Theoretical isotope distribution

Figure 6 Partial MALDI-TOF mass spectrum from PMMA generated by ATRP with ethyl-2-bromoisobutyrate as initiator (inset shows theoretical isotope distribution for lithiated 18-mer of structure 3). (Peak labelled 3 arises from post-source decay of 3 [10].)...

Fig. 3.24. Listing of the theoretical isotopic distribution of Ci6H2oOSi at infinite resolution. The contribution of is not considered, and isotopic peaks above m/z 260 are omitted due to their minor intensities.

Of the remaining candidates, from top to bottom, generate their theoretical isotopic distributions and compare them to the experimental one. Theoretical isotopic distribution of candidate 3 was an obvious... 

FIGURE 32 Theoretical isotopic distribution of elemental composition candidate 7. 

Figure 2 Theoretical isotope distributions of (a) diphenhydramine and (b) thiostrepton. In general, the difference between the monoisotopic and average molecular weight of a molecule increases as molecular weight increases (isotope distributions were generated using Micromass MassLynx 3.1 software).

Figure 6 Theoretical isotope distributions of single- and double-charged gra-macidin-S. (a) The theoretical distribution of the single-charged molecular ion with nominal mass resolution, (b) The double-charged molecular ion with nominal mass resolution, (c) Discrimination of the double-charged isotopes is possible with higher instrument resolution.

Most elements occur naturally as a mixture of isotopes, differing from one another by the number of neutrons present in the nucleus. Natural carbon comprises a mixture of mainly and (98.9 and 1.1% respectively) with a trace of the radioactive isotope Chlorine has isotopes Cl (75.77%) and Cl (24.23%). Thus any mass spectrum will demonstrate a number of molecular ions due to the isotopomers present. Most data systems have programs which allow the input of a molecular formula which generates a theoretical isotopic distribution. This can then be compared with the actual spectrum obtained (Fig. 5.16). It may be necessary to add or subtract a proton from the inputted formula, hydrogen contains 0.015% deuterium. 

At first sight, MS provides information on masses and abundances in the ion mixture obtained from the analyte. Isotope compositions and theoretical isotope distributions link these primary pieces of information. This connection is discussed in Subsection 8.3.3. Ideas from [98,168, 291] will be developed further to calculate match values for molecular formula candidates using mass, intensities and isotope patterns. Such quantities are used for ranking and selection of molecular formula candidates (Subsection 8.4.1). 

In this manner we cannot only describe experimental spectra, but also theoretical isotope distributions and calculated spectra. The atoms of a chemical element X e are not necessarily all of the same mass. The mass of an atom is essentially the mass of its nucleus, which is composed of two types of elementary particles of unit mass, protons and neutrons. In the atoms of a given element X, the number of positively charged protons is fixed, while the number of uncharged neutrons may vary. Such atoms of different mass are isotopes of X (notation for the isotope of mass m X, e.g. C). Natural isotope distributions are known and almost constant, such that mass spectrometry provides information on the elemental composition of an unknown compound through isotope patterns. 

Definition (Theoretical isotope distribution) Let = Xj g n) be a set of chemical elements, and p a molecular formula. Then the theoretical isotope distribution of jS is defined as convolution product... 

In order to calculate theoretical isotope distributions of molecular formulas it is helpful to note the following result ... 

Remark (Recursive method to calculate theoretical isotope distributions) Let /S N be a molecular formula. For the theoretical isotope distribution of jS either of the following is true ... 

The mass of maximal intensity of /S is not obtained as easily, rather, it is taken from the theoretical isotope distribution, which is calculated by folding (see above). In particular, the nominal mass is not necessarily equal to the mass of highest abundance, as demonstrated by the following example ... 

Furthermore, the mass resolution of even recent accurate mass spectrometers is insufficient to identify molecular formulas unambiguously from their theoretical isotope distributions. Kind and Fiehn [159] discuss this in detail, including the influence of various combinations of mass and relative isotopic abundance acciu-acy on formula determination. 

As introduced in Section 8.4, a match value that shows how well the theoretical isotope distribution matches the measured intensities of the isotope peaks in the MS can be... 

Fig. 35. MALDI analysis of a polymethylmethacrylate resin.. Theoretical isotope distribution. From Ref. 66.

Wada, Y. Tamura, J. Musselman, B. D. Kassel, D. B. Sakurai, T Matsuo, T. Electrospray ionization mass-spectra of hemoglobin and transferrin by a magnetic-sector mass-spectrometer—Comparison with theoretical isotopic distributions. Rapid Commun. Mass Spectrom. 1992, 6, 9 13. 

Fig. 10.6. MALDI-FTMS determination of a common industrial polymer, polyoxypropylenediamine (top). The oligomers observed are cationized by sodium attachment and the average molecular mass information is shown in the middle spectrum. The manufacturer s specification of average molecular mass corresponding to 33.1 (mass 2170) repeating units agrees with the ma.ss distribution of 2193. TTie measured isotopic peak distribution for the n = 33 oligomer is compared with the theoretical isotopic distribution in the bottom spectrum. (Source Ref. [37, fig. 2].)...

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