Analysis and elimination of systematic errors originating from Coulomb mutual interaction and image charge in fourier transform ion cyclotron resonance precise mass difference measurements

Abstract

The effect of mutual Coulomb-mediated interactions between ions of two different mass-to-charge ratios (but equal ion cyclotron orbital radii) on their Fourier transform ion cyclotron resonance (FT/ICR) mass spectral frequency difference is derived analytically and measured experimentally. For a cyclindrical ion trap, ion packets are modeled theoretically as infinitely extended lines of charge, and contributions to cyclotron frequency difference due to direct Coulomb repulsion betwen the line charges as well as the forces arising from image charge induced on the trap electrodes by each line charge are calculated. A striking theoretical prediction is that the effect on ICR frequency difference of mutual Coulomb repulsion between ions in a mass doublet may be compensated by the image-charge effect. As a result, there is an optimal (calculable) ion cyclotron orbital radius at which the measured cyclotron orbital frequency difference between ions of two different mass-to-charge ratios is independent of mutual Coulomb-mediated interactions between the two components of the mass doublet! Moreover, if the two mass-doublet component ions are present in equal numbers, then the measured ion cyclotron orbital frequency difference is also independent of all Coulomb-mediated interactions between the two types of ions! Thus, the single largest systematic error in measurement of mass difference in a mass doublet by FT/ICR mass spectrometry may be virtually eliminated by appropriate control of ICR orbital radius and/or by performing measurements at various relative abundance ratios and extrapolating to equal relative abundance of the two mass-doublet components. We report experimental tests and verification of these predictions for two different mass doublets: 3He +/ 3H + (cylindrical trap at 4.7 Tesla) and 12C 1H + 2/ 14 N + (cubic trap at 7.0 Tesla). From the latter measurement, we determine the mass of atomic nitrogen as m( 14N) = 14.003 074 014(19) u.