Random activation energy model and disordered kinetics, from static to dynamic disorder.

We suggest a unified path integral approach for random rate processes with random energy barriers, which includes systems with static and dynamic disorder as particular cases. We assume that the random component of the activation energy barrier can be described by a generalized Zubarev-McLennan nonequilibrum statistical ensemble that can be derived from the maximum information entropy approach by assuming that the time history of the fluctuations of the random components of the energy barrier are known. We show that the average survival function, which is an experimental observable in disorderd kinetics, can be computed exactly in terms of the characteristic functional of this generalized Zubarev-McLennan nonequilibrium statistical ensemble. We investigate different types of disorder described by our approach, ranging from static disorder with infinite memory to random processes with long or short memory, and finally to rapidly fluctuating independent random processes with no memory. We derive expressions of the average survival function for all these types of disorder and discuss their implications in the evaluation of kinetic parameters from experimental data. We illustrate our approach by studying a simple model of dynamic disorder of the renewal type. Finally we discuss briefly the implications of our approach in molecular biology and genetics.

Nonradical mechanisms for the uncatalyzed thermal functionalization of silicon surfaces by alkenes and alkynes: a density functional study.

We propose a new concerted mechanism for the uncatalyzed hydrosilylation of terminal alkenes and alkynes, alternative to the conventional radical-based mechanism. Density functional calculations have been carried out on these and on previously proposed alternative mechanisms for the hydrosilylation of ethylene and acetylene by suitable finite size clusters as models of the thermal functionalization of -SiH3, =SiH2, and [triple bound] SiH groups in flat Si(100) and Si(111) and porous silicon surfaces by alkenes and alkynes. For each step involved in the considered hydrosilylation pathways, we optimized the geometries of reactants and products and located the corresponding transition states. The calculated activation energies for the concerted pathways of ethylene and acetylene are, respectively, 57.6 and 60.9 kcal mol(-1) on -SiH3 and in the ranges 62-63 and 58-61 kcal mol-1 on =SiH2 and 64-66 and 56-61 kcal mol(-1) on SiH. These values are much lower than the activation energies calculated for the corresponding homolytic dissociation of the Si-H bond, which is the preliminary step in the radical path, 85.6, 82-83, and 79-81 kcal mol(-1), respectively, for -SiH3, =SiH2, and [triple bound] SiH groups. Our results thus suggest that the thermal hydrosilylation of alkenes and alkynes on silicon surfaces, for which a radical-based mechanism is currently accepted, may occur through a concerted mechanism.