Least-squares numerical Rayleigh-Ritz and minimum-variance methods for molecular calculations

A general method is presented to find in a least-squares sense a set of orthogonal eigenfunctions and their eigenvalues from local energy and numerical integration methods or by any other dissymmetric approach to solve the eigenvalue problem of a Hermitian operator. By this method a generalization of the minimum variance method to more than one eigenfunction is obtained, which is a variant of Scott's method. Also a new method is derived—called the minimum-overlap method—that is a least-squares numerical version of the standard Rayleigh-Ritz method. Test calculations on the atoms Be and Tm and the molecules H₂ and CO have been performed with both numerical Hartree-Fock and Hartree-Fock-Slater methods. The least-squares solutions are an improvement over other methods in the case of accurate basis sets. Numerical Hartree-Fock calculations of moderate accuracy are found to be considerably faster than the analytic method.     

A luminescence-based probe for sensitive detection of hydrogen peroxide in seconds

Here, we present a fast and simple hydrogen peroxide assay that is based on time-resolved fluorescence. The emission intensity of a complex consisting of terbium ions (Tb³⁺) and phthalic acid (PA) in HEPES buffer is quenched in the presence of H₂O₂ and this quenching is concentration-dependent. The novel PATb assay detects hydrogen peroxide at a pH range from 7.5 to 8.5 and with a detection limit of 150 nmol L⁻¹ at pH 8.5. The total assay time is less than 1 min. The linear range of the assay can be adapted by a pH adjustment of the aqueous buffer and covers a concentration range from 310 nmol L⁻¹ to 2.56 mmol L⁻¹ in total which encompasses four orders of magnitude. The assay is compatible with high concentrations of all 47 tested inorganic and organic compounds. The PATb assay was applied to quantify H₂O₂ in polluted river water samples. In conclusion, this fast and easy-to-use assay detects H₂O₂ with high sensitivity and precision.     

The direct reaction field hamiltonian: Analysis of the dispersion term and application to the water dimer

The induction and dispersion terms obtained from quantum-mechanical calculations with a direct reaction field hamiltonian are compared to second order perturbation theory expressions. The dispersion term is shown to give an upper bound which is a generalization of Alexander's upper bound. The model is illustrated by a calculation on the interactions in the water dimer. The long range Coulomb, induction and dispersion interactions are reasonably reproduced.     

Wake development in staggered short cylinder arrays within a channel

Staggered arrays of short cylinders, known as pin?Cfins, are commonly used as a heat exchange method in many applications such as cooling electronic equipment and cooling the trailing edge of gas turbine airfoils. This study investigates the near wake flow as it develops through arrays of staggered pin fins. The height-to-diameter ratio was unity while the transverse spacing was kept constant at two cylinder diameters. The streamwise spacing was varied between 3.46 and 1.73 cylinder diameters. For each geometric arrangement, experiments were conducted at Reynolds numbers of 3.0e3 and 2.0e4 based on cylinder diameter and velocity through the minimum flow area of the array. Time-resolved flowfield measurements provided insight into the dependence of row position, Reynolds number, and streamwise spacing. Decreasing streamwise spacing resulted in increased Strouhal number as the near wake length scales were confined. In the first row of the bundle, low Reynolds number flows were mainly shear-layer-driven while high Reynolds number flows were dominated by periodic vortex shedding. The level of velocity fluctuations increased for cases having stronger vortex shedding. The effect of streamwise spacing was most apparent in the reduction of velocity fluctuations in the wake when the spacing between rows was reduced from 2.60 diameters to 2.16 diameters.