Effects of Electron Correlation in X‐Ray and Electron Diffraction. IV. Approximate Treatment for Many‐Electron Atoms

A simple scheme is proposed for predicting effects of electron correlation on intra‐atomic electron—electron radial distribution functions and on intensities of x rays scattered by gas atoms. It makes use of a relationship connecting the Coulomb hole function for an electron pair with the corresponding correlation energy. The method is applied to the beryllium atom in its ground state. Results compare favorably with results calculated directly from correlated and Hartree—Fock wavefunctions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71228/2/JCPSA6-45-12-4700-1.pd

Molecular Structure of XeF6. II. Internal Motion and Mean Geometry Deduced by Electron Diffraction

The distribution of internuclear distances in gaseous XeF6 exhibits unusually diffuse XeF6 bonded and F–F geminal nonbonded peaks, the latter of which is severely skewed. The distribution proves the molecule cannot be a regular octahedron vibrating in independent normal modes. The instantaneous molecular configurations encountered by the incident electrons are predominantly in the broad vicinity of C3υC3υ structures conveniently described as distorted octahedra in which the xenon lone pair avoids the bonding pairs. In these distorted structures the XeF bond lengths are distributed over a range of approximately 0.08 Å with the longer bonds tending to be those adjacent to the avoided region of the coordination sphere. Fluorines suffer angular displacements from octahedral sites which range up to 5° or 10° in the vicinity of the avoided region.Alternative interpretations of the diffraction data are developed in detail, ranging from models of statically deformed molecules to those of dynamically inverting molecules. In all cases it is necessary to assume that t1ut1u bending amplitudes are enormous and correlated in a certain way with substantial t2gt2g deformations. Notwith‐standing the small fraction of time that XeF. spends near OhOh symmetry, it is possible to construct a molecular potential‐energy function more or less compatiable with the diffraction data in which the minimum energy occurs at OhOh symmerty. The most notable feature of this model is the almost vanishing restoring force for small t1ut1u bending distortions. Indeed, the mean curvature of the potential surface for this model corresponds to a υ4υ4 force constant F44F44 of 10−2 mdyn/Å or less. Various rapidly inverting non‐OhOh structures embodying particular combinations of t2gt2g and t1ut1u deformations from OhOh symmetry give slightly better radial distribution functions, however. In the region of molecular configuration where the gas molecules spend most of their time, the form of the potential‐energy function required to represent the data does not distinguish between a Jahn–Teller first‐order term or a cubic V445V445 term as the agent responsible for introducing the t2gt2g deformation. The Jahn–Teller term is consistent with Goodman's interpretation of the molecule. On the other hand, the cubic term is found to be exactly analogous to that for other molecules with stereochemically active lone pairs (e.g., SF4, ClF3). Therefore, the question as to why the XeF6 molecule is distorted remains open. The reported absence of any observable gas‐phase paramagnetism weighs against the Jahn–Teller interpretation.The qualitative success but quantitative failure of the valence‐shell–electron‐pair‐repulsion theory is discussed and the relevance of the “pseudo‐Jahn–Teller” formalism of Longuet‐Higgins et al. is pointed out. Brief comparisons are made with isoelectronic ions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70641/2/JCPSA6-48-6-2466-1.pd

Estimating equations for biomarker based exposure estimation under non-steady-state conditions

Unrealistic steady-state assumptions are often used to estimate toxicant exposure rates from biomarkers. A biomarker may instead be modeled as a weighted sum of historical time-varying exposures. Estimating equations are derived for a zero-inflated gamma distribution for daily exposures with a known exposure frequency. Simulation studies suggest that the estimating equations can provide accurate estimates of exposure magnitude at any reasonable sample size, and reasonable estimates of the exposure variance at larger sample sizes

Assessing the effects of exposure timing on biomarker expression using β-estradiol

Temporal and spatial variability in estrogenicity has been documented formanytreated wastewater effluents with the consequences of this variability on the expression of biomarkers of endocrine disruption being largely unknown. Laboratory exposure studies usually utilize constant exposure concentrations which may produce biological effects that differ from those observed in organisms exposed in natural environments. In this study, we investigated the effects of differential timing of exposures with 17β - estradiol (E2) on a range of fathead minnow biomarkers to simulate diverse environmentally relevant exposure profiles. Two 21-day, replicate experiments were performed exposing mature male fathead minnows to E2 at time-weighted mean concentrations (similar average exposure to the contaminant during the 21-day exposure period; 17 ng E2/L experiment 1; 12 ng E2/L experiment 2) comparable to E2 equivalency values (EEQ) reported for several anthropogenically altered environments. A comparable time-weighted mean concentration of E2 was applied to five treatments which varied in the daily application schema: E2 was either applied at a steady rate (ST), in a gradual decreasing concentration (HI), a gradual increasing concentration (LO), applied intermittently (IN), or at a randomly varying concentration (VA). We assessed a range of widely used physiological (vitellogenin mRNA induction and plasma concentrations), anatomical (body and organ indices, secondary sex characteristics, and histopathology), and behavioral (nest holding) biomarkers reported to change following exposure to endocrine active compounds (EACs). All treatments responded with a rise in plasma vitellogenin concentration when compared with the ethanol carrier control. Predicatively, vitellogenin mRNA induction, which tracked closely with plasma vitellogenin concentrations in most treatments was not elevated in the HI treatment, presumably due to the lack of E2 exposure immediately prior to analysis. The ability of treatment male fish to hold nest sites in direct competition with control males was sensitive to E2 exposure and did yield statistically significant differences between treatments and carrier control. Other biological endpoints assessed in this study (organosomatic indices, secondary sex characteristics) varied little between treatments and controls. This study indicates that a broad suite of endpoints is necessary to fully assess the biological consequences of fish exposure to estrogens and that for at least field studies, a combination of vitellogenin mRNA and plasma vitellogenin analysis are most promising in deciphering exposure histories of wild-caught and caged fishes

Error matrices in gas-electron diffraction : II. Influence of weight matrix

The properties of three different forms of error matrices in electron diffraction are investigated, assuming the presence of stationary, Gaussian, Markovian noise in the primary data. The error matrices studied are Mxp based on the optimum weight matrix P the bona fide error matrix Mxw based on the nonoptimum weight matrix W, and the false error matrix Mxo commonly calculated by diffractionists using the formula for the optimum error matrix while incorporating a nonoptimum weighting. Simple formulae relating the elements of the various matrices are derived in the case where W is the best diagonal weight matrix and where geometric constraints are not imposed on parameters. The influence of geometric constraints is tested. Calculations indicate that diagonal weight matrices in ordinary circumstances give results imperceptibly inferior to the results obtained with the best nondiagonal weight matrices. Elements of Mxw closely approach those of Mxp whereas elements of the false error matrix, taken alone, may be very misleading.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33835/1/0000093.pd

Private Drinking Water Wells as a Source of Exposure to Perfluorooctanoic Acid (PFOA) in Communities Surrounding a Fluoropolymer Production Facility

BACKGROUND: The C8 Health Project was established in 2005 to collect data on perfluorooctanoic acid (PFOA, or C8) and human health in Ohio and West Virginia communities contaminated by a fluoropolymer production facility. OBJECTIVE: We assessed PFOA exposure via contaminated drinking water in a subset of C8 Health Project participants who drank water from private wells. METHODS: Participants provided demographic information and residential, occupational, and medical histories. Laboratory analyses were conducted to determine serum-PFOA concentrations. PFOA data were collected from 2001 through 2005 from 62 private drinking water wells. We examined the relationship between drinking water and PFOA levels in serum using robust regression methods. As a comparison with regression models, we used a first-order, single-compartment pharmacokinetic model to estimate the serum:drinking-water concentration ratio at steady state. RESULTS: The median serum PFOA concentration in 108 study participants who used private wells was 75.7 μg/L, approximately 20 times greater than the levels in the U.S. general population but similar to those of local residents who drank public water. Each 1 μg/L increase in PFOA levels in drinking water was associated with an increase in serum concentrations of 141.5 μg/L (95% confidence interval, 134.9-148.1). The serum:drinking-water concentration ratio for the steady-state pharmacokinetic model was 114. CONCLUSIONS: PFOA-contaminated drinking water is a significant contributor to PFOA levels in serum in the study population. Regression methods and pharmacokinetic modeling produced similar estimates of the relationship

Risk Estimation and Value-of-Information Analysis for Three Proposed Genetic Screening Programs for Chronic Beryllium Disease Prevention

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75032/1/0272-4332.00009.pd

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed

Spectral Shape of Relaxations in Silica Glass

Precise low-frequency light scattering experiments on silica glass are presented, covering a broad temperature and frequency range (9 GHz < \nu < 2 THz). For the first time the spectral shape of relaxations is observed over more than one decade in frequency. The spectra show a power-law low-frequency wing of the relaxational part of the spectrum with an exponent $\alpha$ proportional to temperature in the range 30 K < T < 200 K. A comparison of our results with those from acoustic attenuation experiments performed at different frequencies shows that this power-law behaviour rather well describes relaxations in silica over 9 orders of magnitude in frequency. These findings can be explained by a model of thermally activated transitions in double well potentials.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let