Theory Of Vibrational Relaxation Research Articles

Improvement of the output power of optical pumping THz lasers based on the theory of vibrational relaxation

Based on the semiclassical density matrix theory and vibrational relaxation theory, the present paper studies the influences on optical pumping THz lasers output power due to adding an appropriate proportion of buffer gas and appropriately reducing the waveguide core diameter. Results prove that adding appropriate proportion of buffer gas or appropriately reducing the waveguide core diameter can increase the output of light intensity of THz laser. Optimizing the two parameters at the same time can further improve the efficiency of pumping laser energy into THz laser energy, extend the effective activation area of the working cavity, put off the appearance of the pumping saturation effect, and increase the output power of the THz lasers. This research may have a guiding significance for the THz optical pumping laser in improving energy conversion efficiency, and increasing the output power so as to bring about the miniaturization of THz optical pumping laser.

Real and imaginary parts of the vibrational relaxation of acetonitrile in its electrolyte solutions: new results for the dynamics of solvent molecules

Isotropic scattering Raman spectra of liquid acetonitrile (AN) solutions of LiBF 4 and NaI at various temperatures and concentrations have been investigated. For the first time imaginary as well as real parts of the solvent vibrational correlation functions have been extracted from the spectra. Such imaginary parts are currently an important component of modern theories of vibrational relaxation in liquids. This investigation thus provides the first experimental data on imaginary parts of a correlation function in AN solutions. Using the fitting algorithm we recently developed, statistically confident models for the Raman spectra were deduced. The parameters of the band shapes, with an additional correction, of the ν 2 AN vibration (CN stretching), together with their confidence intervals are also reported for the first time. It is shown that three distinct species, with lifetimes greater than ∼10 −13 s, of the AN molecules can be detected in solutions containing Li + and Na +. These species are attributed to AN molecules directly solvating cations; the single oriented and polarised molecules interleaving the cation and anion of a Solvent Shared Ion Pair (SShIP); and molecules solvating anions. These last are considered to be equivalent to the next layer of solvent molecules, because the CN end of the molecule is distant from the anion and thus less affected by the ionic charge compared with the anion situation. Calculations showed that at the concentrations employed, 1 and 0.3 M, there were essentially no other solvent molecules remaining that could be considered as bulk solvent. Calculations also showed that the internuclear distance in these solutions supported the proposal that the ionic entity dominating in solution was the SShIP, and other evidence was adduced that confirmed the absence of Contact Ion Pairs at these concentrations. The parameters of the shape of the vibrational correlation functions of all three species are reported. The parameters of intramolecular anharmonic coupling between the potential surfaces in AN and the dynamics of the intermolecular environment fluctuations and intermolecular energy transfer are presented. These results will assist investigations made at higher and lower concentrations, when additional species and interactions with AN molecules will be present.

Multiphonon vibrational relaxation in liquids: An exploration of the idea and of the problems it causes for molecular dynamics algorithms

The basic solid-state perspective on energy relaxation—that a solute transfers large amounts of energy to its surroundings by exciting overtones of the solid’s phonons—is sufficiently beguiling that it is tempting to try to apply it to high-frequency vibrational energy relaxation in liquids. We suggest that when the phonon concept is suitably adapted this picture does provide a surprisingly realistic and quantitative portrait of vibrational energy dispersal in solution. Within the nonlinear instantaneous-normal-mode/instantaneous-pair theory of vibrational relaxation, relaxation rates can be formally written as a sum over the contributions of successively higher overtones of fundamental solvent frequencies. However the presence of a significant width to the band of fundamental frequencies in the liquid state means that there could, in principle, be complex interferences between multiple contributing overtones, rendering the overtone picture no more than a formal construct. What we find is that such interferences do not occur. Despite the fact the band shape is log normal—with a relatively long band tail—the relaxation is invariably dominated by a single overtone. This same perspective also helps us understand one of the failings of the common velocity-Verlet molecular dynamics algorithm in predicting high-frequency energy relaxation.

Time-dependent theory of vibrational relaxation—application to time-resolved fluorescence

A general time-dependent theory of vibrational relaxation is developed and applied to resonance fluorescence in a two-level model. The transient emission rate and spontaneous emission are calculated for FWHM 8 and 80 fs pulses, respectively. The main properties of time-resolved fluorescence for vibrational relaxation are presented.

Theory for a gas composition sensor based on acoustic properties

Sound travelling through a gas propagates at different speeds and its intensityattenuates to different degrees depending upon the composition of the gas.Theoretically, a real-time gaseous composition sensor could be based on measuringthe sound speed and the acoustic attenuation. To this end, the speed of soundwas modelled using standard relations, and the acoustic attenuation wasmodelled using the theory for vibrational relaxation of gas molecules. Theconcept for a gas composition sensor is demonstrated theoretically fornitrogen–methane–water and hydrogen–oxygen–water mixtures. For athree-component gas mixture, the measured sound speed and acousticattenuation each define separate lines in the composition plane of two of thegases. The intersection of the two lines defines the gas composition. Itshould also be possible to use the concept for mixtures of more than threecomponents, if the nature of the gas composition is known to some extent.

Density dependent vibrational relaxation in supercritical fluids

The vibrational lifetimes of the asymmetric CO stretching mode (1990 cm −1) of W(CO) 6 in the gas phase and as a function of density in supercritical ethane are examined using infrared pump–probe experiments. The gas phase measurement provides the zero density rate constant, which permits the effect of the ethane solvent to be separated from internal relaxation dynamics. The non-exponential gas phase vibrational dynamics are briefly discussed. The density dependence of the lifetime is compared to an extension of a hydrodynamic theory of vibrational relaxation in supercritical fluids to the regime of large wavevector. Agreement between experiment and theory is found to be good.

Instantaneous pair theory for high-frequency vibrational energy relaxation in fluids

Notwithstanding the long and distinguished history of studies of vibrational energy relaxation, exactly how it is that high frequency vibrations manage to relax in a liquid remains somewhat of a mystery. Both experimental and theoretical approaches seem to say that there is a natural frequency range associated with intermolecular motion in liquids, typically spanning no more than a few hundred cm−1. Landau–Teller-type theories explain rather easily how a solvent can absorb any vibrational energy within this “band,” but how is it that molecules can rid themselves of superfluous vibrational energies significantly in excess of these values? In this paper we develop a theory for such processes based on the idea that the crucial liquid motions are those that most rapidly modulate the force on the vibrating coordinate — and that by far the most important of these motions are those involving what we have called the mutual nearest neighbors of the vibrating solute. Specifically, we suggest that whenever there is a single solvent molecule sufficiently close to the solute that the solvent and solute are each other’s nearest neighbors, then the instantaneous scattering dynamics of the solute–solvent pair alone suffices to explain the high-frequency relaxation. This highly reduced version of the dynamics has implications for some of the previous theoretical formulations of this problem. Previous instantaneous-normal-mode theories allowed us to understand the origin of a band of liquid frequencies, and even had some success in predicting relaxation within this band, but lacking a sensible picture of the effects of liquid anharmonicity on dynamics, were completely unable to treat higher frequency relaxation. When instantaneous-normal-mode dynamics is used to evaluate the instantaneous pair theory, though, we end up with a multiphonon picture of the relaxation which is in excellent agreement with the exact high-frequency dynamics — suggesting that the critical anharmonicity behind the relaxation is not in the complex, underlying liquid dynamics, but in the relatively easy-to-understand nonlinear solute–solvent coupling. There are implications, as well, for the independent binary collision (IBC) theory of vibrational relaxation in liquids. The success of the instantaneous-pair approach certainly provides a measure of justification for the IBC model’s focus on few-body dynamics. However, the pair theory neither needs nor supports the basic IBC factoring of relaxation rates into many-body and few-body dynamical components — into collision rates and relaxation rates per collision. Rather, our results favor taking an instantaneous perspective: the relaxation rate is indeed exercise in few-body dynamics, but a different exercise for each instantaneous liquid configuration. The many-body features therefore appear only in the guise of a purely equilibrium problem, that of finding the likelihood of particularly effective solvent arrangements around the solute. All of these results are tested numerically on model diatomic solutes dissolved in atomic fluids (including the experimentally and theoretically interesting case of I2 dissolved in Xe). The instantaneous pair theory leads to results in quantitative agreement with those obtained from far more laborious exact molecular dynamics simulations.

Temperature dependent vibrational lifetimes in supercritical fluids near the critical point

Vibrational relaxation measurements on the CO asymmetric stretching mode (∼1980 cm−1) of tungsten hexacarbonyl (W(CO)6) as a function of temperature at constant density in several supercritical solvents in the vicinity of the critical point are presented. In supercritical ethane, at the critical density, there is a region above the critical temperature (Tc) in which the lifetime increases with increasing temperature. When the temperature is raised sufficiently (∼Tc+70 °C), the lifetime decreases with further increase in temperature. A recent hydrodynamic/thermodynamic theory of vibrational relaxation in supercritical fluids reproduces this behavior semiquantitatively. The temperature dependent data for fixed densities somewhat above and below the critical density is in better agreement with the theory. In fluoroform solvent at the critical density, the vibrational lifetime also initially increases with increasing temperature. However, in supercritical CO2 at the critical density, the temperature dependent vibrational lifetime decreases approximately linearly with temperature beginning almost immediately above Tc. The theory does not reproduce this behavior. A comparison between the absolute lifetimes in the three solvents and the temperature trends is made.

Temperature dependence of vibrational lifetimes at the critical density in supercritical mixtures

Experimental measurements are reported for the temperature dependence of the vibrational lifetime, T1, of the asymmetric CO stretching mode of tungsten hexacarbonyl in supercritical ethane at constant density from just above the critical temperature to substantially higher temperatures. T1 is found initially to increase with temperature along an isochore (reaching a maximum at about 70° above the critical point of ethane), and then subsequently to decrease. Using a recent classical theory of vibrational relaxation, we attempt to rationalize the T1 data. This behavior can be semiquantitatively reproduced by the theory if quantum corrections to the classical rate expressions are assumed to be temperature independent in the limit when the transition energy is much greater than thermal energy. In this case, the theory indicates that the initial increase in T1 with temperature arises because of a competition between properties of the solvent which are changing rapidly as the temperature is raised above the critical temperature. At sufficiently high temperature, properties of the solvent vary slowly with temperature, and the explicit temperature dependence of the vibrational relaxation dominates, producing a decrease in T1 with increasing temperature. The predictions of the theory are also examined when other postulated forms of the quantum correction factors are used, and the implications of these results for theoretical approaches to vibrational relaxation are discussed.

Multiphonon decay of stretch vibrations in zeolites

The vibrational dynamics of free and hydrogen bonded O-H and O-D groups in zeolites are investigated as a function of temperature with picosecond infrared saturation spectroscopy. From the temperature dependence of the population relaxation rare the order of the multiphonon relaxation process is obtained. It is noted that, in contrast with the conventional theory for vibrational relaxation of an oscillator in a dense medium, the absolute decay rate hardly scales with the number N of accepting modes. This leads us to conclude that, in addition to the order N of the relaxation process, the relaxation rate is also determined by the number of possible relaxation channels. From the temperature dependence of the decay rate of H-bonded oscillators we obtain insight in the role of H-bonding in vibrational relaxation in solids. It is found that the hydrogen bond efficiently accepts part of the oscillator energy in the relaxation process.

Diffusional description of vibrational relaxation in a binary mixture of diatomic molecules — quantum oscillators

Abstract The finite-difference equations of diffusional type for the vibrational relaxation process in a binary gas mixture of diatomic molecules - quantum oscillators are derived. The derivation begins with the corresponding complete (with allowance for multiquantum transitions) population balance equations and uses techniques of the finite-difference analysis. The kinetic equations obtained approximately take account of multiquantum transitions and are exact in the case of the one-quantum energy transfer; in the classical limit, these equations are transformed into equations of the classical (or continual) diffusional theory of vibrational relaxation. The time-dependent isothermal problem of vibrational relaxation in a binary mixture of anharmonic oscillators is numerically solved. The results presented illustrate the effect of multi-quantum vibration exchange processes for components with essentially different fundamental vibrational frequencies in various concentrations and initial conditions. A comparison of micro- and macroscopic vibration kinetic descriptions is carried out.

Conditional variation in the kinetic parameters of rare gas halide excimers

In accordance with the theory of vibrational relaxation, a rare gas halide (RgX) excimer or similar electronically excited molecule cannot be characterized by one universal set of kinetic parameters. Both the quenching rate constants and the effective radiative lifetimes are discovered to depend on the internal energy of generated molecules and gaseous-mixture composition. It is emphasized that different values of a kinetic parameter have to be used under steady-state and pulse conditions.

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.

Vibrational relaxation on metal surfaces: Molecular-orbital theory and application to CO/Cu(100)

A nonempirical theory of vibrational relaxation at metal surfaces via nonadiabatic coupling to conduction electrons is presented. Using a single determinant Hartree–Fock (HF) description of the electronic states of the system, an expression for the lifetime of an excited vibration is obtained. Under certain additional assumptions, all the quantities necessary to calculate the lifetime can be obtained from the results of ab initio HF calculations on cluster models of the adsorbate-metal system. As a practical test of this procedure, the lifetime of the excited v=1 vibrational state of CO on Cu(100) is calculated using clusters of 6, 10, and 14 copper atoms. Results ranging between 1.1 and 3.5 ps are obtained, with our preferred procedure yielding 1.7 ps for the largest cluster, in good agreement with experiment. Extensions of this approach may also be valuable for treating other nonadiabatic phenomena at metal surfaces.

A vibrational analysis of the O2 ( A3Σ+u) Herzberg I system using rocket data

An observation of the u.v. nightglow between 2670 and 3040 Å was conducted over White Sands Missile Range on 22 October 1984. A 1 4 m spectrometer operating at 3.5 Å resolution viewed the Earth's limb at tangent heights between 90 and 110 km for 120 s. A total of 41 spectral scans of the nightglow were obtained with the brightest feature being the O 2 ( A 3 Σ u +− X 3 Σ g −) Herzberg I bands. The data were sorted into two groups, one from the top side of the layer and one containing the emission peak, and compared with synthetic spectra. The deduced O 2 ( A 3 Σ u +) vibrational distributions indicate that at low altitudes, the higher vibrational levels ( v ́ > 6) were relatively depleted; however, the magnitude of the vibrational shift is much less than that predicted from theories of vibrational relaxation. It is shown that increasing the electronic quenching of O 2 ( A 3 Σ g +) with respect to the vibrational quenching can reduce the vibrational shift in the model and qualitatively explain the observations; however, several details of the vibrational distribution are not well reproduced.

Sum rules in the theory of vibrational relaxation and unimolecular reactions

For simple models of the relaxation of highly vibrationally excited molecules the average energy transferred per collision <Δϵ⪢ i for molecules with initial energy ϵ i is a significant quantity. For more realistic models <Δϵ⪢ i is generalized to a quantity [Δ qϵ] i which is not strictly an average. We derive a number of sum rules which show the theoretical significance of quantities [Δ qa] i where a i may be some quantity other than ϵ i . For example, if the vibrational relaxation is coupled to reaction, the quantities [Δ qK] i are of importance, K i being the rate constant for reaction of molecules with energy ϵ i .

Studies of chemical reactivity in the condensed phase. IV. Density dependent molecular dynamics simulations of vibrational relaxation in simple liquids

Molecular dynamics simulations of the photodissociation/recombination process for iodine in liquid xenon at several densities are reported in this paper. These simulations were performed to aid in the understanding and interpretation of recent picosecond experimental investigations on model chemical reaction systems. From these calculations, it was found that geminate recombination occurs primarily within a few picoseconds at all densities considered. This is in agreement with previous molecular dynamics simulations with significantly smaller systems, and with the current interpretation of experimental results. Simulated iodine ground electronic state vibrational relaxation times range from about 1 ns at the lowest density to approximately 250 ps at the highest density reported here. In addition, the functional form of the decay of the average iodine vibrational energy was observed to be nearly independent of density. This result is discussed in terms of simple gas phase isolated binary collision models. Various force correlation functions projected onto the iodine vibrational coordinate were also examined, and indicate that the iodine molecule significantly perturbs the local solvent environment. These force correlation functions may be helpful when assessing the usefulness of liquid phase theories of vibrational relaxation of highly excited molecules. Finally, the simulation results on iodine vibrational relaxation are compared with the available experimental data. These comparisons indicate that the molecular dynamics calculations overestimate the rate of vibrational relaxation over the lower third of the iodine ground electronic state potential surface, and that the efficiency of V–TR transfer, relative to V–V transfer, may have been underestimated. The sensitivity of these results to several system parameters are analyzed.

Theory of Vibrational Relaxation of R 2★ Centres in Rare‐Gas Solids. Application to Ne 2★

AbstractA tunnel mechanism of vibrational relaxation is proposed for a class of emission centres which are characterized by a weak coupling to the crystalline environment and have vibrational quanta considerably exceeding phonon energies. For such kind of centres, e.g. for R centres in solidified rare gases, a new relaxation channel, connected with the anharmonicity of vibrations, appears. The theory is applied to the centre Ne in solid Ne: a direct calculation of the probabilities of vibrational transitions is carried out.

Vibrational distribution functions in a mixture of excited isotopic CO molecules

Analytical theories of vibrational relaxation of highly excited diatomic molecules are extended, taking into account the two-quantum V-V transfer and radiative processes. The theoretical vibrational distribution functions obtained in this way are compared with those derived from numerical computations and with experimental distributions observed for a natural-abundance 12C 16O, 13C 16O, 12C 18O mixture in a CO laser type cell. In particular, the isotopic enrichments observed in high vibrational levels are compared to the theoretical ones.

Theory of vibrational relaxation in mixtures of ortho- and para-hydrogen

A numerical study of the vibrational relaxation at 500 K of a mixture of ortho-H2 and para-H2 is described. The required state-to-state rate constants were calculated from the quantum results of Rabitz and co-workers, and missing pieces of data were estimated by interpolation.It is concluded that only one relaxation time will be observed in any mixture of ortho-H2 and para-H2 and that (except at very high dilutions in a third inert gas) the relaxation rate constant will be close to the mean of the individual rate constants for relaxation, weighted according to the respective mole fractions of ortho-H2 and para-H2 present in the mixture.We find that the relaxation process can be modelled very accurately as an electrical RC network, whose time constants can be written down quite easily as sums of the appropriate microscopic rate constants, and by using this model, it is a simple matter to explore the conditions required for a mixture of two gases to exhibit two distinct vibrational relaxation times.