Integer points on hypersurfaces

Very general hypersurfaces in ⁴ contain r ^2+(4/9) integer points in any ball of radiusr>1. As a consequence, an irreducible algebraic hypersurface in ⁿ (wheren4) which is not a cylinder and is of degreed, contains c(d, n)r ^{n–1–(5/9)} integer points in a ball of radiusr. This improves on the known boundc(d, n)r ^n–(3/2).Meinem verehrten Lehrer Professor E. Hlawka zum siebzigsten Geburtstag gewidmetWritten with partial support from NSF-MCS-8211461.     

Comparative studies of static dipole polarizabilities of ionic crystals on the basis of different self-consistent potentials

The static dipole polarizabilities, ^D , have been studied for the ions O^2–, F^–, Na⁺, Mg²⁺, Cl^–, K⁺ and Ca²⁺ in the crystals NaF, KF, NaCl, KC1, MgO and CaO. The starting zero-order wave functions have been generated using various exchange- and exchange-correlation potentials in order to study the effect of these potentials on ^D . The direct contribution to the dipole polarizability, _o ^D , has been determined by the uncoupled Hartree-Fock method. Self-consistency effects have been included by the geometric approximation. The crystal potential is incorporated using the Watson sphere model. Good agreement between theoretical and experimental results are found for those self-consistent potentials which exclude self-interaction.     

Accurate pKa determination for a heterogeneous group of organic molecules.

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.     

Preparation and properties of polymers from aryl cyclic sulfonium zwitterions

A new class of zwitterionic monomers were prepared in which the positive and negative sites are cyclic sulfonium and phenolate. Thermal polymerization occurs by phenolic anionic attack upon the aliphatic carbon α to the sulfonium sulfur. Polymerization proceeds with ring opening and net loss of charge to form nonionic polymers. The monomeric zwitterions are generally hydrated, crystalline solids that are soluble in water or alcohol. Chlorination of the aromatic portion of the molecule yields nonhydrated species. The polymerizations of 1-(4-hydroxy-3-methylphenyl)tetrahydrothiophenium hydroxide inner salt (dihydrate) and 1-(3,5-dichloro-4-hydroxyphenyl)tetrahydrothiophenium hydroxide inner salt were studied. The latter monomer gave a polymer with M?_n of 46,000 when a nucleophile was present as an initiator. The physical properties of this polymer were determined. Cyclization appears to be the main mechanism of termination in the polymerization of zwitterions.     

LiTiCl3: Synthesis and thermal behaviour

LiTiCl₃ is obtained as one example within an ample solid solution, Li_24–2nTi_nCl₂₄ (?4?n?10), by synpropotionation of TiCl₃ and Ti in the presence of LiCl (2:1:3 molar ratio) in sealed tantalum tubes at 750°C. It crystallizes with the inverse spinel-type structure according to (Li_0.67)^[4](Li_0.67Ti_1.33)^[4]Cl₄ with, at 25°C, a = 1048.62(4) pm, space group Fd3m. Thermal expansion is linear with α = 4.85 × 10^?5K^?1 up to about 300°C and thereafter, when the migration of Li⁺ from tetrahedral to octahedral interstices becomes increasingly important, it exhibits a relative decrease resulting, finally, in the phase transition to a NaCl-type structure that is observed for the first time at about 575°C.     

A novel synthesis of substituted 4H-pyrazolo[3,4-d]pyrimidin-4-ones

A novel synthesis of 4H-pyrazolo-[3,4-d]pyrimidin-4-ones is described. This approach utilizes an in situ generated iminochloride as a key precursor for amidine formation, with subsequent base-catalyzed ring closure. This method represents a mild and efficient entry into this ring system which is amenable to diversification of the core template.     

Chlor-dimethylaminosulfonium-Salze Darstellung und IR-Spektren

Chloro-dimethylaminosulfonium Salts. Preparation and I. R. Spectra By reaction of bis-dimethylamino-mono- resp. -disulfane with a mixture of chlorine/antimony(V) chloride the chloro dimethylaminosulfonium hexachloroantimonates(V) [(CH₃)₂N]₂SCI^⊕SbCl₆^? (I) and (CH₃)₂NSCI₂^⊕SbCl₆^? (II) are yielded. The i. r. spectra of these compounds were measured and assigned.     

Acyl- und Alkylidenphosphane. XXII [1]. Synthese und Struktur des 1, 3-Dimethyl-2,2,4,4-tetrakis-(trimethylsilylsulfano)-1,3-diphosphetans

Acyl- and Alkylidenephosphines. XXII. Synthesis and Structure of 1, 3-Dimethyl-2,2,4,4-tetrakis(trimethylsilylsulfano)-1,3-diphosphetane At ?30°C methylbis(trimethylsilyl)phosphine reacts with carbon disulfide to give a red adduct first which rearranges to [bis(trimethylsilylsulfano)methylidene]methylphosphine 1a . In contrast to the thermally stable phenyl derivative 1b [2], this compound with its insufficiently shielded P?C group dimerizes fast with increasing temperature. 1,3-Dimethyl-2,2,4,4-tetrakis(trimethylsilylsulfano)-1,3-diphosphetane 2a formed by this reaction, crystallizes in the triclinic space group P1 with following dimensions of the unit cell, determined at a temperature of measurement of ?80 ± 3°C: a = 1024.7(3); b = 1360.2(5); c = 1326.3(6)pm; α = 117.85(4); ß = 111.05(3); γ = 72.09(3)°; Z = 2. Due to ring folding at the P1? P2 axis of 149.1°, the molecule shows pseudosymmetry C_s. Characteristic averaged bond lengths and angles obtained at an R_w-value of 0.030, are: P? C(endocyclic) 188 and 191; P? CH₃ 184; C? S 183; S? Si 216 pm; C? P? CH₃ 105; P? C? S 113; S? C? S 114; C? S? Si 108; P? C? P 90 and C? P? C 86°.