Quantum harmonic transition state theory—Application to isomerization of stilbene in liquid ethane

Abstract

A harmonic quantum transition state theory, suggested recently by Pollak and Gershinsky ͓in Lectures on Stochastic Dynamics, edited by W. Lutz and T. Poeschel, Lecture Notes in Physics ͑Springer Verlag, New York, 1997͔͒, is applied for the first time to a realistic reacting system. The isomerization of trans-stilbene in the gas phase and in the presence of dense liquid ethane solvent is investigated. We find that the overall quantum effect at room temperature is rather small. The quantum correction to the classical reaction rate estimate is approximately 23% for gas phase stilbene at room temperature. The addition of the dense solvent lowers the correction down to 13%, thus making the reacting system even more ''classical,'' justifying the extensive use of classical molecular dynamics in investigating this reaction.

Viscosity dependence and solvent effects in the photoisomerization of cis-stilbene: Insight from a molecular dynamics study with an ab initio potential-energy function

“…[13][14][15][16] However, this procedure has little predictive power, since the desired results are put in previously, and then reproduced. Moreover, Eli Pollak and co-workers [17][18][19][20] apply sophisticated theories, based on transition state theory, to the photoisomerization of trans-stilbene. This reaction differs from cis-stilbene insofar that it is most probably thermally activated.…”

“…If we take the rule of thumb and say if បӶk B T, then the motion is classical, we must admit that both quantities are almost equal in the case of the cis-stilbene photoisomerization. However, Gershinsky and Pollak 20 report that the influence of quantum effects is small, especially in condensed systems, and that classical molecular dynamics can be relied upon.…”

Theoretical Investigation of the Mechanism of the Water–Gas Shift Reaction on Cobalt@Gold Core–Shell Nanocluster

“…To calculate the rate constants, we employed harmonic transition state theory (hTST) k = v * nobreak0em0.25em⁡ exp ( − E a k B T ) where E a is the activation energy, k B is the Boltzmann constant, T is the temperature in Kelvin, and v * = k normalB T h ∏ i = 1 D [ 1 − exp true( − ℏ ω i normalR k normalB T true) ] ∏ i = 1 D [ 1 − exp true( − ℏ ω i normalS k normalB T true) ] is the quantum mechanically modified form of the prefactors, where D , ω i R , and ω i S are the number of normal modes and the nonimaginary vibrational frequencies of the i th mode in the reactants and saddle-point states, respectively.…”

“…All chemical species were verified by the vibrational frequencies of the adsorbed structures, which were analyzed by diagonalizing the Hessian matrix of selected atoms within the VASP approach. Atomic charges of the selected structures were calculated by utilizing Bader charge 81,82 analysis with a program designed by Henkelman et al 83 To calculate the rate constants, we employed harmonic transition state theory (hTST) 84…”

On the possibility of the Observation of Intramolecular Reaction Dynamics in Liquids by Time-resolved X-ray Scattering

“…The characteristic (quenched) fluorescence varies with the experimental conditions (e.g. gas-jet experiments, pressure-experiments in the liquid phase or studies on stilbene derivatives) between femtoseconds and some picoseconds [19][20][21][22][23][24][25][26][27][28][29][30]. The reaction scheme is complicated by the fact that the formed cis-product can also be excited in the next step of a repetitive experiment (not shown in Fig.…”