Vibrational Relaxation Of Diatomic Molecules Research Articles

Molecular dynamics simulation of the rate of dissociation and of the time of vibrational relaxation of diatomic molecules

A method is described for molecular dynamics calculation of the rate of dissociation and of the time of vibrational relaxation of N2 and O2 diatomic molecules, which involves simultaneous simulation of the entire ensemble of particles based on the classical concepts of the dynamics of molecules with internal degrees of freedom. Agreement between the calculation results and experimental data is discussed.

Towards parallel computing: representation of a linear finite state digital logic machine by a molecular relaxation process

A chemical system displaced not far from equilibrium is shown to offer a physical realization of a linear sequential digital logic machine. The requirement from the system is that its state is described by giving the current values of the concentration of different chemical species. The time evolution is therefore described by a classical master equation. The Landau-Teller process of vibrational relaxation of diatomic molecules in a buffer gas is used as a concrete example where each vibrational level is taken to be a distinct species. The probabilities (= fractional concentrations) of the species of the physicochemical system are transcribed as words composed of letters from a finite alphabet. The essential difference between the finite precision of the logic machine and the seemingly unbounded number of significant figures that could be used to specify a concentration is emphasized. The transcription between the two is made by using modular arithmetic that is, is the arithmetic of congruence. A digital machine corresponding to the vibrational relaxation process is constructed explicitly for the simple case of three vibrational levels. In this exploratory effort we use words of only one letter. Even this is sufficient to achieve an exponentially large number of memory states.

Semiclassical extension of the Landau-Teller theory of collisional energy transfer

A semiclassical version of the quantum coupled-states approximation for the vibrational relaxation of diatomic molecules in collisions with monatomic bath gases is presented. It is based on the effective mass approximation and a recovery of the semiclassical Landau exponent from the classical Landau-Teller collision time. For an interaction with small anisotropy, the Landau exponent includes first order corrections with respect to the orientational dependence of the collision time and the effective mass. The relaxation N(2)(v=1)-->N(2)(v=0) in He is discussed as an example. Employing the available vibrationally elastic potential, the semiclassical approach describes the temperature dependence of the rate constant k(10)(T) over seven orders of magnitude across the temperature range of 70-3000 K in agreement with experimental data and quantum coupled-states calculations. For this system, the hierarchy of corrections to the Landau-Teller conventional treatment in the order of importance is the following: quantum effects in the energy release, dynamical contributions of the rotation of N(2) to the vibrational transition, and deviations of the interaction potential from a purely repulsive form. The described treatment provides significant simplifications over complete coupled-states calculations such that applications to more complex situations appear promising.

Existence of the Bottleneck in Vibrational Relaxation of Diatomic Molecules

Existence of the Bottleneck in Vibrational Relaxation of Diatomic Molecules

Existence of the Bottleneck in Vibrational Relaxation of Diatomic Molecules

High-temperature vibrational relaxation of diatomic molecules is analyzed using master equation and Fokker‐ Planck diffusion equation modeling. Both approaches are based on the nonperturbative forced harmonic oscillator vibrational energy transfer rate model. The results show that the effect of the retarded diffusion at the intermediate vibrational energies during the relaxation process (bottleneck), predicted in the previous studies, does not exist at the high temperatures. It is also shown that the interpretation of the high-temperature vibrational relaxation as a diffusion-type process is inadequate because of the strong effect of multiquantum energy transfer. The obtained results, applied to interpretation of the rates of thermal dissociation, suggest an important role of rotations in molecular activation at the high vibrational energies.

Existence of the bottleneck in vibrational relaxation of diatomic molecules

Existence of the bottleneck in vibrational relaxation of diatomic molecules

Vibrational relaxation of diatomic molecules in liquids

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTVibrational relaxation of diatomic molecules in liquidsCharles B. Harris, David E. Smith, and Daniel J. RussellCite this: Chem. Rev. 1990, 90, 3, 481–488Publication Date (Print):May 1, 1990Publication History Published online1 May 2002Published inissue 1 May 1990https://doi.org/10.1021/cr00101a003RIGHTS & PERMISSIONSArticle Views352Altmetric-Citations125LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts Get e-Alerts

Generalized Brownian dynamics. II. Vibrational relaxation of diatomic molecules in solution

A simple classical stochastic model for diatomic vibrational relaxation, based on the generalized Langevin equation, is presented. The memory function in the generalized Langevin equation is determined directly from equilibrium force autocorrelation functions for the individual atoms of the diatomic dissolved in the solvent of interest. A simple autoregressive (AR) procedure, developed in a preceding paper [D. E. Smith and C. B. Harris, J. Chem. Phys. 92, xxx (1990)], is used for modeling the memory functions to arbitrary order. This model is tested on the system of iodine in Lennard–Jones xenon using fourth order AR approximations for the memory functions, and is found to be very effective in reproducing data from molecular dynamics simulations at two very different densities. Results are discussed in terms of the simplifying assumption that the solvent interaction with the diatomic can be characterized by equilibrium dynamics of single atoms in solution.

The role of rotation in the vibrational relaxation of diatomic molecules

The mechanism by which molecular rotation enhances vibrational relaxation of a diatomic molecule is examined. Three factors are discussed, lowering by rotational transitions of the vibrational energy defect, coupling due to potential matrix elements off-diagonal in rotational state, and additional phase shifts introduced into the incoming and outgoing waves by anisotropy in the intermolecular potential. The distorted wave solution of the coupled states scattering equations elucidates, for H 2(ν = 1)-He and CO(ν = 1)-H 2, the importance of each factor. For H 2He, rotation plays both an energetic and a dynamical role. In the energetic role, rotation of the H 2 lowers the vibrational energy defect and thereby enhances vibrational relaxation. The dynamic contribution takes the form of additional phase shifts introduced into the incoming and outgoing waves by the potential anisotropy. For the relaxation of CO(ν = 1) by H 2, rotational enhancement by H 2 is almost entirely due to lowering of the vibrational energy defect. Our results suggest that molecular anisotropy, particularly in the region of the classical turning point, is an important factor in the rotational enhancement observed in recent comparisons of CSA and IOSA vibrational relaxation rate constants for the N 2He and COHe systems. We further discuss vibrational energy transfer from H 2(ν = 1) to CO(ν = 0, 1, 2). In this case, the role played by H 2 rotation changes markedly as a function of the final CO vibrational state.

Determination of Rate Constants for Vibration‐to‐Vibration Energy Transfer

AbstractThe rate equation lor vibrational relaxation of diatomic molecules is generalized by considering microscopic rate coefficients of the form kα(v + 1)e−C|ΔE|. It is shown that for most molecules of interest the rate equation reduces analytically to the form previously obtained. The consequences of its use and misuse are discussed. A prescription is given for extracting V V rate constants from rate data.

A simple reason for non-linear mixture rules in chemical kinetics. Part 1. Vibrational relaxation of diatomic molecules

The generalized rate law for the vibrational relaxation of diatomic molecules is extended to include inert collision partners. V–V energy transfer processes are accounted for explicitly as are thermal effects. The molecules are treated as Morse oscillators as far as energetics are concerned; however, the microscopic rate constants are Landau–Teller type. It is found that the phenomenon of non-linear mixture rules arises when experimental data are forced to fit a first-order rate law. The persistence of V–V processes at times well-advanced into the relaxation zone is responsible for deviations from linearity. The non-linearities are most pronounced at high temperatures, and can be avoided only by using extremely dilute mixtures. Several sources of ambiguity are pointed out. The type of excitation method influences the initial deviation from a Boltzmann distribution and plays a crucial role in determining the importance of V–V processes and hence the degree of non-linearity. Thus, when the initial distribution is Boltzmann as in shock waves, the mixture rule is found to be absolutely linear for the vibrational relaxation of diatomic molecules.Several examples, heretofore not recognized as such, are pointed out in the literature.

Vibrational relaxation of diatomic molecules: Anharmonic oscillators in a Boltzmann thermostat. Single-component system

Vibrational relaxation of diatomic molecules: Anharmonic oscillators in a Boltzmann thermostat. Single-component system

On rotational and vibrational relaxation of diatomic molecules and a quasi-classical model for rotational relaxation

Differences between vibrational and rotational relaxation patterns disappear and similarities are revealed by transforming from state to energy distribution. This follows from the constant state density of both oscillators and rotors and the exponential gap law governing their relaxation. A simple, parameter-free, rotational model which agrees well with previous results is formulated.

Microscopic and macroscopic analysis of non-linear master equations : vibrational relaxation of diatomic molecules

The thermodynamic and kinetic characteristics of vibrational relaxation of diatomic molecules are studied using HF gas as a model system. The non-linear master equation governing the relaxation is solved numerically using a comprehensive set of exponential gap rate constants. The results indicate a two-stage relaxation mechanism. A very fast V-V dominated stage leading to an intermediate quasi-equilibrium distribution which depends only on the initial mean number of vibrational quanta. During this stage the vibrational distribution can be described as a superposition of the initial and intermediate distributions. A second, very slow, V-T dominated stage ultimately brings the system to complete equilibrium with the heat bath. The relaxation is characterized microscopically by the time evolution of the vibrational distribution and macroscopically by the evolution of the moments. The bridge between the two levels of analysis is provided by the maximal entropy procedure. It is shown that the entropy deficienc...

Vibrational relaxation of diatomic molecules in a non-Boltzmann thermostat

The action of resonance IR laser radiation on a molecular gas leads, at high-power absorption intensity, to a breakdown in the equilibrium (Boltzmann) energy distribution in the internal degrees of freedom [1]. Under realistic conditions, molecular gases usually are (due to small amounts of impurities or isotopic components) multicomponent systems. In this case resonance IR laser radiation (or other methods of selective action), disturbing the distribution function of the primary gas, does not interact directly with impurities. The problem thus arises of determining the distribution function of the impurity gas interacting with the nonequilibrium (non-Boltzmann) thermostat. The present paper, devoted to the solution of this problem, treats the distribution function of harmonic oscillators A, consisting of a small amount of impurities in a system of harmonic oscillators B with given nonequilibrium distribution functions of vibrational energy. The behavior of a system in a nonequilibrium thermostat was first considered in [2, 3] where, as well as in [4, 5], it was shown that in a non-Maxwellian thermostat with a small amount of harmonic oscillator impurities, a Boltzmann distribution in harmonic oscillator vibrational energies is established under stationary conditions, with a temperature differing from the gas-kinetic temperature of the thermostat, defined in terms of the mean-square velocity. The behavior of a small amount of impurities (heavy monoatomic particles and harmonic oscillators) in a non-Maxwellian thermostat of a light gas was further investigated in [6–8]. Unlike the papers mentioned, the present one considers the behavior of a small amount of harmonic oscillator impurities in a thermostat with a Maxwellian velocity distribution and with a nonequilibrium (non-Boltzmann) distribution in vibrational energies.

Vibrational relaxation of diatomic molecules in condensed monatomic media

A model based on binary-like collisions is presented to describe the vibrational relaxation of diatomic molecules in a monatomic medium. For N 2Ar and COAr, it is shown that the oscillatory motion of host atoms undergoing multiquantrum processes is most important in removing vibrational energy. The translational motion of molecules confined to the cell space also contributes to the energy relaxation by removing the energy mismatch.

On the vibrational relaxation of diatomic molecules at intermediate excitation

The theory of quasistationary vibrational distributions of diatomic molecules at low gas temperatures is developed for the case of intermediate excitation temperatures when the flow of quanta is nondiffusional in Treanor's part of the distribution. In certain conditions the distribution contains a region of inversion which is followed by a plateau.

Vibrational Relaxation of Diatomic Molecules in Complex Forming Collisions with Reactive Atoms

Vibrational Relaxation of Diatomic Molecules in Complex Forming Collisions with Reactive Atoms

Vibrational relaxation of diatomic molecules

Vibrational relaxation of diatomic molecules

Model for vibrational relaxation of diatomic molecules in simple monatomic liquids

A simple quantum-mechanical model for the nonradiative vibrational relaxation of a diatomic molecule in a monatomic liquid is developed. The rotation of the diatomic is neglected and it is assumed that only collinear collisions are responsible for the relaxation. The many-body states of the liquid are determined using a cell model and the cell potential is approximated as an infinite square well. The Fermi golden rule for the rate of vibrational relaxation is simplified to obtain a closed expression exhibiting explicit dependences upon the temperature and upon microscopic properties of the system. This expression is then used to predict the vibrational relaxation rates of some selected diatomic molecules (H 2, D 2, O 2, N 2, CO) in liquid rare gases (Ne and Ar).