Vibrational excitation of deuterium fluoride and hydrogen fluoride by atomic and diatomic species

The vibrational excitation of HF and DF and the energy transfer efficiencies for various collision partners were investigated over the temperature and pressure ranges of 1400°K to 4100°K and 0.1 to 0.3 atm, respectively. The extent of excitation was determined as a function of time by continuously monitoring the infrared emission intensity at the center of the 1–0 vibration-rotation band of the molecule. Collisional efficiencies of HF, N₂, O₂, F, Cl, and DF in relaxing HF and of DF, HF, and N₂ in relaxing DF are reported. A comparison with relaxation data for pure HF taken at lower temperature suggests that long-range attractive forces are mechanistically of major importance in the relaxation process. The relatively high efficiency of atomic chlorine in relaxing HF, i.e., (τP)_HF–HF/(τP)_HF–C1 ≥ 5 at 3000°K is discussed in terms of our previous result for atomic fluorine, i.e., (τP)_HF–HF/(τP)_HF–F = 18.     

Deformed Bosons: Combinatorics of Normal Ordering

We solve the normal ordering problem for (A A) ⁿ where A and A are one mode deformed ([A,A ] = [N+1] – [N]) bosonic ladder operators. The solution generalizes results known for canonical bosons. It involves combinatorial polynomials in the number operator N for which the generating function and explicit expressions are found. Simple deformations provide examples of the method.     

Oxygen activation by the noncoupled binuclear copper site in peptidylglycine alpha-hydroxylating monooxygenase. Reaction mechanism and role of the noncoupled nature of the active site

Reaction thermodynamics and potential energy surfaces are calculated using density functional methods to investigate possible reactive Cu/O(2) species for H-atom abstraction in peptidylglycine alpha-hydroxylating monooxygenase (PHM), which has a noncoupled binuclear Cu active site. Two possible mononuclear Cu/O(2) species have been evaluated, the 2-electron reduced Cu(II)(M)-OOH intermediate and the 1-electron reduced side-on Cu(II)(M)-superoxo intermediate, which could form with comparable thermodynamics at the catalytic Cu(M) site. The substrate H-atom abstraction reaction by the Cu(II)(M)-OOH intermediate is found to be thermodynamically accessible due to the contribution of the methionine ligand, but with a high activation barrier ( approximately 37 kcal/mol, at a 3.0-A active site/substrate distance), arguing against the Cu(II)(M)-OOH species as the reactive Cu/O(2) intermediate in PHM. In contrast, H-atom abstraction from substrate by the side-on Cu(II)(M)-superoxo intermediate is a nearly isoenergetic process with a low reaction barrier at a comparable active site/substrate distance ( approximately 14 kcal/mol), suggesting that side-on Cu(II)(M)-superoxo is the reactive species in PHM. The differential reactivities of the Cu(II)(M)-OOH and Cu(II)(M)-superoxo species correlate to their different frontier molecular orbitals involved in the H-atom abstraction reaction. After the H-atom abstraction, a reasonable pathway for substrate hydroxylation involves a "water-assisted" direct OH transfer to the substrate radical, which generates a high-energy Cu(II)(M)-oxyl species. This provides the necessary driving force for intramolecular electron transfer from the Cu(H) site to complete the reaction in PHM. The differential reactivity pattern between the Cu(II)(M)-OOH and Cu(II)(M)-superoxo intermediates provides insight into the role of the noncoupled nature of PHM and dopamine beta-monooxygenase active sites, as compared to the coupled binuclear Cu active sites in hemocyanin, tyrosinase, and catechol oxidase, in O(2) activation.     

The Boson Normal Ordering Problem and Generalized Bell Numbers

For any function F(x) having a Taylor expansion we solve the boson normal ordering problem for $F [(a^\dag)^r a^s]$, with r, s positive integers, $F [(a, a^\dag]=1$, i.e., we provide exact and explicit expressions for its normal form $\mathcal{N} \{F [(a^\dag)^r a^s]\} = F [(a^\dag)^r a^s]$, where in $ \mathcal{N} (F) $ all a's are to the right. The solution involves integer sequences of numbers which, for $ r, s \geq 1 $, are generalizations of the conventional Bell and Stirling numbers whose values they assume for $ r=s=1 $. A complete theory of such generalized combinatorial numbers is given including closed-form expressions (extended Dobinski-type formulas), recursion relations and generating functions. These last are special expectation values in boson coherent states.AMS Subject Classification: 81R05, 81R15, 81R30, 47N50.     

Cross section for b-Jet production in &pmacr;p collisions at radicals = 1.8 TeV

Bottom-quark production in &pmacr;p collisions at sqrt[s] = 1.8 TeV is studied with 5 pb(-1) of data collected in 1995 by the D0 detector at the Fermilab Tevatron Collider. The differential production cross section for b jets in the central rapidity region ( | y(b)|<1) as a function of jet transverse energy is extracted from a muon-tagged jet sample. Within experimental and theoretical uncertainties, D0 results are found to be higher than, but compatible with, next-to-leading-order QCD predictions.