Shell structure and response properties of metal clusters

Electronic shell structure, which was first recognized in sodium clusters, has been observed in alkali and noble metals, as well as in divalent and trivalent metals. Shell structure with modifications is expected to be broadly applicable to most metals. Features in the cluster abundance spectra and in the experimental dipole polarizabilities and ionization potentials correlate well with predictions of electronic level filling in spherical and spheroidal potential wells. The lack of precise quantitative agreement between experiment and theory for the response properties indicates necessary refinements in the self-consistent uniform background jellium model for clusters.     

COSMIC(90): An improved molecular mechanics treatment of hydrocarbons and conjugated systems

Summary Four modifications to the COSMIC molecular mechanics force field are described, which greatly increase both its versatility and the accuracy of calculated conformational energies. The Hill non-bonded van der Waals potential function has been replaced by a two-parameter Morse curve and a new H-H potential, similar to that in MM3, incorporated. Hydrocarbon energies in particular are much improved.A simple iterative Hückel pi-electron molecular orbital calculation allows modelling of conjugated systems. Calculated bond lengths and rotational barriers for a series of conjugated hydrocarbons and nitrogen heterocycles are shown to be as accurate as those determined by the MM2 SCF method.Explicit hydrogen-bonding potentials for H-bond acceptor-donor atom pairs have been included to give better hydrogen bond energies and lengths. The van der Waals radii of protonic hydrogens are reduced to 0.5 Å and the energy well depth is increased to 1.0 kcal mol^-1.Two new general atom types, N⁺ _sp ² and O^- _sp ³ , have been introduced which allow a wide variety of charged conjugated systems to be studied. A minimum of parameterisation is required, as the new types are easily included in the Hückel scheme which automatically adjusts bond and torsional parameters according to the defined bond-order relationships.     

Single Atom Ring Contraction of Peptide Macrocycles Using Cornforth Rearrangement

Site-selective transformations of densely functionalized scaffolds have been a topic of intense interest in chemical synthesis. Herein we have repurposed the rarely used Cornforth rearrangement as a tool to effect a single-atom ring contraction in cyclic peptide backbones. Investigations into the kinetics of the rearrangement were carried out to understand the impact of electronic factors, ring size, and linker type on the reaction efficiency. Conformational analysis was undertaken and showed how subtle differences in the peptide backbone result in substrate-dependent reaction profiles. This methodology can now be used to perform conformation-activity studies. The chemistry also offers an opportunity to install building blocks that are not compatible with traditional C-to-N iterative synthesis of macrocycle precursors.     

Properties of a representation of a basis for the null space

Given a rectangular matrixA(x) that depends on the independent variablesx, many constrained optimization methods involve computations withZ(x), a matrix whose columns form a basis for the null space ofA ^T(x). WhenA is evaluated at a given point, it is well known that a suitableZ (satisfyingA ^T Z = 0) can be obtained from standard matrix factorizations. However, Coleman and Sorensen have recently shown that standard orthogonal factorization methods may produce orthogonal bases that do not vary continuously withx; they also suggest several techniques for adapting these schemes so as to ensure continuity ofZ in the neighborhood of a given point.This paper is an extension of an earlier note that defines the procedure for computingZ. Here, we first describe howZ can be obtained byupdating an explicit QR factorization with Householder transformations. The properties of this representation ofZ with respect to perturbations inA are discussed, including explicit bounds on the change inZ. We then introduceregularized Householder transformations, and show that their use implies continuity of the full matrixQ. The convergence ofZ andQ under appropriate assumptions is then proved. Finally, we indicate why the chosen form ofZ is convenient in certain methods for nonlinearly constrained optimization.The research of the Stanford authors was supported by the U.S. Department of Energy Contract DE-AM03-76SF00326, PA No. DE-AT03-76ER72018; the National Science Foundation Grants MCS-7926009 and ECS-8312142; the Office of Naval Research Contract N00014-75-C-0267; and the U.S. Army Research Office Contract DAAG29-84-K-0156.The research of G.W. Stewart was supported by the Air Force Office of Scientific Research Contract AFOSR-82-0078.     

On exceptional groups of order p5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order $p^5$. For an odd prime p, we classify all pairs $(G,Q)$ where G has order $p^5$ and Q is a distinguished quotient. (The case $p=2$ has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order $p^5$ with at least one exceptional quotient tends to 1/2.     

Bistable behaviour in squeezed vacua: II. Stability analysis and chaos

Linear stability analysis and (numerical) investigation of the periodic and chaotic self-pulsing behaviour are presented for the Maxwell-Bloch equations of a bistable model in contact with a squeezed vacuum field. Effect of the squeeze phase parameter on the period doubling bifurcation that preceeds chaos is examined for the adiabatic and non-adiabatic regimes.     

Measurements of hyperon semileptonic decays at the CERN Super Proton Synchrotron

The charged hyperon beam at the CERN Super Proton Synchrotron (SPS) has been used to collect data on semileptonic decays ofΣ ^?,Ξ ^? andΛ. A magnetic channel selects 100 GeV/c negatively charged particles produced in the forward direction by interaction of the 200 GeV/c SPS proton beam on a BeO target. TheΣ ^? andΞ ^? hyperons are concurrently identified in a DISC ?erenkov counter, and their decay products are analysed by a magnetic spectrometer. Electron-hadron discrimination is achieved by the combined use of lead-glass and lead/scintillator counters, transition radiation detectors, and a ?erenkov counter. In this article we report results on the \(\Sigma ^ - \to \Lambda e^ - \bar v\) decay mode. Measurements of the Λ polarization and of the centre-of-mass distributions (baryon kinetic energy, electron-neutrino correlation, and Dalitz plot distributions) yield the vector to axialvector form factor ratiof ₁/g ₁=+0.034±0.080, in agreement with the value expected from the conserved vector current hypothesis (f ₁/g ₁=0). TheΣ ^?→Λe ^? v→ branching ratio measurement gives a value of (5.41±0.30)×10^?5. The effects of radiative corrections are not included in these results. They are discussed in the text. Results on the otherΞ ^?,Σ ^?, andΛ semileptonic decays are reported in separate articles.     

Acoustic emission from domain wall motion in ferroelectric lead germanate

Simultaneous visual observation and monitoring of the ultrasonic signals show that acoustic emission (AE) produced as Pb₅Ge₃O₁₁c-plate crystals undergo the ferroelectric hysteresis cycle results from domain wall nucleation and collapse. AE activity takes place predominantly at applied electric fields large enough to bring a crystal substantially towards its saturation polarisation. A notable feature observed in Pb₅Ge₃O₁₁ and Pb_5?xBa_xGe₃O₁₁ alloys is the existence of an abrupt threshold electric field, denoted by E_∞ in the high gain limit, for production of AE: as the electric field is increased beyond the threshold value, the amount of AE observed increases by several orders of magnitude. E_∞ depends linearly on the inverse of the c-plate sample thickness (1/d) and also upon sample temperature—falling to a minimum at about 70°C for Pb₅Ge₃O₁₁ and then rising steeply as the Curie temperature (178°C) is approached. E_∞ is also dependent on the rate of change of the applied electric field and as this is increased extrapolates to the high frequency limit of the coercive field. Measurements of crystal polarisation indicate a one-to-one correspondence between AE and the electrical Barkhausen pulses which occur during polarisation reversal—further evidence for domain nucleation and collapse as the source of AE. Optical and AE studies made simultaneously on gadolinium molybdate add confirmation that these particular processes are responsible for the AE produced by ferroelectric crystals.     

Ab initio calculations of the excited states of the permanganate and chromate ions

The excited states of the permanganate and chromate ions are described by better-than-minimal basis set SC FMO CI calculations. The results are compared with the experimental absorption spectra.