Time Evolution of the Scattering Data for the Forced Toda Lattice

Determination of the time evolution of the scattering data for an inverse scattering transform solution of the forced Toda lattice appears to require an overspecification of the boundary condition at the end of the lattice. This appears in the form of an apparent need to specify the values of two functions at the boundary rather than one. We present three different approaches to the resolution of this problem. One approach gives the Maclaurin series (in time) for the scattering data. The second approach gives the scattering data in terms of the solution to a nonlinear, nonlocal partial differential equation. The third approach gives the scattering data in terms of the solution to a linear integral equation. All three approaches reduce to one the number of functions which must be specified to determine a solution. The advantages and limitations of each approach are discussed.     

Internal energy content of n-butylbenzene, bromobenzene, iodobenzene and aniline molecular ions generated by two-photon ionization at 266 nm. A photodissociation study

A technique to investigate photodissociation kinetics on a nanosecond time scale has been devised for molecular ions generated by multiphoton ionization (MPI) using mass-analyzed ion kinetic energy spectrometry. The branching ratio or rate constant has been determined for the photodissociation of the n-butylbenzene, bromobenzene, iodobenzene, and aniline molecular ions generated by MPI at 266 nm. The ion internal energies have been estimated by comparing the measured kinetic data with the previous energy dependence data. The analysis has shown that only those molecular ions generated by two-photon ionization contribute to the photodissociation signals. Around half of the available energy has been found to remain as molecular ion internal energy in the two-photon ionization process. Copyright 1999 John Wiley & Sons, Ltd.     

Gas-phase kinetic and mechanistic studies of some interconverting alkylcyclopropene pairs: involvement of dialkylvinylidene intermediates and their quantitative behaviour

The pyrolyses of two isomeric pairs of alkylcyclopropenes, namely 1,3-dimethyl-(15) and 1-ethyl-cyclopropene (16), and 1,3,3-trimethyl-(5) and 1-isopropyl-cyclopropene (17), have been studied in the gas phase. Complete product analyses at various conversions up to 95% were obtained for the decomposition of each compound at five temperatures over a 40 degrees C range. The time-evolution data showed that the isomerisation reactions 15<==>16 and 5<==>17 were occurring. Kinetic modelling of each system allowed the determination of rate constants for these and all other decomposition processes. Tests confirmed that all reactions were unimolecular and homogeneous. Arrhenius parameters are reported for overall reactions and individual product pathways. Further kinetic analysis allowed us to extract the propensities (at 500 K) for 1,3-C-H insertion of the dialkylvinylidene intermediates involved in the rearrangements as follows: k(prim):k(sec): k(tert)= 1:16.5:46.4. Additional experiments with 13C-labelled cyclopropenes yielded alkyl group migration aptitudes for the dialkylvinylidenes (from the pattern of 13C in the alkyne products) as follows: Me:Et:iPr=1:3.1:1.5. Explanations for these trends are given. Another important finding is that of the dramatic rate enhancements for 1,3-diene product formation from the 1-alkylcyclopropenes; this can be explained by either hyperconjugative stabilisation of the vinylcarbene intermediates involved in this pathway, or their differing propensities to 1,2 H-shift. The observed large variations in product distribution amongst these four cyclopropenes is interpreted in terms of these specific effects on individual pathways.     

Enhanced near-neighbour aggregation of dichloro- and trichloromethane in liquid methane solution from molecular dynamics simulation of radial site–site distribution functions: a simple predictor of solute–solvent compatibility

Molecular dynamics simulations have been performed for a range of equi-site and site–site radial distribution functions for the five-atom halomethane species dichloro-, trichloro-, and tetrachloromethane dissolved in the low-molecular weight hydrocarbons liquefied methane and cyclopropane, with the general aim of using this approach to predict good or bad solvent characteristics. It was found that methane solutions of dichloro- and trichloromethane showed an enhancement of near-neighbour occupancy, the methane solvent seemingly exhibiting a phobic, structure-promoting solvation behaviour towards the two solutes by increasing the number of nearest neighbours above the values that would result from a pure dilution effect caused by the solvent. It was verified that there were no significant regions of solid-like conformations nor remnants of imperfect average homogeneity within the system at the necessarily low temperature (183?K). On the other hand, simulated site–site radial functions with solvents tetrachloromethane and cyclopropane indicate normal solution characteristics towards solutes dichloro- and trichloromethane. The cause of the phobic solvation behaviour of solvent liquid methane towards di- and trichloromethane is not obvious, except that it seemingly involves the presence of hydrogen atoms on the solute species because the site–site centre-of-mass radial distribution functions of tetrachloromethane in liquid methane implied normal solution behaviour.     

Direct coulomb and exchange interaction in artificial atoms

We determine contributions from the direct Coulomb and exchange interactions to the total interaction in artificial semiconductor atoms. We tune the relative strengths of the two interactions and measure them as a function of the number of confined electrons. The electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle-state degeneracy, and find that the spin configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states.     

A conserved helical capping hydrogen bond in PAS domains controls signaling kinetics in the superfamily prototype photoactive yellow protein

PAS domains form a divergent protein superfamily with more than 20?000 members that perform a wide array of sensing and regulatory functions in all three domains of life. Only nine residues are well-conserved in PAS domains, with an Asn residue at the start of α-helix 3 showing the strongest conservation. The molecular functions of these nine conserved residues are unknown. We use static and time-resolved visible and FTIR spectroscopy to investigate receptor activation in the photosensor photoactive yellow protein (PYP), a PAS domain prototype. The N43A and N43S mutants allow an investigation of the role of side-chain hydrogen bonding at this conserved position. The mutants exhibit a blue-shifted visible absorbance maximum and up-shifted chromophore pK(a). Disruption of the hydrogen bonds in N43A PYP causes both a reduction in protein stability and a 3400-fold increase in the lifetime of the signaling state of this photoreceptor. A significant part of this increase in lifetime can be attributed to the helical capping interaction of Asn43. This extends the known importance of helical capping for protein structure to regulating functional protein kinetics. A model for PYP activation has been proposed in which side-chain hydrogen bonding of Asn43 is critical for relaying light-induced conformational changes. However, FTIR spectroscopy shows that both Asn43 mutants retain full allosteric transmission of structural changes. Analysis of 30 available high-resolution structures of PAS domains reveals that the side-chain hydrogen bonding of residue 43 but not residue identity is highly conserved and suggests that its helical cap affects signaling kinetics in other PAS domains.     

NMR Study of CO2 Capture by Butylamine and Oligopeptide KDDE in Aqueous Solution: Capture Efficiency and Gibbs Free Energy of the Capture Reaction as a Function of pH**

We have been interested in the development of rubisco-based biomimetic systems for reversible CO₂ capture from air. Our design of the chemical CO₂ capture and release (CCR) system is informed by the understanding of the binding of the activator CO₂ (^ACO₂) in rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase). The active site consists of the tetrapeptide sequence Lys-Asp-Asp-Glu (or KDDE) and the Lys sidechain amine is responsible for the CO₂ capture reaction. We are studying the structural chemistry and the thermodynamics of CO₂ capture based on the tetrapeptide CH₃CO−KDDE−NH₂ (“KDDE”) in aqueous solution to develop rubisco mimetic CCR systems. Here, we report the results of ¹H NMR and ¹³C NMR analyses of CO₂ capture by butylamine and by KDDE. The carbamylation of butylamine was studied to develop the NMR method and with the protocol established, we were able to quantify the oligopeptide carbamylation at much lower concentration. We performed a pH profile in the multi equilibrium system and measured amine species and carbamic acid/carbamate species by the integration of ¹H NMR signals as a function of pH in the range 8≤pH≤11. The determination of ΔG₁(R) for the reaction R−NH₂+CO₂ R−NH−COOH requires the solution of a multi-equilibrium equation system, which accounts for the dissociation constants K₂ and K₃ controlling carbonate and bicarbonate concentrations, the acid dissociation constant K₄ of the conjugated acid of the amine, and the acid dissociation constant K₅ of the alkylcarbamic acid. We show how the multi-equilibrium equation system can be solved with the measurements of the daughter/parent ratio X, the knowledge of the pH values, and the initial concentrations [HCO₃⁻]₀ and [R-NH₂]₀. For the reaction energies of the carbamylations of butylamine and KDDE, our best values are ΔG₁(Bu)=−1.57 kcal/mol and ΔG₁(KDDE)=−1.17 kcal/mol. Both CO₂ capture reactions are modestly exergonic and thereby ensure reversibility in an energy-efficient manner. These results validate the hypothesis that KDDE-type oligopeptides may serve as reversible CCR systems in aqueous solution and guide designs for their improvement.