Numerical Investigation of Some Aspects of Fourier Transform Ion Cyclotron Resonance Spectroscopy

Chapter 1 A detailed kinematic analysis is presented comparing the use of quadrupole and octopole ion guides in conjunction with external ion source Fourier transform ion cyclotron resonance spectrometers. Methods to determine simply the electric fields for ideal and real quadrupoles and octopoles are presented, with emphasis on the importance of the effective potential in analyzing the design of an ion guide. Trajectory calculations are presented for a wide range of ion guide operating parameters and initial ion energies, along with an evaluation of the range of injected masses. Radial and axial ion energies together with a projection of the off-axis excursions of the ion motion on the plane perpendicular to the axis of the ICR cell are graphically illustrated. The real octopole exhibits more nearly ideal behavior than does a real quadrupole. It does not suffer from the anti-magnetic mirror effect, has uniform mass cutoffs, and has a four times greater maximum mass cutoff for given operating parameters than does a quadrupole. Chapter 2 A detailed analysis of ion motion in a cubic FT-ICR cell reveals dephasing effects of the z-axis (magnetic field direction) oscillations that limit the maximum resolution that can be achieved. With typical ranges of operating conditions using a 1 inch cubic cell in a 7 Tesla field, unit mass resolution is lost in the range between 103 and 104 amu, and peaks may be up to 20 amu in width at the upper end of this range. The finite transient length is due to the coupling between the effective radial force on the ion and the z-axis motion and to a lesser extent, on the instantaneous center of the cyclotron orbit. Operating conditions that minimize the amplitude of the z-axis oscillations and cell designs that incorporate more homogeneous electric fields serve to increase the coherence time and provide higher ultimate resolution" Chapter 3 We report here a detailed numerical study of space charge effects on ion trajectories in a typical FT-ICR experiment. In particular, we focus on ions with high mass to charge ratios, 3000 amu/|e-| ≤ m/z ≤ 10000 amu/|e-|, which are particularly relevant to experimental studies of clusters, polymers, or biomolecules. We assume excitation and trapping voltages of 1 V in the one inch cubic cell and a magnetic field of 7 T. We find essentially no discernable effect on the dephasing time, mass resolution, or mass shifts for ion densities below about 7 x 104 |e-|/cm3. That is, the natural inhomogeneous broadening due to the excitation fields1 is far more deleterious to FT-ICR performance than are space charge effects. Chapter 4 A numerical study of the application of magnetic excitation to FT-ICR is presented. It is concluded that magnetic excitation, which would permit nonstandard cell designs, might be practical for excitation to small final cyclotron radii. For greater degrees of excitation, this technique results in excessive magnetron motion and consequent loss of phase coherence and loss of signal. Unlike conventional rf excitation, the time required for magnetic excitation to a given final radius scales linearly with the mass to charge ratio. The technique is thus most applicable to low mass to charge ratio species. Chapter 5 We present here computational results for the collision cross section and rate constant for proton transfer reactions of a multiply-charged, linear, gas-phase protein. The protein is intended to resemble cytochrome c, with a length of 400 Å, a mass of 12 400 amu. The model protein is studied with proton charges of between 9 and 15 |e-|. The computational reactant is intended to model dimethyl amine, with a mass of 45 amu, a polarizability of 5.0 Å3 (dimethyl amine has a polarizability estimated by the Le Fevre method of 5.86 Å31), and a dipole moment of 1.03 Debye2. Results for low linear charge densities on the protein are interpretable in terms of a geometric model that accounts for the overlap of adjacent spheres of capture of each charge on the protein.