Rapid Generation and Safe Use of Carbenes Enabled by a Novel Flow Protocol with In‐line IR spectroscopy

A powerful new continuous process for the formation and use of donor/acceptor‐substituted carbenes is described. The safety profile of diazo group transfer on methyl phenylacetate was determined including kinetic studies in batch and in flow using in‐line IR analysis. Batch work‐up and liquid chromatography were circumvented by developing an optimized liquid/liquid flow separation method providing aryl diazoacetates in high purity. Fast screening of reaction conditions in flow with in‐line IR analysis allowed rapid reaction optimization. Finally, a multistep process of diazo group transfer, extraction, separation and subsequent diazo decomposition combined with multiple X?H insertion reactions was established.     

Crystal and molecular structure of 5-benzylidene-3-acetyl-2,4-oxolandione

The title compound crystallizes in the monoclinic space groupP2₁/n (No. 14),a=14.923(2),b=4.165(2),c=18.097(2) Å,=106.40(1)°,Z=4. The structure was solved by direct methods, and refined by full-matrix least squares toR=0.048 for 1313 observed reflections. Inter- and intramolecular hydrogen bonding is observed, the latter resulting in the formation of dimers.     

High‐Frequency Fe–H Vibrations in a Bridging Hydride Complex Characterized by NRVS and DFT

High‐spin iron species with bridging hydrides have been detected in species trapped during nitrogenase catalysis, but there are few general methods of evaluating Fe?H bonds in high‐spin multinuclear iron systems. An ⁵⁷Fe nuclear resonance vibrational spectroscopy (NRVS) study on an Fe(μ‐H)₂Fe model complex reveals Fe?H stretching vibrations for bridging hydrides at frequencies greater than 1200 cm^?1. These isotope‐sensitive vibrational bands are not evident in infrared (IR) spectra, showing the power of NRVS for identifying hydrides in this high‐spin iron system. Complementary density functional theory (DFT) calculations elucidate the normal modes of the rhomboidal iron hydride core.     

On a Family of Hyperplane Arrangements Related to the Affine Weyl Groups

Let be an irreducible crystallographic rootsystem in a Euclidean space V, with ⁺ theset of positive roots. For , , let be the hyperplane . We define a set of hyperplanes . This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincaré polynomial of is , where n is the rank of and h is the Coxeter number of the finiteCoxeter group corresponding to .     

Height of flat tori

Relations between the height and the determinant of the Laplacian on the space of -dimensional flat tori and the classical formulas of Kronecker and Epstein are established. Extrema of the height are shown to exist, and results for a global minimum for 2-d tori and a local minimum for 3-d tori are given, along with more general conjectures of Sarnak and Rankin.

     

Efficient Finite Difference Solutions to the Time-Dependent Schrödinger Equation

The matrix elements of the exponential of a finite difference realization of the one-dimensional Laplacian are found exactly. This matrix is used to formulate an efficient algorithm for the numerical solution to the time-dependent quantum mechanical scattering of a single particle from a time-independent potential in one-space and one-time dimension. The method generalizes to higher spatial dimensions, as well as to multiparticle problems.     

Master-slave synchronization and the Lorenz equations

Since the seminal remark by Pecora and Carroll [Phys. Rev. Lett. 64, 821 (1990)] that one can synchronize chaotic systems, the main example in the related literature has been the Lorenz equations. Yet this literature contains a mixture of true and false, and of justified and unsubstantiated claims about the synchronization properties of the Lorenz equations. In this note we clarify some of the confusion. (c) 1997 American Institute of Physics.