Hydrogen bis[tris(4‐fluorophenyl)phosphane oxide] triiodide

In the title compound, C₃₆H₂₅F₆O₂P₂⁺·I₃⁻, hydrogen‐bonded [{(p‐FC₆H₄)₃PO}₂H]⁺ dimers assemble along the crystallographic c axis to form channels that house extended chains of triiodide anions. Although the I—I bond lengths of 2.9452 (14) and 2.9023 (15) Å are typical, the inter‐ion I...I distance of 3.5774 (10) Å is unusually short. A posteriori modelling of nonmerohedral twinning about (100) has been only partially successful, achieving a reduction in the maximum residual electron density from 5.28 to 3.24 e Å⁻³. The inclusion of two low‐occupancy I‐atom sites (total 1.7%), which can be interpreted as translational disorder of the triiodide anions along the channels, reduced the maximum residual electron density to 2.03 e Å⁻³. The minor fractional contribution volume of the nonmerohedral twin domains refined to 0.24 and simultaneous refinement of the inversion twin domains showed the crystal to be a 0.5:0.5 inversion twin.     

Theoretical investigation of paramagnetic NMR shifts in transition metal acetylacetonato complexes: analysis of signs, magnitudes, and the role of the covalency of ligand-metal bonding

Ligand chemical shifts are calculated and analyzed for three paramagnetic transition metal tris-acetylacetonato (acac) complexes, namely high-spin Fe(III) and Cr(III), and low-spin Ru(III), using scalar relativistic density functional theory (DFT). The signs and magnitudes of the paramagnetic NMR ligand chemical shifts are directly related to the extent of covalent acac oxygen-to-metal σ donation involving unoccupied metal valence d(σ) acceptor orbitals. The role of delocalization of metal-centered spin density over the ligand atoms plays a minor secondary role. Of particular interest is the origin of the sign and magnitude of the methyl carbon chemical shift in the acac ligands, and the role played by the DFT delocalization error when calculating such shifts. It is found that the α versus β spin balance of oxygen σ donation to metal valence d acceptor orbitals is responsible for the sign and the magnitude of the ligand methyl carbon chemical shift. A problematic case is the methyl carbon shift of Fe(acac)(3). Most functionals produce shifts in excess of 1400 ppm, whereas the experimental shift is approximately 279 ppm. Range-separated hybrid functionals that are optimally tuned for Fe(acac)(3) based on DFT energetic criteria predict a lower limit of about 2000 ppm for the methyl carbon shift of the high-spin electronic configuration. Since the experimental value is based on a very strongly broadened signal it is possibly unreliable.     

Temperature dependence of OH(8;6) equilibration in an air-like gas ensemble

We present a quantum state-resolved computational investigation of the equilibration of rovibrationally excited OH, present as the minor component in an air-like mixture of N(2) and O(2), over the temperature range 100-1200 K. Generic features of the equilibration that are present over the entire range are identified, and the increase in speed of the principal energy exchange mechanism as the temperature increases is quantified. The data demonstrate that partitioning of excess energy and angular momentum among the modes of the three different molecules is independent of the magnitude of excess energy and of its form. The rotational temperature of OH is found to vary widely over the equilibration process, varying with number of collision cycles and with initial temperature. However, at equilibration, the rotational temperature of OH is invariably the lowest of all modes of all three species present in the ensemble. This suggests that rotational temperatures of OH obtained from rotational state populations are unlikely to provide a reliable guide to other modal temperatures in ensembles of the kind we consider.     

On implicit systems of differential equations

This article considers implicit systems of differential equations. The implicit systems that are considered are given by polynomial relations on the coordinates of the indeterminate function and the coordinates of the time derivative of the indeterminate function. For such implicit systems of differential equations, we are concerned with computing algebraic constraints such that on the algebraic variety determined by the constraint equations the original implicit system of differential equations has an explicit representation. Our approach is algebraic. Although there have been a number of articles that approach implicit differential equations algebraically, all such approaches have relied heavily on linear algebra. The approach of this article is different, we have no linearity requirements at all, instead we rely on algebraic geometry. In particular, we use birational mappings to produce an explicit system. The methods developed in this article are easily implemented using various computer algebra systems.