Concerning atomic radii

The identification of the atomic radius with the distance from the nucleus to the position of the minimum in the internuclear electronic density is studied. It is shown that a set of statistically significant radii may be defined for the atoms of a given column of the periodic table bound to any of the atoms of another column. Sets of radii calculated by modified Anderson-Parr relations are presented. The values obtained are consistent with radii obtained using a minimum in electronic density criterion with electron densities calculated from molecular orbital wave functions or approximated by a sum of atomic densities.     

Termolecular ion-molecule reactions in Titan’s atmosphere. II: The structure of the association adducts of HCNH+ with C2H2 and C2H4

The ion-molecule reactivity of the products formed in the association reactions of HCNH+ with C2H2 (C3H4N+) and C2H4 (C3H6N+) has been investigated to provide information on the structures of the adducts thus formed. The C3H4N+ and C3H6N+ adducts were formed in the reaction flow tube of a flowing afterglow sourced-selected ion flow tube (FA-SIFT) and their reactivity with a neutral molecular "probe" examined. The reactivity of possible known structural isomers for the C3H4N+ and C3H6N+ ions was investigated in both the FA-SIFT and an ion cyclotron resonance spectrometer (ICR). Ab initio investigations of the potential energy surfaces for both structures at the G2(MP2) level have also been performed and structures corresponding to local minima on both surfaces have been identified and evaluated. The results of these experimental and theoretical studies show that at room temperature, the C3H4N+ adduct ion contains two isomers; a less reactive one that is likely to be a four-membered cyclic covalent isomer (approximately 70%) and a faster reacting component that is probably an electrostatic complex (approximately 30%). The C3H6N+ adduct ion formed from HCNH+ + C2H4 at room temperature is a single isomer that is likely to be the four-membered covalently bound cyclic CH2CH2CHNH+ species.     

Valence bond studies of AH2 molecules

Minimal basis set (STO) molecular orbital and valence-bond calculations are reported for the³ B ₁ and¹ A ₁ states of CH₂. The open-shell molecular orbital calculations used the Roothaan formulation. The valence-bond calculations used the Prosser-Hagstrom biorthogonalisation technique to evaluate the cofactors required in using Löwdin's formulae. Optimisation of geometry and orbital exponents in the molecular orbital calculation on the³ B ₁ state gave a geometry of R_C-H=2.11 a.u. and H-C-H=123.2 °. The energy obtained was ?38.8355 a.u. The molecular orbital and valencebond calculations are compared. In the valence-bond calculations the variation with bond-length and bond-angle of the configuration energies was studied. Valence bond “build-up” studies are also reported. Valence-bond calculations using hybrid orbitals instead of natural atomic orbitals showed that the perfect-pairing approximation is not as good for CH₂ as BeH₂. The nature of the lone-pair and bonding orbitals is found to be significantly different between the³ B ₁ and¹ A ₁ states. In the³ B ₁ state the 2s and 2p orbitals are fairly equally mixed between both types of orbital. However in the¹ A ₁ state the bonding orbitals have mainly 2p character and the lone pair orbitals have mainly 2s character. As was found for H₂O, the bonding hybrid orbitals do not follow the hydrogen nuclei as the bond angle varies but continue to point approximately in their equilibrium directions.     

Real‐time measurement of peroxyacetyl nitrate using selected ion flow tube mass spectrometry

The on‐line detection of gaseous peroxyacetyl nitrate (PAN) using selected ion flow tube mass spectrometry (SIFT‐MS) has been investigated using a synthetic sample of PAN in air at a humidity of ～30%. Using the H₃O⁺ reagent ion, signals due to PAN at m/z 122, 77 and 95 have been identified. These correspond to protonated PAN, protonated peractetic acid and its water cluster, respectively. These products and their energetics have been probed through quantum mechanical calculations. The rate coefficient of H₃O⁺ has been estimated to be 4.5 × 10^?9 cm³ s^?1, leading to a PAN sensitivity of 138 cps/ppbv. This gives a limit of detection of 20 pptv in 10 s using the [M+H]⁺ ion of PAN at m/z 122. Copyright © 2010 John Wiley & Sons, Ltd.     

RESTRICTED LIE ALGEBRAS WITH MAXIMAL 0-PIM

In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p ^MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced from the one-dimensional trivial module of a torus of maximal dimension, only if L is solvable.