The uniqueness of the adjoint operation I

Let H be a complex, infinite-dimensional Hilbert space. Let B(H) denote the set of bounded linear operators on H. This paper contains a nonlinear characterization of the adjoint operation on B(H). The statement of this result is:THEOREM:Let h: B(H) B(H)be a function such that h(I)0.Then h(ST)=h(T)h(S)and h(S)S0for all elements Sand Tof B(H)if and only if h(S)=S^* for all S B(H).     

Direct dynamics trajectory study of the reaction of formaldehyde cation with D2: vibrational and zero-point energy effects on quasiclassical trajectories

Quasiclassical, direct dynamics trajectories have been used to study the reaction of formaldehyde cation with molecular hydrogen, simulating the conditions in an experimental study of H2CO+ vibrational effects on this reaction. Effects of five different H2CO+ modes were probed, and we also examined different approaches to treating zero-point energy in quasiclassical trajectories. The calculated absolute cross-sections are in excellent agreement with experiments, and the results provide insight into the reaction mechanism, product scattering behavior, and energy disposal, and how they vary with impact parameter and reactant state. The reaction is sharply orientation-dependent, even at high collision energies, and both trajectories and experiment find that H2CO+ vibration inhibits reaction. On the other hand, the trajectories do not reproduce the anomalously strong effect of nu2(+) (the CO stretch). The origin of the discrepancy and approaches for minimizing such problems in quasiclassical trajectories are discussed.     

Heteroatom transfer to alkenes by N-protected-oxaziridines: new reaction pathways and products

N-Alkoxycarbonyl- and N-carboxamido-oxaziridines are shown to react with aromatic alkenes to give epoxide, aziridine or hydro-oxidation products, in ratios depending on the oxaziridine structure. Chiral oxaziridines can effect epoxidation and hydro-oxidation with promising levels of asymmetric induction.     

Palladium-catalyzed regioselective arylation of imidazo[1,2-a]pyrimidine

Imidazo[1,2-a]pyrimidine can be arylated at the 3-position with aryl bromides in the presence of base and a catalytic amount of palladium. This provides an efficient one-step synthesis of 3-arylimidazo[1,2-a]pyrimidines from the unsubstituted heterocycle. [reaction: see text]     

Half-sandwich titanium(IV) complexes with Kläui's tripod ligand

Treatment of [Ti(O-i-Pr)(2)Cl(2)] with NaL(OEt) (L(OEt)(-) = [CpCo[P(O)(OEt)(2)](3)](-), Cp = eta(5)-C(5)H(5)) afforded [L(OEt)Ti(O-i-Pr)(2)Cl] that reacted with HCl in ether to give [L(OEt)TiCl(3)] (1). The average Ti-O and Ti-Cl distances in 1 are 1.975 and 2.293 A, respectively. Reaction of titanyl sulfate with NaL(OEt) in water followed by addition of HBF(4) afforded [L(OEt)TiF(3)] (2), the Ti-O and Ti-F distances of which are 2.020(2) and 1.792(2) A, respectively. The Zr(IV) analogue [L(OEt)ZrF(3)] (3) was prepared similarly from zirconyl nitrate, NaL(Oet), and HBF(4) in water. The Zr-O and average Zr-F distances in 3 are 2.139(2) and 1.938(2) A, respectively. Treatment of 1 with tetrachlorocatechol (H(2)Cl(4)cat) afforded [L(OEt)Ti(Cl(4)cat)Cl] (4). The average Ti-O(P), Ti-O(C), and Ti-Cl distances in 4 are 1.972, 1.926, and 2.334 A, respectively. Hydrolysis of 4 in the presence of Et(3)N yielded the mu-oxo dimer [(L(OEt))(2)Ti(2)(Cl(4)cat)(2)(mu-O)] (5). The average Ti-O(P), Ti-O(C), and Ti-O(Ti) distances in 5 are 2.027, 1.926, and 1.7977(9) A. Treatment of 1 with 1,1'-binaphthol (BINOLH(2)) in the presence of Et(3)N afforded [(L(OEt))(2)Ti(2)(mu-O)(2)(mu-BINOL)] x 2BINOLH(2) (6.2BINOLH(2)). Complex 1 is capable of catalyzing ring opening of epoxides with Me(3)SiN(3) under solvent-free conditions presumably via a Ti-azide intermediate.     

Studies in bicyclo[3.1.0]hexane methanolysis. Ring opening of activated cyclopropanes under acidic and basic conditions

A bicyclo[3.1.0]hexane, with one cyclopropane carbon flanked by a ketone and an ester or an aldehyde, undergoes methanolysis with cleavage of one of the two activated cyclopropane bonds, depending on the reaction conditions. Acidic conditions yield primarily or exclusively a 4-methoxycyclohexane, while basic conditions yield a 3-methoxymethylcyclopentanone.     

Lewis base activation of lewis acids. Addition of silyl ketene acetals to aldehydes

The weak Lewis acid silicon tetrachloride can be activated by catalytic amounts of the chiral bisphosphoramide (R,R)-3 to form a highly reactive, chiral trichlorosilyl cation which is an extremely effective promoter of aldol addition reactions between aldehydes and silyl ketene acetals. The tert-butyldimethylsilyl ketene acetal of methyl acetate adds nearly instantaneously to aromatic and olefinic aldehydes as well as aliphatic aldehydes (albeit more slowly) with excellent enantioselectivity. The homologous tert-butyldimethylsilyl ketene acetal of tert-butyl propanoate adds with nearly exclusive anti diastereoselectivity to a similar range of aldehydes also with excellent enantioselectivity. The origin of the slower reaction rate with aliphatic aldehydes is revealed to be the formation of chlorosilyl ether adducts.     

New synthetic routes to cationic rhenium tricarbonyl bipyridine complexes with labile ligands

Triflate abstraction from the complex [Re(OTf)(CO)(3)(bipy)] (1) using the salt NaBAr'(4) (Ar' = 3,5-bis(trifluoromethyl)phenyl) in dichloromethane solution in the presence of L = PPh(3), NCMe, NCPh, imines, ketones, Et(2)O, THF, MeOH, and MeI affords cationic complexes [Re(L)(CO)(3)(bipy)](+) as their BAr'(4)(-) salts. The new complexes have been characterized spectroscopically and, for [Re(eta(1)-O=C(Me)R)(CO)(3)(bipy)]BAr'(4) (R = CH(3), 6a; R = Ph, 6b), and [Re(THF)(CO)(3)(bipy)]BAr'(4) (9), also by single-crystal X-ray diffraction. Compared with conventional methodologies, the route reported here allows the coordination of a broader range of weakly coordinating ligands and requires considerably milder conditions. On the other hand, the reactions of lithium acetylides with [Re(THF)(CO)(3)(bipy)]BAr'(4) (9) can be used for the high-yield syntheses of rhenium alkynyls [Re(Ctbd1;CR)(CO)(3)(bipy)] (R = Ph, 12; R = SiMe(3), 13). Complex 9 was found to catalyze the aziridination of benzylideneaniline with ethyl diazoacetate.     

Adsorption, desorption, and clustering of H2O on Pt111

The adsorption, desorption, and clustering behavior of H2O on Pt111 has been investigated by specular He scattering. The data show that water adsorbed on a clean Pt111 surface undergoes a structural transition from a random distribution to clustered islands near 60 K. The initial helium scattering cross sections as a function of temperature are found to be insensitive to the incident H2O flux over a range of 0.005 monolayers (ML)/s-0.55 ML/s indicating that the clustering process is more complex than simple surface diffusion. The coarsening process of an initially random distribution of water deposited at 25 K is found to occur over a broad temperature range, 60相似文献   

Molecular cluster decay viewed as escape from a potential of mean force

We show that evaporation from a quasistable molecular cluster may be treated as a kinetic problem involving the stochastically driven escape of a molecule from a potential of mean force. We derive expressions for the decay rate, and a relationship between the depth of the potential and the change in system free energy upon loss of a molecule from the cluster. This establishes a connection between kinetic and thermodynamic treatments of evaporation, but also reveals differences in the prefactor in the rate expression. We perform constant energy molecular dynamics simulations of cluster dynamics to calculate potentials of mean force, friction coefficients and effective temperatures for use in the kinetic analysis, and to compare the results with the directly observed escape rates. We also use the simulations to estimate the escape rates by a probabilistic analysis. It is much more efficient to calculate the decay rate by the methods we have developed than it is to monitor escape directly, making these approaches potentially useful for the assessment of molecular cluster stability.