Two-dimensional (2d) correlation analysis and the search for intermediates: A strictly mathematical approach to an important mechanistic question

Article abstract of DOI:10.1021/cs502127y

In situ spectroscopic studies of metal-mediated syntheses of new and previously unstudied systems are being increasingly used to better understand speciation and mechanistic aspects. These types of experiments give rise to an interesting question: namely, can one deduce from in situ data alone, and with no a priori chemical knowledge (i.e. chemical assignments), which pure component spectral estimates correspond to intermediates? In the present contribution, a statistical 2D correlation analysis is introduced to solve this problem for unicyclic catalytic systems. Such a methodological development achieves two goals: (1) it allows the experimentalist to concentrate on the most meaningful information at the outset of a new exploratory study (focus on the species directly associated with the catalysis), and (2) it helps to free the experimentalist from chemical bias and prejudice, i.e. believing that a specific organometallic species has to be an intermediate due to one or more chemical arguments, when in fact it may be just a side product or spectator species in the metal-mediated synthesis. The 2D correlation analysis is first tested with a numerically simulated data set and then with a real in situ FTIR data set from an unmodified rhodium-catalyzed hydroformylation. The resulting statistical 2D correlation analysis provides a clear and correct answer.

Full text of DOI:10.1021/cs502127y

Research Article
pubs.acs.org/acscatalysis
Two-Dimensional (2D) Correlation Analysis and the Search for
Intermediates: A Strictly Mathematical Approach to an Important
Mechanistic Question
Qisong Xu, LiangFeng Guo, Tung Nguyen Dinh, Angie Cheong, and Marc Garland*
Institute of Chemical and Engineering Sciences, Agency for Science, Technology and Research, 1 Pesek Road, Jurong Island 627833,
Singapore
ABSTRACT: In situ spectroscopic studies of metal-mediated syntheses of new and
previously unstudied systems are being increasingly used to better understand speciation
and mechanistic aspects. These types of experiments give rise to an interesting question:
namely, can one deduce from in situ data alone, and with no a priori chemical knowledge
(i.e. chemical assignments), which pure component spectral estimates correspond to
intermediates? In the present contribution, a statistical 2D correlation analysis is
introduced to solve this problem for unicyclic catalytic systems. Such a methodological
development achieves two goals: (1) it allows the experimentalist to concentrate on the
most meaningful information at the outset of a new exploratory study (focus on the
species directly associated with the catalysis), and (2) it helps to free the experimentalist
from chemical bias and prejudice, i.e. believing that a specific organometallic species has to
be an intermediate due to one or more chemical arguments, when in fact it may be just a side product or spectator species in the
metal-mediated synthesis. The 2D correlation analysis is first tested with a numerically simulated data set and then with a real in
situ FTIR data set from an unmodified rhodium-catalyzed hydroformylation. The resulting statistical 2D correlation analysis
provides a clear and correct answer.
KEYWORDS: hydroformylation, homogeneous catalysis, in situ FTIR, BTEM, intermediates
1. INTRODUCTION
In the past few decades, in situ spectroscopic studies of metal-
mediated organic syntheses have become considerably more
common,1 and here in situ FTIR2 and in situ NMR3 have
played a central role. A few groups that contributed extensively
to the early developments include those from (1) Monsanto,4
ICI,5 and Zurich,6 focusing on understanding the fundamentals
of organometallic transformations, and those from (2)
Marburg,7 Twente,8 York,9 Oxford,10 Zurich,11 Sheffield/
BP,12 Liverpool,13 Amsterdam,14 and Singapore,15 focusing
more on the catalysis. Catalysis science has benefited
enormously from these early developments, since it was clearly
demonstrated that means could be implemented to better
understand the bracket and arrow (or “black box”) of metal-
mediated homogeneous organic transformations, which are
essential to today’s bulk chemical, fine chemical, and
pharmaceutical industries (Figure 1).16,17
Although these earlier studies established the usefulness of in
situ spectroscopy, it became rather clear that there is often a
large gap between the observations and a confident under-
standing of the catalysis. This situation existed in large part due
to the numerous new spectroscopic bands which arose in many
studies. It became important to find a means of untangling the
spectroscopic information so that proper chemical assignments
could be made and subsequently to get an accurate estimation
of concentrations and rates.
Figure 1. Commonly used and generic representation of a liquid-phase
metal-mediated homogeneous organic transformation, where the
bracket and arrow emphasize the need for a metal and the catalytic
nature of the transformation. A black box has been added for visual
and conceptual emphasis. In situ methods such as FTIR and NMR
have targeted a better understanding (speciation) of the black box.
spectra from a system. The main goal of such numerical work
has been to obtain sets of pure component spectral estimates.18
Examples of such algorithms used in catalysis and based on
entropy minimization include minimization of entropy and
spectral similarity (MESS)19 and pure component decom-
position (PCD),20 which generate the set simultaneously, and
band-target entropy minimization (BTEM), which generates
the pure component spectral estimates one at a time.21
When such pure component spectral estimates are first
generated by the above algorithms, they are all normalized
Received: December 31, 2014
Revised: April 9, 2015
Published: May 14, 2015
In the past decade, advanced signal processing has been
applied on a large scale, to hundreds if not thousands of in situ
© 2015 American Chemical Society
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(usually scaled to unity). Moreover, if the reaction is truly
homogeneous and the species are all distinct small molecules
(in contrast to distributions of colloids etc.), one can introduce
the initial mass balance(s) and solve simultaneously the
stoichiometries corresponding to each spectral estimate.22 By
fitting the normalized pure component spectral estimates onto
the original data, “relative concentration” profiles can be
obtained, and by fitting the calibrated pure component spectral
estimates onto the original data, “real concentration” profiles
can be obtained. If a synthesis is not “clean”, i.e. either colloids
or precipitates form, the initial mass balance is not valid for the
liquid phase for the entire reaction period. Therefore, for many
systems, the absorptivities cannot be calibrated (analogously,
the stoichiometries cannot be determined) and the “real
concentration” profiles cannot be obtained. Thus, the take-
home message is clear; in exploratory studies, the experimen-
talist might be forced to be content with just normalized pure
component spectral estimates and “relative concentration”
profiles. This situation is certainly unfortunate, but it often
represents real-world synthetic situations.
The identification of intermediates is often the primary goal
of an exploratory study.23 This being the case, the first question
is often as follows: what can be further done with just the
normalized pure component spectral estimates and “relative
concentration” profiles? This initial question then gives rise to a
much more specific and very useful question: can one deduce
from in situ data alone, and with no a priori chemical
knowledge, which pure component spectral estimates corre-
spond to intermediates? If such a methodological development
could be achieved, then two problems are overcome: (1) it
allows the experimentalist to concentrate on the most
meaningful information (signals) at the outset of a new
exploratory study (the species directly involved in the catalysis),
and (2) it frees the experimentalist from chemical bias and
prejudice, i.e. believing that an organometallic species has to be
an intermediate when in fact it may be just a side product or a
spectator species in the metal-mediated synthesis.
C5H9CORh(CO)4 and the rate of aldehyde formation. In
other words, C5H9CORh(CO)4 is a true intermediate.26
2.2. Chemicals and Preparations. All solution prepara-
tions and transfers were carried out under a purified argon
(99.9995%, Soxal, Singapore) atmosphere using standard
Schlenk techniques or conducted in a glovebox (MBRAUN
UNIlab). Carbon monoxide (research grade, 99.97%, Soxal,
Singapore) and hydrogen (99.9995%, Soxal, Singapore) were
further purified through columns packed with activated 4 Å
molecular sieves, BTS catalyst, Faujesite (CBV 780 CY (1.6)),
and β-zeolite (CP 811C-300 CY (1.6)) to eliminate trace
amounts of water and Ni(CO)4 from the CO. n-Hexane
(99.5%, Sigma-Aldrich puriss) was purified by distillation from
NaK under argon. Rh4(CO)12 (98%, Strem) was used without
further purification. Cyclopentene (99%, Fluka) was purified by
distillation from maleic anhydride to remove dienes formed by
Diels−Alder cycloaddition, followed by distillation from CaH2
under argon.
2.3. Equipment. The in situ spectroscopic studies were
conducted with the use of a hermetically sealed recycling
reaction system, as shown in Figure 2. The system included (a)
In the present contribution, we introduce a set of purely
statistical tests in order to determine if a normalized pure
component spectrum represents an intermediate in the metal-
mediated synthesis or if it is just a side product or a spectator
species. In order to convey the statistical test results in a clear
manner, the results are assembled in a visual 2D correlation
format. In the first instance, this approach is applied to a known
numerically simulated model system, and in the second
instance, it is applied to the unmodified rhodium-catalyzed
hydroformylation of cyclopentene to form cyclopentanecarbox-
aldehyde using in situ FTIR as the experimental spectroscopy.
The resulting statistical 2D correlation analysis provides a clear
and correct answer in both cases.24
Figure 2. Schematic of the recycling reaction system used for the
present in situ FTIR spectroscopic studies. The HP syringes facilitate
batch−feed operation with perturbations which are especially
important for subsequent BTEM analysis.
an in-house-designed and -fabricated SS316 stirred tank reactor
with an internal volume of 100 mL, (b) 1/16 in. SS316 transfer
lines, (c) a hermetically sealed magnetically coupled gear pump
(Model GAH-X21, Micro pump, USA), (d) an SS316 high-
pressure (HP) flow-through infrared cell with CaF2 windows
separated by a Teflon spacer (path length) of 200 μm in
thickness, (e) high-pressure (HP) SS316 syringe pumps for
injection of solutions (Model PHD 4400, Harvard Instruments,
USA), and (f) a cryostat (Poly-Science, USA). A rather
complete description of the system is provided elsewhere.27
Transport effects in the present system were minimal. The
liquid phase became saturated with dissolved gas on the order
of 6 min, and the recycle time was on the order of τ = 2 min.
Thus, in ca. 6 min (three recycle times), the system is, to a very
good approximation, thoroughly mixed. The rate of conversion
of substrate to product was such that concentrations of
substrate, dissolved CO, and dissolved H2 did not vary more
than 5% over the length of the recycle loop. The present
reaction system belongs to category H of the Hatta reaction
regimes: i.e., an infinitely slow reaction in comparison to mass
transfer.28
2. EXPERIMENTAL ASPECTS
2.1. General Considerations. In the following, the well-
studied unmodified rhodium-catalyzed hydroformylation re-
action is used as a model system.25 Specifically, cyclopentene is
used as the substrate and Rh4(CO)12 as the catalyst precursor.
The catalytic system is homogeneous, with no detectable light
scattering. In situ FTIR normally shows the presence of only
Rh4(CO)12, C5H9CORh(CO)4, and Rh6(CO)16 as observable
organometallics and only cyclopentene and cyclopentanecar-
boxaldehyde as observable organics in the active system. It has
been shown repeatedly that there is a 1:1 relationship between
the instantaneous concentration of the intermediate
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Measurements were performed on a Bruker Vertex 70 FTIR
spectrometer equipped with a DTGS ambient detector and KBr
beam splitter. Spectra were acquired at 2 cm−1 resolution, from
600 to 4000 cm−1, using 16 coadds per spectrum at intervals of
ca. 2 min. Zero filling was used in order to provide data points
with ca. 0.1 cm−1 separation. The other IR measurement
parameters are as follows: order of zero filling, 16; aperture
setting, 6 mm; preamp gain, A; scanning mirror velocity, 10
kHz; use of optical filter, open.
2.4. Experimental Design. An appropriate experimental
design for exploratory studies in combination with BTEM
analysis should involve a few well-chosen perturbations in
reagents. The purpose of these perturbations is to obtain more
variation in the signals present (particularly of the organo-
metallics present). By performing a perturbation, one upsets
the monotonic and asymptotic trajectories of the reactant
concentrations and hence signal ratios. This results in better
pure component spectra estimates.
Moreover, in the present study for 2D correlation analysis, it
will be imperative to aim for very small substrate changes and
low yields of product, since both initial rate and pseudo-steady-
state conditions for the organics are desirable (even though a
batch reactor is being used). Taken together, the two
aforementioned prerequisites must be balanced in a semi-
batch experiment. Table 1 shows such an experimental design.
Evidence to support the proposition that both prerequisties are
satisfied is provided in the sections 4 and 5.
resolution, from 600 to 4000 cm−1, using 16 coadds per
spectrum at intervals of ca. 2 min. Zero filling was used in order
to provide data points with ca. 0.1 cm−1 separation. The n-
hexane calibration gave a molar absorptivity of 2.977 L/(mol
cm) at ν = 1136 cm−1.
3. COMPUTATIONAL ASPECTS
3.1. Spectral Processing. Raw spectra were truncated for
analysis of specific spectral windows. The truncated spectra
were renormalized by using the respective molar absorptivity of
the solvent at its characteristic band, resulting in a set of
dimensionless spectra for further quantitative analysis.30
Equation 1 is the main equation used for initial processing of
exp
k×ν
the experimental spectra, where A is the raw experimental
exp
renorm
k×ν
A
= Γ A
k×k
k×ν
(1)
reaction mixture matrix, Γk×k is a diagonal renormalization
renorm
k×ν
factor, and A
is the dimensionless absorbance matrix. The
index k is the number of experimental spectra, and the index ν
is the number of channels of data in each spectrum. The
dimensionless absorbance matrix is needed in order to account
for changes (i) in reaction volumes either due to thermal/
pressure changes or the addition of additional components
during the reaction (semi-batch operation, perturbations) and
(ii) in the cell path lengthagain due to pressure or
temperature or swelling effects of the O-rings.
3.2. BTEM Analysis and Pure Component Spectral
Estimation. The band−target entropy minimization (BTEM)
algorithm21 was used in order to obtain pure component
spectral estimates of the solutes present in the system, by
analyzing appropriate sets of reaction spectra. BTEM has been
repeatedly used to study complex metal-mediated homoge-
neous catalytic organic syntheses.18,21,23,30
a
Table 1. Experimental Design for the Present Study
perturbation
step
action
timeline
b
e
f
1
2
infuse initial solution
spectral acquisition
spectral acquisition
add CO (20 bar) then
H2 (20 bar)
c
Equation 2 is the main equation used for BTEM analysis,
3
4
5
6
add Rh4(CO)12
t = 0 h
t = 2 h
t = 3.8 h
d
where a1×ν
̂
is a BTEM pure component spectral estimate, T1×z
add Rh4(CO)12
d
add Rh4(CO)12
a1×ν
̂
= T1×zVTz×ν
(2)
end of experiment
t = 4.5 h, end of
acquisition
a
The stock solution was prepared as 11.9 mg of Rh4(CO)12 in 8 mL of
is an optimized transformation vector, and VTz×ν is the matrix of
right singular vectors (obtained from a singular value
decomposition (SVD) of the spectroscopic data A). The
indices are ν for the total number of channels of data in each
spectrum and z for the number of vectors used, where normally
k ≫ z ≫ s, where s is the number of observable species present.
During BTEM analysis, a global search is performed to find the
simplest spectral estimate with the lowest signal entropy.
After an exhaustive one by one spectral search, the relative
b
n-hexane. The reaction temperature was 293 K. Conditions:
cyclopentene (1 mL) in n-hexane solution (32 mL) and then addition
c
of CO (20 bar) and H2 (20 bar). Conditions: 3 mL of stock solution.
d
e
Conditions: 2.5 mL of stock solution. Initial spectra before catalytic
f
reaction. Continuous acquisition.
The data from the last two rows (entries 5,6) in Table 1 were
not used in the final 2D correlation analysis (see section 3.5). It
was found that the conversion of alkene and the yield of
aldehyde were too high and hence the assumption of pseudo-
first-order kinetics is no longer valid. Thus, only data from
times 0−3.8 h (perturbation steps 1−4) were used.
2.5. Calibrations. The solvent intensity was used as an
internal standard. Calibrating or not calibrating the solvent
would not change the final interpretation of the 2D correlation
matrix.29
concentration matrix ck×s
̂
can be calculated as in eq 3, where
renorm
A
is the dimensionless absorbance matrix and (as×ν
generalized inverse of the matrix of normalized BTEM spectral
estimates.
̂
)+ is the
k×ν
renorm
+
ck×s
̂
= A
̂
(as×ν)
k×ν
(3)
Spectra of the solvent n-hexane were acquired using a special
variable path length cell (Model SP07500, with ZnSe window,
Specac U.K.). Seven path lengths (25, 50, 75, 100, 125. 150,
175 μm) were used, and spectra were recorded on a Bruker
Vertex 70 FTIR spectrometer equipped with a KBr beam
splitter and DTGS detector. The system was purged with dry
air at a rate of 10 L/min. Spectra were acquired at 2 cm−1
3.3. Pseudo-Steady-State Single-Product Multipath-
way Unicyclic Catalysis. An accurate working definition for
the catalytic system is needed in order to place the 2D
correlation into the proper perspective. Accordingly, an abstract
block-diagram relationship among precursor(s), degradation
product(s), and a generalized unicyclic catalytic cycle is shown
in Figure 3. The precursor(s) may be metal salt(s) or
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performed either in a single concerted manner or as two
sequential elementary reactions. (6) The object (iii) represents
a classic example of a reservoira species in equilibrium
exchange with an intermediate on a cycle. (7) the symbol ≈
adds further emphasis to the fact that this diagram is general
there may be many more elementary steps present.
Figure 3 was drawn with a number of important points in
mind. One point is that, in general, a single product synthesis
will have multiple, independent reaction pathways, even if it has
an “isolated unicycle mechanism”. This issue can be visualized
more readily by hypothetically “labeling” individual substrate
molecules. In this manner, one can trace each pathway taken.
Thus, suppose for the moment a hypothetically labeled
molecule takes the most probable pathway through the
mechanism. This might be pathway a in Figure 4. The next
Figure 3. Abstract representation of the three distinct pools of metal-
containing species in single-product multipathway unicyclic catalysis.
See text for further explanation.
organometallic(s), and modifiers such as phosphorus- or
nitrogen-containing ligands may be included. The spectator
species are considered to be metal-containing inorganic or
organometallic complexes that are neither precursors nor
intermediates. In other words, they do not participate in
product formation. They may be formed by reaction of the
precursor or an intermediate with impurities, the reactor wall,
and/or reactants. The spectator species may also arise due to
thermal degradation. The gray arrows in Figure 3 are only an
indication of the usual direction for the net flux of metal from
one block to another and in no way are meant to suggest the
reactions are irreversible. Indeed, measurable equilibria between
precursors and intermediates have been observed at least twice
(so-called equilibrium-controlled precursor conversion),26c,31
and selectivities for the conversion of precursors to spectator
species between 0% and 100% have been observed.32 The green
boxes and arrows in the “catalytic block” are used to indicate
the addition of reagents (from the overall reaction, Figure 1) to
the cycle, and the red box and arrow are used to indicate the
singular product of the overall reaction.
The most common graph representation for a catalytic cycle
will be used: namely, the nodes represent intermediates and the
edges represent reactions.33 Moreover, the following features
have been added to the single-product multipathway unicyclic
catalysis. (1) An arrow in the center of the diagram will
represent the direction of next product formation, (2) The dots
represent intermediates having the lowest concentrations. (3)
Black boxes represent intermediates with the highest
concentrations and, therefore, may be observable if appropriate
in situ spectroscopy is used. (4) The branch (i) indicates that
two pathways exist, in this case, due to the presence of isomers.
(5) The branch (ii) indicates that a transformation can be
Figure 4. Four possible pathways highlighted in red, for a
“hypothetically labelled substrate molecule” through the single-product
multipathway unicyclic catalytic cycle: (a) most direct and probable
pathway through cycle; (b) a pathway through an isomer; (c) a
pathway through two-step transformation versus concerted trans-
formation; (d) a pathway involving exchange with the reservoir at least
one time. Additional pathways can be generated as permutations/
combinations of the above four examples.
substrate molecule might take the least likely isomer pathway at
the branch point (i) and complete the pathway (Figure 4b).
The third substrate molecule might take the two-step pathway
at the branch point (ii) and complete the pathway (Figure 4c).
The fourth substrate molecule substrate molecule might take
pathway iii, thereby populating a reservoir at least once during
its journey to product formation (Figure 4d). Then, of course,
there are a number of permutations of the above scenarios that
can be envisaged. In conclusion, Figure 4 shows that,
depending on the pathway taken, there are different
intermediates.
Taking the whole picture into consideration, all nodes must
be considered to be intermediates. Thus, a sufficiently robust
single-product multipathway unicyclic catalytic cycle must
accommodate numerous branching issues and recognize that
all nodes are potential intermediatesdependent on the
specific pathway taken. Another important purpose of Figures
3 and 4 is to bring self-consistency between a mathematically
rigorous description of single-product multipathway unicyclic
catalysis and features which are familiar to the catalytic chemist.
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King and Altman derived a general matrix solution for
enzyme catalysis,34 and this description was expanded by
others.35 Upon close inspection it is evident that enzyme
mathematical results extend directly to the case of homoge-
neous metal-mediated catalysis, given one important prereq-
uisite; each and every intermediate has the same nuclearity, and
therefore there are no bimolecular reactions between
intermediates. Subsequently, one observes that the features
introduced in Figures 3 and 4, i.e. branch points, reservoirs, etc.,
are admissible within the model. The mathematical description
of the activity of such a unicyclic system, in the approximation
of a steady-state or pseudo-steady-state product formation rate
rp, can be expressed in terms of either the concentration of each
and every ith intermediate Ii (eq 4) or the total sum of all
intermediate concentrations (eq 5), where the terms ki and
kTOF contain only constants and terms involving reactant
concentrations (but not concentrations of organometallics):
(for any arbitrary yth species) is generated against each
concentration Cx (for any arbitrary xth species). This produces
a scatterplot for each and every combination of observable
species x and y. Since max{x} = max{y} = sobs, there are a total
of sobs2 scatterplots to be evaluated. These sobs2 scatterplots will
form the basis for the 2D correlation analysis.
For any particular scatterplot, a set of unit tangent vectors
can be calculated from the successive data points (Figure 5).
rp = ki[Ii] ∀ i
(4)
rp = kTOF
[I ]
i
∑
(5)
Figure 5. Representation of a scatterplot where ν0 is a unit vector and
Tn is the successive unit tangent vectors. The x axis can be either real
Specifically, eq 5 is useful as the formal definition for the well-
known turnover frequency (TOF) of a reaction cycle, especially
when it is evaluated in terms of instantaneous reaction rates and
intermediate concentrations at any time t.
̂
̂
concentration Cx or relative concentration Cx. The y axis can be either
̇
absolute real concentration rate |Cy| or absolute relative concentration
̇
̂
rate |Cy|, respectively.
In the context of the present contribution, the most central
and important concept concerning unicyclic mechanisms is that
the resulting system activity is linear in each intermediate
concentration (eq 4). Consequently, in the regression of real
rate data (criterion I) the intercept should be in the close
vicinity of 0 and (criterion II) the slope should be a close
approximation of a straight line, with little or no hint of
curvature. Clearly, the two aforementioned criteria can be
implemented in practice as statistical tests. Criteria I and II will
serve as the starting points for the following 2D correlation
analysis.
3.4. Initial Catalysis Startup. In most real-world
homogeneous catalytic experimentation, the experimentalist
will use a batch reactor, although the past decade has seen more
examples of continuous-flow systems.36 At the moment that all
reactants are brought together, but the fluid elements are not
yet intimately mixed, there are no intermediates yet, and the
catalytic cycle is unpopulated. A finite time is required in order
to start populating the cycle. This finite delay time is also seen
as a delay between the time a substrate goes into a cycle and a
product comes out, and this delay is on the order of TOF−1,
where TOF is the turnover frequency. There are also delay
times associated with mass transfer from the gas phase into the
liquid phase, mixing of the liquid phase, and mixing of all of the
liquid throughout the experimental apparatus shown in Figure
2. Therefore, the earliest part (first few minutes) of initial rate
data will not be appropriate for 2D correlation analysis.
3.5. Scatter Plots and Statistical Analysis. As mentioned
above, careful design of the experiment is essential for
meaningful statistical analysis. Experimental conditions were
chosen with an excess of reactants, and small extents of
reaction, in order to ensure that catalytic system follows
pseudo-first-order kinetics as closely as possible.
The scalar product of each tangent vector with a unit vector
(directed exactly through the origin) gives a series of similarity
coefficients. This sample of coefficients was tested statistically
to assess if the data points satisfy two criteria: (1) they pass
through the point of origin, and (2) they have a general linear
trend.
As mentioned previously in section 3.3, a true intermediate
will possess two necessary characteristics: namely, criterion I,
which is that the intercept is 0, and criterion II, which is that the
slope is a constant. Therefore, restating these criteria in the
framework of Figure 5 provides testable hypotheses.
Criterion I: data points that are directed toward the vicinity
of the origin should have similarity coefficients with values
approaching unity. Thus, the first criterion was assessed by a
hypothesis testthe Sign test. The Sign test is a nonparametric
procedure which tests hypothesis on the median of any
continuous distribution.37 The null hypothesis is that the
sample median of similarity coefficients is close to a specified
median μ while the alternative is that the sample median is
̃
0
lower than μ . The one-tailed test was performed using a lower
̃
0
tail at a significance level of 0.05.
Criterion II: the slopes of the data points are generally
straight and should have mean stationary similarity coefficients.
Thus, the second criterion was assessed by a hypothesis test
the Kwiatkowski−Phillips−Schmidt−Shin (KPSS) test. The
KPSS procedure parametrizes a time series for the hypothesis
test of stationarity.38 The null hypothesis is that the sample of
similarity coefficients is mean stationary while the alternative is
that the sample is a nonstationary unit root series. The one-
tailed test was performed using an upper tail at a significance
level of 0.05.
The statistical analysis proceeds in the following manner.
First, BTEM analysis is applied in order to get the pure
component spectral estimates and the associated relative
If both criteria I and II are fulfilled, then we will say that the
variables are “linearly correlated”. This statistical hypothesis
testing can be applied to the respective scatterplots from
different experiments. The final result is a two-dimensional
̇
concentrations. Next, a trajectory for each rate of change |Cy|
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correlation matrix which identifies possibly high correlation
are set to be k1 = 2.3 × 10−4 s−1 and k2 = 2.5 × 10−3 s−1,
consistent with real experimental data.26 These rate constants
are approximately the apparent rate constants previously
observed in real unmodified hydroformylations at ca. 20 bar
of CO and 20 bar of H2.
In order to keep the test system interesting, a rate expression
is temporarily and artificially imposed in the numerical
simulation for the formation of Rh6(CO)16 (reaction 2c in
Scheme 2). In this proposed expression, it is assumed that the
observable intermediate RCORh(CO)4 degrades to form
Rh6(CO)16 through an unknown but first-order rate process,
where k3 = 10−6 s−1. Indeed, Rh6(CO)16 is frequently observed
from in situ unmodified rhodium-catalyzed hydroformylations,
and the mechanisms by which it forms have not been clearly
identified. Some routes clearly involve reactions with impurities
(water, oxygen); thus, the process is definitely complex. Thus,
for the purpose of our numerical simulations, we assume only
one mechanism and it is first order.
̇
̂
̂
̇
between |Cy| and Cx or |
C
y| and Cx.
3.6. Computational Platforms. All of the simulations and
signal processing were performed with in-house-developed
algorithms (BTEM), using Matlab 7.12.39 Numerical calcu-
lations were performed on an Intel Pentium CPU G640 2.80
GHz processor with 4 GB of RAM.
3.7. Numerical Simulations of Catalytic System. A
semi-batch reaction for the rhodium-catalyzed hydroformyla-
tion of alkene was numerically simulated so that all character-
istics of the system could be controlled. The precursor
Rh4(CO)12 reacts with CO, H2, and alkene to produce an
acylrhodium speciesthe intermediate, the side product
Rh6(CO)16, and a product aldehyde. The simulated reaction
was assumed to be performed at constant temperature and
pressure. The overall reaction can be represented as Scheme 1.
Scheme 1. Overall Hydroformylation of an Alkene
The specific rate expressions for each of the five species are
given respectively in eqs 6−10, where the exponent is a = 0.15,
a value observed experimentally.26
d[Rh4(CO)12]
k
4
= − 1 [Rh4(CO)12][alkene]a
(6)
(7)
dt
A simplified reaction model for unmodified hydroformylation
was constructed for simulating the overall reaction and thus
testing the 2D correlation analysis. The details of this catalytic
mechanism are provided in Scheme 2. Reaction 2a is the
d[RCORh(CO)4]
= +k1[Rh4(CO)12][alkene]a
dt
d[RCHO]
= +k2[RCORh(CO)4]
(8)
dt
Scheme 2. Conversion of the Organometallic Precursor to
the Acyl Intermediate (a), Formation of the Product
Aldehyde and Conversion of the Intermediate Back to Itself
(b), and Unbalanced Reaction for Degradation of the
Intermediate (c)
d[alkene]
= −k2[RCORh(CO)4]
(9)
dt
d[Rh6(CO)16]
= +k3[RCORh(CO)4]
(10)
dt
Given an initial concentration of the each species, this set of
ordinary differential equations (ODEs) was solved numerically
to generate the time-dependent concentration profiles of every
species. A Matlab inbuilt function, ode45 (Runge−Kutta
method), was used to perform the numerical integration
procedure. The amounts of Rh4(CO)12 added in each
perturbation for the simulated batch reaction are given in
Table 2.
Table 2. “Experimental Design” for Numerical Simulation
perturbation
step
action
timeline
0
start of numerical experiment with 0.03 before start of
mol of alkene reaction
conversion of the organometallic precursor Rh4(CO)12 to the
observable intermediate RCORh(CO)4, where R is an alkyl
moiety. Reaction 2b is an overall reaction from the observable
intermediate back to itself and the formation of the product
aldehyde (note that the delay in the catalytic cycle cannot be
fully represented by this equation alone). Reaction 2c is an
unbalanced reaction (vide infra).
Reactions 2a and 2b in Scheme 2 are based on actual detailed
modeling of hydroformylation reactions. Thus, at constant
partial pressures of CO and H2, the rates of formation or
disappearance for the catalyst precursor Rh4(CO)12, the
intermediate RCORh(CO)4, the substrate alkene, and the
product aldehyde are simplifiedonly apparent rate constants
are needed. In this model the respective apparent rate constants
1 (frame 1) add Rh4(CO)12 to 4.10 × 10−5 mol/L
2 (frame 2) add Rh4(CO)12 to 4.10 × 10−5 mol/L
t = 0 h
t = 2 h
t = 4 h
3
end of numerical experiment
The simulation provided concentration profiles for each
solute. To these profiles random noise was added to reflect the
stochastic fluctuations in the experimental conditions. The
simulated system was made to undergo a perturbation by
means of addition of precursor Rh4(CO)12 alone without the
introduction of additional solvent.
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4. RESULTS
Research Article
4.1. Numerical Simulation. The test system outlined in
section 3.7 was numerically simulated. The concentration
profiles are shown in Figure 6. The first frame (frame 1) occurs
Figure 7. Scatterplot matrix produced from numerically simulated data
set. Each entry of the matrix gives a visual display of the possible
̇
relationship between rate |Cy| and concentration Cx. Legend: (1)
Rh4(CO)12; (2) RCORh(CO)4; (3) Rh6(CO)16; (4) aldehyde; (5)
alkene. Blue data points belong to frame 1, and green data points
belong to frame 2. The x axis domain for each entry has the range of
[0, max{Cx}], and the y axis domain for each entry has the range of [0,
Figure 6. Time-dependent concentration profiles of the solutes (with
perturbation at the second hour) for the numerically simulated
hydroformylation reaction. For clarity in presentation, the figure is
plotted with every third data point.
̇
max {|Cy|}].
criterion I (pass through the point of origin) and criterion II
(have a general linear trend), as described in detail in section
3.5. Both hypothesis tests were applied to all possible
scatterplots in all reaction frames, in order to reinforce
conclusions about scatterplots which are truly linear. The
final result of the hypothesis testing on the 2D representation
of the scatterplot matrix was then mapped onto a 2D
correlation matrix, as shown in Figure 8.
between reaction times of 0 and 2 h. The figure also clearly
shows the perturbation introduced at t = 2 h in the 4 h
experiment. The perturbation with the addition of precursor
Rh4(CO)12 at the end of the second hour introduces a second
frame (frame 2). More importantly, it is seen that the
concentrations of the organic species (alkene and aldehyde)
vary only a few percent. This is important, since it fulfils the
prerequisite of pseudo-steady-state conditions, and hence
enforces the likelihood of pseudo-first-order kinetics for true
intermediates (section 3.3).
The solute concentration profiles from Figure 6 were used to
assemble an associated set of instantaneous reaction rates for
each species. Therefore, there is a correspondence between any
species concentration Cx in time and an associated set of
̇
reaction rates for each species rate |Cy|. Taking one species
profile concentration Cx in time and any individual species rate
̇
in reaction time rate |Cy| produces a scatterplot.
All possible scatterplots from both reaction frames were
assembled into a two-dimensional (2D) representation as
shown in Figure 7. This 2D representation acts as a graphical
tool that depicts the relationship among all possible
scatterplots. Each individual scatterplot has a concentration
along the x axis and a rate along the y axis (the absolute value of
the rate is used to keep representations simple). The origin of
each individual scatterplot lies at 0 for both axes, and the
maximum value of each axis corresponds to the maximum value
of the entry observed during the numerical simulation. Thus,
the trends in variables are easily visualized in each individual
scatterplot. A linearly correlated scatterplot has (1) data points
that form generally straight lines, (2) each straight line, or its
extrapolation has an intercept in the vicinity of the origin, (3)
one straight line for frame 1, and (4) one straight line for frame
2. In Figure 7, scatterplots that contain linearly correlated
variables are highlighted in yellow for easy identification. It is
clear that the remaining scatterplots do not satisfy all the
criteria for linearity stated above.
Figure 8. Final 2D correlation matrix of the numerically simulated
catalytic system after application of statistical tests to the scatterplot
matrix. Each entry of the matrix expresses a yes−no answer to the
̇
statistical tests and hence the linearity of rate |Cy| versus concentration
Cx. The value 1 will be assigned to positive results for both the Sign
test and KPSS test, while the value 0 represents otherwise. Legend: (1)
Rh4(CO)12; (2) RCORh(CO)4; (3) Rh6(CO)16; (4) aldehyde; (5)
alkene.
If and only if both tests are positive, a matrix entry of unity is
assigned (yellow); otherwise, a matrix entry of 0 is assigned
(white). On the basis of the 2D correlation matrix shown in
Figure 8, the following can be concluded. (1) The
concentration of species 1 is linearly related to both the rates
of species 1 and species 2. This implies that the concentration
of Rh4(CO)12 is linearly related to the rates of Rh4(CO)12 and
In a more distilled form, it can be said that the data points of
each frame were assessed with respect to only two main criteria:
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RCORh(CO)4. (2) The concentration of species 2 is linearly
related to rates of species 3, species 4, and species 5. This
implies that the concentration of RCORh(CO)4 is linearly
related to the rates of Rh6(CO)16, aldehyde, and alkene.
Reflecting back on the original model (section 2.3), it is verified
that the 2D correlation analysis correctly identifies the linearly
correlated scatterplots. In the numerically simulated system
(Scheme 2) there are three linear rate constants and these rates
involve all five solutes. Rh4(CO)12 and RCORh(CO)4 are
connected by Scheme 2a, RCORh(CO)4 is connected to alkene
and aldehyde by Scheme 2b, and RCORh(CO)4 and
Rh6(CO)16 are connected by Scheme 2c.
4.2. Experimental Test. The aforementioned 2D correla-
tion analysis was then applied to the experimental rhodium-
catalyzed hydroformylation of cyclopentene to cyclopentane-
carboxaldehyde using in situ FTIR as the experimental
spectroscopy. The hydroformylation of alkene was performed
with the experimental conditions specified in section 2.4. The
reaction duration was 3.8 h, with the addition of additional
precursor Rh4(CO)12 and solvent at t = 2 h. A total of 110 raw
spectra were collected. The changes in the intensities of the
absorption bands in the wavenumber range of 1550−2300
cm−1 can be observed in Figure 9.
Figure 10. Five individual BTEM spectral estimates a−e obtained
from the raw data. No assignments have been made at this point.
However, one can note (i) the narrow spectral features of a−c, which
suggest that they may be organometallics, and (ii) the broad spectral
features of d and e, which suggest that they may be organics.
Figure 11. Time-dependent relative concentration profiles of the five
components in the experimental unmodified rhodium hydroformyla-
tion. The time-dependent curves a−e correspond with the individual
BTEM spectra a−e shown in Figure 10.
Figure 9. Raw in situ spectra from the experimental rhodium-catalyzed
hydroformylation of cyclopentene.
substrate and that (ii) pseudo-first-order kinetics are probably
valid for the system, since so little conversion has occurred.
Due to mixing issues in the recycle system (section 3.4) the
first few data points (about three data points corresponding to
ca. 6 min) in frames 1 and 2 were discarded from further
analysis. Therefore, there is a very small discontinuity in time
for the data points between different frames.
Scatterplots were generated from the relative concentrations
data according to section 3.5. The collection of all scatterplots
from both reaction frames were assembled into a scatterplot
matrix, as shown in Figure 12. From a visual inspection of the
scatterplot matrix alone, one entry appears to clearly possess
linearity (in yellow) and three entries might possess linearity
(in gray). All other scatterplots clearly do not fulfill criteria I
and II, as discussed in detail in section 3.5. Both hypothesis
tests were applied to all frames in scatterplots. The final 2D
correlation matrix is shown in Figure 13.
The BTEM algorithm was used to deconvolute the spectral
set in Figure 9 to obtain the set of normalized (uncalibrated)
pure components underlying the raw spectra. In the current
experiment, five normalized pure component spectral estimates
were obtained (excluding the solvent and dissolved CO),as
shown in Figure 10. At this point, the identity of the chemical
species associated with the pure component spectra is
immaterial for the following 2D correlation analysis. The 2D
correlation analysis presented in this contribution is deliberately
constructed to avoid introducing a priori chemical knowledge
on speciation into the analysis of the system.
At the same time, the relative concentration profiles for the
respective components (indices a−e) are obtained from the
BTEM algorithm. These relative uncalibrated concentration
profiles are shown in Figure 11. In this figure, the perturbation
is clearly seen at t = ca. 2 h. Most importantly, we see that the
concentration of the organic reagent e starts at a more or less
maximum value and decreases only a few percent, in a regular
monotonic fashion, over the entire experimental period.
Therefore, we can conclude that (i) e is most likely our
It is seen from Figure 13 that only one entry satisfies both
the Sign test and the KPSS test, and this entry is highlighted in
̂
yellow. This entry is associated with the concentration Cb
̇
̂
versus the rate | d|. Therefore, solely on the basis of the
C
scatterplots, and without recourse to chemical assignments, it
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5. DISCUSSION
5.1. Numerical Simulation. The most important issue
here is the details of the model used. It was assumed that there
are only three reactions, and these were enough to set up a
model system for the numerical simulation. In other words, a
detailed catalytic system, with multiple intermediates, was not
modeled. Moreover, the finite delay time in a catalytic cycle was
deliberately not captured. The reasons for this decision are
straightforward. We simply wanted to verify the validity of the
statistical tests and the 2D correlation as it relates to the
identification of first-order kinetics. In the same manner, the
introduction of a “presumed” first-order process for the
formation of Rh6(CO)16 from intermediates was based on the
same reasoning. When the model system is kept extremely
simple, it is much easier to understand the meaning of the final
2D correlation.
The resulting 2D correlation matrix possessed five yellow
entries (Figure 7). These entries relate (1) the disappearance of
the precursor Rh4(CO)12 and the formation of the intermediate
RCORh(CO)4, (2) the loss of alkene and the formation of
aldehyde due to the intermediate RCORh(CO)4, and finally
(3) the formation of Rh6(CO)16 from the observable
RCORh(CO)4. The first pair of reactions in (1) are easily
understood by inspection of Scheme 2a and the first-order
kinetic expressions given by eqs 6 and 7. The second pair of
reactions in (2) is easily understood in terms of Scheme 2b and
the first-order kinetic expressions given by eqs 8 and 9. Finally,
the reaction in (3) is understood in terms of Scheme 2c and the
first-order kinetic expression given by eq 10which was
deliberately and artificially introduced. Taken together, the
above 2D correlation results are consistent with the model
used. All first-order reactions provide positive results for the
Sign test, as well as the KPSS test.
Figure 12. Scatterplot matrix of the real data set. Each entry of the
matrix gives a visual display of the possible relationship between rate
̇
̂
̂
|Cy| and concentration Cx. Blue data points belong to frame 1, and
green data points belong to frame 2. The yellow entry clearly possesses
linearity, and the three gray entries might possess linearity. The x axis
̂
domain for each entry has the range of [0, max {Cx}], and the y axis
domain for each entry has the range of [0, max {|Cy|}].
̂
5.2. Experimental Test. The experimental system
introduces an entire set of new physical phenomena, and
these affect the kinetics and hence the statistical tests. The
significant issues to consider in the experimental system are (i)
the fact that the system has a finite delay time in the cycle
associated with the turnover frequency, (ii) solvent is actually
introduced with the precursor during the perturbation (this
changes the mass balance in the system, and the concentrations
in a significant way), and (iii) the organometallics are labile and
there are equilibria present. These issues will influence the final
way that the experimental scatterplots look as well as the results
of the statistical tests.
Figure 13. Resulting 2D correlation matrix of the real experimental
hydroformylation system after application of statistical tests. Each
entry of the matrix expresses a yes−no answer to the statistical tests
̇
̂
̂
and hence the linearity of rate |Cy| versus concentration Cx. The value
1 will be assigned to positive results for both the Sign test and KPSS
test, while the value 0 represents otherwise.
Figure 14 is an expanded view of the gray and yellow entries
found previously in Figure 12, which help to clarify further
many of these aforementioned remarks.
can be concluded that there is only one observable intermediate
in the system.
̇
̂
e|] in Figure 14a contains some subtle but
̂
The entry [Cb,|
C
At this point, for the purpose of the present contribution, it
can be revealed that the index b corresponds to RCORh(CO)4
and the index d corresponds to the organic product
cyclopentanecarboxaldehyde. This is indeed the correct overall
and expected conclusion. Only the species RCORh(CO)4 is an
intermediate in the overall catalytic transformation. Neither
index a (Rh4(CO)12) nor index c (Rh6(CO)16) is an
intermediate in the unicyclic catalysis. Finally, there is no
positive cross correlation between the indices d and e (aldehyde
and alkene), since these two species are separated by an entire
cycle of intermediates, and moreover, there is an intrinsic delay
time of ca. 10 min along the cycle (TOF ≈ 0.1 min−1).
noticeable peculiarities. Close inspection shows that (i) there is
significant curvature at the end of frame 1 and the beginning of
frame 2 and (ii) upon dilution of the system between frames 1
and 2, a discontinuity in the curves occurs. Both of these
observations can be traced back to the fact that alkene (species
e) is involved in two overall reactions: namely, transformation
of precursor to RCORh(CO)4 and catalysis. Therefore, if
alkene is involved in two overall reactions, a plot of rate versus
just RCORh(CO)4 must show some curvatures. In contrast,
̇
̂
d|] are both very straight. Thus, entry
̂
frames 1 and 2 in [Cb,|
C
̇
̇
d|]
̂
̂
̂
̂
[Cb,|
C
e|] almost passes the statistical tests, but entry [Cb,|C
certainly passes the statistical tests.
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general case, some of these organometallics will be
intermediates in the synthesis and others will be spectator
species/side products/degradation products. It is quite possible
that the identity of all of these organometallics will prove too
difficult or impossible to determineeven if enormous efforts
using density functional theory (DFT) are performed. The
explanation is simple enough; some of the spectator species/
side products/degradation products will be structurally very
complex large clusters and there are just too many variations.
Moreover, and probably of primary importance, some of the
spectator species/side products/degradation products will be
the result of reactions with unknown impurities.
The present 2D correlation analysis helps to focus attention
on the most important spectroscopic information: namely, the
spectra associated with the intermediates directly involved in
the overall organic synthesis. It is these spectra which are most
important to consider in DFT calculations, and it is these
intermediates which are most important from a stoichiometric
and structural viewpoint. In other words, the present 2D
correlation analysis provides a rational basis for model
reduction. If the experimentalist can deduce the stoichiometry
and the structure of the intermediates, a large part of the central
mechanistic issues is clarified. If the experimentalist can also
determine the identity of most spectator species/side products/
degradation products, that is of course a bonus. However, if
some of the latter determinations are not possible, one still has
a rather clear picture of the salient features of the catalytic
system.
Figure 14. Expanded views of gray and yellow entries from Figure 12:
̇
̇
̇
̇
̂
̂
̂
̂
̂
̂
̂
̂
(a) entries [Cb,|Cd|] and [Cb,|Ce|]; (b) entries [Ca,|Ca|] and [Ca,|Cb|].
5.4. Postanalysis Data Reconciliation and Criteria III
and IV. For a well-designed experimental data set, and at least
in the present case, criteria I and II appear necessary and
sufficient to ensure a proper result.
Blue symbols are given for frame 1, and green symbols are given for
frame 2. In (b), the red filled diamonds are data points where Ca values
̂
̇
̇
̂
̂
are the same. The corresponding values of |Ca| and |Cb| in frames 1 and
̂
2 are obtained for a given Ca value, as shown in the directed dashed
Close inspection of the King and Altman formalism shows
that there are actually two additional criteria which are implicit
in the analytical expressions. Continuing from eq 4, we arrive at
the following.
line. See text for explanation.
The issues of lability and reversibility of the organometallic
transformations is seen by the “offset” in curves for entries
̇
Criterion III: as implied by eq 4, Cp = kiCi and hence an
intermediate i is related to the product p where i ≠ p.40
̇
̇
̂
̂
̂
̂
[Ca,|
C
a|] and [Ca,|C
b|], as shown in Figure 14b. Each frame
̇
̂
x|] (for any
̂
̇
Therefore, all diagonal entries [Cx,|Cx|] or [Cx,|
C
alone gives a good linear plot for the precursor Rh4(CO)12, but
upon combination of both frames, there is a distinct mismatch.
species x) can be confidently set identical with 0 in the 2D
correlation matrix for the identification of intermediates.
̇
̂
a|], there was a decrease in the rate
̂
As observed in entry [Ca,|
C
̇
Criterion IV: as implied by eq 4, Cp = kiCi and hence the rate
of loss of species a (Rh4(CO)12) from frame 1 to frame 2 for a
constant k is implicitly positive (k > 0) for the case relating
̂
given Ca. At the beginning of frame 1, when Rh4(CO)12 is
intermediate i to product p. Therefore, for all constants k found
introduced, there is no RCORh(CO)4 present. However, at the
beginning of frame 2, when Rh4(CO)12 is introduced, there is
quite a lot of RCORh(CO)4 already present. Therefore, for
frame 2, the rate of loss of Rh4(CO)12 is markedly lower.
̇
to be nonpositive (k ≤ 0), the respective entry [Cx,|Cy|] or
̇
̂
y|] (for any pair of species x and y) may be confidently set
̂
[Cx,|C
to 0 in the 2D correlation matrix for the identification of
intermediates.
̇
̂
b|]: a decrease in
̂
Similar observation was noticed in entry [Ca,|
C
In the context of the real catalytic system and the 2D
correlation matrices/entries of Figures 12 and 14, we see that
the rate of formation of species b (RCORh(CO)4) from frame
̇
̂
1 to frame 2 for a given Ca value. Thus, the entries [Ca,|C
̂
̂
̇
a|] and
b|] almost pass the linearity tests (gray shading) but not
entirely.
This demonstrates that the analysis of multiple frames seems
̂
̂
application of criterion III applies to [Ca,|
C
a|]. Thus, this entry
̇
̂
̂
may be confidently set to 0. Presently, it appears that Criteria I
and II are sufficiently strong criteria to evaluate well-designed
experimental data sets with good signal to noise ratios.
Accordingly, it appears that criteria III and IV are, at the
moment, not needed for real data unless difficulties with the
quality of the data is encountered: i.e., insufficient signal to
noise ratios.
[Ca,|
C
to be a particularly useful tool in the 2D correlation in order to
reject potential positive tests. The final outcome is that one and
only one organometallic correlates experimentally with product
formation, and that is RCORh(CO)4.
5.3. Model Reduction. In many or perhaps most
exploratory studies of new metal-mediated syntheses, detailed
spectral analysis will results in the detection of numerous
organometallics (far more than in the present study). In the
5.5. Consequence and Future Studies. The present 2D
correlation analysis was carried out under an explicit
assumption that there is one isolated catalytic cycle. A soluble
and isolated catalytic cycle will have one and only one route for
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product formation, and there will be only one product. Clearly,
this is a specific case for a much broader and more general
situation. Many catalytic systems possess chemoselectivity,
regioselectivity, or stereoselectivity, and therefore, they have by
definition more than one product and more than one cycle of
intermediates leading to product formation. Such systems will
have coupled catalytic cycles, where some but not all
intermediates are common to both cycles. This situation
requires much more consideration with respect to setting up a
properly posed 2D correlation analysis.
REFERENCES
■
(1) Mechanisms in Homogeneous Catalysis: A Spectroscopic Approach;
Heaton, B., Ed.; Wiley-VCH: Weinheim, Germany, 2005.
(2) Haynes, A. The Use of High Pressure Infrared Spectroscopy to
Study Catalytic Mechanisms. In Mechanisms in Homogeneous Catalysis.
A Spectroscopic Approach; Heaton, B., Ed.; Wiley-VCH: Weinheim,
Germany, 2005; pp 107−150.
(3) Viviente, M.; Pregosin, P.; Schott, D. NMR Spectroscopy and
Homogeneous Catalysis. In Mechanisms in Homogeneous Catalysis: A
Spectroscopic Approach; Heaton, B., Ed.; Wiley-VCH: Weinheim,
Germany, 2005; pp 1−80.
More difficult situations could also arise, at least in principle.
Indeed, there are systems that possess more than one
completely independent catalytic cycle leading to product
formation (think of two metals that can perform a hydro-
genation and add them to the same synthesis). Another
complication arises when a catalytic system possesses
intermediates of more than one nuclearity in the same complex
reaction network. A number of synergistic systems have been
shown to function in this manner.41
Moreover, and perhaps the most difficult situation to
consider, is a system which has additional reaction pathways
above and beyond the coupled systems mentioned above.
These more complex systems might have contributions to
product formation due to (1) uncatalyzed thermally induced
product formation, (2) surface-catalyzed reactions at the wall
(perhaps the reactor is not as clean as originally thought), and
(3) surface-catalyzed product formation due to colloids
generated during the reaction. These types of situations, at
least at the moment, appear to be considerably more difficult to
treat using the approach we have introduced. The main reason
is that it is difficult to quantify some of the time-dependent
quantities involved in points (1)−(3) above.
(4) Tinker, H.; Morris, D. Rev. Sci. Instrum. 1972, 43, 1024−1028.
(5) Whyman, R. J. Chem. Soc. D 1970, 23, 1194−1195.
(6) Bor, G.; Dietler, U.; Noack, K. J. Chem. Soc., Chem. Commun.
1976, 22, 914−916.
(7) Mirbach, M. J. Organomet. Chem. 1984, 265, 205−213.
̆
(8) Alemdaroglu, N.; Penninger, M.; Oltay, E. Monatsh. Chem. 1976,
107, 1153−1165.
(9) Duckett, S.; Newell, C.; Eisenberg, R. J. Am. Chem. Soc. 1994,
116, 10548−10556.
(10) Brown, J.; Kent, A. J. Chem. Soc., Chem. Commun. 1982, 723−
725.
(11) Garland, M.; Bor, G. Inorg. Chem. 1989, 28, 410−413.
(12) Haynes, A.; Maitlis, P.; Morris, G.; Sunley, G.; Adams, H.;
Badger, P.; Bowers, C.; Cook, D.; Elliott, P.; Ghaffar, T.; Green, H.;
Griffin, T.; Payne, M.; Pearson, J.; Taylor, J.; Vickers, P.; Watt, R. J.
Am. Chem. Soc. 2004, 126, 2847−2861.
(13) Heaton, B.; Jacob, C.; Monks, G.; Hursthouse, M.; Ghatak, I.;
Somerville, R.; Heggie, W.; Page, P.; Villax, I. J. Chem. Soc., Dalton
Trans. 1996, 1, 61−67.
(14) van Rooy, A.; Orij, E.; Kamer, P.; van Leeuwen, P.
Organometallics 1995, 14, 34−43.
(15) Li, C.; Guo, L.; Garland, M. Organometallics 2004, 23, 2201−
2204.
(16) More recently, important in situ FTIR contributions have been
made by a number of groups. Particularly noteworthy is the large
contribution from Rostock, Germany (LIKAT): (a) Christiansen, A.;
Efforts are underway to generalize the formulation of the
present 2D correlation analysis in order to address as many of
the aforementioned scenarios as possible.
Li, C.; Garland, M.; Selent, D.; Ludwig, R.; Franke, R.; Borner, A.
̈
ChemCatChem 2010, 2, 1278−1285. (b) Christiansen, A.; Li, C.;
Garland, M.; Selent, D.; Ludwig, R.; Spannenberg, A.; Baumann, W.;
Franke, R.; Borner, A. Eur. J. Org. Chem. 2010, 14, 2733−2741. (c)
̈
6. CONCLUSION
Reference 20.
(17) For the purpose of the present contribution, we will exclude
consideration of at-line mass spectrometry work, although it has
provided a wealth of new information on homogeneous catalysis:
(a) Chen, P. Angew. Chem., Int. Ed. 2003, 42, 2832−2847.
(b) Henderson, W.; McIndoe, J. C. Mass Spectrometry of Inorganic
and Organometallic Compounds: Tools-Techniques-Tips; Wiley-Inter-
science: New York, 2005.
(18) Garland, M., Processing Spectroscopic Data. In Mechanisms in
Homogeneous Catalysis: A Spectroscopic Approach; Heaton, B., Ed.;
Wiley-VCH: Weinheim, Germany, 2005; pp 151−193.
(19) Li, C.; Chew, W.; Garland, M. Appl. Spectrosc. 2003, 57, 491−
498.
In the present contribution, a strictly mathematical 2D
correlation analysis has been developed in order to identify
the intermediates participating in a unicyclic catalytic cycle. The
analysis has been successfully tested on a numerical model and
then on a set of experimental data for a rhodium-catalyzed
hydroformylation of alkene. Without any prior chemical
knowledge of the reaction, but with proper experimental
design, the present approach allows an experimentalist to focus
on the most meaningful spectroscopic information at the
exploratory stage of a research program. Efforts are underway in
our laboratory to extend the concept of 2D correlation to more
complex catalytic systems.
(20) (a) Kubis, C.; Ludwig, R.; Sawall, M.; Neymeyr, K.; Borner, A.;
̈
Wiese, K. D.; Hess, D.; Franke, R.; Selent, D. ChemCatChem 2010, 2,
287−295. (b) Kubis, C.; Selent, D.; Sawall, M.; Ludwig, R.; Neymeyr,
K.; Baumann, W.; Franke, R.; Borner, A. Chem. - Eur. J. 2012, 18,
̈
AUTHOR INFORMATION
■
8780−8794.
Corresponding Author
(21) (a) Chew, W.; Widjaja, E.; Garland, M. Organometallics 2002,
21, 1982−1990. (b) Widjaja, E.; Li, C.; Garland, M. Organometallics
2002, 21, 1991−1997. (c) Widjaja, E.; Li, C.; Chew, W.; Garland, M.
Anal. Chem. 2003, 75, 4499−4507.
*E-mail for M.G.: marc_garland@ices.a-star.edu.sg.
Notes
The authors declare no competing financial interest.
(22) Widjaja, E.; Li, C.; Garland, M. J. Catal. 2004, 223, 278−289.
(23) Garland, M.; Li, C.; Guo, L. ACS Catal. 2012, 2, 2327−2334.
(24) In order to avoid unnecessary confusion, we note that the term
“2D correlation analysis” arises in quite a few areas of the mathematical
and physical sciences. In the area of chemistry and spectroscopy, one
of the most well-known forms is the Noda transform, which arises in
ACKNOWLEDGMENTS
■
Support from the Agency for Science, Technology and
Research (A*STAR) of Singapore is gratefully acknowledged.
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DOI: 10.1021/cs502127y
ACS Catal. 2015, 5, 3588−3599

ACS Catalysis
Research Article
the application of the Hilbert transform to raw spectroscopic data sets:
Noda, I.; Ozaki, Y. Two-Dimensional Correlation Spectroscopy-
Applications in Vibrational and Optical Spectroscopy; Wiley: New
York, 2005. Furthermore, BTEM has been used to untangle spectra
prior to further application of the Noda transform: Widjaja, E.; Tan,
B. H.; Garland, M. Appl. Spectrosc. 2006, 60, 294−303. The type of
2D correlation analysis introduced in the present contribution does
not use any of the mathematical constructs of the Noda Transform,
the Hilbert Transform, nor synchronous/asynchronous maps in any
way.
(25) van Leeuwen, P., Claver, C. Rhodium Catalyzed Hydro-
formylation; Springer, Heidelberg, Germany, 2002.
(26) (a) Garland, M.; Pino, P. Organometallics 1991, 10, 1693−1704.
(b) Feng, J.; Garland, M. Organometallics 1999, 18, 417−427. (c) Fyhr,
C.; Garland, M. Organometallics 1993, 12, 1753−1764.
(27) Gao, F.; Ng, K.; Li, C.; Krummel, K.; Allian, A.; Garland, M. J.
Catal. 2006, 237, 49−57.
(28) Garland, M. Transport Effects in Homogeneous Catalysis. In
Encyclopedia of Catalysis; Horvath, I., Ed.; Wiley: New York, 2002; pp
550−577.
(29) In the present case, we have chosen to calibrate the solvent.
However, it should be noted that there are two choices for 2D
correlation: namely, (1) no calibration of the solvent and (2)
calibration of the solvent to obtain an absorptivity. If (1) is chosen,
then any arbitrary nonzero absorptivity can be assigned: for example,
setting the absorptivity to unity.
(30) Chew, W.; Widjaja, E.; Garland, M. Appl. Spectrosc. 2007, 61,
734−746.
(31) Liu, G.; Li, C.; Guo, L.; Garland, M. J. Catal. 2006, 237, 67−78.
(32) Liu, G.; Hakimifard, M.; Garland, M. J. Mol. Catal. A: Chem.
2001, 168, 33−37.
(33) (a) Masters, C. Homogeneous Transition-metal Catalysis: A Gentle
Art; Springer: Heidelberg, Germany, 2013. (b) Temkin, O.;
Zeiggarnik, A.; Bonchev, D. Chemical Reaction Networks: A Graph−
Theoretical Approach; CRC Press: Boca Raton, FL, 1996.
(34) King, E.; Altman, C. J. Phys. Chem. 1956, 60, 1375−1378.
(35) Chou, K. J. Biol. Chem. 1989, 264, 12074−12079.
(36) (a) Zagajewski, M.; Behr, A.; Sasse, P.; Wittman, J. Chem. Eng.
Sci. 2014, 115, 88−94. (b) Zagajewski, M.; Dreimann, J.; Behr, A.
Chem. Ing. Tech. 2014, 86, 449−457. (c) Behr, A.; Witte, H.; Kamper,
̈
A.; Haßelberg, J.; Nickel, M. Chem. Ing. Tech. 2014, 86, 458−466.
(d) Roda−Monsalvez, N.; Tran, D.; Battilocchio, C.; Labes, R.;
Ingham, R.; Hawkins, M.; Ley, S. Org. Biomol. Chem. 2015, 13, 2550−
2554. (e) Brzozowski, M.; O’Brien, M.; Ley, S.; Polyzos, A. Acc. Chem.
Res. 2015, 48, 349−362.
(37) Montgomery, D.; Runger, G. Applied Statistics and Probability for
Engineers, 2nd ed.; Wiley: New York, 1999.
(38) Kwiatkowski, D.; Phillips, P.; Schmidt, P.; Shin, Y. Journal of
Econometrics. 1992, 54, 159−178.
(39) MATLAB version 7.12.0 (R2011a); The MathWorks Inc.,
Natick, MA, 2011.
(40) Note that in simple catalytic systems, which are the focus of the
present contribution, the possibility of autocatalysis will not be
considered.
(41) (a) Li, C.; Widjaja, E.; Garland, M. J. Am. Chem. Soc. 2003, 125,
5540−5548. (b) Li, C.; Chen, L.; Garland, M. J. Am. Chem. Soc. 2007,
129, 13327−13334. (c) Li, C.; Cheng, S.; Tjahjono, M.; Schreyer, M.;
Garland, M. J. Am. Chem. Soc. 2010, 132, 4589−4599.
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DOI: 10.1021/cs502127y
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