Uniform semiclassical self-consistent-field calculations of vibrational resonance energies and widths

Using the Breit—Wigner definition of a resonance, we calculate both resonance positions and widths for a model non-separable hamiltonian, using a uniform semiclassical self-consistent-field (SCF) method. Excellent agreement with recent complex-coordinate quantum SCF calculations is obtained.     

Benzene in the extended hückel approximation: an unexpected geometry

The equilibrium geometry predicted by the extended Hückel method for benzene with D_6h symmetry is found to correspond to a saddle point on the potential surface. The search for a more stable D_3h structure leads to the prediction that benzene is unstable in the EHT approximation. It is concluded that EHT calculations of molecular conformation are much less than has apparently been previously recognized.     

Raman spectra of ionic liquids: a simulation study of LaCl3 and its mixtures with alkali chlorides

Theoretical Raman spectra of the elpasolite-structured crystal Cs2NaLaCl6 and of molten mixtures of LaCl6 with NaCl and CsCl have been obtained from computer simulations in order to examine how the Raman spectra reflect the coordination structure around the La3+ ions. This system is a model for many other trivalent metal halides and for examining how the network structure of the pure melts is broken down by the addition of alkali halides with different structure-breaking powers. The results suggest a way of reconciling the conclusions of Raman studies about the structures of the melts with those of neutron and x-ray-diffraction studies, which have already been examined with the same simulation methods. The Raman spectra, both polarized and depolarized, are calculated from a model for the dependence of the polarizability of the system on the ionic coordinates which was inspired by electronic structure calculations of the polarizabilities of ions in a condensed phase environment. Some results on the lifetimes of the coordination complexes responsible for the appearance of the discrete Raman bands are discussed.     

KT-nearfields of rank 2

Summary Nearfields of rank 2 over their kernel which are not Dickson nearfields have recently been constructed by H. Zassenhaus. Here it is shown that KT-nearfields of rank 2 over their kernels and of characteristic 2 are necessarily Dickson nearfields which are coupled to quadratic field extensions and their Dickson group is isomorphic to ₂. Using results of Gröger one obtains all KT-nearfields of rank 2 over the field of rational numbers.     

Gap-Free Set Partitions

A set partition is called “gap-free” if its block sizes form an interval. In other words, there is at least one block of each size between the smallest and largest block sizes. Let B(n) and G(n), respectively, denote the number of partitions and the number of gap-free partitions of the set [n]. We prove that      

Stereochemical analysis of isopentenyl diphosphate isomerase type II from Staphylococcus aureus using chemically synthesized (S)- and (R)-[2-2H]isopentenyl diphosphates

[chemical reaction: see text]. To study the catalysis of isopentenyl diphosphate (IPP) isomerase type II from Staphylococcus aureus, which is a flavoprotein catalyzing the interconversion of IPP and dimethylallyl diphosphate, we have chemically synthesized (S)- and (R)-[2-2H]IPP and carried out stereochemical analysis of the reaction. Our results show that the C-2 deprotonation of IPP by this enzyme is pro-R stereospecific, suggesting a similar stereochemical course as the type I enzyme.     

Facile syntheses of unsolvated UI3 and tetramethylcyclopentadienyl uranium halides

In the course of comparing the reaction chemistry of (C5Me5)3U, 1, and its slightly less crowded analogue (C5Me4H)3U, 2, new syntheses of UI3, (C5Me4H)3U, (C5Me4H)3UCl, 3, and (C5Me5)3UCl, 4, have been developed. Additionally, (C5Me4H)3UI, 5, and (C5Me4H)2UCl2, 6, have been identified for the first time. A facile synthesis of unsolvated UI3 is reported that proceeds in high yield with inexpensive equipment from iodine and hot uranium turnings. Both UI3 and UI3(THF)4 react with KC5Me4H in toluene to make unsolvated (C5Me4H)3U in higher yield than in previous reports that involve reduction of tetravalent (C5Me4H)3UCl, 3. A more atom-efficient synthesis of complex 3 is also reported that proceeds from reduction of t-BuCl, PhCl, or HgCl2 by 2. Similarly, (C5Me4H)3U reacts with PhI or HgI2 to generate (C5Me4H)3UI. These studies also provided a basis to improve the synthesis of (C5Me5)3UCl from 1 by employing t-BuCl or HgCl2 as the halide source. Like (C5Me5)3UCl, the (C5Me4H)3UCl complex reacts with HgCl2 to form (C5Me4H)2 and (C5Me4H)2UCl2, 6, but unlike (C5Me5)3UX (X = Cl or I), the less substituted (C5Me4H)3UX complexes do not reduce t-BuCl or PhX. The synthesis of 6 from (C5Me4H)MgCl x THF and UCl4 is also included.     

Triphenylphosphonium-alloxan betaines

Alloxan and 1,3-dimethylalloxan react with triarylphosphines to generate zwitterionic adducts involving the phosphorus and the C-5 carbonyl oxygen atoms of alloxan. The adducts, unlike alloxan, did not induce permanent hyperglycemia but one analog did effect a transient rise in blood glucose.     

Bile acids LXIX. Selective K-Selectride reduction of 3,7-diketo steroids

The K-Selectride reduction at low temperature (-45°C) of 7-oxo-5α-holestan-3β-yl acetate and methyl 7-oxo-3α-hydroxy-5(β-cholanoate resulted in almost quantitative yield of the 7α-alcohol in the 5α-compound but only moderate yield of the 5β-analog. The simultaneous reduction of two carbonyl groups in the 3 and 7 positions afforded good to excellent yields of the diaxial diol in planar steroids (methyl 3,7-dioxo-5α-cholanoate, 3,7-dioxo-5α-cholestane and methyl 3,7-dioxo-5α-cholestan-27-oate) and only 14% of 3α,7α-(OH)₂ from methyl 3,7-dioxo-5β-cholanoate.     

Gödel axiom mappings in special relativity and quantum-electromagnetic theory

Exponential mappings into an imaginary space or number field for the axioms of a theory, which are in the form of propositional constants and variables, make possible: (a) an understanding of the meaning and differences between the Lorentz transformation constants, such that their product is still equal to one, but the axioms at each end of the transformations are logically inverse and separately consistent; (b) an interpretation of the psi function phase factor which is part of the axiomE=hf; (c) the unification of the quantum-mechanical psi function and the electromagnetic wave function. Thus, those statements whose mechanisms are unknown (the axioms of the theory) are to be assigned the axiom propositional number symbol and are to be associated with the complex probability eⁱ, which is a uniform factor of the energy equations expressing the physical state. Such probabilistic axiom functions can be associated with both the special theory of relativity and the quantum-electromagnetic theory.