Mass spectrometric separation and quantitation of overlapping isotopologues. H2O/HOD/D2O and H2Se/HDSe/D2Se mixtures
Juris Meija
0
1
2
Zoltan Mester
0
1
2
Alessandro D'Ulivo
0
1
2
0
Published online May 19, 2006 Address reprint requests to Dr. Z. Mester,
Institute for National Measure ment Standards, National Research Council Canada
, 1200 Montreal Rd., Ontario K1A 0R6,
Canada
1
Laboratory of Instrumental Analytical Chemistry, Institute for Chemical and Physical Processes, Research area of Pisa, National Research Council of Italy
,
Pisa, Italy
2
Institute for National Measurement Standards, National Research Council Canada
,
Ottawa
, Ontario,
Canada
Three conceptually different mathematical methods are presented for accurate mass spectrometric determination of H2O/HOD/D2O and H2Se/HDSe/D2Se concentrations from mixtures. These are alternating leastsquares, weighted twoband target entropy minimization, and a statistical mass balance model. The otherwise nonmeasurable mass spectra of partially deuterated isotopologues (HOD and HDSe) are mathematically constructed. Any recorded isotopologue mixture mass spectra are then deconvoluted by leastsquares into their components. This approach is used to study the H2O/D2O exchange reaction, and is externally validated gravimetrically. The H2O/D2O exchange equilibrium constant is also measured from the deconvoluted 70 eV electron impact GC/MS data (K 3.85 0.03). (J Am Soc Mass Spectrom 2006, 17, 1028 1036) 2006 American Society for Mass Spectrometry

Icomposition only, such as H2O and D2O. These
comsotopologues are compounds that differ in isotopic
pounds play an important role in analytical chemistry,
especially in quantitative analysis where most of the
modern internal quantitation methods are based on
isotopologues. The massdomain separation of isotopologues,
such as HBr and DBr, is a trivial task since there is no mass
spectral overlap on the 81Br molecular ions of the two
species. However, the presence of two hydrogen atoms (as
in H2O or H2Se) makes the direct estimate of each
isotopologue impossible from its electron impact mass spectra.
The mass spectrum of H2O has two abundant signals at
m/z 18 and 17, the mass spectrum of D2O has two
abundant signals at m/z 20 and 18. HOD, whose mass
spectrum cannot be directly measured, is expected to have
three abundant ions at m/z 19, 18, and 17. Due to the
abovementioned spectral overlaps, a 1:1 mixture of H2O
and D2O gives a ratio of the molecular ions (at m/z 18
and 20) of about 1.3:1 (see Scheme 1). It is evident from this
that deconvolution of the mass spectra is needed to
estimate the individual amounts of H2O, HOD, and D2O
from the composite mass spectra. To do this, however, one
needs to obtain the reference mass spectrum of pure HOD.
This is not possible since HOD (or any other mixed
isotopologue that exchanges its protons and deuterons)
cannot exist in the absence of H2O and D2O due to the
rapid isotopeexchange equilibrium 2HOD ` H2O
D2O.
Using the best available commercial highresolution
mass spectrometers, one can possibly address the H2O/
HOD/D2O system (requiring m/ m 12,000 to fully
resolve isobars OD and H2O ); however, to do the same
for heavier element hydrides, such as HDSe or AsH2D,
mass resolving power of at least 50,000 is required. Such
resolution currently is attainable only for GCFTMS
instrumentation. Gasphase IR spectroscopy could be an
alternative option to the above mentioned problem.
While introduction of deuteriumlabeled reagents
potentially offers new information, such as quantitation or
reaction mechanism elucidation, the interpretation of
experimental data becomes cumbersome due to the possible
spectral overlaps. The aim of this study is to outline
mathematical approaches to solve these problems: (1)
extraction/reconstruction of pure isotopologue mass
spectra; (2) estimation of isotopologue concentration
profiles from the mass spectra of their mixtures.
The following reagents were used: NaBH4 pellets (Alfa
Aesar, Ward 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
solution of NaBH4 prepared in H2O was stabilized by
Scheme 1. Statement of the problem: Amounts of individual water isotopologues cannot be
estimated from their EI mass spectra without deconvolution.
adding NaOH up to 0.1 M final concentration. A
solution of NaBD4 (0.25 M), prepared in D2O
was stabilized by adding NaOD up to 0.1 M final
concentration.
An enriched isotopic standard solution of 260 g
mL 1 82Se(IV) in HNO3 aqueous media (Oak Ridge
National Laboratory, Oak Ridge, TN) was used to spike
the reaction media in septumsealed vials for cold vapor
generation of their corresponding hydrides. All other
reagents were of analytical grade.
A HewlettPackard 6890 gas chromatograph
(Wilmington, DE) operated in the splitless mode and
equipped with a HewlettPackard 5973 mass selective
detector was fitted with a DB1 capillary column (30
m 0.25 mm i.d. 1 m; Vallobond VB1). A 5 mL
gastight syringe (Hamilton, Reno, NV) was
employed for sampling headspace gases from reaction
vials.
Screw cap reaction vials fitted with
PTFE/silicone septa (510 mL, 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 min 1.
H2Se generation. The reaction vial (10 mL) containing 2
mL of 1 M HCl, about 10 g of 82Se(IV) and a Teflon
coated stirbar was capped and two stainless steel
needles were inserted into the septum. Vigorous
stirring of the solution was started and nitrogen was then
introduced through one needle to purge atmospheric
oxygen from the headspace of the vial. The two needles
were then removed and 1 mL of 0.25 M NaBH4 solution
was injected using a plastic syringe fitted with a
stainless steel needle. Headspace gases (23 mL) were
subsequently sampled with a gas tight syringe and injected
into the GC/MS. Mass spectrum of pure H2Se was
obtained.
D2Se generation. Generation of pure D2Se was
attempted using fully deuterated reaction media. A
procedure similar to that described for H2Se generation
was adopted with the following modifications. In a 5
mL vial containing 0.5 mL of 1 M DCl spiked with 0.05
mL of 82Se(IV) aqueous standard solution, atmospheric
oxygen was degassed and 0.5 mL of 0.25 M NaBD4
solution was injected.
H/D exchange experiments. Pure H2Se was prepared as
described above. Two aliquots of the H2Se headspace
gas (each of 35 mL volume) were collected in a rapid
sequence. The first aliquot was injected into a 5 mL
reaction vial (the exchange vial) containing 1 mL of 0,
3 and 6 M DCl in D2O and continuously shaken
throughout the experiment. The second H2Se
headspace aliquot was injected into the GC/MS to verify
the isotopic composition of the synthesized H2Se. The
isotopic composition of the injected hydride in the
headspace of the exchange vial was checked at
regular intervals by GC/MS. Previous experiments in
which H2Se was injected onto a column pretreated
with DCl vapors have demonstrated that the H/D
exchange does not take place in the GC capillary
column [1].
Results and Discussion
The first aim of the study is the extraction of pure
component mass spectra from their mixtures. In
mathematical terms, this is an inverse problem of
spectral reconstruction: given composite spectra,
extract the individual component mass spectra and
their concentration. In information theory, this is
referred to as the blind source separation and
independent component analysis. The H2O/HOD/D2O
system resembles a socalled gray system because we
have partial knowledge of the spectra of the
components involved. Also, the number of components is
known.
Reconstruction of HOD Mass Spectrum
Alternating leastsquares model. Any mass spectra of the
H2O, HOD, and D2O mixture can be represented in a
general equation:
This demonstrates that the observed [normalized]
mass spectrum is a weighted sum of all the isotopomer
mass spectra. Weighting factors, a, are the amount
fractions of each isotopomer in the mixture. Eq 1 can be
rewritten as I F a , where I5 1 is the observed
mass spectrum vector of the mixture (5 is the number of
m/z channels), F5 3 is the matrix of three individual
component mass spectra (stacked together), a3 1 is their
abundance (amount fraction) vector and 5 1 is the
instrumental noise vector [2]. In an alternating
leastsquares method (also known as iterative leastsquares),
many possible (alternating) sets of HOD mass spectra
are generated, which then are used (onebyone) to
reconstruct the mass spectra of the H2O/HOD/D2O
mixtures. A large set of possible HOD mass spectra can
be obtained using the uniformly distributed random
number generator. Three random numbers, xi [0. . .1],
are generated in each set of calculations: x1, x2, and x3,
which correspond to m/z 16, 17, and 18 intensities
(normalized) in the HOD mass spectrum; m/z 19
intensity, x4 1 x1 x2 x3. If x4 0, another set of
random numbers is generated until x4 0. Each of the
generated (nonnegative) HOD spectra is then used in
eq 1 to reconstruct a given experimental mass spectrum
of the H2O/HOD/D2O mixture using the leastsquares
optimization. A HOD mass spectrum that fits the
experimental mass spectra with the smallest residual error
is the result of the least square optimization
I F min G a
Here, a global minimum, min(G), of the variance of
the residual errors is sought. Alternating leastsquares
have been used previously in spectroscopy to
reconstruct the infrared spectra of HOD and eventually
determine the individual amounts of H2O, HOD, and
D2O in the H2O/D2O mixtures [3, 4]. This technique is
also of general interest in solving liquid
chromatography mass spectrometry coelution problems [5].
In the case of the H2O/D2O system, the mass spectra
of H2O, D2O, and that of the resulting mixture are
known. The remaining five independent variables,
a(H2O), a(HOD), and the intensities of m/z 16, 17, and
18 in the mass spectrum of HOD, are unknown. Other
variables: a(D2O) and I(HOD, m/z 19), are dependent
since both concentrations and mass spectra are
normalized to unity. As well, I(HOD, m/z 20) 0. Note that the
system is underdetermined by one dimension (four
independent measurements and five unknown
variables) and, therefore, it is impossible to obtain an
analytical solution of the HOD mass spectrum. Instead,
we can obtain the range of solutions that are consistent
with certain assumptions discussed below.
Since the system described above is
underdetermined, contextual information has to be supplied. Such
information can be the expected intensity of the HOD
molecular ion. The normalized molecular ion intensities
for H2O and D2O are 0.799 0.001 ( 2s) and 0.803
0.001, respectively; therefore it is reasonable to assume
that the intensity of the HOD molecular ion is expected
to be within that range. Note that the real isotope
dilution analytical protocols operate on the very same
basic assumption. The reconstructed mass spectrum of
HOD using the alternating leastsquares algorithm with
the above mentioned restriction (assumption) is shown
in Figure 1.
Entropy minimization model. Mass spectra of pure
components can be reconstructed using entropy
minimization as recently outlined by Zhang et al. [6]. In essence,
this approach is a pattern discovery (recognition) via
entropy minimization. The objective function to be
minimized thus is the entropy of the extracted mass
spectrum. In information theory, entropy is a measure
of the average amount of information required to
describe the distribution of some variable of interest. The
most commonly used measure of entropy was
introduced by Shannon (S plnp) [7]. This classical entropy
definition was previously used in reconstruction of
continuous NMR, Raman, and IR spectra where p has
been quantitatively linked with the first or higher order
derivatives [8 12]. However, such an entropy definition
(smoothness of the spectra) cannot be transferred in the
context of mass spectrometry where the individual
masses are discrete by their nature and, thus, a
modified nonlogarithmic entropy definition is used in this
model recently developed by the Garland group [6, 12].
An overall weighted two bandtarget entropy
minimization algorithm can be outlined in the following
steps. First, a mass spectral data matrix Ik n is compiled
from k mass spectra each having n masstocharge
channels (k number of possible isotopologues). Each
mass spectrum is normalized to unity total ion
intensity. Second, a singular value decomposition of Ik n
matrix is performed [13]. This procedure represents any
k n matrix as a product of three matrices (Uk n and
Vn n are orthonormal, e.g., UTU VTV 1):
This leads to the diagonal singular value matrix
and the right singular value matrix VT. The obtained
singular value decomposition is used further for noise
reduction [14]. The main idea is that the experimental
Ik n matrix contains components of large and low
variation. It can be shown that the small singular values
Figure 1. Construction of HOD mass spectrum using three conceptually different approaches:
alternating leastsquares (a), weighted two bandtarget entropy minimization (b), and statistical mass
balance model (c).
in mainly represent the noise. This noise is eliminated
by keeping only the first j nonzero singular values (j
k) [15]. It is worth mentioning that the matrix range
(which equals j) represents the number of individual
compounds whose spectra are to be deconvoluted. The
j j
The pure component mass spectra can be obtained
using the transformation matrix T:
The presence of matrix in this equation serves as a
weighting procedure, making the model more robust.
Mass spectral reconstruction of j independent
components now becomes a problem of finding all T vectors.
There are certain restrictions any candidate T vector
must comply with. First, it has to produce a
nonnegative pure component spectrum estimate A1 n.
Choosing the two target bands (m/z channels) Ax and Ay
is the crucial step of the method. During this step A1 n
matrix is normalized with respect to the total intensity
of the target bands:
A1 n
Depending on the targeted m/z channels, mass
spectra of different isotopologues are extracted. For
example, targeting the m/z 18 and 20 yields a mass
spectrum of D2O, targeting m/z 17 and 18 yields a
H2O mass spectrum, and targeting m/z 17 and 19 or
18 and 19 results in retrieval of the HOD spectrum.
Second, component contribution (concentration) in each
of the k mass spectra also has to be nonnegative:
Ik n AnT 1
A1 n
The objective function (entropy) to be minimized is
simply the sum of the channel intensities in the
reconstructed mass spectrum:
A1 n
Minimization of the objective function (in terms of T
vector) is usually achieved using the simulated
annealing algorithm, which is a good choice for a global
minimum search in many dimensions [16, 17]. In our
situation, the number of dimensions is small (three for
the H2O/HOD/D2O system); therefore we use the
exhaustive random search.
As mentioned above, the model seeks the lowest
entropy (most simple) mass spectra within the
nonnegativity constraints. In a particular H2O/HOD/D2O
example, the three component concentration and mass
spectral information is condensed into five spectral
channels; therefore the system is undetermined and an
infinite number of HOD mass spectra can be obtained.
Since one of such possible solutions is a HOD spectrum
with no fragment ions, this is the obvious minimum
entropy result (the simplest mass spectrum). In other
words, additional contextual information is needed to
separate the mathematical solution from the chemically
meaningful solution of the HOD mass spectrum. The
same applies to the reconstruction of the HDSe mass
spectrum. The blind deconvolution lowest entropy
result for the HOD mass spectrum is (0.000; 0.000; 0.000;
1.000; 0.000). This result clearly has no chemical
meaning, especially considering the experimentally
measured mass spectra of H2O and D2O. When the
abundance of the HOD molecular ion is set within the range
of H2O and D2O molecular ions, the reconstructed mass
spectrum of HOD using the weighted twoband target
entropy minimization algorithm (targeting m/z 18
and 19) with the above mentioned restriction of
molecular ion intensity is (0.017; 0.056; 0.126; 0.801; 0.000) as
shown in Figure 1. Although these two results are
quantitatively different, nevertheless, they are nearly
identical when compared using the spectral contrast
angle (99% similarity). Clearly, the spectral contrast
angle is not a good choice for comparing the
experimental and the reconstructed spectra due to its
insensitivity to low intensity ions. This was also recently
pointed out by Zhang who proposed using the ratio of
the geometric and the arithmetic means as a similarity
measure between the mass spectra [18]. Using this
criterion, the similarity between constrained and
unconstrained HOD spectra becomes 89%. In the first
unconstrained bandtarget entropy minimization
reconstruction of mass spectra, the Garland group achieves
76 92% similarity (calculated using the ratio of
geometric and arithmetic means) between the reference and
measured spectra in a four component mixture
(ethanol, acetone, hexane, and toluene in the m/z 10 100
range) [6].
Clearly, when dealing with underdetermined
overlapping isotopologue systems, ion intensities in the
extracted pure component mass spectra can be biased if
no contextual feedback is provided. As we have seen,
although such bias might be of little importance for
spectral recognition, it is, nevertheless, significant for
quantitative purposes.
Statistical model. To predict mass spectra of
isotopologues one needs to consider two factors: differences in
symmetry numbers for particular fragmentation
pathways (e.g., loss of H from H2O versus HOD) and
possible rate constant differences between the two
isotopic pathways (loss of H versus loss of D from the
same ion) [19]. All the possible fragmentation reaction
pathways can be written for H2O, HOD, and D2O, and
for each of the reactions we can assign a probability
coefficient that accounts for the mass balance between
the precursor and fragment ions including the statistical
factor as shown in Scheme 2. This model assumes that
the probability of a certain ligand is directly
proportional to its amount in the precursor ion. In other words,
the loss of an H from H2O is assumed to be twice as
probable as from HOD . Autoionization (formation of
H3O , D3O , H2DO , and HD2O ) is excluded from
this scheme due to its small contribution ( 1%). These
mathematical coefficients are obtained from the
experimental mass spectra of pure H2O and D2O and then are
used to reconstruct the mass spectrum of HOD as
Scheme 2. Statistical mass balance model of the H2O and D2O
mass spectra used to reconstruct the mass spectrum of the HOD.
Coefficients k represent the reaction probabilities.
shown in Scheme 2. In this model, the (normalized)
intensity of m/z 17 for H2O is kH1(1 kH2) and 0.5kD1(1
kH2) for HOD.
One can immediately see from this scheme, that
the system is (again) underdetermined: with three
independent variables (kH1, kH2, and kH) and only two
independent measurements, the intensities of H2O
(m/z 18) and OH (m/z 17), since the intensity of the
remaining ion (O ) in a normalized mass spectra is
bound to the sum of all the other relative ion
intensities. The same applies for D2O coefficients. In other
words, one can have an infinite number of solutions
to the model described above. Despite this, we can
assign all the possible values of kH1 and kD1 (kH1 and
kD1 [0. . .1]) and for each of these values (kH2, kH)
and (kD2, kD) are calculated. Any set of kH1, kH2, and
kH has to fit the experimental mass spectrum of H2O
within the specified error threshold. The same
applies for D2O. Also, any negative values of k are
eliminated from the solution set. This procedure is
essentially a nonnegative leastsquares optimization
[20]. Once all the possible sets of (kH1, kH2, kH) and
(kD1, kD2, kD) are identified, mass spectra of HOD are
then obtained for every possible combination
between those two sets according to the Scheme 2.
Interestingly enough, the obtained ion abundances in
mass spectra of HOD are insensitive to the particular
values of k used. This is because the ion intensities in
the HOD mass spectrum are functions of the ratios
between the kHi and kDi:
Im/z 19 0.5I(H2O, m/z 18) 0.5I(D2O, m/z 20)
Im/z 18 0.5I(H2O, m/z 17)(1 kD2)/(1 kH2)
Im/z 17 0.5I(D2O, m/z 18)(1 kH2)/(1 kD2)
Even though the complete mass spectrum of HOD
(m/z 16. . .19) cannot be experimentally obtained, the
ratio of HOD to OH can be measured from a mixture
of D2O with a small amount ( 5%) of H2O. In such
mixtures virtually all of the 1H isotopes are in the form
of HOD. Besides that, odd m/z values have zero
intensity in the D2O mass spectrum. Hence, the ratio of m/z
19/17 in such D2O/H2O mixtures is a direct estimation
of a partial HOD mass spectrum. Since the intensity of
m/z 17 is low, the uncertainty of the experimental 19/17
ratio is rather large. Nevertheless, the average
experimental value of 14 6 ( 2s) is comparable to the
alternating leastsquares estimate of 16 3, the entropy
minimization estimate of 14.5 0.3 and the statistical
massbalance estimate of 8.9 0.1.
Alternating leastsquares and entropy minimization
yield virtually identical mass spectra of HOD. Although
the m/z 17 and 18 ion intensities in the HOD mass
spectrum as obtained from the statistical model appears
qualitatively very different from the other two
estimates, the spectral similarity of the HOD mass spectra
among all three models exceeds 99.8% (calculated either
as the spectral contrast angle between the unity length
normalized spectra [21] or as the ratio of the geometric
and arithmetic mean between them [18]). For reference
purposes, all the mass spectra are tabulated in Table 1.
Reconstruction of HDSe Mass Spectrum
Reconstruction of selenium hydride mass spectra is a
problem similar to that of the water example. The
difficulty of the pure component spectra reconstruction,
however, is increased because the D2Se mass spectrum
is difficult to obtain even by reaction of trace amounts
of Se(IV) with NaBD4 in deuteriumonly medium (DCl
NaBD4, x(D) 97%) as discussed previously in the
Experimental section.
Accordingly, alternating leastsquares cannot be
used to reconstruct the mass spectrum of HDSe since no
experimental estimate of D2Se is available. In spite of
this, Figure 2 shows the entropy minimization estimates
of H2Se, HDSe, and D2Se mass spectra (containing only
82Se isotope). The H2Se mass spectrum was recovered
by targeting the m/z 82 and 84, HDSe by targeting m/z
82 and 85, and the D2Se mass spectrum was
recovered by targeting the m/z 82 and 86. To reduce the
bias in recovered ion intensities, the molecular ion in
the HDSe mass spectrum was forced to be in the range
of H2Se and D2Se molecular ion intensities. One can see
that the reconstructed H2Se mass spectrum agrees well
with the experimental measurements (Figure 2). The
m/z 16
17
18
19
20
m/z 82
83
84
85
86
0.0170.0170.020
0.0900.0560.054
0.0920.1260.124
0.8010.8010.800
aExperimental mass spectra. 0.01615 means 0.0161 0.0005 (2s)
bStatistical mass balance model
cWeighted two bandtarget entropy minimization
dAlternating least squares reconstruction
e
c
and 0.3
n
u
b
ea 0.2
v
ilt
a
e
R 0.1
Figure 2. Reconstructed mass spectra of H282Se, HD82Se, and D282Se using bandtarget entropy
minimization and statistical mass balance model.
HDSe mass spectrum was also modeled using the
statistical mass balance model assuming that the ion
intensities in the D2Se mass spectrum are the same as
those in H2Se spectrum. Using these assumptions, the
obtained HDSe mass spectrum agrees rather well with
the lowest entropy estimate (Figure 2). For reference
purposes, all the mass spectra are tabulated in Table 1.
Quantitation of Isotopologues
Using the Reconstructed Mass Spectra
H2O/HOD/D2O. The extracted HOD mass spectra
using alternating leastsquares or entropy minimization
approaches are identical (see Figure 1) and, therefore,
the deconvoluted isotopologue concentrations will be
the same using the two models. In contrast to this, the
average m/z 17 and 18 ion intensities in the HOD
mass spectrum obtained from the statistical models are
different (see Figure 1); nevertheless, the spectral
similarity [18] or spectral contrast angle [22] between the
three extracted HOD mass spectra is 99%. The HOD
mass spectra (as obtained from statistical and
alternating leastsquares models) are then used for
determination of H2O, HOD, and D2O amount fractions in various
H2O/D2O mixtures with varying amount fraction of
deuterium, x(D), using the linear leastsquares isotope
pattern reconstruction (Figure 3), [2]. The accuracy of
the deconvoluted isotopologue concentrations was
verified using the gravimetrically prepared mixtures of
H2O and D2O with known D/H ratios. A total H/D
amount ratio between the two gravimetrically prepared
H2O/D2O mixtures with n(H)/n(D) 2.005 was
determined as 2.03 0.02 ( 2s, n 10) and 2.02 0.02 ( 2s,
n 10) using alternating leastsquares and statistical
models, respectively. Also, the H2O/HOD/D2O
concentration profiles are in good agreement with earlier
studies (see Figure 4 in Libnau et al. [3]).
Mixtures of H2O and D2O are characterized by the
equilibrium H2O D2O ` 2HOD and isotopic
selfexchange reaction of water in gaseous or liquid phases
has been the subject of numerous investigations and
debates over the past decades [24, 25]. Although
seemingly simple system, estimates of the H2O/D2O isotope
exchange equilibrium constant (in both gaseous and
liquid phases) range between 3.41 and the geometric
mean of 4.0 [3, 26]. This value has been recently
(re)estimated using IR and NMR techniques [3, 27].
Using the above described HOD reconstruction/
deconvolution algorithm, we can easily calculate the
equilibrium constant from the amount fractions of H2O,
HOD, and D2O. Replicate measurements in the range of
x(D) 50 70% lead to the average value of K 3.85
0.03 ( 2s) using the alternating leastsquares
deconvolution and entropy minimization model. K values
obtained from the statistical mass balance model were by
7% lower. This in good agreement with the best
theoretical value of 3.85 [23]. The two most recent liquid
phase equilibrium constant measurements (at 298 K)
are 3.86 0.07 [3] and 3.86 0.01 [27]. Note that the
Alternating least squares
Statistical mass balance
Range for the possible HDSe or HOD molecular
ion intensity is needed to obtain accurate mass
spectra of HDSe and HOD.
Range for the possible HDSe and HOD molecular
ion intensity is expected to be within the
values from H2Se, D2Se and H2O, D2O spectra.
Probability of ligand loss is directly proportional
to its amount in the precursor ion.
difference between liquid and gasphase equilibrium
constants is estimated to be only 0.03 [28]. Previous
direct mass spectrometric measurements (carried out in
the 1960s) have led to the values of K 3.75 0.07 [29]
and 3.76 0.02 [26]; however, these measurements
have been performed at electron accelerating voltages
from 3 eV (H2O) [25] to 1213 eV (H2Se and H2S) [30] to
eliminate any fragment formation. Although this
classical approach avoids the need for deconvolution, it is
clearly not of practical use for a variety of analytical
purposes due to the deterioration of method sensitivity
and robustness.
H2Se/HDSe/D2Se. Various gaseous mixtures of H2Se/
HDSe/D2Se were obtained when H282Se (generated
from 82SeO32 and 2 M HCl/NaBH4) was introduced in
the headspace of D2O/DCl environment. In such
conditions rapid H/D exchange takes place resulting in a
rise of HD82Se and D282Se concentrations in the
headspace. The resulting mixtures were then analyzed using
GC/MS, and their composite mass spectra were
decomposed using the weighted two bandtarget entropy
minimization algorithm and the statistical model. The
relative amount fractions of isotopologues as obtained
from both models are in good agreement and are not
biased.
Based on reaction purities of reagents, the estimated
H atom fraction in the reaction solution was 7%. The
obtained mixture contained 43% H2Se and 44% HDSe,
and only 13% D2Se (63% atom fraction of H).
Decreasing the volume of the spike of 82Se(IV) aqueous
standard solution to 0.01 mL (H atom fraction in reaction
solution 3%) improved the purity of the D282Se, but it
was unsuccessful in the production of pure D2Se: the
composition of the resulting mixture was 10% H2Se,
26% HDSe, and 64% D2Se. Total hydrogen
incorporation in this mixture is 23%, which is far from the
isotopic distribution of the solvent (3% H and 97% D).
The present findings contradict the previous
hypothesis, which assumed that the isotopic composition of
hydrogen selenide is similar to that of the solvent due to
the rapid H/D exchange (as a consequence of the
strongly acid nature of H2Se and D2Se) [1]. More
experiments are needed to understand the mechanism
controlling the isotopic composition of hydrogen
selenide generated by borohydride from aqueous selenite
solutions. Clearly, the deconvolution model for mass
spectra will be of paramount importance for the
realization of this difficult task.
We have shown that the concentration profiles of the
overlapping isotopologues can be accurately extracted
from their mixture mass spectra. Three conceptually
different mathematical strategies are compared to
achieve this aim (see Table 2). To our knowledge, this is
the first attempt to investigate the quantitative aspects
of the reconstruction of unknown isotopologue mass
spectra. The above mentioned strategies can be
employed to quantitatively assess isotopologue
concentrations from their overlapping 70 eV electron impact
spectra and can be successfully extended to more
complicated isotopologue systems, such as AsH3/AsH2D/
AsHD2/AsD3, to study the hydride generation
mechanism.
Acknowledgments
JM thanks the National Science and Engineering Research Council
of Canada for the postdoctoral fellowship.
References