Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Gallium cluster "magic melters"

Calorimetry measurements (using a method based on multicollision induced dissociation) have been performed for unsupported gallium clusters, Gan+ (n = 30-50 and 55). Melting transitions have been identified from spikes in the heat capacities recorded as a function of temperature. There are enormous fluctuations in the melting temperatures and the heats of fusion with cluster size. Clusters with n = 31, 33, 37, and 45-47 are "magic melters" with particularly well-defined melting transitions. There is a strong correlation between the heats of fusion, entropies of fusion, and the stabilities of the clusters. However, these quantities are not strongly correlated with the melting temperatures.     

Chemo‐ and Enzyme‐Catalyzed Reactions Revealing a Common Temperature‐Dependent Dynamic Solvent Effect on Enantioselectivity

The enantiomeric ratio E of enzyme‐catalyzed (Candida antarctica lipase and lipase PS) and chemo‐catalyzed (L ‐proline‐based diamines) acylation reactions of 1‐(naphthalen‐2‐yl)ethanol, 2‐phenylpropanol, and 2‐benzylpropane‐1,3‐diol is dependent on solvent and temperature. Plots of ln E vs. 1/T showed the presence of inversion temperatures (T_inv). The T_inv values for the bio‐catalyzed and the chemo‐catalyzed reactions are fairly in agreement, and correspond as well to the T_NMR values obtained by variable‐temperature ¹³C‐NMR experiments on the substrates in the same solvent of the resolution. This result demonstrates that clustering effects in the substrate solvation manage the chemical and the enzymatic enantioselectivity, and, moreover, that the solute? solvent cluster is always the real reacting species in solution for chemical as well as for enzymatic reactions.     

Novel mass spectral fragmentation of heptafluorobutyryl derivatives of acyl analogues of platelet-activating factor

Direct derivatization of the acyl analogue of platelet-activating factor (acyl-PAF) with heptafluorobutyric anhydride results in replacement of the phosphocholine moiety with a heptafluorobutyryl (HFB) group. Electron capture (EC) mass spectrometric analysis of this compound that makes use of negative ion detection along with subsequent accurate mass measurement and tandem mass spectrometry studies revealed that in addition to expected fragmentation due to losses of elements of HF, ketene, and/or acetic acid, there is a rearrangement reaction between the HFB group and the substituent on carbon-2 of the glycerol backbone. For 2-acetyl isomers, this fragmentation yields a characteristic ion at m/z 237; for 1-acetyl isomers, the analogous ion is observed at [M-135]⁻, along with a corresponding carboxylate anion. The use of the HFB derivative is invaluable for analysis of PAF homologues and analogues because it provides detailed structural information in combination with the high sensitivity of a gas chromatography combined with EC-mass spectrometry assay.     

Structural studies of ammonia and metallic lithium-ammonia solutions

The technique of hydrogen/deuterium isotopic substitution has been used to extract detailed information concerning the solvent structure in pure ammonia and metallic lithium-ammonia solutions. In pure ammonia we find evidence for approximately 2.0 hydrogen bonds around each central nitrogen atom, with an average N-H distance of 2.4 A. On addition of alkali metal, we observe directly significant disruption of this hydrogen bonding. At 8 mol % metal there remains only around 0.7 hydrogen bond per nitrogen atom. This value decreases to 0.0 for the saturated solution of 21 mol % metal, as all ammonia molecules have then become incorporated into the tetrahedral first solvation spheres of the lithium cations. In conjunction with a classical three-dimensional computer modeling technique, we are now able to identify a well-defined second cationic solvation shell. In this secondary shell the nitrogen atoms tend to reside above the faces and edges of the primary tetrahedral shell. Furthermore, the computer-generated models reveal that on addition of alkali metal the solvent molecules form voids of approximate radius 2.5-3.0 A. Our data therefore provide new insight into the structure of the polaronic cavities and tunnels, which have been theoretically predicted for lithium-ammonia solutions.     

Enantioreversal in the sharpless asymmetric epoxidation reaction controlled by the molecular weight of a covalently appended achiral polymer

Polymers such as poly(ethylene glycol) (PEG) have proven use in a variety of applications including organic synthesis. We now disclose our investigations into the recently disputed report that PEG tartrate esters can reverse the enantioselectivity of the Sharpless asymmetric epoxidation reaction. The results presented herein have clarified that the enantioselectivity of this reaction can be reproducibly reversed solely as a function of the molecular weight of the appended PEG. By preparing a range of tartrate ligands with varying PEG chains lengths, the reversal was found to occur within a molecular weight change of only 800. As the PEG chain did not affect the inherent chirality of the ligand, the enantioreversal was proposed to occur as a result of two Ti-ligand complexes which differ in their molecularity of ligand, one monomeric in ligand and the other dimeric. Support for this hypothesis was given through equilibrium measurements which revealed that the predominant species in Ti/PEG tartrate ester mixtures is a distinct 2:1 Ti-ligand complex, as opposed to the 2:2 Ti-ligand complex of traditional Sharpless asymmetric epoxidations. In total, these data represent an unrecognized property of PEG-supported catalysts that could open up new venues in the control of asymmetric reactions by means of achiral appended polymers.     

The Michael addition of indoles to alpha,beta-unsaturated ketones catalyzed by CeCl3.7H2O-NaI combination supported on silica gel

Alkylation of indoles by means of the Michael addition has been the subject of a number of investigation. It is well established that regioselectivity in the additions of indoles to electron-deficient alkenes is strongly controlled by the reaction medium. In a continuation of the work on developing greener and cleaner technologies, the cerium(III) chloride heptahydrate and sodium iodide combination supported on silica gel catalyzes the alkylation of various indoles with alpha,beta-unsaturated ketones giving 3-(3-oxoalkyl)indole derivatives in good yields. The substitution on the indole nucleus occurred exclusively at the 3-position, and N-alkylation products have not been observed.     

Quantum chemical studies of dioxygen activation by mononuclear non-heme iron enzymes with the 2-His-1-carboxylate facial triad

Density functional theory with the B3LYP hybrid functional has been used to study the mechanisms for dioxygen activation by four families of mononuclear non-heme iron enzymes: alpha-ketoacid-dependent dioxygenases, tetrahydrobiopterin-dependent hydroxylases, extradiol dioxygenases, and Rieske dioxygenases. These enzymes have a common active site with a ferrous ion coordinated to two histidines and one carboxylate group (aspartate or glutamate). In contrast to the heme case, this type of weak field environment always leads to a high-spin ground state. With the exception of the Rieske dioxygenases, which have an electron source outside the active site, the dioxygen activation process passes through the formation of a bridging-peroxide species, which then undergoes O-O bond cleavage finally leading to the four electron reduction of O(2). In the case of tetrahydrobiopterin- and alpha-ketoacid-dependent enzymes, the O-O heterolysis yields a high-valent iron-oxo species, which is capable of performing a two-electron oxidation chemistry on various organic substrates. For the other two families of enzymes (extradiol dioxygenases and Rieske dioxygenases) the substrate oxidation and the O-O bond cleavage are found to be coupled. In the extradiol dioxygenases the product of the O-O bond cleavage is a ferric iron with an oxy-substrate with a mixture of radical and anionic character, which is essential for the selectivity of the catechol cleavage.