Molecular dynamics are computed for a model SN2 reaction Cl−+CH3Cl→ClCH3+Cl− in water and are found to be strongly dependent on the instantaneous local configuration of the solvent at the transition state barrier. There are significant deviations from the simple picture of passage over a free energy barrier in the reaction coordinate, and thus, a marked departure from transition state theory occurs in the form of barrier recrossings. Factors controlling the dynamics are discussed, and, in particular, the rate of change of atomic charge distribution along the reaction coordinate is found to have a major effect on the dynamics. A simple frozen solvent theory involving nonadiabatic solvation is presented which can predict the outcome of a particular reaction trajectory by considering only the interaction with the solvent of the reaction system at the gas-phase transition barrier. The frozen solvent theory also gives the transmission coefficient κ needed to make the transition state theory rate agree with the outcome of the molecular dynamics trajectories. This theoretical κ value, which is the implementation for the SN2 reaction of the van der Zwan–Hynes nonadiabatic solvation transmission coefficient, is in good agreement with the trajectory results. In contrast, a Kramers theory description fails dramatically.
AppendixVibrational state densities for c~clo~entene, l-meth~lc~clo-pentene, and vinylcyclopropane were computed from harmonic oscillator models by exact count.'9 Fundamental vibrational wavenumbers used were: ~yclopentene(2), 50. In methylcyclopropane and vinylcyclopropane the methyl and vinyl groups were treated as torsional vibrations of 170 and 5o cm-l, respectively. Registry No.A method is illustrated for computing the contours of electronic absorption bands from classical equilibrium or nonequilibrium molecular dynamics (or equally for equilibrium systems from Monte Carlo or explicit integration over coordinates). The inputs to the calculations are the potential energy curves for the different electronic states and the electronic transition dipole moments between the states as functions of nuclear coordinates. A simple quantum correction by temperature scaling is demonstrated for the thermal equilibrium case. A test is carried out for the I2 visible absorption spectrum involving transitions from the ground X Og+('Z) to the excited A lJ311), B 0,,t(311) and B" l,,('II) states, for thermal equilibrium gas-phase 12.The electronic band contours are computed and shown to be remarkably similar to the measured contours. This method and others such as the methods of Lax, Lee, Tellinghuisen, and Moeller and the Landau-Zener-Stuckleberg-Tully-Preston surface hopping approach are shown all to be mutually equivalent, while the usual reflection method is shown to be related but nonequivalent.
An analytic theory for SN2 reactions in polar solvents in the nonadiabatic solvation limit is presented and used to interpret the computer simulation results of the preceding paper by Bergsma et al. The theory is based on the nonadiabatic solvation limit of previous studies by van der Zwan and Hynes and incorporates the solvent approximately but explicitly via a coordinate additional to the intrinsic reaction coordinate. Central results include: an explicit expression for the reaction transmission coefficient κ, the dependence of reaction probability on kinetic energy, the interpretation of κ in terms of nonequilibrium solvation entropy effects, and the deviation of the reaction coordinate from that assumed in the standard equilibrium solvation transition state theory view of the reaction.
Molecular dynamics are computed for model atom transfers A+BC→AB+C in rare gas solvents at liquid densities. We find that the reaction dynamics can be understood in terms of a simple picture which consists of three stages: (1) activation of reactants, (2) barrier crossing, and (3) deactivation of products. The effects seen in stages (1) and (3) can be largely interpreted in terms of existing models of energy and phase decay in solution, while the effects seen in stage (2) can be largely interpreted in terms of gas phase A+BC barrier crossing dynamics. We find that transition state theory is in perfect agreement with the simulations for the 20 and 10 kcal/mol barrier reactions and is a very good description for a 5 kcal/mol reaction barrier. At low barrier curvature, dynamical effects due to the solvent are shown to induce some recrossings of the transition state barrier, thus causing rate constants calculated by simple transition state theory to be slightly too high. The Grote–Hynes modification of transition state theory, which considers the effect of the time dependent friction of the solvent on the dynamics at the transition state, predicts corrections to the rate constants in good agreement with the results from the simulations.
The nitrogen and β-hydrogen hyperfine splitting constants (hfsc) for phenyl, 4-nitrophenyl, 4-pyridyl, benzoyl, and trichloromethyl spin adducts of α-phenyl tert-butyl nitrone (PBN) as well as for the tert-butoxyl adduct of 5,5-dimethylpyrroline-N-oxide (DMPO) have been obtained as a function of solvent (30 solvents). A useful linear relationship between the β-H hfsc and the N-hfsc of each aminoxyl is found except for the benzoyl adduct of PBN. Some speculations regarding the structural significance of these correlations is presented.
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