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UHRMS Formula Assignment: Diophantine-Based Recalibration Yields Lorentzian Mass Error Distribution as the Limiting

Neda Safaridehkohneh1, Albrecht Ott1

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Journal of the American Society for Mass Spectrometry
|December 26, 2025
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Summary

This study introduces a Diophantine method for molecular formula assignment in ultrahigh-resolution mass spectrometry (UHRMS). The novel approach improves spectral interpretation accuracy for complex samples by statistically analyzing mass errors.

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Area of Science:

  • Analytical Chemistry
  • Spectrometry
  • Computational Chemistry

Background:

  • Ultrahigh-resolution mass spectrometry (UHRMS) is crucial for analyzing complex molecular mixtures.
  • Fourier transform techniques (FTICR-MS, FT-Orbitrap-MS) offer high resolution but pose interpretation challenges.
  • Nontargeted analysis of complex samples often results in difficult spectral interpretation.

Purpose of the Study:

  • To introduce a novel Diophantine method for accurate molecular formula assignment in UHRMS.
  • To address challenges in spectral interpretation for complex samples.
  • To enhance the statistical consistency and accuracy of molecular formula determination.

Main Methods:

  • Development and application of a Diophantine method for molecular formula assignment.
  • Statistical analysis of random mass error using Gaussian distribution.
  • Distinguishing systematic calibration errors from random mass errors.
  • Quantification of random mass error as Lorentzian distribution.

Main Results:

  • The Diophantine method enables statistically consistent molecular formula assignment.
  • Systematic errors from suboptimal calibration can be effectively distinguished from random errors.
  • The method quantifies random mass error, consistent with Fourier transform-based instruments.
  • Molecular formula assignments approach the theoretical limit of achievable accuracy.

Conclusions:

  • The Diophantine method offers a robust approach to molecular formula assignment in UHRMS.
  • This method significantly improves spectral interpretation accuracy for complex samples.
  • The technique is self-consistent and pushes the boundaries of mass spectrometry accuracy.