions in the liquid phase. Taking into account the points that (1) intermolecular interactions are primarily of atom–atom origin, and (2) the relaxation resulting from quasielastic collisions are considered to be dominant, we have calculated how the eigenvector (on the Cartesian coordinate basis) of an initially excited normal mode is transformed when the three components corresponding to one atom are displaced without change in the vibrational energy. On this basis, the relative efficiency of intramolecular energy flow from the initial state has been estimated. Calculations on the CH stretches of dichloromethane and the OH stretch of methanol are compared with existing experimental results.

Experimental and Theoretical Analysis of Non‐linear Vibrational Relaxation of Polyatomic Molecules Strongly Excited by Resonant Laser Radiation

We present a very simple theoretical model aimed at the analysis of non‐linear relaxation processes in molecular gases in the presence of partial molecular dissociation induced by vibrational–vibrational exchange between highly excited molecules. The model has a phenomenological character, since it analyzes the behavior of a system of anharmonic diatomic molecules, which is a very rough approximation of a polyatomic molecule such as SF6. Nonetheless, it provides an interesting key for the interpretation of a number of peculiar features characterizing our experimental observation, with which a comparison is made. In particular, the model takes realistic account of the influence of dissociation processes on the relaxation time.

Classical and semiclassical aspects of dissipative molecular processes: Radiative and nonradiative vibrational relaxation in polyatomic molecules

The time dependence of spontaneous emission from isolated, highly vibrationally excited molecules is studied from the point of view of the classical and semiclassical mechanics of dissipatively perturbed Hamiltonian systems. A correlation function expression for the time-dependent emission spectrum serves as a starting point for quasiclassical approximations. These in turn lead to an investigation of the classical dynamics of model molecular systems in which small, energy-nonconserving terms have been added to Hamilton’s equations. Numerical calculations show rich dynamical behavior which can be qualitatively understood in terms of the resonance structure of the unperturbed system. For example, trajectories tend to be captured by zones of nonlinear resonance. This ‘‘mode locking’’ produces a characteristic cleanup of an emission spectrum that otherwise is rather congested at these energies. The close connection between spectra and dynamics suggests that the classical dynamics of dissipatively perturbed systems may provide a useful language for interpreting radiative and condensed-phase vibrational relaxation, and possibly some types of intramolecular relaxation phenomena as well.

Threshold energy dependence of intramolecular vibrational relaxation in polyatomic molecules

We report the results of calculation of the intramolecular vibrational relaxation (IVR) rate of an isolated polyatomic molecule in a broad range of energies. The energy dependence of the relaxation rate was found to feature threshold properties: the relaxation rate was zero below some critical energy E c and non-zero at higher energies. We believe that such a threshold behavior can be associated with the development of a dynamic chaos in the system. Calculations were made by the method of Green functions with the use of a self-consistent quasiharmonic resonance approximation. We obtained a closed set of non-linear algebraic equations for quasiharmonic frequencies and relaxation rates of the molecular vibrational modes, and numerically analyzed the solutions of the set for molecules with 9 and 18 degrees of freedom. The numerical results obtained for relaxation rates agree well with the available experimental data. We demonstrate here the possibility of the existence of highly excited long-lived states in some systems.

A semiclassical model for intramolecular vibrational relaxation of local mode overtone in polyatomic molecules

A combination of the semiclassical perturbation (SCP) approximation and a kinetic coupling model gives rise to simple analytic formulae for the description of local mode overtone absorption spectra and the associated intramolecular vibrational relaxation in polyatomic molecules. Application to the CH(CD) stretch local mode overtones of C6H6 (C6D6) gives results which are in reasonable agreement with experimental observations. The SCPkinetic coupling model is thus seen to provide a very useful description of this intramolecular dynamics.

Simple quantum models for atom-polyatomic (V, T) collisional energy transfers: an exploratory study

A general quantum model for treating vibrational relaxation in polyatomic molecules is presented and its application to CO2 relaxation in collision with helium is discussed. A drastic simplification of the large expansion over molecular states, which is usually needed for complex targets, is here achieved by treating each normal mode independently and by then coupling each manifold of levels via the intermolecular potential through an analytic expansion of the latter that yields simple expressions for the coupling matrix elements. The effects of the physical factors which are here disregarded and/or simplified by the model are discussed and qualitatively assessed by comparison with previous calculations on the same system.

Transient structural response to photoexcitation in polyacetylene

An equation-of-motion procedure to study intramolecular vibrational relaxation in polyatomic molecules is developed and applied to study the transient structural response of a polyene to photoexcitation. The lattice response at short times (\ensuremath{\sim}20 fs) following excitation is characterized by an adiabatic relaxation which is highly specific to the exciting frequency. For longer times (20-1000 fs) this relaxation is strongly modified by the nonadiabatic relaxation of the excited carrier and takes the form of a splash in the bond-alternation profile, which reflects the transient distribution of the excited carrier in energy.

The restricted quantum exchange theory of intramolecular T1 and T2 relaxation rates

We present a theory for intramolecular vibrational relaxation in polyatomic molecules. The theory postulates the existence of a restriction on the magnitudes of matrix elements connecting zero-order states which favors coupling between vibrational modes. Specifically, the matrix elements are assumed to depend on two parameters, one determining the overall magnitude of coupling, and the other the rate of falloff with increasing quantum exchange. We use this ’’restricted quantum exchange’’ (RQE) hypothesis to derive analytic expressions for T1 (energy-transfer) and T2 (coherence-loss) relaxation rates which depend only on the two coupling parameters, the average molecular frequency, the number of modes, the energy in the molecule, and (for T1) the size of the energy transfer. In the derivation we obtain analytic expressions for the number of pairs of states on an energy shell related to each other by exchange of a fixed number of quantua M. The analysis has been carried out for arbitrary M, allowing us formally to include the effects of all higher order couplings and to show rigorously when they can be eliminated. The resulting T1 and T2 relaxation rates and associated linewidths exhibit saturation with increasing vibrational energy, a property which has been shown to be essential to obtaining reasonable cross sections for multiphoton excitation. We propose on the basis of restricted quantum exchange a simple explanation for the observed narrowing of the linewidths of benzene with increasing vibrational quantum number.

ChemInform Abstract: ON THE SYSTEMATICS OF VIBRATIONAL RELAXATION IN POLYATOMIC MOLECULES

Chemischer InformationsdienstVolume 12, Issue 10 Physical Organic Chemistry ChemInform Abstract: ON THE SYSTEMATICS OF VIBRATIONAL RELAXATION IN POLYATOMIC MOLECULES A. E. DEPRISTO, A. E. DEPRISTOSearch for more papers by this author A. E. DEPRISTO, A. E. DEPRISTOSearch for more papers by this author First published: March 10, 1981 https://doi.org/10.1002/chin.198110042AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume12, Issue10March 10, 1981 RelatedInformation

On the systematics of vibrational relaxation in polyatomic molecules

The systematic variation of vibrational relaxation rates with initial excitation, i.e., the quantum number scaling, is investigated for collisions involving polyatomic molecules. We consider the contrasting behavior of diatomic and polyatomic relaxation and the impact of the more varied behavior in polyatomics on experimental measurements. Particular emphasis is placed on the effect of collision-induced intramolecular vibrational transitions on the rate scaling. The theory utilized to accomplish such an analysis involves an extension of the energy corrected (ECS) scaling relationship to polyatomic vibrational transitions. This development is presented for vibrationally inelastic processes in a single electronic level. We apply the theory to the inversion of total rates for bending mode relaxation in CF2. The resulting state-to-state rates display peculiarities which reflect both the energy spectrum of the CF2 molecule and the nature of the collision partner.

Restricted quantum exchange theory for intramolecular vibrational relaxation in polyatomic molecules

We pose and solve a new quantum statistical counting problem and develop it further to obtain a theory for intramolecular vibrational coupling. Simple analytical expressions are presented for T 1 and T 2 relaxation rates. The formulas predict, in agreement with experiments, that high energy linewidths are nearly energy independent.

Vibrational energy relaxation in liquids

A theory of vibrational relaxation of polyatomic molecules in liquids is presented which expresses the rate of decay of a vibrational state in terms of atomic force autocorrelation functions. These force correlation functions can be estimated from hydrodynamics or from an independent binary collision model. The results of calculations on small molecules dissolved in inert, cryogenic solvents are discussed, including the dependence of the rates on the details of the intramolecular potential surface.

Coherence transfer processes in vibrational relaxation of polyatomic molecules in condensed media

The vibrational relaxation of a polyatomic molecule in a condensed host is studied by a consideration of two molecular vibrations. Relaxation processes, intermode coupling terms and vibrational frequency fluctuation contributions are retained. Population decay ( T 1), dephasing ( T 2), and coherence transfer rates are evaluated through second order in the limit where the host bath dynamics are rapid compared to these molecular timescales. The rates are expressed in terms of temperature and frequency dependent bath correlation functions. For the special case of a three level system (the ground state and ones where one of the two vibrational modes is excited) the important effects of anharmonicity are incorporated. It is shown that certain coherence transfer terms involve zero frequency bath correlation functions, so they should be larger than the high frequency ones which obey modified energy gap laws. A discussion is presented of the types of interactions which may contribute to these coherence transfer processes.

Mechanisms of vibrational relaxation in polyatomic molecules

Mechanisms of vibrational relaxation in polyatomic molecules

Vibrational relaxation of polyatomic molecules in a field of monochromatic radiation behind the leading edge of a shock wave

Vibrational relaxation of polyatomic molecules in a field of monochromatic radiation behind the leading edge of a shock wave

Vibrational relaxation in polyatomic molecules: SF6

Vibrational relaxation in mixtures of 5%, 10%, and 25% SF6 in Ar has been studied behind incident shock waves over the temperature range 450–1050 K by time-resolved measurement of postshock density gradients using a laser beam deflection technique. Short extrapolation of the results obtained yields excellent agreement with ultrasonic data in the range 200–420 K. Contrary to original reports, results from infrared fluorescence and double resonance measurements at 300 K are shown to be in disagreement with the ultrasonic data. A discussion of relaxation behavior in polyatomic molecules under differing conditions of departure from equilibrium shows that such a discrepancy is to be expected in general.