Comparison and interconversion of the two most common frequency-to-mass calibration functions for Fourier transform ion cyclotron resonance mass spectrometry

In a perfect three-dimensional axial quadrupolar electrostatic potential field, Ledford et al. showed that the frequency-to-mass calibration relation m/z = A(L)/v + B-L/v(2) is valid for ions of any mass-to-charge ratio, m/z < (m/z)(critical) = e B(0)(2)a(2)/4V(trap)alpha, in which v is the "reduced" (observed) ion cyclotron frequency, e is the electronic (elementary) charge, z is the number of elementary charges per ion, B-0, is magnetic field induction, a is a characteristic trap dimension, v(trap) is the potential applied to each trap endcap, alpha is a constant determined by the trap geometrical configuration, and A(L) and B-L are constants that are determined by fitting experimental ion cyclotron resonance (ICR) frequencies for ions of at least two known masses in a Fourier transform ICR (FT-ICR) mass spectrum. In the further limit that m/z much less than (m/z)(critical), Francl et al. obtained a different frequency-to-mass relation m/z = A(F)/(B-F + v). Here, we rederive both frequency-to-mass relations to derive a simple conversion between A(L) and B-L, versus A(F) and B-F (e.g, for comparing calibrated FT-ICR mass spectral data from different vendors). For accurate mass measurement, the conversion introduces a small error (a few parts per billion) that can usually be neglected. More important, by applying both calibration equations to the same experimental time-domain data, we find that mass accuracy resulting from the two calibration functions (or their interconversion) is indistinguishable, because Ledford et al,'s validity criterion, m/z < 0.001 (m/z)(critical), is generally satisfied for modern high-field instruments with optimized cell geometry. Interestingly, a small difference may result when different forms of the same calibration function are employed, presumably due to different roundoff errors in the calculation. (C) 2000 Elsevier Science B.V.