Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Adsorbate conformation determines catalytic chemoselectivity: crotonaldehyde on the Pt(111) surface

Molecular orientation, which depends on surface coverage, determines whether or not catalytic hydrogenation is chemoselective.     

Efficient epoxidation of a terminal alkene containing allylic hydrogen atoms: trans-methylstyrene on Cu{111}

The selective oxidation of trans-methylstyrene, a phenyl-substituted propene that contains labile allylic hydrogen atoms, has been studied on Cu{111}. Mass spectrometry and synchrotron fast XPS were used to detect, respectively, desorbing gaseous products and the evolution of surface species as a function of temperature and time. Efficient partial oxidation occurs yielding principally the epoxide, and the behavior of the system is sensitive to the order in which reactants are adsorbed. The latter is understandable in terms of differences in the spatial distribution of oxygen adatoms; isolated adatoms lead to epoxidation, while islands of "oxidic" oxygen do not. NEXAFS data taken over a range of coverages and in the presence and absence of coadsorbed oxygen indicate that the adsorbed alkene lies essentially flat with the allylic hydrogen atoms close to the surface. The photoemission results and comparison with the corresponding behavior of styrene on Cu{111} strongly suggest that allylic hydrogen abstraction is indeed a critical factor that limits epoxidation selectivity. An overall mechanism consistent with the structural and reactive properties is proposed.     

Critical influence of adsorption geometry in the heterogeneous epoxidation of "allylic" alkenes: structure and reactivity of three phenylpropene isomers on Cu(111)

It has long been conjectured that the difficulty of heterogeneously epoxidizing higher alkenes such as propene is due to the presence in the molecule of "allylic" H atoms that are readily stripped off by the oxygenated surface of the metal catalyst resulting in combustion. Here, taking advantage of the intrinsically higher epoxidation selectivity of Cu over Ag under vacuum conditions, we have used three phenylpropene structural isomers to examine the correlation between adsorption geometry and oxidation chemistry. It is found that under comparable conditions alpha-methylstyrene, trans-methylstyrene, and allylbenzene behave very differently on the oxygenated Cu(111) surface: the first undergoes extensive epoxidation accompanied by relatively little decomposition of the alkene; the second leads to some epoxide formation and extensive alkene decomposition; and the third is almost inert with respect to both reaction pathways. This reactive behavior is understandable in terms of the corresponding molecular conformations determined by near-edge X-ray absorption fine structure spectroscopy and density functional theory calculations. The proximity to the surface of the C=C function and of the allylic H atoms is critically important in determining reaction selectivity. This demonstrates the importance of adsorption geometry and confirms that allylic H stripping is indeed a key process that limits epoxidation selectivity in such cases.     

Halogen-induced selectivity in heterogeneous epoxidation is an electronic effect--fluorine,chlorine, bromine and iodine in the Ag-catalysed selective oxidation of ethene

Selectivity promotion in the Ag-catalysed heterogeneous epoxidation of ethene correlates with halogen electron affinity showing that it is an electronic phenomenon rather than a steric or geometrical effect.