Mass spectrometric separation and quantitation of overlapping isotopologues. Deuterium containing hydrides of As, Sb, Bi, Sn, and Ge

Journal of The American Society for Mass Spectrometry, Feb 2007

Mass spectra of fully and partially deuterated As, Sb, Bi, Ge, and Sn hydrides have been obtained using several mathematical approaches aimed at signal extraction and reconstruction. Study of such hydride mixtures is important for the elucidation of hydride generation mechanisms. In this approach, mass spectra of partially deuterated isotopomers, i.e., AsH2D and AsHD2, are extracted using the weighted two-band target entropy minimization method. Alternatively, these mass spectra were constructed from the mass spectra of fully deuterated and hydrogenated hydrides using the statistical approach in fragmentation pathways. Concentration profiles of all deuterated hydrides were obtained from their overlapping mixture mass spectra using least-squares deconvolution.

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Mass spectrometric separation and quantitation of overlapping isotopologues. Deuterium containing hydrides of As, Sb, Bi, Sn, and Ge

Juris Meija 0 1 2 Zoltan Mester 0 1 2 Alessandro D'Ulivo 0 1 2 0 Published online November 7, 2006 Address reprint requests to Dr. Z. Mester, Institute for National Measure- ment Standards, National Research Council Canada , 1200 Montreal Road, M-12, Ottawa , ON K1A 0R6, Canada 1 Institute for Chemical and Physical Processes, Laboratory of Instrumental Analytical Chemistry, National Research Council of Italy , Pisa, Italy 2 Institute for National Measurement Standards, National Research Council Canada , Ottawa , Ontario, Canada Mass spectra of fully and partially deuterated As, Sb, Bi, Ge, and Sn hydrides have been obtained using several mathematical approaches aimed at signal extraction and reconstruction. Study of such hydride mixtures is important for the elucidation of hydride generation mechanisms. In this approach, mass spectra of partially deuterated isotopomers, i.e., AsH2D and AsHD2, are extracted using the weighted two-band target entropy minimization method. Alternatively, these mass spectra were constructed from the mass spectra of fully deuterated and hydrogenated hydrides using the statistical approach in fragmentation pathways. Concentration profiles of all deuterated hydrides were obtained from their overlapping mixture mass spectra using least-squares deconvolution. (J Am Soc Mass Spectrom 2007, 18, 337-345) 2007 American Society for Mass Spectrometry - HNaBH4 with various elements is a widely used ydride generation by aqueous phase reaction of analytical technique for ultra trace determination of elements such as As, Sb, Bi, Ge, Pb, Hg, Se, Te, and Sn [1]. More recently, this reaction has been extended to generation of volatile species of In, Tl, Cd, Cu, and many other transition and noble metals [2]. Although hydride generation was first introduced in 1973, the reaction mechanisms relating to the interaction of aqueous tetrahydroborate(III) with ionic or molecular analytes are almost unknown. Nascent hydrogen hypothesis was very popular for a long time even though there were no supporting experimental data [3]. The first systematic investigations of the hydride generation mechanism appeared only recently using the approach of introducing the deuterium labeled reagents to elucidate the details of the hydride formation followed by mass spectrometric measurements [4]. Unfortunately, one cannot separate the various isotopologic hydrides such as AsH3, AsH2D, AsHD2, or AsD3 using conventional capillary gas chromatographic systems. Neither can these compounds be well separated in the mass domain since the electron impact mass spectra of these hydrides greatly overlap. Also, to the best of our knowledge, there are no experimental strategies for obtaining pure intermediate isotopologues such as AsH2D and AsHD2, not even to record their true mass spectra. In other words, while introducing the deuterium labeled reagents potentially offers new information about the hydride formation mechanism, the interpretation of the experimental data becomes cumbersome. The aim of this study is to mathematically solve the above mentioned problem to investigate the mechanism of hydride formation and H/D exchange reactions of the various (semi)metal hydrides. Using deconvolution methods, such as weighted two-band target entropy minimization [5 8], any recorded mass spectra of deuterium-labeled hydrides can be deconvoluted into the pure mass spectra of each isotopologue without having standard mass spectra of these compounds. The first part of this study described the mathematical approaches used to achieve the above stated aim [9] and in this manuscript we are extending the work to metal hydrides of the IV and V main group elements. Reagents and Materials The following reagents were used: NaBH4 pellets (Alfa Aesar, Word Hill, MA); NaBD4 pellets (99% D, Cambridge Isotope Laboratories, Andover, MA); 37% DCl in D2O (99.5% D, Aldrich, St. Louis, MO); 30% NaOD in D2O (99% D, Aldrich) and D2O (99% D, Aldrich). A stock solution of NaBH4 (1.0 M) in H2O was stabilized by adding NaOH up to 0.5 M. A stock solution of NaBD4 (1.0 M) in D2O was stabilized by adding NaOD up to 0.5 M. Working solutions of pure 0.2 M NaBH4, 0.2M NaBD4, as well as mixed 0.2 M (NaBH4 NaBD4) were prepared before experiments by adding 4 mL of H2O to x L of 1.0 M NaBH4 y L of 1.0 M NaBD4 (x 1000, 900, 750, 500, 250, 100, and 0 L; x y 1000 L). The resulting concentration of NaOH in the final solutions is 0.1 M NaOH. A 0.2 M NaBD4 solution in D2O and 0.1 M NaOD were prepared for hydride generation in fully deuterated reaction medium. Cold vapor generation of hydrides was performed in septum-sealed vials using solutions of 500 g mL1 As(III) and Bi(III), and 100 to 300 g mL1 (in acidified aqueous media) of 123Sb(III), 73Ge(III), and 118Sn(IV) (Oak Ridge National Laboratory, Oak Ridge, TN). All other reagents were of analytical grade. A Hewlett-Packard 6890 gas chromatograph (Wilmington, DE) operated in the splitless mode and equipped with a Hewlett-Packard 5973 mass selective detector (operated at 70 eV) was fitted with a DB-1 capillary column (30 m 0.25 mm i.d. 1 m; ValcoBond VB-1). A 5 mL gas-tight Hamilton syringe was used for sampling headspace gases from reaction vials; 10 mL screw cap reaction vials, fitted with PTFE/silicone septa (Pierce Chemical Co., Rockford, IL), were used according to experimental requirements. The GC was operated under the following conditions: injector temperature 150 C; oven temperature 35 C (isothermal). The carrier gas was He at 1.2 mL min1 . Hydride Generation Procedure The 10 mL reaction vial containing 2 mL of acid (1 M HCl or DCl for As, Sb, and Bi and 0.01 M HCl or DCl for Ge and Sn), approximately 2 to 10 g of the element ions and a Teflon coated stir-bar was capped and two stainless steel needles were inserted through the septum. Vigorous stirring of the solution was started and nitrogen was then introduced through one needle to purge the atmospheric oxygen from the headspace of the vial. The two needles were then removed and 1 mL of 0.2 M reducing solution (NaBH4, NaBD4 or NaBH4, and NaBD4 mixture) was injected using a plastic syringe fitted with a stainless steel needle. Headspace gases (2 to 3 mL) were subsequently sampled with a gas tight syringe and injected into the GC/MS. Collection of Mass Spectra Mass spectra of the hydride mixtures were obtained by integrating the overall chromatographic peaks. Average background intensities were subtracted. The obtained L1-normalized (A i 1) mass spectra were sufficiently stationary, i.e., constant in their statistical parameters over time. For example, results of 10 duplicate experiments using various mixtures of NaBH4 and NaBD4 in HCl showed the relative mass spectral intensity variations in the order of 1.5%. Average mass spectra of 2 to 4 measurements were used for spectral reconstruction and deconvolution. For reconstruction of AsHnDm, SbHnDm, and BiHnDm spectra (4 spectra, 7 m/z channels each) seven different mixture mass spectra were used (each being average of 2 to 4 replicate measurements). For SnHnDm and GeHnDm (5 spectra, 9 m/z channels) 12 mixture spectra were used in each case. All computations were carried out using the commercially available MathCad v.12.0 package (Mathsoft Engineering and Education, Inc.). Reconstruction of the mass spectra was done using the statistical mass balance method [9] and the weighted two-band-target entropy minimization algorithm (developed by the Garlandgroup[5 8]anddiscussedoriginallybyZhanget al.[5];seealsothefirstpartofthisstudy[9]).Standard simulated annealing minimization procedure was used to search for global minima, i.e., pure component mass spectra. Concentration profiles of the individual isotopologues were obtained using a least-squares isotope patternreconstructionasdescribedelsewhere[10,11]. A non-negative least-squares minimization routine was used for the reconstruction of more complex Ge and Sn hydride mass spectra to avoid the occurrence of negativecontributions[12].Spectralcontrastanglebetween the two mass spectra was calculated as follows: where Ai and Bi are the ion intensities on the ith m/z channel. For spectral comparison purposes, all the mass spectra were normalized with respect to their L2-norm, i.e., A i2 Bi2 1, unlike the conventional L1-norm (A i Bi 1) for the reasons discussed elsewhere [13].L1-normwasusedinspectralreconstruction,entropy minimization and in least-squares reconstruction. Results and Discussion The maximum number of hydrogen atoms, n, in simple metal and nonmetal volatile hydrides ranges from 1 to 4 and introducing deuterium in these hydrides can result in a maximum of (n 1) partially deuterated isotopologues with a total of (n 1) hydrides formed. The simplest case of n 1 represents hydrides such as HCl, HBr, (CH3)2AsH or CH3HgH. The mass-domain separation of these isotopomers is a trivial task (especially when enriched isotopes of the analyte elements Scheme 1. Statistical mass balance model of the EH3 and ED3 mass spectra (E As, Sb or Bi) that is used to reconstruct the mass spectra of the EH2D and EHD2. Coefficients k represent the reaction probabilities. k11 (kH11 kD11)/2 and k21 (kH21 kD21)/2. are used) since there is no mass spectral overlap on the molecular ions of the two species, e.g., D81Br and H81Br can be directly measured. In the case of n 2, the system becomes more complex. Direct estimation of H2O, HOD, and D2O from their electron impact mass spectra is impossible since H2O overlaps with OD (originating from HOD and D2O). In the first part of this study, we described the mass spectral deconvolution of the systems with n 2 using three conceptually differentapproaches[9]andhereweextendtheintroduced methods to the mass spectral reconstruction of hydrides with n 3 and 4. Deconvolution of EH3/EH2D/EHD2/ED3 Mass Spectra Electron impact mass spectra of the partially deuterated (semi)metal hydrides cannot be obtained due to the difficult chromatographic separation and their large spectral overlap. Mass spectra of AsH2D and AsHD2 for example cover m/z channels from 75 to 79 and 75 to 80, respectively. In the following paragraphs we will apply theband-targetentropyminimization[5,8]andmass balance[9]modelstoobtainthemassspectraofthe partially deuterated hydrides of As, Sb, Bi, Ge, and Sn. Unlike in the systems with n 2 (H2O, H2Se), the alternatingleast-squaresmodel[9]cannotbeextended to hydrides with n 2 due to the rapid increase in the number of unknown variables. In the case of As, 12 unknown variables (three concentrations, nine ion intensities for AsH2D and AsHD2) are present while only six independent measurements are available from the normalized mass spectra of m/z 75 to 81). Statistical Mass Balance Model Statistical reconstruction of the individual deuterated hydride isotopologue mass spectra has been attempted previously.Reconstructionofdeuterateddiborane[14], methane[15],andethane[16]massspectrahasbeen reported. Reconstructed mass spectra of deuteromethanes have even found application in methane H/D exchangestudiesovervariouscatalysts[17]. Reconstruction mixed isotopomer mass spectra of arsenic, antimony, and bismuth hydrides can be achieved in a manner similar to that used for H2O and H2Seisotopologues[9].Inprinciple,thestatisticalmass balance model reconstructs the mass spectra of isotopologues EH2D and EHD2 using the mass spectra of EH3 and ED3 (E As, Sb, Bi). All the possible fragmentation reaction pathways can be written for EH3, EH2D, EHD2 and ED3 (see Scheme 1). For each of the reactions, a probability coefficient k is assigned that accounts for the mass balance between the precursor ion and its fragment ion along with the statistical reaction probability factor. The individual ion intensities for EH2D and EHD2 mass spectra are derived using the symmetry numbers for each fragmentation reaction. In other words, the loss of the H radical from EH3 (represented by the kH1) is assumed to be three times as probable as the loss of H from the EHD2 (represented by [1/3]kH1). Symmetry numbers for the loss of HD are determined by assuming that the probability of HD elimination is the arithmetic average between the H2 and D2 elimination reactions. Consider the fragmentation EH2D EH (loss of HD). There are two combinations for HD elimination from the EH2D whereas there are three combinations to remove H2 or D2 from EH3 and ED3, respectively. Thus, the symmetry number for the loss of HD in the pathway EH2D EH is [2/3]. Reaction probability coefficients are obtained from the experimental mass spectra of pure EH3 and ED3 and are used to reconstruct the mass spectra of EH2D and EHD2. For example, coefficients kHi and the experimentally measured mass spectrum of EH3 are linked via the following equations: I EH3 I EH2 I EH I E There are three independent measured variables and five unknowns in this system of equations. Because this system is under-determined, one can have an infinite number of solutions to the model described above. Despite that, it is feasible to assign values to all the possible combinations of kH1, kH2 and kD1, kD2 (kH1, kH2, kD1, kD2 [01]) and, for each of these values, calculate the corresponding values of kH3, kH11, kH21, and kD3, kD11, kD21. Any negative k values are excluded from the solution set. This procedure is essentially a nonnegative least-squares optimization [12] where any combination of non-negative kH1, kH2, kH3, kH11, and kH21 that fit the mass spectra of EH3 is obtained. The same applies to ED3. Once all the possible sets of kHi and kDi are identified, mass spectra of EH2D and EHD2 are then obtained for every possible combination between those two sets according to Scheme 1. Despite the under-determined nature of the model, the obtained ion intensities for mass spectra of AsH2D and AsHD2 are rather insensitive to the particular valuesofk used(Figure1).Thisisbecauseofthefact that the m/z 78, 79, and 80 intensities depend on either the ratio or the difference between the kHi and kDi. Since the differences in AsH3 and AsD3 mass spectra are small (in terms of the ion intensities), so are the differences between the possible kHi and kDi values. It is interesting to note up front that despite the simplicity of this model, the ion ratios in the predicted isotopologue mass spectra agree rather well with the experimental measurements. Weighted Two-Band Target Entropy Minimization Model Band-target entropy minimization is an alternative approachtoreconstructcomponentmassspectra[5,8]. One of the most prominent features of the band target entropy minimization is the selection of the target m/z channels. Given a mass spectra with n channels one has n(n 1) combinations of two-band targets (including situations where both bands represent the same m/z channel). In the case of arsenic hydride mixtures, 28 different targets over a seven channel mass spectra (m/z 75 to 81) leads to four distinct mass spectra as shown inFigure2.Notethatthekeytoretrievingacomponent mass spectrum using this technique is the existence of a unique m/z channel that bears the highest intensity ion among all the other component spectra. AsH3 has such an ion at m/z 78, AsH2D at m/z 79, AsHD2 at m/z 80, and AsD3 at m/z 81. Two of the retrieved profiles agree with the experimental spectra of AsH3 and AsD3; however, closer inspection of the remaining two spectra shows abnormally large molecular ions. This is not consistent with the observed ion intensity relationships in isotopologue mass spectra since it is reasonable to assume that the molecular and elemental ion intensities of isotopologues have to range between the intensities of fully hydrogenated and deuterated compounds. When such contextual knowledge was included in the weighted two-band target entropy minimization algorithm the obtained AsH2D and AsHD3 mass spectra were in good agreementwiththestatisticalmodel(Figure2top)and the experimental data (see Validation section). Note that the biased ion ratios cannot be regarded as a failure of the entropy minimization model, rather as a consequence of the extremely dense spectral overlaps in this particular situation. For reference purposes, the reconstructed As, Sb, and Bi hydride isotopologue mass spectra are given in the Table1. To the best of our knowledge, this is the first study of the individual metal hydride isotopologue mass spectra, thus it is of interest to discuss the spectral similarity of these spectra. Spectral contrast angle is widely used similarity criteria in diverse fields, including mass spectrometry[13,18].InspectingthespectrafromTable1,it can be observed that the spectral similarity between successive isotopologues (AsH3 versus AsH2D; AsH2D versus AsHD2; AsHD2 versus AsD3) is rather constant. This can be illustrated by plotting the congruence angle amongtheisotopologuesinpolarcoordinates(Figure3) [19].Thus,alltheisotopologuemassspectra(including the Sn and Ge hydrides as discussed later) share an equal degree of dissimilarity. If this rule has a general extension, it will ensure that the spectral similarity of 0.145 | 0.145 0.421 | 0.420 0.106 | 0.105 0.328 | 0.328 0.000 | 0.001 0.000 | 0.000 0.000 | 0.000 0.142 | 0.139 0.278 | 0.262 0.176 | 0.177 0.066 | 0.079 0.341 | 0.343 0.000 | 0.000 0.000 | 0.000 0.139 | 0.135 0.141 | 0.086 0.281 | 0.324 0.064 | 0.006 0.031 | 0.103 0.344 | 0.346 0.000 | 0.000 0.133 | 0.136 0.008 | 0.000 0.421 | 0.431 0.003 | 0.000 0.088 | 0.088 0.022 | 0.000 0.325 | 0.345 aExperimental mass spectra. bBand-target entropy minimization. Ions that were forced to zero are marked with an asterisk (). Molecular ion intensity of EH 2D and EHD2 was forced to be within the EH3 and ED3 values. cStatistical mass balance model. Maximum difference between the kHi and kDi was allowed to be 50% (1000 simulations). any isotopologue mass spectra is governed by the orthogonality (dissimilarity) between the fully hydrogenated and fully deuterated hydride mass spectra. Among the periodic trends seen in the mass spectra of the element hydrides, the intensity of the molecular ion diminishes with the increase of the atomic number. In other words, heavy element hydrides are more prone to fragmentation. Deconvolution of EH4/EH3D2/EH2D2/EHD3/ED4 Mass Spectra Aqueous phase reaction of borohydride, BH4 , with Ge(IV) and Sn(IV) species forms GeH4 and SnH4 respectively. However, in the presence of deuterated borohydride, BD4 , four more hydrides can form: EH3D, EH2D2, EHD3, and ED4 (E 73Ge, 118Sn) depending on the BH4 /BD4 ratio. Also, various partially deuterated hydrides can be obtained when GeH4/GeD4 and SnH4/ SnD4 are subjected to H/D exchange reactions at different pH. Germanium and tin hydride mass spectra are different from the As, Sb, and Bi hydride in a sense that the molecular ion is practically absent. Also, the number of isotopologues is by one larger than in the case of group V element hydrides. For these reasons the Ge and Sn hydride isotopologue mass spectra are substantially overlapping and the retrieval of all five isotopologue mass spectra using the band-target entropy minimization model was not successful. GeH4, GeD4, and SnH4, SnD4 mass spectra can be easily recovered using the restrictions analogous to As, Sb, and Bi spectra. Alternating the band-targets for germanium hydride mixtures, for example, leads to the retrieval of only GeH4, GeD4, and GeHD3 spectra. Accurate ion intensities, however, cannot be ensured for GeH3D, GeH2D2, GeHD3, and their Sn analogues for two reasons. First, no feasible verification of the ion intensities can be done (due to the absence of the molecular ions) and, secondly, there is no safe way to ensure that pure spectra (and not linear combinations of several spectra) are retrieved from the entropy minimization. At the expense of additional assumptions (such as the pure GeD4 and GeH4 spectra), the statistical model, however, is not affected by the dense spectral overlaps; hence, it can be used to reconstruct all the isotopologues of Ge and Sn hydridesasshowninTable2. Despite some difficulties of implementing the weighted two-band target entropy minimization model in the particular case of Ge and Sn hydride mixtures, it has an important advantage in retrieval of fully deuterated hydride reference spectra. Due to the high reactivity of GeD4 and SnD4, the H/D exchange process makes it extremely hard to obtain mass spectra with no impurities from the first exchange products GeHD3 and SnHD3. Isotope Effects in Fragmentation When comparing the mass spectra of the various isotopologues clearly the ion ratios within each mass spectrumaredifferent(Figure4).Forexample,theratioof AsD3 /As in the mass spectrum of AsD3 is 2.43 0.04 (2s) whereas the AsH 3 /As ratio in the mass spectrum of AsH3 differs by 7% (2.26 0.01). Similar comparison of the molecular ion and elemental ion ratios for Sb and Bi hydrides show 15 and 50% differences, respectively. This is clearly due to the isotope aStatistical mass balance model. Maximum difference between the kHi and kDi was set to 50%. bExperimental GeD4 spectrum contains rather large amounts of GeHD3 and GeH2D2 (10%). Constrained entropy minimization was used to recover the pure GeD4 mass spectra (m/z 76 and 78 were forced to be 0.001). cExperimental SnD4 mass spectrum contains about 5% SnHD3. Thus, all the calculations were preformed in two iterations. In the first iteration the raw SnD4 spectrum was used and in the second iteration the contribution of the SnHD3 spectrum was removed from the contaminated experimental SnD4 mass spectrum. effects in the fragmentation pathways. We can see that on average, the loss of hydrogen predominate the loss of deuterium in 70 eV electron impact mass spectra of As, Sb, Bi, Ge, and Sn hydrides. Note that staggeringly large isotope effects in EI mass spectra are not uncommon. Such effects, for example, have been observed for methane isotopologue CHD3 where the loss of H greatlypredominatesthelossofD[20].Similarobservations are known for hydrocarbon electron impact spectra, where deuterium is also less easily split off than hydrogen[21]. For As, Sb, and Bi the ratios of the molecular ions to the elemental ions are shown (e.g., AsD3 /As ). For Ge and Sn, the largest fragment ion is used due to the absence of the molecular ions (e.g., SnH3 /Sn ). Because the ion ratios in the mass spectra of fully deuterated hydrides are different from those in fully hydrogenated species, prediction of the partially deuterated hydride mass spectra with the statistical mass balance model requires the use of both spectra (i.e., kHi and kDi). It is interesting to note that the magnitude of the isotope effects in the group V metal hydrides (As-Sb-Bi) increases with the increase of the atomic number. The explanation of this effect is, however, well beyond the scope of this manuscript. Validation of the Reconstructed Mass Spectra Although it is practically impossible to obtain pure mass spectra of the partially deuterated species (unless scrupulous separation is performed), nevertheless, it is possible to obtain experimental evidence of certain ion ratios for the AsHD2, SbHD2, and BiHD2 mass spectra from rather simple experiments. When 75As, 123Sb, and 209Bi hydrides are generated in an environment that contains 90% deuterium (as BD 4 ), it is reasonable to assume that the generated hydride mixtures will contain mostly 75AsD3, 123SbD3, 209BiD3, some amounts 75AsHD2, 123SbHD2, 209BiHD2, and virtually no other species such as AsH3 or AsH2D. The same principle is also observed, for example, in a H2O/HOD/D2O system. In such mixtures ions with even m/z ratios originate from the 75AsHD2, 123SbHD2, and 209BiHD2 and have no contributions from the fully deuterated compounds. Thus, the even m/z ion ratios can be compared to the theoretical estimates from the statistical, and entropy minimization models as shown in Table 3. Hydrides for this experiment were generated using a 90:10 mixture of equimolar NaBD4 and NaBH4 solutions. Using the coefficients and the symmetry numbers from Scheme 1, it is easy to show that the m/z 80: 78 ratio in the AsHD2 mass spectrum according to the statistical mass balance model is m z 80 : 78 This estimate is in good agreement with the experimental results as shown in Table 3. Similarly one can obtain the estimates of the SbH2D, SbHD2, and BiH2D, BiHD2 mass spectra (see Table 3). The agreement of the statistical model with experimental values is striking and the constrained band Experimentala Entropy modelb aObtained from the AsD3/AsHD2 and SbD3/SbHD2 mixtures generated with NaBD4 NaBH4 (90:10) ( 2s are reported). SnHD3/SnD4 and GeHD3/GeD4 mixtures were obtained from NaBD4 in H2O. bConstrained weighted two-band target entropy minimization (restrictions in the molecular ion intensity were applied). Values obtained from blind deconvolution are given in the parenthesis. cm/z 126 intensity is very small (0.004) in blind deconvolution. dm/z 121 intensity is very small (0.01) in blind deconvolution. target entropy minimization leads to mass spectra that agree with experimental evidence. Applying restrictions on particular ion intensities is, perhaps, feasible, only in isotopologue systems where partial knowledge is always present (since the molecular formulas are known). Similarly, we have shown that it is possible to obtain accurate spectral intensities from the band-target entropy minimization algorithm when certain m/z channels are forced to zero (as in the case of the GeD4 mass spectrum). In practice, such restriction can be useful when the task is to extract the mass spectrum of a particular component. For example, when a mass spectrum of AsH3 is required, the intensities of the channels 75 m/z 78 can be set to zero. Isotopic Conversion of the Mass Spectra So far only the mass spectra of monoisotopic element hydrides have been considered. Unlike arsenic and bismuth, antimony, germanium and tin are not monoisotopic, therefore the mass spectra of the hydrides are more complex when natural isotopic compositions are used for hydride generation. Fortunately, the isotopic conversion of mass spectra is feasible. The reconstructed mass spectra of 123SbH2D and 123SbHD2 can be convoluted with the natural isotope pattern of antimony to obtain the spectra of SbH2D and SbHD2. As an illustrative example, the mass spectrum of SbH3 can be obtained when the mass spectrum of 123SbH3 is convoluted with the Sb isotope pattern. If each of the mass spectra is represented as a vector An 1 and Bm 1, then the transformed mass spectra C(m n 1) 1 is obtained by summing the secondary diagonals (skew diagonals) of the matrix A BT. For the 123SbH3 SbH3 conversion the following operations have to be performed: Such convolution is in agreement with the experimental results obtained from Ge and Sn hydrides generated from monoisotopic and natural abundance elements under identical conditions. Note that for isotope pattern conversions with more than one hetero-element this calculation becomes iterative [22]. An alternative matrix-based isotopic conversion algorithm is also described in the literature (both agree) [23]. Concentration Profiles of Isotopologues The ultimate aim of this study was to be able to obtain accurate concentration profiles for the deuterated element hydrides. To achieve this, various ratios of BH4 /BD4 were used to generate the arsenic hydrides and the collected normalized mass spectra (m/z 75 to 81) of the hydride mixtures were then inspected. Amount fraction of each compound in the analyzed gas mixtures was calculated from the observed composite mass spectra using the isotope pattern reconstruction [10, 11]. In this procedure, the amount fractions of all four arsenic hydride isotopologues are obtained from the linear fit of the following equation: The left side of the equation is the average mixture mass spectrum (from n 4 experiments) and right side contains the four mass spectra of the individual isotopologues (from Table 1). Least-squares fitting of this mass spectrum leads to the relative isotopologue abundances 0.18, 0.43, 0.31, and 0.09 for AsH3, AsH2D, AsHD2, and AsD3 respectively. Figure 5 shows the deconvoluted concentration profiles of the arsenic hydride isotopologues generated using various amounts of NaBD4 in the mixture of NaBD4 and NaBH4 (from pure NaBH4 to pure NaBD4). From these profiles one can see that the sequential hydrogen and deuterium incorporation into the metal hydrides approximately follows the binomial probability distribution [24]: where xD and xH are the deuterium and hydrogen amount fractions in the borohydride mixtures (BD4 / BH4 ). Any deviations from this equation are the result of kinetic effects of H and D transfer. Increasing the amount of deuterium in the borohydride results in the systematic increase of deuterated arof NaBD4 in the mixtures of NaBD4 and NaBH4. Isotopologue mass spectra were obtained from the statistical model (black circles) and the entropy minimization approach (open circles). senic hydrides: starting from the AsH2D, then followed by AsHD2 and ultimately, NaBD4 produces almost pure AsD3. The differences in concentration profiles as obtained from the statistical model and the constrained rather small and are acceptable for analytical purIn this study, we have shown that the statistical mass balance model is very efficient in predicting the ion intensities in the complex mass spectra of As, Sb, Bi, Ge, and Sn hydride isotopologues. This model constructs the mass spectra of EH2D and EHD2 isotopologues from the experimental mass spectra of EH3 and ED3. Alternatively, weighted two-band target entropy minimization can also extract the EH2D and mass spectra from the mixtures of isotopologues with unknown concentration and having no need to know EH3 and ED3 spectra. We have shown that accurate ion intensities can be predicted for these compounds thus solving mass spectrometric problems, virtually intractable before: using the predicted mass spectra we are now able to estimate the individual isotopologue concentration in unknown mixtures that is essential for investigations of the hydride exchange reaction mechanisms [25]. Acknowledgments JM thanks the National Science and Engineering Research Council of Canada for the postdoctoral fellowship.

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Juris Meija, Zoltan Mester, Alessandro D’Ulivo. Mass spectrometric separation and quantitation of overlapping isotopologues. Deuterium containing hydrides of As, Sb, Bi, Sn, and Ge, Journal of The American Society for Mass Spectrometry, 2007, 337-345, DOI: 10.1016/j.jasms.2006.09.018