Initial oxidation and hydroxylation of the Ge(100)-2 x 1 surface by water and hydrogen peroxide

We use density functional theory to investigate the surface chemistry of initial oxidation and hydroxylation of the Ge(100)-2 x 1 surface by water and hydrogen peroxide. Comparison of the reaction of water on the Si(100)-2 x 1 and Ge(100)-2 x 1 surfaces shows that the kinetics of oxidation of the Ge(100)-2 x 1 surface with water is slower. Our calculations also show that oxidation products on the Ge(100)-2 x 1 surface are less thermodynamically stable than on Si. We also investigate two competing dissociation reactions of H2O2 on the Ge(100)-2 x 1 surface. We find that dissociative adsorption via cleavage of the OH bond is less exothermic than OO dissociation. Furthermore, interdimer OO dissociation has a lower activation barrier than interdimer or intradimer OH dissociation, although interdimer dissociation products are found to be less stable compared than those formed from intradimer dissociation reactions. Finally, we find that the oxidation products formed from hydrogen peroxide are more stable than those formed from water.     

Two-step strong order 1.5 schemes for stochastic differential equations

A general class of linear two-step schemes for solving stochastic differential equations is presented. Necessary and sufficient conditions on its parameters to obtain mean square order 1.5 are derived. Then the linear stability of the schemes is investigated. In particular, among others, the stability regions of generalizations of the classical two-step schemes Adams-Bashford, Adams-Moulton, and BDF are obtained.     

Pathways and rate coefficients for the decomposition of vinoxy and acetyl radicals

The potential in the vicinity of the stationary points on the surface for the decomposition of ground-state vinoxy and acetyl radicals has been calculated using the RQCISD(T) method extrapolated to the infinite-basis set limit. Rate coefficients for the decomposition pathways of these two radicals were computed using the master equation and variational transition state theory. Agreement between our calculated rate coefficients for H + CH(2)CO <--> CH(3) + CO and experimental data is very good, without the need for empirical adjustments to the ab initio energy barriers. Multireference configuration-interaction calculations indicate two competitive channels for vinoxy decomposition, with the channel leading to H + CH(2)CO being preferred at photodissociation energies. However, at typical combustion conditions, vinoxy decomposes primarily to CO and methyl. In contrast, decomposition of acetyl shows only one decomposition channel, leading to CO and methyl. The implications of a low-lying exit channel for the calculation of theoretical rate coefficients are discussed briefly.     

The reaction of acetylene with hydroxyl radicals

The potential energy surface for the reaction between OH and acetylene has been calculated using the RQCISD(T) method and extrapolated to the complete basis-set limit. Rate coefficients were determined for a wide range of temperatures and pressures, based on this surface and the solution of the one-dimensional and two-dimensional master equations. With a small adjustment to the association energy barrier (1.1 kcal/mol), agreement with experiments is good, considering the discrepancies in such data. The rate coefficient for direct hydrogen abstraction is significantly smaller than that commonly used in combustion models. Also in contrast to previous models, ketene + H is found to be the main product at normal combustion conditions. At low temperatures and high pressures, stabilization of the C2H2OH adduct is the dominant process. Rate coefficient expressions for use in modeling are provided.     

Reactions over multiple, interconnected potential wells: unimolecular and bimolecular reactions on a C3H5 potential

In this article we analyze quantitatively and discuss in detail a number of reactions that take place on a C3H5 potential. These reactions include the reaction of hydrogen atoms with allene and propyne, the reaction of methyl with acetylene, the isomerization of cyclopropyl to allyl, and the dissociation of allyl, 1-propenyl, and 2-propenyl. The theory employs high-level electronic-structure methods to characterize the potential energy surface, RRKM theory to calculate microcanonical, J-resolved rate coefficients, and master-equation methods to determine phenomenological rate coefficients, k(T,p). The agreement between our theory and the experimental results available is very good. The final theoretical results are cast in a form that is convenient for use in chemical kinetics modeling.     

Generalized Appell bases

In the context of Köthe spaces we study the bases related with the backward unilateral weighted shift operator, the so-called generalized derivation operator, extending known results for spaces of analytic functions. These bases are a subclass of Sheffer sequences called generalized Appell sequences and they are closely connected with the isomorphisms invariant by the weighted shift. We use methods of the non classical umbral calculi to give conditions for a generalized Appell sequence to be a basis.     

The reaction of n- and i-C4H5 radicals with acetylene

In this article, we discuss the reactions of i-C4H5 and n-C4H5 with acetylene. Both have been proposed as possible cyclization steps, forming benzene or fulvene, in rich flames burning aliphatic fuels. The relevant parts of the potential energy surface were determined from rQCISD(T) calculations extrapolated to the infinite-basis-set limit. Using this information in a Rice-Ramsperger-Kassel-Marcus-based master equation, we have calculated thermal rate coefficients and product distributions for both reactions as a function of temperature and pressure. The results are cast in forms that can be used in modeling, and the implications of the results for flame chemistry are discussed.