Tandem mass spectrometric accurate mass performance of time-of-flight and Fourier transform ion cyclotron resonance mass spectrometry: a case study with pyridine derivatives

The interpretation of mass spectra is a key process during compound identification, and the combination of tandem mass spectrometry (MS/MS) with high-accuracy mass measurements may deliver crucial information on the identity of a compound. Obtaining accurate mass data of fragment ions in MS/MS reveals the particular problem of mass calibration when a lockmass, which is frequently used to obtain accurate masses in MS, is absent. An alternative technique is to recalibrate the MS/MS spectrum using a reference MS/MS spectrum acquired under the same conditions. We have tested and validated this approach using a hybrid quadrupole/orthogonal acceleration reflectron-type time-of-flight (TOF) mass spectrometer. The results were compared with those obtained under similar conditions on a Fourier transform ion cyclotron resonance (FT-ICR) instrument. We found that the mass accuracy observed with such an "external" recalibration on the TOF instrument in MS/MS is identical to what can be obtained on a similar instrument operating in one-dimensional MS mode using the lockmass technique. However, mass accuracy in both cases is one order of magnitude inferior to that obtained using FTMS, and also inferior to that observed using sector field MS when operated at comparable resolution. Nevertheless, for small (<200 Da) molecules, this mass accuracy was still sufficient to have the "true" elemental composition identified as the first hit in about 70% of all cases. It was possible to elucidate the fragmentation mechanism of eight azaheterocycles containing a pyridine moiety, where the accurate mass data from the TOF instrument allowed distinction between two alternative fragmentation pathways.     

Bulk and compound-specific isotopic characterisation of illicit heroin and cling film

Comparative analysis involves various but complementary methods and can be used for forensic intelligence purposes to group seizures of heroin into batches. Much forensic analysis now combines expertise in the traditional area of drugs investigation with a detailed understanding of supply, packaging, distribution, and drugs intelligence. It was the intention of this research to determine whether illicit heroin seizures and packaging material can be grouped according to isotopic compositions, and to explore factors that affect the isotopic compositions. In order to achieve these aims, 14 samples of seized heroin, thirteen provided by Avon and Somerset Constabulary (UK), were analysed by elemental analysis/isotope ratio mass spectrometry (EA/IRMS) and gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS) for carbon and hydrogen isotopes. These tests elucidated that a combination of the delta13C, delta15N, delta18O and delta2H results from EA/IRMS is able to distinguish between most samples of bulk heroin. We speculate that the delta13C values of the alkaloids, obtained by GC/C/IRMS, give indications of different geographical or temporal origins of some of the heroin samples. GC/C/IRMS of the cutting agent, caffeine, provides a means to link dilution events. Fifteen retail cling film samples and seven cling film samples from heroin seizures were analysed by EA/IRMS. A multivariate comparison of the carbon, hydrogen and oxygen isotope ratios was able to distinguish between most of the samples. This technique enabled the cling films from the heroin to be grouped according to seizure. Three solvents were tested on two samples of cling film of known composition. Methanol and chloroform were both found to extract material from PVC and from non-PVC cling films. Water-treated PVC was indistinguishable from the untreated PVC and thus water was found to be the most suitable solvent when washing cling film prior to IRMS analysis.     

Using the homotopy method to find periodic solutions of forced nonlinear differential equations

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x + k [xdot] + g(x,t) = ε(t) where k is a constant; g is continuous, continuously differentiable with respect to x, and is periodic of period P in the variable t; ε(t) is continuous and periodic of period P, and when ?g/?x satisfies some additional boundedness conditions. This means that there exist initial values x(0) = α* and [xdot] (0) = β* so that the solution to the corresponding initial value problem is periodic of period P and is unique (up to a translation of the time variable) with this property. The proof of this result is constructive, so that starting with any initial conditions x(0) = α and [xdot](0) = β, a path in the phase plane can be produced, starting at (α, β) and terminating at (α*, β*). Both the theoretical proof and a constructive proof are discussed and a Mathematica implementation developed which yields an algorithm in the form of a Mathematica notebook (which is posted on the webpage http://pax.st.usm.edu/downloads). The algorithm is robust and can be used on differential equations whose terms do not satisfy Li and Shen's hypotheses. The ideas used reinforce concepts from beginning courses in ordinary differential equations, linear algebra, and numerical analysis.     

Fourier series and elliptic functions

Non-linear second-order differential equations whose solutions are the elliptic functions sn(t, k), cn(t, k) and dn(t, k) are investigated. Using Mathematica, high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are correct to at least 11 decimal places. These formulas have the advantage over numerically generated data that they are computationally efficient over the entire real line. This approach is seen as further justification for the early introduction of Fourier series in the undergraduate curriculum, for by doing so, models previously considered hard or advanced, whose solution involves elliptic functions, can be solved and plotted as easily as those models whose solutions involve merely trigonometric or other elementary functions.     

The Gibbs' phenomenon and harmonic oscillators with periodic forcing

We present an interesting nonlinear equation originating from a geometrical problem. We show how it can be solved numerically, how algorithmic differentiation is useful, and how the problem can also be solved analytically using the computer algebra system Maple.     

Lineshapes in quasi-elastic scattering from species hopping between non-equivalent surface sites

We present an analytic model applied to quasi-elastic scattering from an adsorbed surface species undergoing jump diffusion between adsorption sites described by a Bravais lattice combined with a basis of multiple points. The model allows for hops between adsorption sites which are both symmetrically and energetically inequivalent. We give results for 1-D hopping, which are applicable to a species jumping between the top and bridge sites along the [11?0] direction on an fcc-(110) surface or for jumps along a step edge. In 2-D, results for hopping between fcc and hcp hollow sites and between the bridge sites of an fcc-(111) surface are presented. These examples give characteristic signatures which will allow these forms of motion to be recognized in experimental data and will enable the underlying physical parameters to be extracted by comparison with the analytical forms derived here.     

A total synthesis of xestodecalactone a and proof of its absolute stereochemistry: interesting observations on dienophilic control with 1,3-disubstituted nonequivalent allenes

A concise total synthesis of xestodecalactone A, utilizing a Diels-Alder strategy is described. The focal Diels-Alder reaction relied on an "ynoate" dienophile to rapidly assemble the required resorcylinic acid scaffold. During this study, Diels-Alder cycloaddition reactions involving 1,3-disubstituted nonequivalent allene dienophiles were studied, and some surprising results were encountered.     

The Ni + O2 reaction: a combined IR matrix isolation and theoretical study of the formation and structure of NiO2

The reaction of Ni atoms with molecular oxygen has been reinvestigated experimentally in neon matrices and theoretically at the DFT PW91PW91/6311G(3df) level. Experimental results show that i) the nature of the ground electronic state of the superoxide metastable product is the same in neon and argon matrices, ii) two different photochemical pathways exist for the conversion of the superoxide to the dioxide ground state (involving 1.6 or 4 eV photons) and iii) an important matrix effect exists in the Ni + O(2)--> Ni(O(2)) or ONiO branching ratios. Theoretical results confirm that the electronic ground state of the metastable superoxide corresponds to the singlet state, in agreement with former CCSD(T) calculations, but in contradiction with other recent works. Our results show that the ground electronic state of the dioxide is (1)Sigma(+)(g) with the lowest triplet and quintet states at slightly higher energy, consistent with the observation of weak vibronic transitions in the near infrared. The potential energy profiles are modelled for the ground state and nine electronic excited states and a pathway for the Ni(triplet) + O(2)(triplet) --> Ni(O(2)) or ONiO (singlet) reaction is proposed, as well as for the Ni(O(2)) --> ONiO photochemical reaction, accounting for the experimental observations.