Isotope distribution calculator

Figure 6.8 shows an example of a calculation based on a method developed by Hsu and carried out on a personal computer. Some isotope distribution calculators are also available on-line on the Internet [14,15],... 

From the binding energies calculated for the different cluster compositions, we determined abundance mass spectra for heated CggLi clusters from a simple Monte Carlo simulation. Figure 11 shows the simulated mass spectra resulting from these calculations, including the Li and Cgo isotope distributions. The peaks at A = 12 and at x = 6 + n (where n is the cluster charge) observed in the experiment (Fig. 9) are well reproduced. For more details, see ref. [12]. 

Table 3.2. Calculated isotopic distributions for carbon based on the C content according toIUPAC. lUPAC 1998. [4]...

The polynomial approach is the logical expansion of the binomial approach. It is useful for the calculation of isotopic distributions of polyisotopic elements or for formulas composed of several non-monoisotopic elements. [2,14] In general, the isotopic distribution of a molecule can be described by a product of polynominals... 

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. 

Note If the isotopic distribution is broad and/or there are elements encountered that have a lowest mass isotope of very low abundance, it is recommended to base calculations on the most abundant isotope of the respective element. 

Kubinyi, H. Calculation of Isotope Distributions in Mass Spectrometry. A Trivial Solution for a Non-Trivial Problem. Anal. Chim. Acta 1991, 247, 107-119. 

A case study of the identification of a counterfeit drug molecule is discussed in Section IX. C. This is a step-by-step discussion of the experimental procedure using FTMS to address this important issue. After the exact mass of the unknown componnd has been determined, the next step is to derive its elemental composition. The minimnm and maximum number of expected atoms present in the componnd mnst be specified in the search criteria to allow the compnter program to calculate possible elemental compositions. A nniqne fit of only one elemental composition is rarely obtained. The nnmber of possible compositions increases with the increasing nnmber of elements present and with increasing mass. However, other information, snch as the number of double bond eqnivalency and the isotopic distribution of the parent ion mass spectrnm, can be used to reduce the possible elemental compositions to a reasonable nnmber. Fnrther discussion can be fonnd in Section IX. C. 

Figure 5A, B shows the isotopic distribution, of protonated bosentan (C27H30N5O6S, Mr 552.6) with a mass resolution of 0.5 and 0.1 at FWHM, respectively. It is worthwhile to observe the mass shift of the most abundant ion from m/z 552.2006 to m/z 552.1911. This value does not change with a mass resolving power of 15 000 (Fig. 1.5C) or even 500000 (Fig. 1.5D). Accurate mass measurements are essential to obtain the elemental composition of unknown compounds or for confirmatory analysis. An important aspect in the calculation of the exact mass of a charged ion is to count for the loss of the electron for the protonated molecule [M+H]+. The mass of the electron is about 2000 times lower than of the proton and corresponds to 9.10956 x 10 kg. The exact mass of protonated bosentan without counting the electron loss is 552.1917 units, while it is 552.1911 units with counting the loss of the electron. This represents an error of about 1 ppm.

As in the case of the land surface burst, complete characterization of the particle population requires only that particle mass, a volatile species, and a refractory species distribution with particle size be determined. All other isotopic distributions may be deduced from the istotope partition calculations described above. In the subsurface detonation, the earliest aerial cloud sample was obtained in the cloud 15 minutes after detonation. The early sample was, therefore, completely representative of the aerial cloud particle population. In Figure 5 the results of the size analysis on a weight basis are shown. Included for comparison is a size distribution for the early, local fallout material. The local fallout population and the aerial cloud population are separated completely from the time of their formation. 

The data, except for the 0-0.1 /x fraction, fall on a straight line. However, the value of f calculated from the intercept is larger by about a factor of 100 than the value of r calculated from the slope. On the basis of this limited trial, the fit of the data to this form of distribution function appears to be quite unsatisfactory. A correct form of distribution function should apply to the entire class of airburst populations, and additional work now underway is devoted largely to resolving the problem of determining an appropriate form of distribution function to apply to airburst particle size distributions. However, there may be no simple function which reflects adequately the over-all behavior of the particle population. Indeed, Johnson (5) was able to demonstrate that his experimental results on isotope distribution with particle size were compatible with theoretical distributions obtained by following a modified version... 

Equation (115) is the same as (6) studied by James and co-workers (62) in the CO reduction of RhCl3.] The labeling experiment also revealed information on the stability of the hydroxycarbonyl intermediate in (115). If this species, Rh—COOH, was formed in an equilibrium concentration, then proton transfer and the reverse reaction would lead to incorporation of labeled oxygen in the carbonyl ligand and therefore to the observation of doubly labeled C02. However, comparison of the abundances of the three isotopic carbon dioxide molecules found (masses 44, 46 and 48) with distributions calculated assuming (i) equilibrium formation of the hydroxycarbonyl and (ii) immediate decomposition of the intermediate clearly showed that the hydroxycarbonyl intermediate reacts to form C02 immediately after it is formed, with no indication of a substantial equilibrium or incorporation of lsO in the carbonyl ligand. 

Now if a molecule contains more than one chlorine atom, the appearance of isotope clusters can be calculated by the probabilities of isotope distributions and the natural abundances of die isotopes. For example, if a molecule contains two chlorine atoms such as o-dichlorobenzene, dien diere will be peaks at M, M + 2, and M + 4 for molecules which have two 35C1, one 35C1 and one 37C1, and two 37C1 (Figure 11.48). 

Finally, the isotopic distribution of the parent ion can serve as a fingerprint for a given metal composition. The isotopic distribution of the parent ion of H2FeRuOs2(CO),3 is shown in Fig. 2. The wide isotopic distribution from mle 911 to mle 895 arises because iron, ruthenium, and osmium have, respectively, 4, 9, and 7 naturally occurring isotopes of appreciable abundance. The various combinations, taken together with the appropriate weighting factors, give the calculated distribution shown in Fig. 2. If the metal composition of a particular cluster is uncertain, the experimental isotopic distribution may be compared with that calculated for a number of trial compositions, and thus the correct composition can often be uniquely determined. 

Another method has been developed for calculating isotope distributions starting from a molecular formula and elemental isotopic abundances [16,17], This method uses Fourier transforms to do the multiple convolutions required to determine molecular isotope distributions and calculates ultrahigh-resolution distributions over a limited mass range. Because discrete Fourier transforms can be calculated very efficiently, this new way of looking at... 

Rockwood, A.L. and VanOrden, S.L. (1996) Ultrahigh-speed calculation of isotope distributions. Anal. Chem., 68 (13), 2027-30. 

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