Quasirationale singularitäten

It Is shown that Elkik's results on deformations of rational singularities hold without Cohen-Macaulay assumptions: let f:XS be flat with normal fibres X_s and desingularisations _s:Y_sX_s; then the sets are open for all d.     

Heats of crystallization of potassium chloride and magnesium chloride hexahydrate from aqueous solutions at 298.15 K. A critical review

Published data on the heats of crystallization from aqueous solutions of potassium chloride and magnesium chloride hexahydrate are critically reviewed and compared with those evaluated from solubility and activity data. The recommended values of the heats of crystallization are −13.8±0.1 kJ mole⁻¹ for KCl and −15.8^−0.3_+2.8 kJ mole⁻¹ for MgCl₂·6 H₂O. A test of the mutual consistency of data for dissolution heats, temperature dependence of solubility and concentration dependence of activity and/or osmotic coefficient is a side-issue of the review.     

Real-space post-Hartree-Fock correlation models

Real-space models of nondynamical correlation between electrons of opposite spin and of parallel spin in multicenter (molecular) systems are discussed. These models are designed to be partnered with Hartree-Fock or exact Kohn-Sham exchange. Thus the numerous and well-known problems of local density-functional exchange-correlation approximations, especially in stretched odd-electron systems, are circumvented.     

Reaction barrier heights from an exact-exchange-based density-functional correlation model

A recent exact-exchange-based density-functional model of nondynamical and dynamical correlation [A.D. Becke, J. Chem. Phys. 122, 064101 (2005)] is tested on 70 barrier heights for a variety of reaction types: hydrogen transfer reactions, heavy-atom transfer reactions, nucleophilic substitutions, association reactions, and unimolecular rearrangements, including both even- and odd-electron systems. The mean absolute error with respect to accurate reference data is 1.4 kcal/mol. This is achieved without any refitting of the parameters of the model to the barrier height data.     

Synthesis of erythro-alpha-amino beta-hydroxy carboxylic acid esters by diastereoselective photocycloaddition of 5-methoxyoxazoles with aldehydes

A new photoaldol route to alpha-amino-beta-hydroxy carboxylic acid esters is initiated by the photocycloaddition of aromatic or aliphatic aldehydes to 5-methoxyoxazoles. The 4-unsubstituted 5-methyloxazole 1 gave the cycloadducts 8a-f in high yields and excellent exo-diastereoselectivities. Hydrolysis of 8a-f gives the N-acetyl alpha-amino-beta-hydroxy esters 9a-f, which could be subsequently converted into the corresponding Z-didehydro alpha-amino acids 10a-f. Quartenary alpha-amino-beta-hydroxy esters 12, 14, 16, 18, and 20, which are stable against dehydration, were obtained from the 4-alkylated 5-methoxyoxazoles 2-6, in most cases highly erythro-selective due to the high degree of stereocontrol (exo) at the photocycloaddition (to give 11, 13, 15, 17, and 19) level. The relative configurations of the N-acetyl alpha-amino-beta-hydroxy esters were determined by NMR spectroscopy and comparison with chiral pool-derived compounds as well as by X-ray structure determination of the ester 23, formed by hydrolysis of the cycloadduct 22, derived from photocycloaddition of propionaldehyde to the isoleucine-derived oxazole 21.     

Studies of the Reaction Behavior of Nitryl Compounds Towards Azides: Evidence for Tetranitrogen Dioxide,N4O2

The reaction behavior of NaN₃, AgN₃, and Me₃SiN₃ towards FNO₂, CINO₂, NO₂SbF₆, and NO₂BF₄ was investigated. At -30°C or below in a solvent-free system sodium azide did not react with CINO₂, NO₂BF₄, or NO₂SbF₆. Below -30°C silver azide did not react either with neat C1NO₂. Treatment of Me₃SiN₃ with pure C1NO₂ led to the formation of C1N₃, N₂O, and Me₃SiOSiMe₃. A mechanism for this reaction has been proposed. Pure chlorine azide was isolated by fractional condensation and identified by its low-temperature Raman spectrum (liquid state). The reaction of Cp₂Ti(N₃)₂ with C1NO₂ also yielded C1N₃ as the only azide-containing reaction product. Treatment of FNO₂ with NaN₃ at temperatures as low as -78°C always ended in an explosion which was probably due to the formation of FN₃ as one of the reaction products. The reaction of NO₂SbF₆ with NaN₃ in liquid CO₂ (-55°C· T· -35°C) as the solvent afforded a new azide species which was stable at low temperature in solution only and was investigated by means of low-temperature Raman spectroscopy. The obtained vibrational data give strong evidence for the presence of tetranitrogen dioxide, N₄O₂, which can be regarded as nitryl azide (NO₂N₃). The structure and vibrational frequencies of N₄O₂ were computed ab initio at correlated level (MP2/6-31 + G^*). In liquid xenon (-100°C· T· -60°C) NaN₃ did not react with NO₂SbF₆. A previous literature report on the preparation of N₄O₂ could not be established.