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.     

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.     

Improvements to the distance geometry algorithm for conformational sampling of cyclic structures

Modifications to the distance geometry algorithm as embodied in the program DGEOM have been made to improve sampling capabilities. Specifically, torsion angle sampling replaces distance sampling for 1,4 atomic relationships and correlated distance sampling is disabled. The effects of these modifications are illustrated by comparing the different sets of conformations produced for butane. In addition, these changes are shown to increase the conformational sampling of two medium-sized rings, cycloheptadecane and caprylolactam. The current results for these molecules are compared to those of other conformational searching methods.     

The dipole moment of HNO in its ÃA″ excited state determined using optical—optical double resonance stark spectroscopy

The Stark splittings and rotational asymmetry splittings of a number of levels of the ùA″ excited state of HNO have been measured using the sub-Doppler technique of optical—optical double resonance, μ_a is found to be 1.08 ± 0.01 D for the 100 vibronic state, and 1.05 ± 0.01 D for the 020 vibronic state. These values are to be compared with a recently determined ground state value of μ_a = 0.996 D. The asymmetry splittings of some of the levels studied are considerably larger than predicted from the known rotational constants, indicating minor rotational perturbations.     

The use of bis(diphenylphosphino)amines with N-aryl functionalities in selective ethylene tri- and tetramerisation

A systematic study was conducted on the Cr catalysed tri- and tetramerisation of ethylene using bis(diphenylphosphino)amine ligands with N-aryl functionality. This study revealed that the oligomerisation reaction product selectivity is primarily dependent on the structure and size of the N-aryl groups.

Addition of sufficient steric bulk to the N-phenyl group via ortho-alkyl substitution increased the combined 1-hexene and 1-octene selectivity (overall alpha selectivity) to above 82% at an overall 1-octene selectivity of 56%. The introduction of a single carbon spacer between the N-atom and the aryl-moiety, as well as the addition of branching on this carbon, resulted in further selectivity improvements, achieving an overall 1-octene selectivity of 64% and an overall alpha selectivity of 84%. This was obtained at catalyst productivities in excess of 1,000,000 g/g Cr/h.     

Multiphoton ionisation spectroscopy of H2S: a reinvestigation of the 1B1-1A1 band at 139.1 nm

The 3 + 1 multiphoton ionisation (MPI) spectrum of the ¹B₁-¹A₁ transition in H₂S at 139.1 nm has been recorded in both linearly and circularly polarised light. The rotational structure shows marked differences from that of the one-photon absorption spectrum. Properties of the excited state revealed through analysis of this structure include confirmation of its ¹B₁ character, refined values for its A, B and C rotational constants and the operation of an energy-dependent predissociation mechanism. It is shown that the third-rank tensor component of the transition operator dominates over the first-rank component in this MPI band. The orbital nature of this ¹B₁ excited state is considered.     

Higher spin BRS cohomology of supersymmetric chiral matter inD=4

We examine the BRS cohomology of chiral matter inN=1,D=4 supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators _{(a, b)} are products of the elementary chiral superfieldsS and and the derivative operatorsD , and . Such superfields _{(a, b)} can be chosen to have a symmetrized undotted indices _i and b symmetrized dotted indices . The result derived here is that each composite superfield _(a,b) is subject to potential supersymmetry anomalies ifa–b is an odd number, which means that _(a,b) is a fermionic superfield.