Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes. Research partially supported by NSF under award DMS-0434393. Research partially supported by the Australian Research Council Discovery Porject DP0343616.     

Mössbauer and infrared spectroscopic studies of novel mixed valence states in cobaltous ferrocyanides and ferricyanides

Novel mixed valence states have been obtained by the treatment of cobaltous ferrocyanides (Co⁺²Fe^II) and ferricyanides (Co⁺²Fe^III) in an ozone flow. The CN stretching bands occur at 2085 cm^–1 for Co⁺²Fe^II and at 2160 cm^–1 for Co⁺²Fe^III. After the ozonization process of Co⁺²Fe^II, an intense band approximately at 2125 cm^–1 is detected. This intermediate band must correspond to a mixed valence state of the type: Fe^II–CN–Co²⁺–NC–Fe^III Mössbauer spectra recorded in situ during the ozonization of Co⁺²Fe^II show the presence of two components: a doublet with isomer shift and quadrupole splitting values close to the cobalti ferricyanide and a very broad line for the mixed valence state. From the Mössbauer and infrared spectra of the aged samples of the Co⁺²Fe^II after ozonization, a relaxation process to the initial state of the samples is observed but the mixed valence state is stable.     

Theoretical study of PO and PO−

The diatomic systems, PO and PO^– are studied, using numerical Hartree-Fock (NHF) and coupled-cluster calculations. The latter employs a hybrid NHF and Slater orbital basis set. Highly accurate CCSD methods predict bond lengths accurate to <0.004 Å and frequencies to 60 cm^–1. In addition the electron affinity of PO is computed to be 0.89 eV compared to an experimental value of 1.09±0.01. Comparisons are made with SCF and MBPT(2) results for PO⁺ using conventional basis sets.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayGuggenheim Fellow     

Transport and kinetics at microheterogeneous electrodes: Part V. The methylviologen/platinum system

Results are reported for the reaction of methylviologen radical cation, MV⁺ with platinum colloidal particles, studied by stopped flow spectrophotometry. The rate of the reaction depends on the gaseous pretreatment of the particles. For particles reduced by hydrogen, the kinetics are usually first order with respect to MV⁺. The reaction is also first order in the concentration of platinum, and is inhibited in a first order manner by the product MV²⁺. This inhibition suggests that MV²⁺ is adsorbed on the particle surfaces, and this has been confirmed by ac, ring—disc electrode studies on macroscopic platinum electrodes. At high concentrations of MV⁺ some deviation from first order kinetics is observed. These results are all explained by a kinetic model in which either the desorption of MV²⁺ or the adsorption of MV⁺ is the rate limiting process. The rate of consumption of MV⁺ on an oxidised surface is an order of magnitude faster than that on the reduced surface. Ring—disc studies show that this is because the MV⁺ is not producing H₂ but is reducing the surface oxide. The results are shown to fit a simple model which takes into account this titration of the oxide layer. The model also explains why the rate on partially oxidised surfaces will appear to have an order greater than one in [Pt].     

Singular value decomposition applied to the compression of T3 amplitude for the coupled cluster method

We apply the singular value decomposition to compress the degrees of freedom of T3 amplitude for the CCSDT-1 method (compressed CCSDT-1). This method enables us to make the number of the T3 amplitudes less than that of the T2 amplitudes, making CCSDT-1 calculations much less expensive without losing accuracy. We perform test calculations on some atoms and molecules to investigate the applicability of this method. Computational results for the electronic energies as well as timings of these calculations are presented.     

Long-range magnetic ordering in iron jarosites prepared by redox-based hydrothermal methods

The iron jarosites, plumbojarosite, Pb0.5Fe3(OH)6(SO4)2, argentojarosite, AgFe3(OH)6(SO4)2, and thallium jarosite, TlFe3(OH)6(SO4)2, along with the selenate-capped jarosite analogues of potassium, KFe3(OH)6(SeO4)2, and rubidium, RbFe3(OH)6(SeO4)2, have been prepared in their analytically pure forms by employing redox-based hydrothermal methods. The crystal structures of these materials have been determined, and all are found to be essentially isostructrual including Pb0.5Fe3(OH)6(SO4)2, which is distinct from the structure reported for naturally mined samples. All iron jarosites show long-range order (LRO), signified by a sharp transition temperature, T(N), which falls in the narrow temperature range of 61.4 +/- 5 K. The mechanism responsible for this ordering has been established by examining magnetostructural correlations for the jarosites possessing various interlayer cation and capping groups. We show that all magnetic properties of jarosites, including LRO, find their origin in the basic magnetic unit, the intralayer Fe3(mu-OH)3 triangle. Field-dependent magnetization experiments are consistent with the antiferromagnetic stacking of an out of plane moment developed from spin canting within Fe3(mu-OH)3 triangles. Together with the previously reported AFe3(OH)6(SO4)2 (A = Na+, K+, Rb+ and NH4+) jarosites, these compounds provide a framework for probing magnetic ordering in a spin frustrated lattice of the largest series of isoelectronic and isostructural kagomé systems yet discovered.