Model Of Vibrational Energy Transfer Research Articles

Quantum dynamics of vibrational energy flow in oscillator chains driven by anharmonic interactions

A new model of vibrational energy transfer in molecular systems taking into account anharmonic (third order) interactions of localized vibrations with a chain of harmonic oscillators is developed. The role of the energy spectrum of the chain and of the magnitude of the non-linear coupling is discussed in detail by an exact numerical solution of the quantum dynamical problem based on the tensor-train (matrix product state) representation of the vibrational wave function. Results show that the type of wave packet motion is determined by the eigen-spectrum of the chain and by its excitation time. It is found that when the excitation of the chain takes place on a much shorter timescale than the energy transfer along the chain the vibrational wave packet moves in a ballistic way independently of the length of the chain. On the other hand when the excitation of the chain takes place on the timescale of the energy transfer along the chain the overall motion becomes superballistic. These findings shed new light on recent observations of ballistic energy transfer along polymethylene chains.

Three-dimensional analytic probabilities of coupled vibrational-rotational-translational energy transfer for DSMC modeling of nonequilibrium flows

A three-dimensional, nonperturbative, semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom, and between two rotating diatomic molecules (Forced Harmonic Oscillator–Free Rotation model) has been extended to incorporate rotational relaxation and coupling between vibrational, translational, and rotational energy transfer. The model is based on analysis of semiclassical trajectories of rotating molecules interacting by a repulsive exponential atom-to-atom potential. The model predictions are compared with the results of three-dimensional close-coupled semiclassical trajectory calculations using the same potential energy surface. The comparison demonstrates good agreement between analytic and numerical probabilities of rotational and vibrational energy transfer processes, over a wide range of total collision energies, rotational energies, and impact parameter. The model predicts probabilities of single-quantum and multi-quantum vibrational-rotational transitions and is applicable up to very high collision energies and quantum numbers. Closed-form analytic expressions for these transition probabilities lend themselves to straightforward incorporation into DSMC nonequilibrium flow codes.

Near-resonant energy transfer from vibrationally excited OH(v),v= 9, 8, 1 to CO2

[1] The transfer of vibrational energy from chemiluminescent OH, produced predominately by the H + O3 → OH (v) + O2 reaction, is of importance in modeling the airglow from the atmospheres of Earth, Mars, and Venus. We have calculated the energy transfer probability per collision as function of temperature for the near-resonant processes OH (v) + CO2 (00001) → OH(v − 1) +CO2 (mnpqr) for v = 1, 8, and 9 in the 100 – 350 K temperature range. We show that the measured room temperature values of the removal rate coefficient of OH(v = 9, 8) and OH(v = 1) by CO2, are in agreement with the ones calculated for the vibration-to-vibration (VV) energy transfer (ET) processes OH (v) + CO2 (00001) → OH (v − 1) + CO2 (00011) and OH (1) + CO2 (00001) → OH (0) + CO2 (1001 n) n =1, 2, respectively. The emission from the latter levels of CO2 in the terrestrial mesosphere is not self-absorbed leading to the possibility that these levels may be important contributors to the 4.3 μm emission. Our calculation favors the “Collisional Cascade” model of vibrational energy transfer from OH to CO2 that predicts about 50 times more radiation in the Martian Meinel bands over that predicted by the “Sudden Death” model. These two models of Martian atmosphere predict vastly different steady-state populations of the vibrational levels of OH and should, because of the chemical reactions, of other trace species, e.g., H, O, and CO, as well.

Three-Dimensional Analytic Model of Vibrational Energy Transfer in Molecule-Molecule Collisions

Athree-dimensionalsemiclassicalanalyticmodelofvibrationalenergytransferincollisionsbetweentworotating diatomic molecules has been extended for molecule ‐molecule collision. The model is based on analysis of classical trajectories of free-rotating (FR) molecules acted upon by a superposition of repulsive exponential atom-to-atom potentials. The energy transfer probabilities have been evaluated using the nonperturbative Forced Harmonic Oscillator (FHO) model. The model predicts the probabilities for vibrational energy transfer as functions of the total collision energy, orientation of molecules during a collision, their rotational energies, and impact parameter. The model predictions have been compared with the results of three-dimensional close-coupled semiclassical trajectorycalculationsusingthesamepotentialenergysurface.Thecomparisondemonstratesnotonlyremarkably good agreement between the analytic and numerical probabilities across a wide range of collision energies, but also shows that the analytic FHO-FR model correctly reproduces the probability dependence on other collision parameters such as rotation angles, angular momentum angles, rotational energies, and impact parameter. The model equally well predicts the cross sections of single-quantum and multiquantum transitions and is applicable up to very high collision energies and quantum numbers. Most importantly, the resultant analytic expressions for the probabilities do not contain any arbitrary adjustable parameters commonly referred to as steric factors . The present work essentially completes development of the analytic rate database for vibrational energy transfer among air species, increasing the range of applicability of the FHO-FR model.

Three-dimensional analytic model of vibrational energy transfer in molecule-molecule collisions

Three-dimensional analytic model of vibrational energy transfer in molecule-molecule collisions

Three-dimensional nonperturbative analytic model of vibrational energy transfer in atom–molecule collisions

A three-dimensional semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom has been developed. The model is based on analysis of classical trajectories of a free-rotating (FR) molecule acted upon by a superposition of repulsive exponential atom-to-atom potentials. The energy transfer probabilities have been evaluated using the nonperturbative forced harmonic oscillator (FHO) model. The model predicts the probabilities for vibrational energy transfer as functions of the total collision energy, orientation of a molecule during a collision, its rotational energy, and impact parameter. The model predictions have been compared with the results of three-dimensional close-coupled semiclassical trajectory calculations using the same potential-energy surface. The comparison demonstrates not only remarkably good agreement between the analytic and numerical probabilities across a wide range of collision energies, but also shows that the analytic FHO-FR model correctly reproduces the probability dependence on other collision parameters such as rotation angle, angular momentum angle, rotational energy, impact parameter, and collision reduced mass. The model equally well predicts the cross sections of single-quantum and multiquantum transitions and is applicable up to very high-collision energies and quantum numbers. Most importantly, the resultant analytic expressions for the probabilities do not contain any arbitrary adjustable parameters commonly referred to as “steric factors.” The model provides new insight into kinetics of vibrational energy transfer and yields accurate expressions for energy-transfer rates that can be used in kinetic modeling calculations.

A discrete-continuum hybrid model for vibrational energy transfer at the gas–solid interface. II. The quantal evolution of coupled localized-collective motions

We analyze a new approach to the vibration of inhomogeneous surfaces whereby surface defects and their surroundings are properly treated as discrete atoms while the remainder of the solid is represented by an elastic continuum of equivalent mass density and elasticity with quantized vibrational waves. Such a hybrid treatment is aimed at describing defect-local motion while fully coupled to collective vibrational waves in a quantum-mechanical fashion appropriate to inelastic gas–surface scattering. We assess how the hybrid model reproduces the response of the surface by following the quantum-statistical moments of vibrational displacements as the collision progresses. The results suggest that the discrete-continuum approach can provide a powerful tool for describing collisional excitation of defect-laden surfaces within a fully quantal treatment of surface motion.

A simple numerical model of vibrational energy transfer in polyatomic gases

A numerical procedure is developed for the accurate modelling of vibrational-vibrational and vibrational-translational energy transfer in molecular gases. The harmonic approximation necessary for an analytical solution is unnecessary and experimentally observed level energies are used. Rate constants, deduced by curve fitting results from this model to thermal lens data, are significantly different from those deduced from an analytical solution, e.g. for CO 2, k 1=350 Torr −1 s −1 and k 2 = 370 Torr −1 s −1 for the scheme CO 2(010) + CO 2(000) ⇌ CO 2(000) + CO 2(000), Δ H = − 667 cm −1 and CO 2(001) + CO 2(OOO) ⇌ CO 2 (030) + CO 2(000), Δ H = −417 cm −1, where k 1 and k 2 are the rate constants for the forward processes.

A hybrid model for vibrational energy transfer at the gas–solid interface: Discrete surface atoms plus a continuous elastic bulk

We introduce a discrete-continuum hybrid treatment of solid vibrations in order to describe the collisional excitation of adsorbate and defect modes by atom impacts. The inhomogeneous surface is represented by: (a) one or more atom clusters corresponding to the defect sites and their immediate neighbors, which are harmonically coupled to (b) an elastic continuous bulk. The model thus aims at reproducing the long-wavelength spectrum of the lattice as well as the high-frequency localized modes contributed by adsorbates and surface defects. The hybrid model is tested against lattice results in one-dimensional simulations that allow for analytic solution of the surface motion (which would be unfeasible for three-dimensional imperfect lattices); hybrid and lattice results are thus compared in detail under identical conditions. The model is also evaluated under the worst possible conditions for the continuum approximation, since collinear collisions correspond to three-dimensional situations in which the transferred momentum and, therefore, short-wavelength excitations are maximal. Comprehensive tests are presented for He atoms scattering from CO chemisorbed on Pt and on Ni substrates, and from N2 adsorbed on W. The scattering dynamics is treated by time-correlation functions of the transition operator previously developed for polyatomic targets [J. Chem. Phys. 84, 3162 (1987); 85, 2300 (1987); 86, 750 (1987)]. All the energetically open states are thus incorporated, as well as the thermal average over initial states, without need of basis-set expansions. Distributions of transferred energy are presented as would be observed in a one-dimensional scattering ‘‘experiment’’ using impact energies between 0.1 and 1 eV and with the solid at nonzero temperature. The collisional spectra obtained from the hybrid models are found to be in excellent agreement with those of the corresponding inhomogeneous lattices throughout wide ranges of impact velocity, surface initial temperature (including 0 K) and transferred energy. The results indicate that discrete-continuum treatments provide a powerful tool for analyzing the transfer of energy at the gas–adsorbate–solid interface.

Vibrational energy transfer study of C 6H 6 by IR-UV double resonance

Collision-induced vibrational energy transfer of benzene is studied by means of infrared-ultraviolet double resonance (IRUVDR). The time-dependent population and depopulation of the vibrational mode v 6 is measured after excitation of the vibrational mode v 18. The rate constant for v 18 → v 6 V-V energy transfer is obtained. The experiment.is also carried out using rare gases as collision partners. A simplified model for vibrational energy transfer is discussed.

Semiclassical three-dimensional model for vibrational energy transfer in diatomic molecules

A semiclassical model for calculation of rate constants for vibrational excitation in diatomic gases at low temperatures (below 1000 K) is suggested. The model has been tested by its ability to predict the relaxation times of hydrogen (τ H 1 in the temperature region 40–1000 K. The agreement with experimental values is excellent. The isotopic ratio τ D 2/τ H 2 as a function of temperature is predicted.

Semi-classical three-dimensional model for vibrational energy transfer in diatomic molecules

Semi-classical three-dimensional model for vibrational energy transfer in diatomic molecules

Simple quasi-accommodation model of vibrational energy transfer. Low-pressure thermal methyl isocyanide isomerization

Simple quasi-accommodation model of vibrational energy transfer. Low-pressure thermal methyl isocyanide isomerization