Isotopic pattern calculation

Fig. 3.27. The isotopic pattern calculated for [M+H]" of bovine insulin at different resolutions (Rio%). Note that the envelope at R = 1000 is wider than the real isotopic pattern.

The WebElements site (www.webelements.com/) contains chemical and physical data of the elements. This site also has on-line isotope pattern calculators. 

Dichloromethane extracts and thermal desorption The chromatograms of the samples (Fig. 12) showed main peaks at 9.04, 11.61, 13.85, 17.45 and 17.87 min. Chlorodiphenylarsine (Clark I, 9.04 min), Triphenylarsine (11.61 min) and Bis(diphe-nylarsine)oxide (17.45 min, main degradation product of Clark I) could be identified using library searches. Bis(diphenylarsine) (17.87 min) has been identified by means of its mass spectra according to Schoene et al. (1995). Isotopic pattern calculation indicated the peak at retention times 13.85 min to contain sulfur. By comparison of the mass spectrum the substance could be identified as Diphenylthiophenylarsine as proposed by Schoene et al. (1995). 

Arnold, L.J. Mass spectra and the Macintosh Isotope pattern calculator. A program to calculate isotopic ratios for molecular fragments (CS). J. Chem. Educ. 69, 811 (1992)... 

This includes the Periodic Table database, an Isotope Pattern Calculator, and an Element Percentage Calculator. This is a true periodic table with data supplied by Mark Winter at the Department of Chemistry, University of Sheffield. 

Applications With the current use of soft ionisation techniques in LC-MS, i.e. ESI and APCI, the application of MS/MS is almost obligatory for confirmatory purposes. However, an alternative mass-spectrometric strategy may be based on the use of oaToF-MS, which enables accurate mass determination at 5 ppm. This allows calculation of the elemental composition of an unknown analyte. In combination with retention time data, UV spectra and the isotope pattern in the mass spectrum, this should permit straightforward identification of unknown analytes. Hogenboom et al. [132] used such an approach for identification and confirmation of analytes by means of on-line SPE-LC-ESI-oaToFMS. Off-line SPE-LC-APCI-MS has been used to determine fluorescence whitening agents (FWAs) in surface waters of a Catalan industrialised area [138]. Similarly, Alonso et al. [139] used off-line SPE-LC-DAD-ISP-MS for the analysis of industrial textile waters. SPE functions here mainly as a preconcentration device. 

The calculation of isotopic patterns as just shown for the carbon-only molecule Qo can be done analogously for any X-rl element. Furthermore, the application of this scheme is not restricted to molecular ions, but can also be used for fragment ions. Nevertheless, care has be taken to assure that the presumed isotopic peak is not partially or even completely due to a different fragment ion, e.g., an ion containing one hydrogen more than the presumed X-rl composition. 

Fig. 3.2. Calculated isotopic patterns for carbon. Note the steadily expanding width of the pattern as X+2, X+3, X+4,... become visible. At about C90 the X-i-1 peak reaches the same intensity as the X peak. At higher carbon number it becomes the base peak of the pattern.

Again, we obtain w+1 terms for the isotopic pattern of w atoms. The binomial approach works for any di-isotopic element, regardless of whether it belongs to X+1, X+2 or X-1 type. However, as the number of atoms increases above 4 it is also no longer suitable for manual calculations. 

Example The isotopic pattern of CI2 is calculated from Eq. 3.9 with the abundances a = 100 and = 31.96 as (100 + 31.96) = 10000 -1- 6392 + 1019. After normalization we obtain 100 63.9 10.2 as the relative intensities of the three peaks. Any other normalization for the isotopic abundances would give the same result, e.g., a = 0.7578, b = 0.2422. The calculated isotopic pattern of CI2 can be understood from the following practical consideration The two isotopes Cl and Cl can be combined in three different ways i) Cl2 giving rise to the monoisotopic composition, ii) Cl Cl yielding the first isotopic peak which is here X-i-2, and finally iii) Cl2 giving the second isotopic peak X+4. The combinations with a higher number of chlorine atoms can be explained accordingly. 

Note For a rapid estimation of the isotopic patterns of chlorine and bromine the approximate isotope ratios Cl/ Cl = 3 1 and Br/ Br =1 1 yield good results. Visual comparison to calculated patterns is also well suited (Fig. 3.3). 

Fig. 3.3. Calculated isotopic patterns for combinations of bromine and chlorine. The peak shown at zero position corresponds to the monoisotopic ion at m/z X. The isotopic peaks are then located at m/z = X+2, 4, 6,. .. The numerical value of X is given by the mass number of the monoisotopic combination, e.g., 70 u for CI2.

Note Mass spectrometers usually are delivered with the software for calculating isotopic distributions. Such programs are also offered as internet-based or shareware solutions. While such software is freely accessible, it is still necessary to obtain a thorough understanding of isotopic patterns as a prerequisite for the interpreting mass spectra. 

Fig. 3.6. Calculated isotopic pattern of the molecular ion of ethyl propyl thioether, C5H12S with the respective contributions of and C to the M+1 and of and C2 to the M+2 signal indicated.

Fig. 3.7. Calculated isotopic pattern of tetrabutyltin, CigHsgSn, with labels to indicate major isotopic contributions.

The treatment of polyisotopic elements does not require other techniques as far as calculation or constmction of isotopic patterns are concerned. However, the appearance of isotopic patterns can differ largely from what has been considered so far and it is worth mentioning their peculiarities. 

Fig. 3.10. Calculated and experimental (FD-MS, cf. Chap. 8.5.4) isotopic pattern of a ruthenium carbonyl porphyrin complex. The isotopic pattern supports the presumed molecular composition. The label is attached to the peak corresponding to the ° Ru-contaming ion. Adapted fromRef. [17] with permission. IM Publications, 1997.

Isotopic patterns provide a prime source of such additional information. Combining the information from accurate mass data and experimental peak intensities with calculated isotopic patterns allows to significantly reduce the number of potential elemental compositions of a particular ion. [31] Otherwise, even at an extremely high mass accuracy of 1 ppm the elemental composition of peptides, for example, can only be uniquely identified up to about 800 u, i.e., an error of less than 0.8 mmu is required even if only C, H, N, O and S are allowed. [27,32,33]... 

Example The [M-Cl]" ion, [CHCl2], represents the base peak in the El spectrum of chloroform. The results of three subsequent determinations for the major peaks of the isotopic pattern are listed below (Fig. 3.15). The typical printout of a mass spectrometer data system provides experimental accurate mass and relative intensity of the signal and an error as compared to the calculated exact mass of possible compositions. For the [ CH Cl2] ion, the experimental accurate mass values yield an average of 82.9442 0.0006 u. The comparatively small absolute error of 0.6 mmu corresponds to a relative error of 7.5 ppm. 

Note The assignment of empirical formulae from accurate mass measurements always must be in accordance with the experimentally observed and the calculated isotopic pattern. Contradictions strongly point towards erroneous interpretation of the mass spectrum. 

The calculation of isotopic patterns of molecules of several 10 u is not a trivial task, because slight variations in the relative abundances of the isotopes encountered gain relevance and may shift the most abundant mass and the average mass up or down by 1 u. In a similar fashion the algorithm and the number of iterations employed to perform the actual calculation affect the final result. [16]... 

Fig. 3.26. Calculated isotopic patterns of large polystyrene ions. Adapted from Ref. [38] with permission. American Chemical Society, 1983.

The calculated and experimental isotopic patterns have to agree with the molecular formula postulated (Chap. 3.2). 

Example The positive-ion FAB spectrum of tetramesitylporphyrin, C56H54N4, in NBA matrix exhibits IVF and [M-i-H] ions (Fig. 9.8). [96] The presence of both species can be recognized by comparison of experimental and calculated M-i-1 intensity of the isotopic pattern. This difference can only be explained by assuming about 20 % [M+H]" ion formation. The diffuse groups of signals around m/z 900 reveal the formation of some adduct ions with the matrix, e.g., [M-i-Ma-i-H-HiO] at m/z 918. 

Fig. 9.8. Partial positive-ion FAB spectram of a tetramesitylporphyrin in NBA matrix. Comparison of the experimental and calculated isotopic patterns reveals the presence of M and [M+H] ions. Adapted from Ref. [96] by permission. M Publications, 1997.

Fig. 9.11. Negative-ion FAB mass spectra of a Bunte salt. The insets compare experimental and calculated isotopic patterns of the [C-I-2A] and [2C-I-3A] cluster ions. By courtesy of M. Grunze, University of Heidelberg.

Observed and Calculated Isotopic Pattern for the Parent Ion Cluster of [(CeF5)2PFe(CO)3]2... 

Although isotopic patterns and deconvolutions may be calculated manually (6), to achieve full potential a computer is virtually a necessity. Manual calculations often omit the 1.1% contribution for for molecules with large ligands, thirty carbons are not unusual, and these would give a 33% contribution to the m/e value, greater than that from the nominal mass by one mass unit. 

Various computer programs are mentioned in the literature for calculating isotopic patterns (182, 240-242) and the least-squares... 

Fortunately, as larger peptides and proteins are analyzed a distribution of ions is obtained. Even though we cannot look at the individual charge states from the isotopic pattern (because the resolving power of the instruments are too low) we can deduce the charge state by looking at two consecutive peaks in the mass spectrum [m/z and m/(z+1)]. All commercial instruments now allow for these calculations to be carried out very easily. 

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