Truncated Newton method for sparse unconstrained optimization using automatic differentiation

When solving large complex optimization problems, the user is faced with three major problems. These are (i) the cost in human time in obtaining accurate expressions for the derivatives involved; (ii) the need to store second derivative information; and (iii), of lessening importance, the time taken to solve the problem on the computer. For many problems, a significant part of the latter can be attributed to solving Newton-like equations. In the algorithm described, the equations are solved using a conjugate direction method that only needs the Hessian at the current point when it is multiplied by a trial vector. In this paper, we present a method that finds this product using automatic differentiation while only requiring vector storage. The method takes advantage of any sparsity in the Hessian matrix and computes exact derivatives. It avoids the complexity of symbolic differentiation, the inaccuracy of numerical differentiation, the labor of finding analytic derivatives, and the need for matrix store. When far from a minimum, an accurate solution to the Newton equations is not justified, so an approximate solution is obtained by using a version of Dembo and Steihaug's truncated Newton algorithm (Ref. 1).This paper was presented at the SIAM National Meeting, Boston, Massachusetts, 1986.     

Ring expansion of 5- to 6-member zirconacycles by carbenoid insertion

A wide range of carbenoids (1-lithio-1-halo species), including those with α-SiR₃, OEt, SPh, SO₂Ph, P(O)(OEt)₂, and CN substituents, insert into 5-member zirconacycles (saturated and unsaturated, mono- and bi-cyclic) to afford functionalized 6-member zirconacycles. 1-Lithio-1-haloalkenes insert to afford 6-member zirconacycles with an alkylidene substituent next to the metal. Unexpected double insertion of some carbenoids, and evidence for endocylic β-hydride transfer processes provide additional mechanistic interest.     

A Reality Proof in PT-Symmetric Quantum Mechanics

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral equivalences inspired by the correspondence are also discussed.     

Synthesis of substituted 5-aminomethyl tetrahydro-isoquinolines and dihydro-isoindoles

The synthesis of ten substituted aminomethylene tetrahydro-isoquinolines is described, proceeding in eight steps from 5-hydroxyisoquinoline via reductive amination of N-Boc tetrahydro-isoquinoline 5-carboxaldehyde. Likewise, reductive amination was used to prepare four substituted dihydro-isoindoles from the corresponding aldehyde. The dihydro-isoindole ring system was conveniently accessed via a 2+2+2 cycloaddition reaction.     

The effect of a magnetic field on the singlet/triplet ratio in geminate ion recombination

Excited state formation by ion recombination in solutions of fluorene in squalene has been studied by pulse radiolysis at the center of a large electromagnet. The products of the slower part of the ion recombination are affected by an applied magnetic field. The fluorescence yield increases by a factor of about 1.5 whereas the triplet yield decreases.     

Simulation of the electronic and vibrational structure of hydrogenated amorphous silicon using cluster models

A set of simple models of hydrogenated amorphous silicon (a-Si:H) consisting of hypothetical silane molecules with diamond or similar lattices was studied by the semiempirical AM1 method. Densities of states and infrared spectra were calculated for the silane molecules and similar molecules with dangling bonds disorder, and with boron or phosphorus substitution to simulate doping. Some examples are presented, and a comparison is made with experimental properties of a-Si:H. It is proposed to use these models in a study of the Staebler–Wronski photodegradation of a-Si:H and other aspects of amorphous silicon technology. © John Wiley & Sons, Inc.     

Resolving the different dynamics of the fluorine sublattices in the anionic conductor BaSnF(4) by using high-resolution MAS NMR techniques

19F and (119)Sn MAS NMR spectroscopy have been used to investigate the fluoride ion conductor, BaSnF(4), a member of the MSnF(4) family of fluorite-related anionic conductors containing double layers of Sn(2+) and M(2+) cations. Two fluorine sublattices were observed by (19)F MAS NMR, which could be assigned to specific sites in the lattice. The first sublattice is due to fluorine atoms located in Ba(2+) double layers and is rigid on the MAS NMR time scale at room temperature. The second sublattice comprises the fluoride ions between the Ba(2+) and Sn(2+) layers, and the few fluorine atoms that inhabit the Sn(2+)-Sn(2+) double layers. These ions are in rapid exchange with each other, and an extremely short correlation time tau(C) for the motion of these ions of <3 x 10(-)(5) s is obtained at -100 degrees C. T(1) measurements indicate that tau(C) approaches 10(-)(8) s at room temperature. (19)F-to-(119)Sn cross-polarization (CP) experiments confirmed the assignments of the resonances, and that the fluorine atoms located next to the tin atoms are extremely mobile at room temperature (and thus do not contribute to the CP process). Two-dimensional (19)F exchange experiments showed that exchange between the rigid and mobile lattice does occur, but at a much slower rate (tau(C) approximately 10 ms at 250 degrees C). Low-temperature (19)F MAS and (19)F-to-(119)Sn CP NMR spectra demonstrate that the motion of the fluoride ions has almost completely frozen out by -150 degrees C. The results are consistent with rapid two-dimensional (anisotropic) conductivity involving the fluoride ions between the Ba and Sn layers. Conductivity in three dimensions requires hops between the ions in the BaF(2)-like layers and the mobile ions. This process does occur, but with exchange rates that are at least 6-7 orders of magnitude slower.