Brillouin scattering in oligobutene

The quantum mechanical relaxation rate for a high-frequency vibrational mode is evaluated for a one-dimensional model system having two diatomic molecules involved in a collinear collision. The thermally averaged rate is obtained as an integral over energies for the relative translation of the two molecules. These calculations show that energies several times K(B)T make the largest contributions to the rate. Several orders of magnitude of cancellation due to phase interference is found in the evaluation of the coupling matrix elements between the initial and final states, and this is one of the main factors leading to the very small value for the relaxation rate. The region near the classical turning point in the relative translational motion of the colliding molecules dominates the calculation of the contribution to the rate at each energy. Calculations using low-order expansions of the translational potential energy and the interstate coupling about this turning point provide good approximations to the exact quantum mechanical rate. This suggests a possible method for performing calculations of the rate by means of realistic simulations of liquid systems.

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On the Importance of the Classically Forbidden Region in Calculations of the Relaxation Rate for High-Frequency Vibrations: A Model Calculation

Herman

Ding

2007

J. Phys. Chem. A

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Solvent induced vibrational relaxation in diatomics. I. Derivation of a local relaxation rate

Herman

1987

The Journal of Chemical Physics

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Articles you may be interested inSemiclassical surfacehopping approximations for the calculation of solventinduced vibrationalrelaxation rate constants Theory of vibrational energy relaxation in liquids: Diatomic solutes in monatomic solvents J. Chem. Phys. 88, 4415 (1988); 10.1063/1.453800 Solvent induced vibrational population relaxation in diatomics. II. Simulation for Br2 in ArA local rate is derived for the vibrational population relaxation of a diatomic in a simple liquid or dense gas. The total relaxation rate of the system is obtained as the canonical ensemble average of the local rate. The rate expression is amenable to computer simulations in which the canonical average is performed by a Monte Carlo procedure. The vibrational motion is separated from the other degrees of freedom by an adiabatic approximation which treats the vibration as fast compared with the other motions. The adiabatic vibrational energies and the nonadiabatic couplings between vibrational states depend on the solvent configuration. These vibrational energies and couplings are obtained from quantum perturbation theory. The transitions between vibrational states are described semiclassically and the canonical averaging uses the classical canonical density for solvent configurations. The resulting procedure is a mixed quantum-semiclassical-dassical simulation technique.

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Solvent induced vibrational population relaxation in diatomics. II. Simulation for Br2 in Ar

Herman

1987

The Journal of Chemical Physics

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Results are presented from a computer simulation of the population relaxation of the lowest (1→0) vibrational transition for a system of Br2 in a dense Ar fluid at 300 K. The calculate relaxation time is 253 ps. The method of calculation is a mixed quantum–semiclassical–classical simulation procedure. The vibrational state energies and wave functions are obtained from perturbation theory for fixed values of the rotational and translational variables. The relaxation rate for the vibrational transition is evaluated using a semiclassical surface hopping theory of nonadiabatic processes. The configurations of rotational and vibrational variables are sampled from a classical canonical ensemble density using standard Monte Carlo sampling. The relative efficiency of the rotations and translations in promoting the vibrational population relaxation is examined, and the use of perturbation theory and some assumptions of the model are tested numerically.

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Brillouin scattering in oligobutene

Cited by 3 publications

References 13 publications

On the Importance of the Classically Forbidden Region in Calculations of the Relaxation Rate for High-Frequency Vibrations: A Model Calculation

On the Importance of the Classically Forbidden Region in Calculations of the Relaxation Rate for High-Frequency Vibrations: A Model Calculation

Solvent induced vibrational relaxation in diatomics. I. Derivation of a local relaxation rate

Solvent induced vibrational population relaxation in diatomics. II. Simulation for Br2 in Ar

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