Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

Easy preparation of cobalt corrole and hexaphyrin and isolation of new oligopyrroles in the solvent-free condensation of pyrrole with pentafluorobenzaldehyde

[reaction: see text] Following the discovery that meso-substituted corroles are formed in solvent-free condensation of pyrrole with aldehydes, we demonstrate that a small variation in the methodology is suitable for facile synthesis of cobalt(III) corrole and hexaphyrin. These compounds, as well as three noncyclic products, were fully characterized by spectroscopy and X-ray crystallography.     

Macrocyclization on the fullerene core: Direct regio- and diastereoselective multi-functionalization of [60]fullerene,and synthesis of fullerene-dendrimer derivatives

The macrocyclization between buckminsterfullerene, C₆₀, and bis-malonate derivatives in double Bingel reaction provides a versatile and simple method for the preparation of covalent bis-adducts of C₆₀ with high regio- and diastereoselectivity. A combination of spectral analysis, stereochemical considerations, and X-ray crystallography (Fig. 2) revealed that out of the possible in-in, in-out, and out-out stereoisomers, the reaction of bis-malonates linked by o-, m-, or p-xylylene tethers afforded only the out-out ones (Scheme 1). In contrast, the use of larger tethers derived from 1,10-phenanthroline also provided a first example, (±)- 19 (Scheme 2), of an in-out product. Starting from optically pure bis-malonate derivatives, the new bis-functionalization method permitted the diastereoselective preparation of optically active fullerene derivatives (Schemes 4 and 5) and, ultimately, the enantioselective preparation (enantiomeric excess ee > 97%) of optically active cis-3 bis-adducts whose chirality results exclusively from the addition pattern (Fig. 6). The macrocyclic fixation of a bis-malonate with an optically active, 9,9′-spirobi[9H-fluorene]-derived tether to C₆₀ under generation of 24 and ent- 24 with an achiral addition pattern (Scheme 4) was found to induce dramatic changes in the chiroptical properties of the tether chromophore such as strong enhancement and reversal of sign of the Cotton effects in the circular dichroism (CD) spectra (Figs. 4 and 5). By the same method, the functionafized bis-adducts 50 and 51 (Schemes 10 and 11) were prepared as initiator cores for the synthesis of the fullerene dendrimers 62 , 63 , and 66 (Schemes 12 and 13) by convergent growth. Finally, the new methodology was extended, to the regio- and diastereoselective construction of higher cyclopropanated adducts. Starting from mono-adduct 71 , a clipping reaction provided exclusively the all-cis-2 tris-adduct (±)- 72 (Scheme 14), whereas the similar reaction of bis-adduct 76 afforded the all-cis-2 tetrakis-adduct 77 (Scheme 15). Electrochemical investigations by steady-state voltammetry (Table 2) in CH₂Cl₂ (+0.1M Bu₄NPF₆) showed that all macroeyciic bis(methano)fullerenes underwent multiple reduction steps, and that regioisomerism was not much influencing the redox potentials, All cis-2 bis-adducts gave an instable dianion which decomposed during the electrochemical reduction. In CH₂Cl₂, the redox potential of the fullerene core in dendrimers 62, 63 , and 66 is not affected by differences in size and density of the surrounding poly(ether-amide) dendrons. The all-cis-2 tris- and tetrakis(meihano)fullercnes (±) -72 and 77 , respectively, are reduced at more negative potential than previously reported all-e tris- and tetrakis-adducts with methane bridges that are also located along an equatorial belt. This indicates a larger perturbation of the original fullerene π-chromophore and a larger raise in LUMO energy in the former derivatives.     

Charge-remote fragmentation and the two-step elimination of alkanols from fast atom bombardment-desorbed (M + H)+, (M + Cat)+, and (M - H)− ions of aromatic β-hydroxyoximes

Aromatic β-hydroxyoximes undergo unusual fragmentation reactions as protonated or cationized species, as radical cations, or as (M - H)^? ions, As protonated species, they expel OH ’ from the oxime functionality in violation of the even electron rule. Parallel eliminations of alkyl radicals follow OH’ loss when the aromatic ring is substituted with an alkyl chain. Alkyl radical losses appear to be characteristic of radical cations that can isomerize to ions in which the alkyl chain bears a radical site and the charged site is the conjugate acid of a basic functionality (e.g., oxime or imine). Evidence for the mechanisms was found in the ion chemistry of oxime and imine radical cations. The imine reference compounds were conveniently generated by fast atom bombardment-induced reduction of oximes, removing the requirement for using conventional chemical synthesis. Protonated imines and the (M - H)^? ions of oximes fragment extensively via charge-remote processes to eliminate the elements of alkanes. This chemistry is not shared by the protonated oximes.     

Discovery of O-GlcNAc transferase inhibitors

O-GlcNAcylation of serine and threonine residues is a dynamic and essential post-translational modification involved in signaling pathways in eukaryotes. Studies of O-GlcNAcylation would be aided by small-molecule inhibitors of O-GlcNAc transferase (OGT), the sole enzyme know to mediate this modification, but discovery of such molecules has been hampered by poor expression of cloned OGT and lack of suitable high-throughput screens. This Communication describes the development an expression system to access large amounts of the catalytic domain of OGT and the implementation of a fluorescence-based substrate analogue displacement assay that has led to the discovery of a set of OGT inhibitors. This work lays the foundation for both structural and functional analysis of the catalytic domain of OGT.     

Supramolecular assemblies of a naturally derived sophorolipid

Acidic sophorolipid (SL) molecules derived from yeasts represent a novel type of asymmetrical bolaamphiphiles due to their unique structural features that include an asymmetrical polar head size (disaccharide vs COOH), a kinked hydrophobic core (cis-9-octadecenoic chain), and a non-amide polar-nonpolar linkage. Light microscopy, small- and wide-angle X-ray scattering, FT-IR spectroscopy, and dynamic laser light scattering were used to investigate the supramolecular structures of the self-assembled aggregates of SL molecules at different pH values. In acidic conditions (pH < 5.5), giant twisted and helical ribbons of 5-11 microm width and several hundreds of micrometers length were observed for the first time. Increase in solution pH values slowed ribbon formation, decreased ribbon yield, and increased the helicity and entanglements of the giant ribbons. An interdigitated lamellar packing model of acidic SL-COOH molecules with a long period of 2.78 nm, stabilized by both the strong hydrophobic association between the cis-9-octadecenoic chains and strong disaccharide-disaccharide hydrogen bonding, is proposed. The neutralization of SL-COOH in water to SL-COONa produced clear solutions with the formation of short-range ordered aggregates. At concentrations below 1.0 mg/mL, the size of self-assembled aggregates increased as the concentration increased. At concentrations above 1.0 mg/mL, narrowly distributed micellar aggregates with a constant hydrodynamic radius (R(h)) of about 100 nm are formed. The large micelles show strong angular dependence with the fast mode appearing at scattering angle theta >/= 60 degrees.     

The mechanisms of decomposition of the 1- and 2-phenyltetralin radical cations

Mechanisms for decomposition of 1- and 2-phenyltetralins were investigated using low resolution mass spectrometry and metastable ion techniques. Four primary decompositions were observed for 1-phenyltetralin radical cations: (1) the loss of C₆H₆ via a 1,4-elimination; (2) the elimination of ethene via competing losses from carbons 3 + 4 and carbons 2 + 3; (3) the loss of C₈H₈, probably through a stepwise Diels-Alder cycloreversion to expel styrene; and (4) the loss of methyl radical involving carbon 2 and possibly carbon 4. Three major decompositions were observed for 2-phenyltetralin radical cations: (1) the loss of C₈H₈, possibly through a Diels-Alder cycloreversion to expel styrene; (2) the loss of C₆H₆ via a 1,3 elimination; and (3) the loss of methyl radical from carbon 1. Various exchange reactions occur prior to these losses, but they proved to be incomplete even for metastable ions.