Including correlation effects in an improved spreadsheet calculation of combined standard uncertainties

A spreadsheet method allowing rapid calculation of combined standard uncertainties is described. The model used allows explicitly for correlation effects, and requires a user to enter only the parameters, the calculation used to obtain the final result (including relevant influence factors), the individual standard uncertainties for the parameters, and estimates of correlation coefficients where necessary. The estimation of correlation coefficients in common cases is discussed, and it is shown that correlation is likely to be practically significant only when the correlated contribution to individual standard uncertainties is significantly over about 30% of the relevant standard uncertainty, leading to correlation coefficients |r| greater than 0.1. The implementation includes a more robust differentiation algorithm than previously reported for spreadsheet use, and initial preparation of the spreadsheets has been automated. The principle is illustrated with a simple example. Electronic Supplementary Material  Supplementary material is available in the online version of this article at and is accessible for authorized users.

Complete curve fitting of extraction profiles for estimating uncertainties in recovery estimates

This paper reports the use of improved numerical approaches to modelling extraction profiles, and shows that the approach substantially reduces statistical prediction uncertainties compared to those obtained on the basis of a three-point extrapolation from the later part of the extraction curve. Numerical fitting of manually obtained polycyclic aromatic hydrocarbon extraction data to a spherical particle diffusion model showed uncertainties typically reduced by a factor of three (with extremes at 1.02 and 770). Application to pressurised fluid extraction study of pelletised poly(vinylchloride) containing 30 mass% di(2-ethylhexyl)phthalate also showed good improvements. However, this high precision data showed small but significant lack of fit resulting in residual correlation and visibly biased prediction (more so than simple extrapolation). Re-fitting and uncertainty estimation using a first-order autoregression approximation to the covariance matrix produced more realistic uncertainty estimates and closer parameter estimates and is accordingly recommended for treating residual correlation from other causes, but did not entirely alleviate the problem. Different shape models (spherical, plane sheet and cylindrical) were applied without accounting fully for fitting error, and particle size effects were eliminated by modelling a simple size distribution. However, an approximate model based on linearly concentration-dependent diffusion coefficient showed excellent fit, confirming concentration-dependence as the most likely cause. This semiempirical model led to an uncertainty in total extractable material, at 0.2% of the total extractable value (with allowance for correlation). This is potentially good enough for recovery estimation and correction in certification of reference materials for validation purposes.     

Gas-phase reactions of organic radicals and diradicals with ions

Reactions of polyatomic organic radicals with gas phase ions have been studied at thermal energy using a flowing afterglow-selected ion flow tube (FA-SIFT) instrument. A supersonic pyrolysis nozzle produces allyl radical (CH2CHCH2) and ortho-benzyne diradical (o-C6H4) for reaction with ions. We have observed: [CH2CHCH2 + H3O+ --> C3H6+ + H2O], [CH2CHCH2 + HO- --> no ion products], [o-C6H4 + H3O+ --> C6H5+ + H2O], and [o-C6H4 + HO- --> C6H3- + H2O]. The proton transfer reactions with H3O+ occur at nearly every collision (kII approximately with 10(-9) cm3 s(-1)). The exothermic proton abstraction for o-C6H4 + HO- is unexpectedly slow (kII approximately with 10(-10) cm3 s(-1)). This has been rationalized by competing associative detachment: o-C6H4 + HO- --> C6H5O + e-. The allyl + HO- reaction proceeds presumably via similar detachment pathways.     

Generalization of Dewar's half-electron method for calculating energies of open-shell electronic states

Dewar's “half-electron” model for calculating electronic energies of certain open-shell doublet and triplet states is extended so as to be applicable to the lowest-energy open-shell state of any given symmetry and multiplicity.     

Mechanistic study of enantiomeric recognition with native gamma-cyclodextrin by capillary electrophoresis,reversed-phase liquid chromatography,nuclear magnetic resonance spectroscopy,electrospray mass spectrometry and circular dichroism techniques

The possible mechanisms for the chiral recognition of 2(S)-(3,5-bis-trifluoromethyl-phenyl)-2-[3(S)-(4-fluorophenyl)-4-(1H-[1,2,4]triazol-3-ylmethyl)-morpholin-2(R)-yloxy]-ethanol (compound A) and its enantiomer with native gamma-cyclodextrin (gamma-CD) were investigated using capillary electrophoresis (CE), reversed-phase liquid chromatography (RPLC), proton (1H), fluorine (19F) and carbon (13C) nuclear magnetic resonance spectroscopy (NMR), electrospray mass spectrometry (ESI-MS) and circular dichroism (CD). All experiments provided clear evidence of the formation of diastereomeric complexes between the enantiomers and gamma-CD. Proton, fluorine and carbon NMR spectra suggested that both aromatic rings, with mono-fluoro and bis-tri-fluoro functional groups, on the guest molecule were partially included into the cavity of the gamma-CD. ESI-MS spectra indicated that the diastereomeric complexes have a 1:1 stoichiometric ratio. The binding constants of the diastereomeric complexes obtained by CE, RPLC and CD were compared. The effects of the gamma-CD concentration, organic modifiers and temperature on the CE-chiral separation were also investigated.