Photophysical and ab Initio Studies of Mononuclear Copper(I) Complexes

Described are the photophysical properties of the mononuclear copper(I) complexes CuL(4)(+) (L = pyridine (py), 4-methylpyridine, 4-phenylpyridine, or acetonitrile), Cu(lut)(3)(+) (lut = 2,6-lutidine), and Cu(lut)(2)(+). Each of these compounds as their solid PF(6)(-) salts display a relatively long-lived (>1 &mgr;s), visible range emission at both ambient temperature and at 77 K but not in fluid solutions. Also reported are the results for ab initio calculations at the restricted Hartree-Fock self-consistent field level to probe the natures of lower energy excited states of the hypothetical species CuL(n)()(+) (L = NH(3), CH(3)CN, or py; n = 1-4). These results point to an assignment of the lowest energy, luminactive excited states as being largely metal centered, d --> s in character for each of the above complexes with the possible exception of the CuL(4)(+) species where L is py or a substituted analogue. In the case of Cu(py)(4)(+) the ab initiocalculations indicate a metal-to-ligand charge transfer to be the lowest energy Franck-Condon state, although the similarities of emission band shapes, energies, and lifetimes among the various complexes suggest a common d --> s assignment.     

A simple regioselective synthesis of ethyl 1,5-diarylpyrazole-3-carboxylates

Improved procedures for the regioselective preparation of ethyl 1,5-diarylpyrazole-3-carboxylates are described. The new procedures utilize readily prepared lithium aroylpyruvate intermediates which, when combined with arylphenylhydrazine hydrochlorides form 1,5-diarylpyrazole-3-carboxylates regioselectively in good to excellent yield.     

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.     

Numerical implementation of coherence for the example of the “Swiss Cross”

Summary We consider the two-dimensional Helmholtz equation u+u=0 inD with the boundary conditionsu=0 on D. D is the Swiss Cross — a region consisting of five unit squares. A method based on the concept of Coherence is utilized to determine an approximation for the first eigenvalue= ₁ more accurate than calculated by classical difference methods. The numerical result is used to illustrate isoperimetric upper and lower bounds for ₁, and to test some conjectures on its relations with torsional rigidity.Dedicated to the memory of Professor Lathar Collatz     

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      

Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space

We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceH _? ⁿ . We show that there exists a Γ-invariant real hypersurfaceF ?H _? ⁿ such that the Dirichlet fundamental polyhedron for Γ centered at z₀ has two sides (resp. infinitely many sides) if and only ifz ₀ ∈F (resp.z ₀ ?F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofH _? ⁿ is developed in terms of these horospherical coordinates.     

The oxidative decarboxylation of polyaminocarboxylic acids

Summary The rates of oxidation of four chelating agents, NTA, EDTA, CDTA, and DTPA with Ce(IV), in sulfuric acid media, were determined spectrophotometrically by a stopped-flow technique. The reductive ability is in the order CDTA > EDTA > DTPA > NTA. The influence of varying the acidity of the medium was studied, and in each case a maximum in the rate constant vs. [H⁺] plot was observed. A possible interpretation of the reactivities and the influence of acidity is advanced.

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Oxydative Decarboxylierung von PolyaminocarbonsäurenII. Vergleichende kinetische Untersuchung der Oxydation von NTA, ÄDTA, CDTA und DTPA mit Ce(IV) in saurer Lösung

Zusammenfassung Die Oxydationsgeschwindigkeiten von 4 Chelaten (NTA, ÄDTA, CDTA und DTPA) mit Ce(IV) in saurer Lösung wurden spektrophotometrisch mit Hilfe der stopped-flow-Technik bestimmt. Die Reduzierfähigkeit nimmt in der Reihenfolge CDTA > ÄDTA > DTPA > NTA ab. Der Einfluß verschiedener Säuregehalte in der Lösung wurde untersucht, und in jedem Fall wurde ein Maximum in der graphischen Darstellung der Geschwindigkeitskonstante gegen [H⁺] beobachtet. Eine mögliche Erklärung des Reaktionsvermögens und des Säureeinflusses wird gegeben.

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Part I: Z. Anal. Chem. 246, 231 (1969).