Theory of vibrational energy transfer between simple molecules in nonreactive collisions (original) (raw)
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Energy transfer in collisions between two vibrating molecules
Chemical Physics Letters, 1985
We study vrbrarional energy transfer in rnelastic collmear collisions betBeen IWO diaromrc molecules The system is represemed by IWO linearly driven parametric oscillators with a bilinear_ time-dependent residua1 coupling between them. We amu& for Ihe time evolution of the Irncarly dnvcn par;lmetric osciilarow with an operator algebra. and use perturbation theory and basis expansions LO include the residual couphng Rcsulls are prcserued Ior H,-FH and N2-CO. Direct twequantum transitions are found to be important even Zor low relst~rr collrs~on enrrgics.
Progress on the modeling of the collisional energy transfer mechanism in unimolecular reactions
Berichte der Bunsengesellschaft für physikalische Chemie
Words: Computer Experiments / Elementary Reactions / Energy Transfer / Molecular Collisions Statistical Theory The RRKM theory of unimolecular reaction rates is a statistical mechanical theory based on an assumption of microcanonical equilibrium in the reactant phase space. The energy transfer in reactant medium collisions was originally described by a canonical strong collision assumption, i.e., an assumption of full thermal equilibration in each collision. In our work we first introduce a microcanonical strong collision assumption which gives the RRKM theory a consistent form. we then introduce parametrizations of the degree of weakness (nonergodicity) of the collisions. A concept of collision efficiency is defined. The weakness of the collision is expressed in terms of reduced subsets of active reactant and medium degrees of freedom. The corresponding partially ergodic collision theory (PECT) yields physical functional forms of the collisional energy transfer kernel P (E ' , E). In order to resolve the energy and temperature dependence and the dependence on interaction strength a multiple encounter theory is introduced (PEMET). Initially each encounter may be described by a semiempirical PECT model. Eventually the encounters may be resolved by quantum dynamical calculations of the semiclassical or CAQE (classical approach/quantum encounter) type. Simple statistical collision models only distinguish between "hits and misses". In reality the energy transfer efficiency exhibits characteristic fall off with increasing impact parameter b. This b-dependence can be explicitly accounted for in the master equation for the reaction rate coefficient.
A molecular dynamics investigation of energy transfer efficiency in collisions of diatomic molecules
Chemical Physics, 1993
Diatomic collisional energy transfer has been studied wtth the aim of aiding the development of accurate representation of the activation-deactivation mechanism in gas phase reaction rate theory. We seek to determine the dependence of the energy transfer efficiency on the parameters describing the colliding molecules, i.e. mass, vibrationaf frequency, inte~olecular potential and initial energy or temperature. While weak van der Waals type interactions give rise to very poor energy transfer efftciency scaling up the mteractions to the strength of weak chemical bonds increases the energy transfer efftciency dmmatic~ly up to nearly statistical bmit values. The dependence on mass and vibrattonal frequency is found to be weaker. The interaction strength is resolved into two factors, hardness of encounter and attractive strength. Varying these factors independently by a modification of the intermolecular atomic pair potential, both are found to contribute strongly to the observed energy transfer efftciency. Two temperatures, 160 and 1500 K, are consIdered and the sensitivity to the lntermo~ecuiar potential 1s found to be distinctly greater at the lower temperature. The average energy transferred per colliston (AE) is obtamed as a function of the internal energy of the target molecule at normal and high interaction strength.
Zeitschrift für Physikalische Chemie, 2015
The relation between time-dependent population of vibrational state and collision-induced state-to-state rate coefficients is discussed within the Landau–Teller kinetic equations for the relaxation of harmonic oscillators in a heat bath. In particular, the increase of the populations in the first and the second vibrational state of an initially cold oscillator shows a considerable variety of its relation to a single Landau–Teller state-to-state rate coefficient. It is suggested that this variety should be kept in mind when experimental studies of the relaxation of specific level are analyzed.
Chemical Physics Letters, 1999
An analytical expression is derived for average vibrational energy lost or gained D E per collinear collision of an v atom and a diatom. The derivation, based on classical mechanics, uses the perturbative method of the variation of constants ² : and is valid in the weak coupling limit. Second-order results for D E are obtained in terms of power spectra of the v uncoupled vibrational and translational degrees of freedom. The classical results are compared to perturbative quantum calculations, and differences between the two are described.
A Symmetrization Rule for Collision Energies in Molecular Vibrational Transitions
In order to reduce the discrepancies between first-order transition probabilities (P) relevant to inelastic-molecular-collision problems as calculated using classical (C) models and the quantum-mechanical (QM) results, ZE~]~R (1,~) first suggested a (~ symmetrization rule ~) for the relative collision velocity v of a molecular system exercising vibrational transitions and translational energy variations dining the collision. Quantummechanical expressions for transition probabilities depend on both the initial and final molecular velocities vi and vf characterizing the inelastic reaction channel, while classical and semi-classical expressions only depend on a unique collision velocity v, since the translational energy of the system is supposed to be conserved in classical models. Z~ER noted that, if in the classical expression of the transition probability Pc(v) the velocity v is replaced by (vi + v~)/2, i.e. the arithmetical mean between the initial and final velocities, the classical result is found notably to approach the quantum mechanical result, so that Since in classical mechanics the distance x covered in the time interval T by a particle with constant acceleration a and initial velocity vi is (2) x(T) ~-vlT +-aT ~ --T 2 2 '
Possible quantum effects in collisional energy transfer in highly excited molecules
Chemical Physics Letters, 1990
It has been observed that classical trajectory calculations of energy transfer rates in large highly excited molecules with He bath gas give values much higher than experiment. This might be caused by quantum effects in which contributions from higher partial waves do not contribute to energy transfer. Experimental means of testing this postulate are proposed.
Theoretical investigation of collisional energy transfer in polyatomic intermediates
International Reviews in Physical Chemistry, 2013
Quantum scattering calculations on collisional rotational and vibrational energy transfer in small hydrocarbon reactive intermediates are highlighted. This review focuses on recent theoretical studies of energy transfer in methylene (CH 2 ), in both its ground tripletX 3 B 1 and low-lying singletã 1 A 1 electronic states, and in the methyl (CH 3 ) radical. Propensities in the state-to-state cross sections are shown to depend upon the two types of anisotropies that are present in potential energy surfaces of systems involving nonlinear polyatomic molecules. Computed rate constants for rotational and vibrational relaxation are compared with available experimental data. In addition, collisional transfer between the CH 2X andã states is addressed. Collision-induced intersystem crossing is shown to be mediated by spectroscopically perturbed rotational levels of mixed electronic character.