Effects of Hydrodynamic Backflow on the Transmission Coefficient of a Barrier-Crossing Brownian Particle

Abstract

The slow power law decay of the velocity autocorrelation function of a particle moving stochastically in a condensed-phase fluid is widely attributed to the momentum that fluid molecules displaced by the particle transfer back to it during the course of its motion. The forces created by this backflow effect are known as Basset forces, and they have been found in recent analytical work and numerical simulations to be implicated in a number of interesting dynamical phenomena, including boosted particle mobility in tilted washboard potentials. Motivated by these findings, the present paper is an investigation of the role of backflow in thermally activated barrier crossing, the governing process in essentially all condensed-phase chemical reactions. More specifically, it is an exact analytical calculation, carried out within the framework of the reactive-flux formalism, of the transmission coefficient κ­(t) of a Brownian particle that crosses an inverted parabola under the influence of a colored noise process originating in the Basset force and a Markovian time-local friction. The calculation establishes that κ­(t) is significantly enhanced over its backflow-free limit.

Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects

“…However, the assumption of instantaneous friction, employed in early theories, breaks down whenever there is no pronounced separation between time scales of fast solvent relaxation and slow diffusion along the reaction coordinate, which is the case even for the simplest pair reactions in water. , One strategy is to circumvent such non-Markovian effects and to reduce friction memory by using suitable multidimensional reaction coordinates that explicitly account for solvent degrees of freedom. − Alternatively, the generalized Langevin equation (GLE), , which explicitly accounts for time-dependent friction due to solvent relaxation, can be used to model reaction rates − and transition-path times. − …”

“… 10 , 11 One strategy is to circumvent such non-Markovian effects and to reduce friction memory by using suitable multidimensional reaction coordinates that explicitly account for solvent degrees of freedom. 12 − 15 Alternatively, the generalized Langevin equation (GLE), 16 , 17 which explicitly accounts for time-dependent friction due to solvent relaxation, can be used to model reaction rates 18 − 34 and transition-path times. 35 − 37 …”

Molecular hydrodynamic theory of the velocity autocorrelation function

“…[121][122][123] Memory kernel reconstruction methods 36,38,41 may, for instance, enable data-driven insights into these connections, helping to extend the present methodology to driven hydrodynamic Brownian motion in complex fluids. [123][124][125][126][127][128][129][130][131] Also fruitful would be to explore applications to supercooled, [132][133][134][135] supercritical, [136][137][138] and ionic and dielectric fluid systems. 76,[139][140][141][142][143][144] In the case of a dilute gas, a → a 0 .…”