Calculations of the effects of substituents on bond localization in annelated cyclopentadienyl radicals

UB3LYP/6-31G(d) calculations have been performed in order to predict the ground states, 2A2 or 2B1, of cyclopentadienyl radicals that are mono- and bis-annelated with a wide variety of substituents. Unlike the case in the annelated cyclooctatetraenes, studied by Baldridge and Siegel, our calculations find that the sizes of the coefficients of the degenerate MOs at the annelated carbons are more important than the symmetries of the substituent's frontier orbitals in determining the mode of bond localization in the annelated cyclopentadienyl radicals.     

Pressure Buildup During CO<Subscript>2</Subscript> Injection into a Closed Brine Aquifer

CO₂ injected into porous formations is accommodated by reduction in the volume of the formation fluid and enlargement of the pore space, through compression of the formation fluids and rock material, respectively. A critical issue is how the resulting pressure buildup will affect the mechanical integrity of the host formation and caprock. Building on an existing approximate solution for formations of infinite radial extent, this article presents an explicit approximate solution for estimating pressure buildup due to injection of CO₂ into closed brine aquifers of finite radial extent. The analysis is also applicable for injection into a formation containing multiple wells, in which each well acts as if it were in a quasi-circular closed region. The approximate solution is validated by comparison with vertically averaged results obtained using TOUGH2 with ECO2N (where many of the simplifying assumptions are relaxed), and is shown to be very accurate over wide ranges of the relevant parameter space. The resulting equations for the pressure distribution are explicit, and can be easily implemented within spreadsheet software for estimating CO₂ injection capacity.     

An examination for mathematical modelling

First year mathematics degree students at Leicester Polytechnic attend a course in mathematical modelling. The aim is to introduce the students to mathematical modelling concepts and to model development. Work is set and marked during the course and this forms a vital part of the students' assessment. In addition to this, however, the students are assessed by means of a three hour examination at the end of the year. This examination is significantly different from the normal ‘five out of eight’ type. The philosophy and organization of the examination are discussed in this paper. An example of a particular examination, that for June 1986, is included as an appendix to illustrate the points made in the discussion.     

Photoelectron Spectroscopy and Theoretical Studies of PCSe−, AsCS−, AsCSe−, and NCSe−: Insights into the Electronic Structures of the Whole Family of ECX− Anions (E=N,P, As; X=O,S, Se)

The newly synthesized phosphorus‐ and arsenic‐containing analogues of the thio‐ and seleno‐cyanate anions, PCSe^?, AsCS^?, and AsCSe^?, as well as the known ion NCSe^? were investigated in the gas phase by negative‐ion photoelectron spectroscopy (NIPES), velocity‐map imaging (VMI) spectroscopy, and quantum‐chemical computations. The electron affinities (EA), spin–orbit (SO) splittings, and “symmetric”/“asymmetric” stretching frequencies of the neutral radicals ECX^. (E=N, P, As; X=S, Se), generated by electron detachment from the corresponding anions, were obtained from the spectra. The calculated EAs, SO splittings, and vibrational frequencies are in excellent agreement with the experimental measurements. These newly obtained values, when combined with those previously determined for the lighter analogues, show interesting trends on descending the pnictogen and chalcogen series. These trends are rationalized based on electronegativity arguments, the electron distributions in the HOMOs, and NBO/NRT analyses.     

Photoelectron Spectroscopy and Theoretical Studies of PCSe−, AsCS−, AsCSe−, and NCSe−: Insights into the Electronic Structures of the Whole Family of ECX− Anions (E=N,P, As; X=O,S, Se)

The newly synthesized phosphorus‐ and arsenic‐containing analogues of the thio‐ and seleno‐cyanate anions, PCSe^?, AsCS^?, and AsCSe^?, as well as the known ion NCSe^? were investigated in the gas phase by negative‐ion photoelectron spectroscopy (NIPES), velocity‐map imaging (VMI) spectroscopy, and quantum‐chemical computations. The electron affinities (EA), spin–orbit (SO) splittings, and “symmetric”/“asymmetric” stretching frequencies of the neutral radicals ECX^. (E=N, P, As; X=S, Se), generated by electron detachment from the corresponding anions, were obtained from the spectra. The calculated EAs, SO splittings, and vibrational frequencies are in excellent agreement with the experimental measurements. These newly obtained values, when combined with those previously determined for the lighter analogues, show interesting trends on descending the pnictogen and chalcogen series. These trends are rationalized based on electronegativity arguments, the electron distributions in the HOMOs, and NBO/NRT analyses.     

Designing A Reactor to Generate Hydrogen Bubbles

Hydrogen is produced by the reaction between zinc and hydrochloric acid. This reaction is used to illustrate the importance of considering thermodynamics when designing a chemical reactor. The gas released is collected in soap bubbles that rise in the air, indicating that a lighter than air gas has been produced. The bubbles can be lit to add a dramatic effect to the demonstration. The reaction is highly exothermic, raising the temperature of the reaction materials and the reactor. Batch operation of this reactor would require short cooling periods between reactions. Alternatively, a modification of the design is suggested to allow for continuous cooling of the vessel, which would allow semicontinuous operation of the reactor. (Zinc would have to be periodically replenished as it is consumed in the reaction.) The consequences associated with the cooling of the vessel are discussed.     

A simple quantitative HPLC assay for ifosfamide in biological fluids

A high performance liquid chromatography method is described for measuring Ifosfamide (I) in human serum. This involves solvent extraction, reverse phase HPLC and UV detection at 190 nm. Standard curves of peak height x detector sensitivity versus I concentration in serum were linear with a lower limit of detection of 100 ng/ml. Authentic 14C-labelled I cochromatographed with standard I and with I found in serum from treated patients. The concentration-time curves of I determined by both HPLC and gas chromatography were indistinguishable. We conclude that this method is suitable for determining I pharmacokinetics in biological specimens.     

RHF and two-configuration SCF calculations are inappropriate for conjugated diradicals

Restricted Hartee Fock (RHF) and two-configuration self-consistent field (TCSCF) calculations provide qualitatively correct molecular orbitals for the two open-shell electrons in diradicals. Nevertheless, these calculations fail to give correct relative energies and in some cases they even lead to incorrect geometries. Examples of these failures are given for both singlet and triplet states of some conjugated diradicals. In several cases these failures are related to the “doublet instability problem” in RHF calculations on radicals. It is argued that unrestricted Hartee-Fock (UHF) calculations on triplet states are more likely that RHF to provide accurate geometries.     

Very-low-lying electronic states result from n --> pi excitations in open-shell annulenes, annelated with alpha-dicarbonyl groups

UB3LYP/6-31G* calculations find that alpha-dicarbonyl-annelated cyclopentadienyl radical 1 has a sigma ground state, which is formed by excitation of an electron from the in-phase combination of carbonyl lone-pair orbitals into the singly occupied pi orbital. Similarly, tetrakis-annelated cyclooctatetraene 3 is calculated to have very-low-lying singlet and triplet excited states, which result from excitations of electrons from the b1g combination of lone pair orbitals into the empty pi nonbonding MO of the COT ring.