Simple physical models for coulomb‐induced frequency shifts and coulomb‐induced inhomogenous broadening for like and unlike ions in fourier transform ion cyclotron resonance mass spectrometry

Abstract

Two simple models which correspond more closely to physical reality than some prior models are proposed to account for the Coulomb-induced frequency shifts to lower frequency, which have been observed in Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. The first model consists of two different-mass point charges which undergo cyclotron orbits with the same orbit centers at their respective cyclotron frequencies. The model predicts that each excited cyclotron motion should induce a negative frequency shift in the other's cyclotron motion. The model predicts a zero frequency shift for ions of the same mass. The physical hasis for the Coulomb-induced shift is most easily seen in a coordinate frame which rotates at the cyclotron motion of the ion whose frequency is shifted. It is noted that a prior model for Coulomb-induced frequency shifts is more appropriate for scanning ICR than FT-ICR and the reason is described for the correctness of the predictions of this less appropriate model. A second model, the line model, is created by extension of the point model. The line model gives rise to a position-dependent frequency shift which is synonymous with inhomogeneous Coulomb broadening. When a non-quadrupolar electrostatic trapping field is included in the model, 'like' ions become 'unlike' and Coulomb-shifting and Coulomb-broadening apply, as for 'like' ions. The analysis predicts that ICR cells which are designed to have negligible trapping fields over most of their volume will be less sensitive to Coulomb shifting/hroadening than ordinary ICR cells.

Experimental evidence for space-charge effects between ions of the same mass-to-charge in Fourier-transform ion cyclotron resonance mass spectrometry

“…Wineland and Dehmelt have stated that ions of the same mass-to-charge can not induce a spacecharge shift in their own frequencies [19], and others have repeated this claim [20,21]. In recent years, however, the space-charge induced frequency shift has been shown to be different between ions of different m/z value than between ions of the same m/z value.…”

Sub part-per-million mass accuracy by using stepwise-external calibration in fourier transform ion cyclotron resonance mass spectrometry

“…Although sub part-per-million (ppm) mass accuracy can be achieved by FT-ICR [26,27,31], the typical accuracy level is usually in the 1 to 10 ppm range. For external calibration, the mass accuracy in a FT-ICR experiment depends on the number of ions in the analyzer cell because a space-charge frequency shift causes the observed cyclotron frequency to decrease with increasing ion population [32][33][34][35][36][37][38][39]. Analyte separation before mass spectrometry is often necessary for proteome samples to reduce the sample complexity and to improve the detection dynamic range.…”

Mass measurement errors caused by “local” frequency perturbations in FTICR mass spectrometry

“…However, the mass accuracy in an FTICR experiment depends crucially on the number of ions used for the measurement [9,[11][12][13][14][15][16][17][18]. When online separations are used, the analyte ion production rates vary widely, and the ion population in the trap cannot be easily or precisely controlled.…”