Short Time Scale Dynamics and the Correlation between Liquid and Gas Phase Vibrational Energy Relaxation Rates

Computational design of faster rotating second-generation light-driven molecular motors by control of steric effects

We report a systematic computational investigation of the possibility to accelerate the rate-limiting thermal isomerizations of the rotary cycles of synthetic light-driven overcrowded alkene-based molecular motors through modulation of steric interactions. Choosing as a reference system a second-generation motor known to accomplish rotary motion in the MHz regime and using density functional theory methods, we propose a three-step mechanism for the thermal isomerizations of this motor and show that variation of the steric bulkiness of the substituent at the stereocenter can reduce the (already small) free-energy barrier of the rate-determining step by a further 15-17 kJ mol(-1). This finding holds promise for future motors of this kind to reach beyond the MHz regime. Furthermore, we demonstrate and explain why one particular step is kinetically favored by decreasing and another step is kinetically favored by increasing the steric bulkiness of this substituent, and identify a possible back reaction capable of impeding the rotary rate.

Short time scale dynamics and a second correlation between liquid and gas phase chemical rates: diffusion processes in noble gas fluids

A theoretical formula for single-atom diffusion rates that predicts an isothermal correlation relation between the liquid (l) and gas (g) phase diffusion coefficients, D(T, ρl) and D(T, ρg) is developed. This formula is based on a molecular level expression for the atom’s diffusion coefficient, D(T, ρ), and on numerical results for 1715 thermodynamic states of 25 rare gas fluids. These numerical results show that at fixed temperature, T, the decay time, τDIF, which governs the shortest time decay of an appropriate force autocorrelation function, F(t) F0, is density (ρ)-independent. This independence holds since τDIF arises from the ρ-independent shortest time inertial motions of the solvent. The ρ independence implies the following l−g diffusion coefficient correlation equation: D−1(T, ρl) = (ρl/ρg) D−1(T, ρg) [ρl−1F0,l2/ρg−1F0,g2]. This relation is identical in form to the familiar (isolated binary-collision-like) empirical correlation formula for vibrational energy relaxation rate constants. This is because both correlation relations arise from inertial dynamics. Inertial dynamics always determines short-time fluid motions, so it is likely that similar correlation relations occur for all liquid phase chemical processes. These correlation relations will be most valuable for phenomena dominated by short time scale dynamics.