SiO bonded interactions in coesite: a comparison of crystalline, molecular and experimental electron density distributions

Bond critical point properties of electron density distributions calculated for representative Si₅O₁₆ moieties of the structure of coesite are compared with those observed and calculated for the bulk crystal. The values calculated for the moieties agree with those observed to within ∼5%, on average, whereas those calculated for the crystal agree to within ∼10%. As the SiOSi angles increase and the SiO bonds shorten, there is a progressive build-up in the calculated electron density along the bonds. This is accompanied by an increase in both the curvatures of the electron density, both perpendicular and parallel to each bond, and the Laplacian of the electron density distribution at the bond critical points. The cross sections of the bonds at the critical points become more circular as the angle approaches 180o. Also, the bonded radius of the oxide anion decreases about twice as much as that of the Si cation as the SiO bond length decreases and the fraction of s-character of the bond is indicated to increase. A knowledge of electron density distributions is central to our understanding of the forces that govern the structure, properties, solid state reactions, surface reactions and phase transformations of minerals. The software (CRYSTAL95 and TOPOND) used in this study to calculate the bond critical properties of the electron density and Laplacian distributions is bound to promote a deeper understanding of crystal chemistry and properties. Received: 23 February 1998 / Revised, accepted: 16 July 1998     

Field calibration of a formula for entrance mixing of river inflows to lakes: Lake Taupo,North Island,New Zealand

Field measurements were used to validate predictions for the initial dilution of negatively buoyant, cold‐water inflows to Lake Taupo, as part of a study to quantify mixing processes associated with the two largest inflows to the lake. The predictions were made using a formulation originally derived for positively buoyant, warm‐water inflows to cooling ponds. The formulation predicts the total dilution of an inflow during its inertia‐dominated phase between its entrance to the lake and the point where buoyancy forces are great enough to cause the inflow to plunge and form a submerged density current. In one of the measured inflows, the inflowing jet was free to entrain from both sides; in the other, entrainment was restricted on one side by attachment of the inflowing jet to the shoreline of a bay just upstream of the plunge point. In the former example, the unmodified coefficients from the cooling pond formulation provided an excellent prediction of initial dilution. In the latter example, entrainment was reduced and different coefficients were derived. In both examples the inflows remained attached to the lake bed throughout their course until their liftoff at depths of 45–55 m to form interflows. The difference between coefficients for the two inflows indicates that the coefficient values should be considered site‐specific. The formulation is not valid for inflows that separate from the bottom of the inflow channel before plunging. The entrance mixing formulation was incorporated in a more general model of lake stratification, DYRESM, which already includes a well‐documented routine for routing underflows down submerged channels on the bed of a lake. Application of the model to the inflows measured in Lake Taupo gave good results for two model outputs that were not involved in the calibration of the entrance mixing formulation, but that are affected by the result of the initial dilution calculation—the temperatures in the river plume after it has plunged, and the insertion depth.     

The bottom sediments of the Amazon shelf and tropical Atlantic Ocean

Analytical results of bottom sampling of the equatorial Atlantic Ocean affected by the Amazon River show a concentration of material smaller than 2 μ along the shore northwest of the mouth of the Amazon River for 2000 km. A zone having a high percentage of material coarser than 20 μ extends outward from the Amazon River and along the outer continental shelf northwestward for 2000 km. Areas having high carbonate percentages are encountered only on the outer shelf and in deep water.     

Fluxes of organic carbon in Manukau Harbour, New Zealand

We collated information on the sources and sinks of organic carbon in Manukau Harbour, a shallow temperate estuary. Two contrasting inner harbor regions were considered; the northern region, which is urbanized and receives a major load of sewage wastewater, and the southern region, where allochthonous inputs are dominated by the runoff from small rural streams. Although high levels of dissolved nitrogen in the wastewater supported phytoplankton blooms in the northern region, total primary production there was similar to that in the southern region (ca. 300 g C m^?2yr^?1). By contrast, high concentrations of organic carbon in the wastewater resulted in an additional input to the northern region of 120 g C m^?2 yr^?1. Loads from runoff and streams to both regions were low. At 350 g C m^?2 yr^?1, total respiration in the northern region exceeded total production, so the region was slightly heterotrophic. Respiration was lower in the southern region (270 g C m^?2 yr^?1), which was net autotrophic. Some carbon was exported from each region to the outer harbour (50–80 g C m^?2 yr^?1). Dissolved oxygen levels in the northern region were somewhat depleted at times; and the high numbers of microzooplankton indicated consumption was enhanced there. Apart from a relatively small area of organic enrichment close to the wastewater discharge, benthic consumers in the harbor appeared to be limited by physical disturbance (by wind-waves) rather than by food availability. Improved wastewater treatment is expected to substantially reduce the allochthonous input to the northern region, with the total input of carbon in the future being only slightly higher than that to the southern region.     

Bond length variation in hydronitride molecules and nitride crystals

Bond lengths calculated for the coordination polyhedra in hydronitride molecules match average values observed for XN bonds involving main group X-cations in nitride crystals to within 0.04 Å. As suggested for oxide and sulfide molecules and crystals, the forces that determine the average bond lengths recorded for coordinated polyhedra in hydronitride molecules and nitride crystals appear to be governed in large part by the atoms that comprise the polyhedra and those that induce local charge balance. The forces exerted on the coordinated polyhedra by other parts of the structure seem to play a small if not an insignificant role in governing bond length variations. Bonded radii for the nitride ion obtained from theoretical electron density maps calculated for the molecules increase linearly with bond length as observed for nitride crystals with the rock salt structure. Promolecule radii calculated for the molecules correlate with bonded and ionic radii, indicating that the electron density distributions in hydronitride molecules possess a significant atomic component, despite bond type.     

Evidence of systematic errors in FK5

Analyses of FK5 stars observed in 1986 with the Carlsberg Automatic Meridian Circle on La Palma and the automatic meridian circle at Bordeaux Observatory produce evidence of systematic errors in the FK5 reaching 0 ^. 1 in size.     

Glonass Laser Ranging Accuracy With Satellite Signature Effect

GLONASS satellites have been tracked by the worldwide laser ranging networkas well as by the GLONASS-borne microwave-based technique. Owing to thelarge size of their corner cube reflector arrays, the amount of ranging data is enough to determine their orbits from laser ranging data alone. We found, however, that the large size of the array affected the accuracy of measurement to an extent that is dependent on the characteristics of the ranging systems. An azimuthal variation of the reflector array response was also detected in observations from single-photon laser ranging. Orbital analysis reveals that the effect makes the measured range on average 22 mm shorter than expected in the absence of the large array, which explains more than half of the offset of 39 mm previously discovered between microwave and laser orbits.     

A population analysis for Be and B oxyanions

Mulliken bond overlap populations calculated for beryllium and boron oxyanions isolated from a number of minerals and synthetic compounds correlate with observed bond lengths with shorter bonds tending to involve larger overlap populations. As the populations were calculated assuming constant bond lengths and observed valence angles, the correlations are asserted to reflect the angular geometry impressed on the oxyanions by neighboring cations. Extended Hückel theory shows that the dependence of overlap population upon valence angles is greater for boron than for beryllium oxyanions. This is consistent with the observation that bond length variations in boron oxyanions are greater than those in corresponding beryllium oxyanions. As expected, observed bond lengths correlate with valence angles with the shorter bonds tending to be involved in wider angles.Now at Department of Geophysical Sciences, University of Chicago, Chicago, Illinois 60637, USANow at Geochemistry Branch, Phillips Petroleum Co., Bartlesville, Oklahoma 74004, USANow at Department of Geology, University of Toledo, Toledo, Ohio 43606, USA     

Experimental and theoretical bond critical point properties for model electron density distributions for earth materials

Generalized X-ray scattering factor model experimental electron density distributions and bond critical point, bcp, properties generated in recent studies for the earth materials stishovite, forsterite, fayalite and cuprite with high energy single crystal synchrotron X-ray diffraction data and those generated with high resolution diffraction data for coesite and senarmonite were found to be adequate and in relatively good agreement, ~5% on average, with those calculated with quantum chemical methods with relatively robust basis sets. High resolution low energy single crystal diffraction data, recorded for the molecular sieve AlPO₄-15, were also found to yield model electron density distribution values at the bcp points for the AlO and PO bonded interactions that are in relatively good to moderately good agreement with the theoretical values, but the Laplacian values of the distribution at the points for the two bonded interactions were found to be in relatively poor agreement. In several cases, experimental bcp properties, generated with conventional low energy X-ray diffraction data for several rock forming minerals, were found overall to be in poorer agreement with the theoretical properties. The overall agreement between theoretical bcp properties generated with computational quantum methods and experimental properties generated with synchrotron high energy radiation not only provides a basis for using computational strategies for studying and modeling structures and their electron density distributions, but it also provides a basis for improving our understanding of the crystal chemistry and bonded interactions for earth materials. Theoretical bond critical point properties generated with computational quantum methods are believed to rival the accuracy of those determined experimentally. As such the calculations provide a powerful and efficient method for evaluating electron density distributions and the bonded interactions for a wide range of earth materials.Dedicated to Professor Robert F. Stewart of Carnegie Mellon University on his retirement for his brilliant and original work modeling electron density distributions.