Vibrational Transition Rates Research Articles

Master Equation Study of Vibrational and Rotational Relaxations of Oxygen

Transition rates in collisions for each vibrational and rovibrational state are generated by means of the quasi-classical trajectory method using potential energy surfaces of different fidelities. The first potential energy surface, obtained via the double many-body expansion method, is adopted to obtain vibrational transition rates assuming transrotational equilibrium. The trajectory simulation on a simpler potential surface, based on the two-body pairwise interaction, generates a complete set of rates for each internal state. Vibrational and rotational relaxations of oxygen in a heat bath of parent atoms are modeled by a system of master equations at translational temperatures between 1000 and 20,000 K. It is shown that the vibrational relaxation becomes less efficient at high temperatures, in contrast with the conventional equation for relaxation time proposed by Millikan and White (“Systematics of Vibrational Relaxation,” Journal of Chemical Physics, Vol. null, No. null, 1963, Paper 3209). Rotational and vibrational relaxation times are the same order of magnitude in the range of temperatures observed in hypersonic flows. The excitation of the vibrational mode in collisions under typical postshock conditions occurs earlier than in other molecular systems. The exchange channel plays an important role in the internal energy randomization.

Algorithm for reconstructing vibrational relaxation times in excitable gases by two-frequency acoustic measurements

Vibrational relaxation time is a parameter describing the macroscopic behavior of vibrational energy transition rate between molecular internal degrees of freedom (DOF) and external DOF in excitable gas, which determines the relaxation frequency of the maximum point in acoustic absorption spectrum. To measure the vibrational relaxation time, the traditional methods are used to obtain the acoustic absorption spectra by changing the ambient pressure at several operating frequencies. However, these traditional methods are not suitable for real-time measurement due to the complexity of equipment implementation and the non-ideality of test gas under high pressure. In order to solve those problems, we have developed an algorithm [2013 Meas. Sci. Technol. 24 055002] to capture the primary vibrational relaxation processes only based on the measurements of sound absorption and sound speed at two operating frequencies and a single pressure. But the algorithm only can reconstruct the absorption maximum and it cannot capture the relaxation time with high precision. To measure the frequency dependence of the complex effective specific heat of the relaxing gas, an algorithm synthesizing relaxation processes is given by Petculescu and Lueptow [2005 Phys. Rev. Lett. 94 238301]. In its derivation process, relaxational angular frequency was set to be the inverse ratio to relaxation time. However, the relaxational angular frequency was measured in the adiabatic process of transmission thermodynamic, while the relaxation time was obtained in the thermodynamic isothermal process, the derivation confused the two thermodynamic processes, making the algorithm unable to capture the relaxation frequency with high precision. In order to estimate the relaxation time with higher accuracy, in this paper we first obtain the theoretical relationship among the relaxation times under the three types of thermodynamics conditions, i. e., isothermal, adiabatic constant pressure and adiabatic constant volume. Then we correct the relaxation time derivation and propose our corrected algorithm to reconstruct the relaxation frequencies and relaxation times under the conditions of isothermal, adiabatic constant pressure and adiabatic constant volume. In experiments and simulations, the relaxation times and relaxation frequencies reconstructed by our corrected algorithm for various gas compositions including carbon dioxide, methane, chlorine, nitrogen, and oxygen around room temperature are consistent with the experimental data.

Chemical reaction rates and non-equilibrium pressure of reacting gas mixtures in the state-to-state approach

Viscous gas flows with vibrational relaxation and chemical reactions in the state-to-state approach are analyzed. A modified Chapman–Enskog method is used for the determination of chemical reaction and vibrational transition rates and non-equilibrium pressure. Constitutive equations depend on the thermodynamic forces: velocity divergence and chemical reaction/transition affinity. As an application, N2 flow with vibrational relaxation across a shock wave is investigated. Two distinct processes occur behind the shock: for small values of the distance the affinity is large and vibrational relaxation is in its initial stage; for large distances the affinity is small and the chemical reaction is in its final stage. The affinity contributes more to the transition rate than the velocity divergence and the effect of these two contributions are more important for small distances from the shock front. For the non-equilibrium pressure, the term associated with the bulk viscosity increases by a small amount the hydrostatic pressure.

Insight into Action Spectroscopy for Single Molecule Motion and Reactions through Inelastic Electron Tunneling

We propose a versatile formula that describes action spectra for vibrationally mediated reactions of single molecules with a scanning tunneling microscope. Spectral fitting of the formula to CO hopping and the configurational change of the cis-2-butene molecule on Pd(110) enables us to determine the vibrational energy, reaction order, and transition rate associated with anharmonic coupling between the modes excited by tunneling electrons and the reaction-coordinate modes. The formula proposed here is general and easy to apply to any vibrationally mediated motion and reaction of single molecules.

Electronic damping of anharmonic adsorbate vibrations at metallic surfaces

The nonadiabatic coupling of an adsorbate close to a metallic surface leads to electronic damping of adsorbate vibrations and line broadening in vibrational spectroscopy. Here, a perturbative treatment of the electronic contribution to the lifetime broadening serves as a building block for a new approach, in which anharmonic vibrational transition rates are calculated from a position-dependent coupling function. Different models for the coupling function will be tested, all related to embedding theory. The first two are models based on a scattering approach with (i) a jellium-type and (ii) a density functional theory based embedding density, respectively. In a third variant a further refined model is used for the embedding density, and a semiempirical approach is taken in which a scaling factor is chosen to match harmonic, single-site, first-principles transition rates, obtained from periodic density functional theory. For the example of hydrogen atoms on (adsorption) and below (subsurface absorption) a Pd(111) surface, lifetimes of and transition rates between vibrational levels are computed. The transition rates emerging from different models serve as input for the selective subsurface adsorption of hydrogen in palladium starting from an adsorption site, by using sequences of infrared laser pulses in a laser distillation scheme.

Vibrational relaxation in the Kubo oscillator: Stochastic pumping of heat

We present a model for a molecular level heat pump that operates when a stochastic time dependent force modulates the molecular vibrational energies. The model consists a molecular unit, represented by a Kubo oscillator, coupled to two solids characterized by distinct spectral properties and kept at unequal temperatures. In the fast modulation limit we derive expressions for the vibrational energy transition rates in the Kubo oscillator, and show that they do not trivially correspond to the population transition rates, unlike the field-free (or adiabatic) limit. We discuss the operation principle of the pump and manifest, analytically and numerically, directing of heat against a temperature gradient for a broad range of system and bath parameters. The present formalism could also describe a unidirectional exciton energy flow in a metal-molecule-metal junction under random noise.

Modeling of a Vibrational Transition Collisional Model for Diatomic Molecules (1st Report, Vibrational Transition Probability)

The direct simulation Monte Carlo (DSMC) method is widely used for simulating rarefied gas flows, and in most cases, the phenomenological model with a local equilibrium assumption is chosen as a collision model. Since most collisions in the rarefied gas regime are binary ones, to make the vibrational transitional collision model for the DSMC method without the local equilibrium assumption, binary collision processes of diatomic molecules were analyzed. The semiclassical approach, in which the vibrational motion is treated quantum mechanically and other degrees of freedom are investigated with the classical mechanics, was introduced. The scheme was verified using the vibrational transition rate coefficient comparing with the empirical relation and the existent numerical results. The transition probability was obtained as a function of the initial translational and rotational energy. From collinear collisions, the transition probability can be described with a simple function of the relative translational energy. The total rotational energy of collisional pairs is appeared to be important for general collisions with rotational energies.

Theoretical study of vibration-phonon coupling of H adsorbed on a Si(100) surface

In this paper a perturbation-theory study of vibrational lifetimes for the bending and stretching modes of hydrogen adsorbed on a Si(100) surface is presented. The hydrogen-silicon interaction is treated with a semiempirical bond-order potential. Calculations are performed for H-Si clusters of different sizes. The finite lifetime is due to vibration-phonon coupling, which is assumed to be linear or bilinear in the phonon and nonlinear in the H-Si stretching and bending modes. Lifetimes and vibrational transition rates are evaluated with one- and two-phonon processes taken into account. Temperature effects are also discussed. In agreement with the experiment and previous theoretical treatment it is found that the H-Si (upsilon(s) = 1) stretching vibration decays on a nanosecond timescale, whereas for the H-Si (upsilon(b) = 1) bending mode a picosecond decay is predicted. For higher-excited vibrations, simple scaling laws are found if the excitation energies are not too large. The relaxation mechanisms for the excited H-Si stretching and the H-Si bending modes are analyzed in detail.

Nonequilibrium kinetics of a radiative CO flow behind a shock wave.

An investigation is presented of a highly nonequilibrium CO flow with consistently coupled vibrational energy exchanges, chemical reactions, and radiation. A detailed state-to-state model taking into account vibration-vibration, vibration-translation, and vibration-electronic transitions, dissociation-recombination reactions, and radiative transitions between vibrational and electronic states is developed on the basis of kinetic theory methods. A closed set of master equations for vibration-electronic level populations, number densities of atomic species, radiation intensity, temperature, and velocity is derived, and a one-dimensional inviscid carbon monoxide flow behind a plane shock wave is studied numerically. Several models of vibrational transition and dissociation rates in high temperature carbon monoxide are tested, and a model satisfying both accuracy and feasibility requirements is recommended. The role of various energy transfers and chemical reactions in the formation of nonequilibrium vibrational distributions in a shock heated CO flow is studied, and the influence of state-to-state distributions on macroscopic flow parameters and radiation intensity is discussed.

Simulations of the Vibrational Relaxation of I2 in Xe

The vibrational relaxation of an I2 molecule in a xenon fluid has been simulated by three methods. The conventional perturbation theory approach based on an equilibrium molecular dynamics (MD) simulation is compared with purely classical nonequilibrium MD and mixed quantum−classical surface-hopping MD simulations. Relaxation times and state-to-state vibrational transition rate constants obtained with these three approaches are compared and information that can be extracted concerning the mechanism of vibrational relaxation is examined. Both harmonic and anharmonic solutes are considered as are some common approximations invoked in obtaining vibrational relaxation times.

Reactive and nonreactive vibrational energy exchanges in nonequilibrium hypersonic flows

The generalized depletion equations, considering state-to-state kinetics of dissociating nitrogen, were solved to predict the extent of vibrational depletion for 4000 and 6000 K. Two different vibrational transition rate sets were used in the depletion analysis. One was based on the Schwartz–Slawsky–Herzfeld (SSH) theory and the other based on the analytical methods of Capitelli, Billing, Fisher, Doroshenko and co-workers. Transition rates based on the SSH theory predicted a lower depletion due to very high rates in the upper levels. With the objective of delineating the vibration–vibration (V–V) exchanges and vibration–translation (V–T) transfers in nonreactive, vibrationally excited gas dynamic flows, the flowfield simulations of blunt body and expanding nozzles were performed. For vibrational cooling cases (where vibrational temperature is greater than translational temperature) of flow past blunt body and the nozzle flows, the population distribution showed the Treanor-like distribution only at low translational temperatures. This non-Boltzmann behavior and the corresponding low state densities establish the dominance of the V–T energy transfers and the relatively minor role of V–V exchanges for hypersonic gasdynamic flows.

Vibrational Relaxation of Chemically Excited SiO (ν = 1—5) Produced in the Reaction of Silane with O(1D)

Abstract The state-resolved vibrational relaxation process of SiO was monitored in the excimer laser photolysis of N2O/SiH4/He mixtures, where vibrationally hot SiO (Tv = 5200 K) was produced by the reaction of SiH4+ O(1D). A frequency-doubled optical parametric oscillator was used as a widely tunable source to probe SiO (v = 0—7) by the laser-induced fluorescence technique. From an analysis of the observed relaxation profiles, the vibrational transition rate constants in collisions with He and N2O were evaluated against the vibrational level v = 1—5 of SiO. Previous theories for the V-T and V-V energy transfer were compared with the present experimental results.

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.

Dependence of level-resolved energy transfer on initial vibrational level in Li2A1Σu+−Ne collisions

We have investigated collision induced rotational and vibrational energy transfer in the Li2 A1Σu+(vi,ji=30)−Ne system experimentally under single-collision conditions at an effective temperature of 691 K. Over 800 inelastic rate constants have been measured, with the initial vibrational level vi ranging from 2 to 24 and −2≤Δv≤+2. Increasing vi results in a linear increase in the vibrational transition rate constants, which is accompanied by a decrease in the rotationally inelastic transition rate constant. The total inelastic rate constant increases with vi only at the highest values of vi. Net vibrational energy transfer 〈ΔE〉 calculated using rotationally summed rate constants is qualitatively consistent with a simple model. However, explicit inclusion of rotation gives quite different values of 〈ΔE〉. The experimental results are compared with our three-dimensional trajectory calculations on an ab initio potential surface and on a simple repulsive potential surface.

Prediction of Vibrational Relaxation in Hypersonic Expanding Flows Part I: Model Development

A number of experiments in nozzles have indicated that the Landau-Teller vibrational relaxation model fails to accurately predict the relaxation process in expanding flows. In the present study vibrational transition rate equations are solved and the detailed calculations are used to develop a simplified relaxation model. The present simplified relaxation model allows both non-BoItzmann population distributions in vibrationally heating and cooling flows. This simplified model also includes the effect of anharmonicity on vibrational transition rates and energy transfer.

Prediction of Vibrational Relaxation in Hypersonic Expanding Flows Part 2: Results

This article examines the range of applicability and performance of the Landau-Teller vibrational relaxation model and a simplified anharmonic model in expanding flows. The simplified relaxation model allows both non- Boltzmann population distributions and includes anharmonic transition rates and energy transfer. A coupled set of vibrational transition rate equations and quasi-one-dimensional fluid dynamic equations is solved. The calculations are compared with experimental results obtained in nozzles. The predictions of the detailed master equation solver are in excellent agreement with experimental results. Although the simplified anharmonic model requires significantly less computational time than the master equation solver, it gives good agreement with the detailed solver and with experimental test results. tionally efficient than a detailed master equation solver, while maintaining reasonable accuracy over a wide range of con- ditions. In the present study calculations are performed with the simplified anharmonic model and with the Landau-Teller model. These results are compared with experimental data and with results obtained by solving the vibrational master equation. The vibrational relaxation processes of N2 and CO in cool- ing flows are studied. For the detailed calculations, a coupled set of vibrational master equations and quasi-one-dimensional fluid dynamic equations is solved. Vibration-translation (V- T) transition rates are computed from a modified version of the Schwartz, Slawsky, and Herzfeld2 (SSH) theory, and vi- bration-vibration (V-V) exchange rates are computed by con- sidering both long-range and short-range intermolecular forces. The transition rates are validated with available experimental data and other theoretical models. The reader is referred to a prior study by Ruffin3 for a detailed description of the quasi- one-dimensional solver and the transition rates. The quasi- one-dimensional solver is used to predict the steady-state flow in nozzles and to conduct idealized studies of vibrational re- laxation under isothermal conditions. The present computational schemes are compared with ex- perimental data obtained in expanding nozzles. Relaxation predictions are compared with the most reliable experimental results, which use direct measurement techniques for popu- lation distributions and have very low levels of impurities in the test gas. Anharmonic and harmonic oscillator predictions are also compared in external flows around a blunt re-entry vehicle. The present study also seeks to address three questions related to the simplified anharmonic model: 1) How accurate is the model compared to master equation solutions and experimental data? 2) What is its range of applicability ? 3) Is the computational requirement prohibitive for use in multidimensional flow codes? The accuracy of the model for a wide range of conditions in isothermal relaxations is studied in the next section. The range of applicability is also discussed later in that section. In the subsequent section the model is compared to experimental data and master equation solutions in nonisothermal gasdynamic flows. Both of the next two sections include assessments of the model's computational requirements.

Vibrational relaxation of anharmonic oscillators in expanding flows

Although the Landau-Teller vibrational model accurately predicts vibrational excitation process in post-shock and compressing flows, it under-predicts the rate of de-excitation in cooling and expanding flows. In the present paper, detailed calculations of the vibrational relaxation process of N2 and CO in cooling flows are conducted. A coupled set of vibrational transition rate equations and quasi-one-dimensional fluid dynamic equations is solved. Multiple quantum level transition rates are computed using SSH theory. The SSH transition rate results are compared with available experimental data and other theoretical models. Vibration-vibration exchange collisions are responsible for some vibrational relaxation acceleration in situations of high vibrational temperature and low translational temperature. The present results support the relaxation mechanisms proposed by Bray and by Treanor Rich and Rehm.

Rate parameters for coupled rotation-vibration-dissociation phenomena in H2

The effects of molecular rotation on coupled vibration-dissociation phenomena in H2 undergoing a nonequilibrium relaxation in a heating and cooling environment were studied theoretically. The rate coefficients for the collisional bound-bound and bound-free transitions, calculated by a quasi-classical trajectory method, were fed into the master equation, which was numerically solved to determine the rotational and vibrational population densities and bulk thermodynamic properties. Results indicate that the vibrational transition rates of H2 increase monotonically with the vibrational levels, faster than in the Landau-Teller (1936) model, and that the rotation of the molecules helps relax the low vibrational levels, serves as a temporary storage of vibrational energy during the relaxation, and thereby delays the dissociation process. The average energy loss due to the dissociation was determined to be about 80-90 percent of the total dissociation energy.

Vibrational relaxation in fluids: A many body scattering formalism

We derive an expression for the vibrational energy relaxation rate constant for dilute diatomic molecules in a structureless fluid. Our approach is based on a many-body scattering formalism within the Markov approximation. Using a quantum scattering formalism allows us to formally separate the inelastic part of the problem from the bath dynamics. We assume that the vibrational transition rate is small, and accordingly we treat the inelastic potential as a perturbation. Also, we assume that the translational motion of the diatom and the bath can be treated classically. The separation of the inelastic interaction from the bath dynamics allows the bath motion to be written in terms of a classical time correlation function of the bath density relative to the diatom. The bath, though, evolves under two Hamiltonians; one with the diatom in its initial state and the other with the diatom in its final state. A method is introduced to approximate this time correlation function in terms of single Hamiltonian correlation functions. We discuss the approximations inherent in our method and also those in the independent binary collision (IBC) model.

Vibrational nonequilibrium dissociation of Br2 in collisions with Ar and Br atoms

The collision induced dissociation processes in dilute mixtures of Br2–Ar and Br2–Br are investigated. Vibrational transition rates and dissociation rates from individual vibrational levels are derived from quasiclassical Monte Carlo trajectory calculations where only vibrational nonequilibrium effects are considered. The full transition rate matrix is completed by a moment analysis of the trajectory results. From the steady state solution of vibrational-level master equations, it is found that steady state populations in excited vibrational states are largely depleted but the nonequilibrium dissociation rates are about 30%–75% less than the equilibrium rates. The low activation energy observed in the previous experiments in the dissociation process, Br2+Br→Br+Br+Br cannot be explained by the present analysis.