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.     

Nature et stabilité des complexes métalliques de cryptands dinucléants en solution II. Polythiamacrotricycles et monocycles apparentés

Nature and Stability of Some Metallic Complexes of Dinucleating Cryptands in Solution II. Polythiamacrotricycles and Related Monocyclic Subunits The stability constants of the Cu²⁺ and Ag⁺ complexes of the cylindrical macrotricycle 1a (1,7,13,19-tetraaza 4,16-dioxa 10,22,27,32-tetrathiatricyclo[17.5.5.5]tetratriacontane) have been determined by pH-metry, as well as those of the Cu²⁺, Co²⁺, Zn²⁺, Cd²⁺, Pb²⁺, and Ag⁺ complexes of the monocyclic subunit 2a (1,7-dimethyl-1,7-diaza 4,10-dithiacyclododecane), in aqueous solutions (NaClO₄) at 25°. In the Cu(II) systems, equilibria were reached slowly, and the results established by pH-metry were confirmed by UV/VIS spectrophotometric studies. The tricycle 1a forms dinuclear cryptates with copper and silver, with overall stability constants log β₂₁₀ (Cu₂- 1a )⁴⁺ = 18.5, log β_21-2 (Cu₂- 1a (OH)₂)²⁺ = 4.8, log β₂₁₀(Ag₂- 1a )²⁺ = 23.0. Ag⁺ also forms a mononuclear (Ag- 1a )⁺ complex, with log β₁₁₀ = 13.1, but no mononuclear species were detected in the Cu- 1a system. The absorption spectra of the bis-Cu(II) complexes of 1a and 2a in aqueous medium, MeOH and propylene carbonate (PC) are given, as well as those, in MeOH and PC, of the bis-copper complexes of the related monocycles 3 and 4 (1,7-diaza-4,10,13-trithiacyclopentadecane and 1.10-diaza 4,7,13,16-tetrathiacyclooctadecane, respectively), and tricycle 5 with two benzyl groups in the lateral chains. The complexing properties of the polyoxa- and polythia macrotricycles (Parts I and II of this series) are compared to those of other bis-chelating ligands, the bicyclic bis-tren and the monocyclic bis-dien.     

The structural characteristics of organozinc complexes incorporating N,N'-bidentate ligands

Dimethylzinc reacts with an excess of N-2-pyridylaniline 6 to give the homoleptic species, Zn[PhN(2-C(5)H(4)N)](2) 8. Single crystal X-ray diffraction reveals a solid-state dimer based on an 8-membered (NCNZn)(2) core motif. Zn[CyN(2-C(5)H(4)N)]Me (Cy =c-C(6)H(11)) 10, prepared by the combination of ZnMe(2) with the corresponding cyclohexyl-substituted pyridylamine, is also dimeric in the solid state but reveals a central (ZnN)(2) metallacycle. Employment of (p-Tol)NH(2-C(5)H(4)N)(p-Tol = 4-MeC(6)H(4)) 11 yielded the tris(zinc) adduct Zn(3)[(p-Tol)N(2-C(5)H(4)N)](4)Me(2) 12, which incorporates a central chiral molecule of 'Zn[(p-Tol)N(2-C(5)H(4)N)](2)' 12a, that bridges two 'Zn[(p-Tol)N(2-C(5)H(4)N)]Me' 12b units. A similar trimetallic structure is noted when the pyridylaniline substrate 11 is replaced with the bicyclic guanidine 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine (hppH), affording Zn(3)(hpp)(4)Me(2) 13. Spectroscopic studies point to retention of the solid-state structure of in hydrocarbon solution. Reaction of 13 with dimesityl borinic acid, Mes(2)BOH (Mes = mesityl), affords Zn(3)(hpp)(4)(OBMes(2))(2) 14 in which the trimetallic core is retained. This reactivity is in contrast to the closely related reaction of dimeric Zn[Me(2)NC[N(i)Pr](2)]Me 15 with Mes(2)BOH, which yielded Zn[Me(2)NC[N(i)Pr](2)][OBMes(2)].Me(2)NC[N(i)Pr][NH(i)Pr] 16 as a result of protonation at the guanidine ligand in addition to the Zn-Me bond.     

Dimetallic complexes of a structurally versatile pyridazine-containing Schiff-base macrocyclic ligand with pendant pyridine arms

The new [2 + 2] Schiff-base macrocyclic ligand L2, containing pyridazine head units and pyridine pendant arms, was synthesised as [Ba(II)2L2(ClO4)4(OH2)] 1 from the barium(II) ion templated condensation reaction of 3,6-diformylpyridazine and N1-(2-aminoethyl)-N1-(methylene-2-pyridyl)-ethane-1,2-diamine. Subsequent transmetallation reactions of 1 with copper(II), iron(II) and manganese(II) perchlorates led to the formation of [Cu(II)2L2](ClO4)4.2MeCN 2, [Fe(II)2L2(MeCN)2](ClO4)4 3 and two manganese complexes, 4 and 5, with the same formula, [Mn(II)2L2(MeCN)(OH2)](ClO4)4, but slightly different crystal structures, respectively. Single-crystal X-ray structural analyses reveal the variety of structures which can be supported by L2 in order to meet the coordination environment preferences of the incorporated metal ions. The barium(II) ions in 1 have an irregular ten-coordinate geometry whereas the copper(II) ions in 2 have a square pyramidal geometry and the iron(II) ions in 3 have an octahedral geometry, while in 4 and 5 every manganese(II) ion is seven-coordinate and the environment can be best described as distorted pentagonal bipyramidal. In 1, 4 and 5 the pyridazine moieties bridge the metal centres [Ba(1)...Ba(2) 4.9557(3)A 1; Mn(1)...Mn(2) 4.520(1)A 4; Mn(1)[dot dot dot]Mn(2) 4.3707(8)A 5] but this is not observed in the copper(II) and iron(II) complexes, 2 and 3, in which the metal ions are well separated [Cu(1)...Cu(2) 5.9378(6)A 2; Fe(1)...Fe(2) 5.7407(12)A 3]. In the cyclic voltammogram of [Cu2(II)L2](ClO4)4.2MeCN 2 in MeCN vs. Ag/AgCl two separate reversible one-electron transfer steps are observed [E(1/2)=0.04 V, DeltaE= 0.12 V and E(1/2)= 0.20 V, DeltaE=0.12 V; K(c)=510; in this system E(1/2)(Fc+/Fc)=0.42 V and DeltaE(Fc+/Fc)=0.08 V]. The other complexes cannot be reversibly reduced/oxidised.     

Targeting cell surface receptors with ligand-conjugated nanocrystals

To explore the potential for use of ligand-conjugated nanocrystals to target cell surface receptors, ion channels, and transporters, we explored the ability of serotonin-labeled CdSe nanocrystals (SNACs) to interact with antidepressant-sensitive, human and Drosophila serotonin transporters (hSERT, dSERT) expressed in HeLa and HEK-293 cells. Unlike unconjugated nanocrystals, SNACs were found to dose-dependently inhibit transport of radiolabeled serotonin by hSERT and dSERT, with an estimated half-maximal activity (EC(50)) of 33 (dSERT) and 99 microM (hSERT). When serotonin was conjugated to the nanocrystal through a linker arm (LSNACs), the EC(50) for hSERT was determined to be 115 microM. Electrophysiology measurements indicated that LSNACs did not elicit currents from the serotonin-3 (5HT(3)) receptor but did produce currents when exposed to the transporter, which are similar to those elicited by antagonists. Moreover, fluorescent LSNACs were found to label SERT-transfected cells but did not label either nontransfected cells or transfected cells coincubated with the high-affinity SERT antagonist paroxetine. These findings support further consideration of ligand-conjugated nanocrystals as versatile probes of membrane proteins in living cells.     

Chiral base route to functionalised cyclopentenyl amines: formal synthesis of the cyclopentene core of nucleoside Q

A chiral base route to a range of highly functionalised amino cyclopentenes has been developed. The key asymmetric step involved the chiral lithium amide base-mediated rearrangement of a protected trans-4-hydroxy cyclopentene oxide to give an allylic alcohol (88% ee). Subsequent Overman rearrangement gave a protected trans-1,2-aminocyclopentenol whereas Mitsunobu substitution with BocNHNs gave a protected cis-amino cyclopentenol. Both are proven intermediates for natural product synthesis. The protected cis-aminocyclopentenol was transformed in a few steps into a precursor of the cyclopentene core of nucleoside Q, a natural product whose deficiency in animals is related to tumour growth.