Termolecular kinetics for the Mu + CO + M recombination reaction: A unique test of quantum rate theory

The room-temperature termolecular rate constants, k0, for the Mu + CO + M<==>MuCO + M (M = He, N2, Ar) recombination reaction have been measured by the muSR technique, and are reported for moderator gas pressures of up to approximately 200 bar (densities less, similar 0.4 x 10(22) molec cm(-3)). The experimental relaxation rates reveal an unusual signature, in being dominated by the electron spin-rotation interaction in the MuCO radical that is formed in the addition step. In N2 moderator, k0 = 1.2+/-0.1 x 10(-34) cm(6) s(-1), only about 30% higher than found in Ar or He. The experimental results are compared with theoretical calculations carried out on the Werner-Keller-Schinke (WKS) surface [Keller et al., J. Chem. Phys. 105, 4983 (1996)], within the framework of the isolated resonance model (IRM). The positions and lifetimes of resonance states are obtained by solving the complex Hamiltonian for the nonrotating MuCO system, using an L2 method, with an absorbing potential in the asymptotic region. Accurate values of the vibrational bound and resonance states of MuCO reveal unprecedented isotope effects in comparisons with HCO, due to the remarkable effect of replacing H by the very light Mu atom (m(Mu) approximately (1/9)m(H)). Due to its pronounced zero-point energy shift, there are only two (J = 0) bound states in MuCO. Contributions from nonzero J states to the termolecular rate constants are evaluated through the J-shifting approximation, with rotational constants evaluated at the potential minimum. The value of the important A constant (181 cm(-1)) used in this approximation was supported by accurate J = K = 1 calculations, from which A = 180 cm(-1) was obtained by numerical evaluation. The calculations presented here, with a "weak collision factor" beta c = 0.001, indicative of the very sparse density of MuCO states, give a very good account of both the magnitude and pressure dependence of the experimental rates, but only when the fact that the two initially bound (J = 0) states become resonances for J > 0 is taken into account. This is the first time in IRM calculations of atom-molecule recombination reactions where J not equal to 0 states have proven to be so important, thus providing a truly unique test of quantum rate theory.     

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].     

Transmissive olefination route to putative "morinol I" lignans

A series of morinol-type lignans were rapidly assembled using a Grignard-based transmissive olefination. In combination with palladium-catalyzed arylations, the strategy provides stereoselective access to (7Z,7'E), (7E,7'E), and (7E,7'Z) morinol diastereomers and the (7Z,8'E) and (7E,8'E) conjugated analogues. Critical for the E/Z stereoselectivity is a new, general method for converting alkenenitriles to alkenemethanols that circumvents the enal E/Z isomerization commonly encountered during conventional i-Bu(2)AlH reduction.     

Synthesis and characterisation of macromolecules containing multiple tetrazole functionalities

The synthesis of tetra-tetrazole macromolecules, containing various aromatic cores including benzene, pyridine and pyrazine directly attached to the tetrazole moieties, is described. This variation allowed for the generation of ligands with greater potential for metal ion complexation. Metal ion complexation reactions of the tetra-tetrazole macromolecules with the chelating pyridyl-tetrazole arms result in the formation of metal complexes where the metal ion was bound at the pendant arms rather than at the central core.     

Raman,infrared, SERS and theoretical study of 3‐(1‐phenylpropan‐2‐ylamino) propanenitrile,fenproporex

Infrared, Raman and surface‐enhanced Raman scattering (SERS) spectra of 3‐(1‐phenylpropan‐2‐ylamino)propanenitrile (fenproporex) have been recorded. Density functional theory (DFT) with the B3LYP functional was used for optimizations of ground state geometries and simulation of Raman and SERS vibrational spectra of this molecule. Bands of the vibrational spectra were assigned in detail. The comparison of SERS spectra obtained by using colloidal silver and gold nanoparticles with the corresponding Raman spectrum reveals enhancement and shifts in bands, suggesting a possible partial charge‐transfer mechanism in the SERS effect. Information about the orientation of fenproporex on the nanometer‐sized metal structures is also obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

Large deviations and moments for the Euler characteristic of a random surface

We study random surfaces constructed by glueing together N/k filled k‐gons along their edges, with all (N ? 1)!! = (N ? 1)(N ? 3)···3 · 1 pairings of the edges being equally likely. (We assume that lcm{2,k} divides N.) The Euler characteristic of the resulting surface is related to the number of cycles in a certain random permutation of {1,…,N}. Gamburd has shown that when 2 lcm{2,k} divides N, the distribution of this random permutation converges to that of the uniform distribution on the alternating group A_N in the total‐variation distance as N → ∞. We obtain large‐deviations bounds for the number of cycles that, together with Gamburd's (Ann Probab 34 (2006), 1827–1848) result, allow us to derive sharp estimates for the moments of the number of cycles. These estimates allow us to confirm certain cases of conjectures made by Pippenger and Schleich (Random Struct Algorithm 28 (2006), 247–288). © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Optimal exit probabilities and differential games

The problem considered is to control the drift of a Markov diffusion process in such a way that the probability that the process exits from a given regionD during a given finite time interval is minimum. An asymptotic formula for the minimum exit probability when the process is nearly deterministic is given. This formula involves the lower value of an associated differential game. It is related to a result of Ventsel and Freidlin for nearly deterministic, uncontrolled diffusions.This research was supported in part by the Air Force Office of Scientific Research under AF-AFOSR 76-3063C and in part by the National Science Foundation, NSF-76-07261.