Marcus originally derived the Marcus equation to predict Brønsted coefficients for electron-transfer reactions. However in the literature it is often assumed that Marcus' result can be extended to predict positions of the transition state for atom-transfer reactions. In this paper we use ab initio methods to examine the potential energy surface and transition state of a series of hydrogenolysis reactions of the form H• + CH3CH2R → CH4 + •CH2R, with R = H, CH3, CF3, CN, NH2, and C5H6, in order to see if the Marcus equation can be extended to atom-transfer reactions. The calculations show that the molecular orbitals of the system look “reactant-like” moving up the potential energy surface toward the transition state, and then switch to “product-like” moving down to products, in qualitative agreement with what one would expect from the Marcus equation. However, the curve crossing from “reactant-like” to “product-like” molecular orbitals does not occur at the saddle point in the potential energy surface. Rather the curve crossing occurs at a point part way down to products. Also most of the barrier to reaction is associated with rearrangements of the electron clouds due to Pauli repulsions when the reactants come together and not with the bond destruction and bond formation processes. These rearrangements are not considered in the Marcus equation. We do not yet know if our results are special to the reactions here or are general. However, it does appear that some key physics is missing when one extends the Marcus model to atom- or ligand-transfer reactions. One can represent the key physics with a modified bond additivity potential, however.

This paper describes a sliding-mode observer design for state estimation of a motorized seat belt (MSB) system. The MSB system is an active safety system that can protect passengers and improve passenger convenience by several operations, which prevent and warn to passengers about dangerous driving conditions and reduce the dangerous situation caused by slack and poor return of seat belt. To realize these operations, state information such as the belt winding velocity and tension of belt are required. However measuring this information with sensors increases the system cost and complexity. In this paper, a sliding-mode observer, which estimates requisite state information, is proposed. The designed sliding-mode observer is robust towards system uncertainties and parameter variation and is verified in matched and mismatched parameter cases.