Calculation of isotope distributions in mass spectrometry. A trivial solution for a non-trivial problem

Abstract

Isotope peak patterns in the mass spectra of chemical compounds result from the occurrence of polyisotopic elements. The various approaches and programs published for calculating such isotope distributions are complex or of limited applicability or have insufficient accuracy because of rounding errors, or need too much calculation time. The algorithm described here is simple, easy to understand, highly accurate and extremely fast. Instead of the known procedures involving stepwise development or expansion of polynomial expressions, the isotope distributions are calculated by combining precalculated patterns of hypothetical atom clusters. For large organic molecules, the calculation time is reduced by several orders of magnitude compared to the stepwise procedure, and accuracy is increased compared to the use of polynomial expressions with inappropriate neglect of smaller terms. Typical examples are discussed to illustrate the scope and limitations of this approach. Additional features of the program are the calculation of isotope peak patterns of mixtures and the calculation of high-resolution masses and intensities for any mass within a given isotope distribution.