Tackling calibration problems of spectroscopic analysis in high-throughput experimentation

Article abstract of DOI:10.1021/ac048421c

High-throughput experimentation and screening methods are changing work flows and creating new possibilities in biochemistry, organometallic chemistry, and catalysis. However, many high-throughput systems rely on off-line chromatography methods that shift

Full text of DOI:10.1021/ac048421c

Anal. Chem. 2005, 77, 2227-2234
Tackling Calibration Problems of Spectroscopic
Analysis in High-Throughput Experimentation
Susana C. Cruz, Gadi Rothenberg, Johan A. Westerhuis,* and Age K. Smilde‡
†
†
,‡
van t’ Hoff Institute for Molecular Sciences and Swammerdam Institute for Life Sciences, University of Amsterdam,
Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands
High-throughput experimentation and screening methods
are changing work flows and creating new possibilities in
biochemistry, organometallic chemistry, and catalysis.
However, many high-throughput systems rely on off-line
chromatography methods that shift the bottleneck to the
analysis stage. On-line or at-line spectroscopic analysis
is an attractive alternative. It is fast, noninvasive, and
nondestructive and requires no sample handling. The
disadvantage is that spectroscopic calibration is time-
consuming and complex. Ideally, the calibration model
should give reliable predictions while keeping the number
of calibration samples to a minimum. In this paper, we
employ the net analyte signal approach to build a calibra-
tion model for Fourier transform near-infrared measure-
ments, using a minimum number of calibration samples
based on blank samples. This approach fits very well to
high-throughput setups. With this approach, we can
reduce the number of calibration samples to the number
of chemical components in the system. Thus, the question
is no longer how many but which type of calibration
samples should one include in the model to obtain reliable
predictions. Various calibration models are tested using
Monte Carlo simulations, and the results are compared
with experimental data for palladium-catalyzed Heck
cross-coupling.
make good use of HTE tools. In many cases, the problem has
shifted from performing the experiments to monitoring them and
analyzing the data. This is especially important when multiple
samples must be taken, e.g., in kinetic studies and catalysis
3
research. The coupling of parallel reactors and chromatographic
analysis often creates a bottleneck.4 Alternatively, one can use
,5
in situ or operando spectroscopy, which features fast and nonin-
6
vasive reaction sampling. Until now, however, on-line spectro-
scopic monitoring has been limited to simple reaction mixtures,
mainly because of problems associated with spectral overlapping.
Deconvolution of the spectra is possible by means of multivariate
calibration techniques that enable the efficient extraction of
information concerning analytes of interest from multicomponent
7
mixtures. As we recently showed, it is possible to combine in
situ spectroscopy with multivariate calibration techniques to
monitor the kinetics of complex reactions, such as C-C cross-
coupling8 and metal nanocluster formation. However, multi-
variate calibration requires a large number of calibration samples,
the collection of which is often difficult and time-consuming,
creating a new bottleneck.
,9
10
Combinatorial catalysis, for example, is composed of two
important stages: catalyst screening/discovery and catalyst
optimization. In the screening stage, a large set of catalysts is
tested under a few experimental conditions. In this stage, precision
is not very important, since the main question here is, “Is the
catalyst active?syes/no”. Positive answers to this question will
proceed further to the optimization stage, where more experi-
mental parameters are included. If one wants to use spectroscopic
analysis in this type of system, the calibration model should be
adaptable to both “discovery” and “optimization” modes.
The question is how can one analyze complex reaction
mixtures in situ with a minimal calibration effort. The selection
of calibration samples is a topic that has received the attention of
The last 150 years have witnessed radical changes in chemistry
as far as research areas are concerned, but the basic laboratory
work flow is still quite similar to that employed by Perkin in the
19th century. The incorporation of high-throughput experimenta-
tion (HTE) work flows in research laboratories, however, is
changing this. HTE and combinatorial chemistry tools have
surmounted the science barrier and became enabling technolo-
1,2
gies. Robot systems can now perform thousands of experiments
per day, yielding mind-boggling amounts of data. This techno-
logical revolution is not only about “performing experiments
faster”. It has important psychological consequences: the value
of the basic scientific unit operation (the laboratory experiment)
has changed, and chemists must accept this change if they are to
(3) Lavastre, O. Actual. Chim. 2000, 42-45.
(
(
(
(
4) Boelens, H. F. M.; Iron, D.; Westerhuis, J. A.; Rothenberg, G. Chem. Eur.
J. 2003, 9, 3876-3881.
5) Rothenberg, G.; Boelens, H. F. M.; Iron, D.; Westerhuis, J. A. Chim. Oggi
2003, 21, 80-83.
6) Rothenberg, G.; Boelens, H. F. M.; Iron, D.; Westerhuis, J. A. Catal. Today
2
003, 81, 359-367.
7) Bro, R. Anal. Chim. Acta 2003, 500, 185-194.
*
Corresponding auhor. E-mail: j.a.westerhuis@uva.nl.
van t’ Hoff Institute for Molecular Sciences.
Swammerdam Institute for Life Sciences.
(8) Cruz, S. C.; Aarnoutse, P. J.; Rothenberg, G.; Westerhuis, J. A.; Smilde, A.
K.; Bliek, A. Phys. Chem. Chem. Phys. 2003, 5, 4455-4460.
(9) Rothenberg, G.; Cruz, S. C.; Van Strijdonck, G. P. F.; Hoefsloot, H. C. J.
Adv. Synth. Catal. 2004, 346, 467-473.
†
‡
(
1) Pescarmona, P. P.; van der Waal, J. C.; Maxwell, I. E.; Maschmeyer, T. Catal.
Lett. 1999, 63, 1-11.
(10) Wang, J.; Boelens, H. F. M.; Thathagar, M. B.; Rothenberg, G. ChemPhys-
(
2) Reetz, M. T. Angew. Chem., Int. Ed. 2001, 40, 284-310.
Chem 2004, 5, 93-98.
1
0.1021/ac048421c CCC: $30.25 © 2005 American Chemical Society
Analytical Chemistry, Vol. 77, No. 7, April 1, 2005 2227
Published on Web 02/25/2005

several researchers.11-14 The goal is to choose the smallest set of
prepared calibration samples that can be used without significantly
compromising the model’s prediction ability. In many situations,
a large number of samples from the system has been obtained,
and the exact analyte concentration in the samples is determined
using a reference method (often GC). Calibration samples are
usually selected from a list of possible candidates using methods
spectrum which is orthogonal to the spectra of the other
components” and is uniquely related to the concentration of the
analyte of interest.24
The reason we chose the NAS approach in this study is that
applies well to a HT environment. The separation of the interfer-
ence space from the analyte space (see explanation below) using
blank samples makes it easy to extend the calibration model to
new situations. One does not need to know in advance the future
composition of the system. Rather, by using blank samples
1
1
12
such as Kennard-Stone design, simulated annealing, genetic
algorithms, successive projections algorithms,14 or random
1
3
1
5
selection.
(samples that contain a mixture of interferences but no analyte),
In this paper, we investigate a different situation, wherein prior
to analysis a number of calibration samples are being prepared
by weighing the appropriate amounts of each component, and then
the prepared sample is measured. Here we use the net analyte
signal (NAS) approach with blank samples, a combination that
fits well to HT setups. Two sources of error are important in this
situation: the concentration error and the spectral error. We
examine strategies to minimize the calibration effort in in situ
spectroscopic analysis using both computer simulations and the
Heck cross-coupling as an experimental example.
it is possible to add new interferences sequentially to the
calibration model. For example, one can calibrate a system
containing one analyte and five interferences (of which, say, three
are solvents), using the models shown below. Then, if one wants
to test five other solvents in this system, one additional sample of
each of these solvents is sufficient to evaluate the model’s
performance.
The absorbance spectrum of a mixture of K spectroscopic
active substances (k ) 1, ..., K) is measured at J wavenumbers.
Assume that the analyte of interest, analyte k, is one component
in this mixture. All the remaining components are called the
interferences. Each spectrum represents a vector in the J
dimensional space, and its length and direction translate, respec-
tively, the spectrum’s intensity and shape.
Let R be the matrix composed of spectra with the analyte of
interest, formed by the absorbance spectra of samples containing
the analyte and R-k the matrix composed by the interferences
(formed by spectra of samples that do not contain analyte, i.e.,
blank samples). A spectrum containing analyte k can then be
decomposed, by definition, into two orthogonal parts: one part
orthogonal to the interference space and one part that lies in the
interference space. The latter can be described by a linear
combination of the interferences. The unique direction useful for
quantification of analyte k, which defines the NAS direction, is
THEORY
NAS Approach. There are several techniques for multivariate
calibration, the ones most frequently used being classical least
squares, principal component regression, and partial least squares
16
(
PLS). Multivariate calibration models are usually built from large
sets of samples that include all the possible variability in the data.
The collection of the spectra of these samples is usually difficult
17-23
and time-consuming. Calibration free monitoring
is appealing,
but these methods are not easy to apply since they often give no
unique solution and several constraints are required.
Here we chose to use the NAS approach, which is a fairly new
2
4
technique used in calibration. It was first introduced by Lorber
in 1986 and was subsequently applied in several studies.8,10,25-34
The NAS for a given component is defined as “the part of its
therefore orthogonal to R-k
.
(
11) Wu, W.; Walczak, B.; Massart, D. L.; Heuerding, S.; Erni, F.; Last, I. R.;
Prebble, K. A. Chemom. Intell. Lab. Syst. 1996, 33, 35-46.
Temperature is usually considered as an interference, and its
variability should be included in the calibration model. However,
our previous studies on this chemical system showed that, in this
case, temperature has little effect on the spectra.8
(
12) Kalivas, J. H. J. Chemom. 1991, 5, 37-48.
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C. B.; Jos e´ , G. E.; Pasquini, C.; Raimundo, I. M., Jr.; Rohwedder, J. R.
Chemom. Intell. Lab. Syst. 2004, 72, 83-91.
NAS-based calibration techniques differ in the manner in which
the matrix R-k is defined. Lorber, for example, used pure
component spectra.25 The problem with this approach is that the
samples are very far from reaction conditions. Furthermore, the
spectrum of a pure component is often different from the spectra
at low concentration in a solvent. Also, the Beer-Lambert law is
only valid for low/medium concentrations. Instead of pure spectra,
Goicoechea and Olivieri used samples with analyte k to define
(
(
(
15) Miller, J. N.; Miller, J. C. Statistics and Chemometrics for Analytical Chemistry,
4
th ed.; Prentice Hall: Upper Saddle River, NJ, 2000.
16) Martens, H.; Næs, T. Multivariate Calibration; John Wiley & Sons Ltd.: New
York, 1989.
17) Sans, D.; Nomen, R.; Sempere, J. Comput. Chem. Eng. 1997, 21, S631-
S636.
(
(
18) Jiang, J. H.; Ozaki, Y. Appl. Spectrosc. Rev. 2002, 37, 321-345.
19) Ozaki, Y.; Sasic, S.; Jiang, J. H.; Siesler, H. W. Macromol. Symp. 2002, 184,
2
29-247.
20) Sasic, S.; Kita, Y.; Furukawa, T.; Watari, M.; Siesler, H. W.; Ozaki, Y. Analyst
000, 125, 2315-2321.
30
-k
R . The analyte part of each spectrum is removed by scaling
(
(
2
all samples to equal analyte content and then a centering step
removes the analyte contribution.
21) Windig, W.; Antalek, B.; Sorriero, L. J.; Bijlsma, S.; Louwerse, D. J.; Smilde,
A. K. J. Chemom. 1999, 13, 95-110.
(
(
22) Bijlsma, S.; Smilde, A. K. Anal. Chim. Acta 1999, 396, 231-240.
23) Bijlsma, S.; Boelens, H. F. M.; Hoefsloot, H. C. J.; Smilde, A. K. Anal. Chim.
Acta 2000, 419, 197-207.
(30) Goicoechea, H. C.; Olivieri, A. C. TrAC-Trends Anal. Chem. 2000, 19, 599-
605.
(
(
(
(
(
(
24) Lorber, A. Anal. Chem. 1986, 58, 1167.
25) Lorber, A.; Faber, K.; Kowalski, B. R. Anal. Chem. 1997, 69, 1620-1626.
26) Faber, N. M. J. Chemom. 1998, 12, 405-409.
27) Faber, N. M. Anal. Chem. 1999, 71, 557-565.
28) Faber, K.; Lorber, A.; Kowalski, B. R. J. Chemom. 1997, 11, 419-461.
29) Boque, R.; Larrechi, M. S.; Rius, F. X. Chemom. Intell. Lab. Syst. 1999, 45,
(31) Olesberg, J. T.; Arnold, M. A.; Hu, S. Y. B.; Wiencek, J. M. Anal. Chem.
2000, 72, 4985-4990.
(32) Ferre, J.; Faber, N. M. Chemom. Intell. Lab. Syst. 2003, 69, 123-136.
(33) Skibsted, E. T. S.; Boelens, H. F. M.; Westerhuis, J. A.; Witte, D. T.; Smilde,
A. K. Appl. Spectrosc. 2004, 58, 264-271.
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97-408.
2004, 76, 2656-2663.
2228 Analytical Chemistry, Vol. 77, No. 7, April 1, 2005

The approach employed here makes use of spectra of blank
samples. In this case, the interference space can be directly
8,34
determined from R-k
.
This approach allows the calibration effort
to be reduced, and even more important, with only a few samples
it is possible to assess whether the calibration is feasible at all. A
detailed explanation of the NAS approach as used here was
8
published elsewhere. It is important to realize the consequences
this approach has on the design of the calibration samples used.
The samples used to define the interference space are free of
analyte, and thus, the analyte contribution appears only in the
samples used to define the analyte space.
After finding the unique direction related with the concentra-
tion of analyte, NAS
direction are calibrated to concentration according to eq 1, where
is the concentration of analyte k.
k
, the projections of new spectra on this
Figure 1. Single-component samples vs multicomponent samples.
Single-component samples are formed by one component mixed in
solvent (solid lines) and multicomponent samples by two or more
components in solvent (broken lines). For simplicity, the figure relates
to a system with three components (A, B, C) in a solvent. The solid
lines represent single-component samples, e.g. {A + solvent}, and
the broken lines represent multicomponent samples, e.g. {A + B +
C + solvent}.
c
k
NAS ) bc + e
(1)
k
k
The slope b of this calibration line is fitted using calibration
samples in a least-squares way and e is the residual. The NAS
direction is directly proportional to the concentration of the
analyte, so the multivariate problem reduces to a univariate one.
Even in the case of spectral overlap, it is possible to minimize
the number of calibration samples to the number of chemical
of samples. Another way of solving the problem, demonstrated
in this paper, is to assess the solution by use of computer
simulations. The simulated calibration samples should be signifi-
cantly realistic and include error values. Each sample should be
generated as a linear combination of the underlying pure com-
ponent spectra. When these are not available, they can be
calculated from measured spectra of mixtures of the components.
We included two sources of error in the simulated calibration
samples: a spectral error, which is dependent on the spectrometer
used, and a concentration error. The latter deserves special
attention: In this study, the calibration samples are prepared
before analysis by weighing the appropriate amounts of each
2
4,25
components in the system.
The samples are divided in two
groups: K - 1 samples with no analyte, to define the interference
space (the blank samples), and one sample containing analyte to
define the analyte space. The fundamental question is no longer
how many samples but rather which type of samples: Which K -
1
1
samples should be selected to optimally describe the K -
-dimensional interference space, and which sample should be
selected to define the NAS direction in order to have the minimum
prediction error for new samples.
Single-Component versus Multicomponent Samples. The
reaction takes place in a solvent, and therefore, the calibration
samples are conveniently prepared in solvent. One can prepare
samples with only one component mixed with the solvent (called
component. Let C
component k to be calculated:
k
be the concentration, in weight fraction, of
K
C ) m / mk
(2)
k
k
∑
‘
“single-component samples”) or samples with many or all the
components in the solvent (“multicomponent samples”). Figure
shows this concept for a system with four components (A, B,
k)1
1
C, and solvent). The concept of single-component samples is
simpler, as each component (except for the solvent) is present in
only one sample. On the other hand, multicomponent samples
are more difficult to visualize once each component is present in
more samples.
It is assumed that the masses of the components (m
are independent. The variance in the concentration, σ
found by error propagation theory as the weighed sum of the
variances of the different sources of error in the preparation of
the sample (see Appendix).
1 2 K
, m , ..., m )
2
R
, is then
Which type of samples should be included in the calibration
model? In high-throughput laboratories, the samples are usually
prepared by robots, and therefore, any type of sample is easy to
prepare. However, this is not the case for standard analytical
laboratories where multicomponent samples take more effort and
time to prepare. Also, multicomponent samples contain more
sources of error as one weighs more components. Here we will
examine which type of samples should be included in the
calibration model to obtain reliable concentration predictions.
The most informative way to evaluate which samples to include
in the calibration model is to make a feasibility study with
experimental data, but that is exhaustive and time-consuming,
especially when the experimental design leads to a large number
The calibration samples are simulated as a linear combination
of the underlying pure component spectra. The errors are included
according to eq 3 (for derivation see Appendix), where N denotes
all the components in the mixture except for the solvent (N ) 1,
..., K - 1), and the subscript sol stands for the solvent component.
N
N
Sa ) ( (con + wgEr )‚P + (con
-
wgEr )‚P ) +
n sol
∑
n
n
n
sol
∑
n)1
n)1
spEr (3)
The vector S
sample to prepare, con
a
is the simulated spectrum of the calibration
is the concentration ratio for component
n
Analytical Chemistry, Vol. 77, No. 7, April 1, 2005 2229

n (calculated relative to the concentration of a pure sample of this
component), P is the pure component spectra of component n
estimated from samples at reaction level, and wgEr and spEr are
introduce offsets or slope changes to the spectra that can be
corrected for by spectral preprocessing methods.27 The simulated
data were offset corrected prior to application of the calibration
model.
n
normal distributed random errors, with zero mean and variances
2
σ
R
and SE, respectively. SE is the variance of the spectral error
Although multivariate techniques are full spectral methods, the
performance of the methods usually improves when a suitable
and depends only on the spectrometer used.
35
A calibration model based on the NAS approach is then
developed for each set of K calibration samples and studied with
the aid of simulations. The predictive ability of the models can
be evaluated by examining the root-mean-square of the error in
prediction, RMSEP.
wavelength region is selected. NIR measurements are disturbed,
36
for example, by water vapor in the following areas: 5102-5618
-
1
and 6667-7463 cm . As the NMP solvent is highly hygroscopic,
8
-1
the spectral range used for quantification was 5950-6300 cm
.
In the following sections, PhI is considered as the analyte, but
the same approach can be applied to any of the other components.
Simulations. A computer simulation program for generation
of multivariate data, calibration, and validation of the results was
developed in Matlab.37 For each simulation, a number of samples
were generated as a linear combination of the underlying pure
component spectra (eq 3 above). The spectra were superimposed
with normally distributed noise, with zero mean and variances of
V
1/2
2
(
c - cˆ )
∑
v v
v)1
RMSEP )
(
)
(4)
V
Here, c
v
is the known analyte concentration in sample v, cˆ
v
is
the predicted concentration from the calibration model, and V is
the number of validation samples. The spectra from which the
concentrations are predicted are a function of the concentration
error and the spectral error, as are the RMSEP values. A single
simulation will not necessarily provide a representative result, and
hence, one runs many simulations to get more realistic results.
Each calibration model will, therefore, generate a large number
of RMSEP values. To compare the different models, the RMSEP
values for each model are condensed into an average value, the
average error of prediction (AEP, eq 5), where NR is the number
of simulations per model (nr ) 1, ..., NR).
-
5
-6
5
× 10 (au) and 7 × 10 (au) for the spectral error and the
concentration error, respectively. These spectra were analyzed
3
8
with the NAS software toolbox developed in our group. Each
simulation was run 200 times to ensure sufficiently precise
sampling distribution (increasing the number of simulations from
2
00 to 10 000 gave results within (6%, confirming the robustness
of the models).
Model Validation. The validation of each model is based on
3
0 samples, designed to mimic reaction conditions. For example,
a sample with high concentration of reactants has a low concen-
tration of product. Sample concentrations were in the range of
NR
0
.0-0.3 M for all components except for the solvent, which had
∑
RMSEPnr
concentrations of 8.7-10 M.
nr)1
AEP )
(
)
(5)
NR
RESULTS AND DISCUSSION
The model system considered in this study is the Heck reaction
between PhI with NBA to give n-butyl cinnamate (NBC) in NMP
EXPERIMENTAL SECTION
Materials and Instrumentation. Near-infrared spectra were
3
(eq 6). Et N was used as a base.
recorded on a Perkin-Elmer Spectrum GX FT-IR instrument from
5 000 to 2700 cm . The spectra were recorded as single scans
2.4 s/scan), 2-cm- resolution and 0.4-cm path length. Unless
-
1
1
(
1
noted otherwise, all chemicals were purchased from commercial
firms and used as received. n-Butyl acrylate (NBA) and n-methyl
pyrrolidinone (NMP) were purified prior to use by filtration over
a plug of basic alumina (∼150 mesh, 58 Å). The palladium catalyst
2
was synthesized in situ by adding 1 mol % Pd(OAc) and 6 mol %
3
P(Ph) ligand.
Reaction progress was monitored using fiber optics with
starting concentrations of ∼0.20 M of n-butyl acrylate (NBA), an
3
excess of triethylamine (Et N), and an excess of iodobenzene
Samples of pure NMP and of mixtures of known concentrations
(
(
PhI). Each reaction was carried out in a batch reactor at 60 °C
thermoregulated by a water bath). The reaction volume was set
of the components were measured using Fourier transform near-
infrared (FT-NIR) spectroscopy. Each measured sample can be
expressed as a linear combination of the underlying pure
component spectra (concentration of each component multiplied
by its pure spectrum). The pure component spectra (Figure 2)
were then obtained from these equations in a least-squares way.
to ∼40 mL. All liquid components were introduced in the stirred
reactor. The ligand was dissolved in NMP in a glass vial, prior to
2
adding the Pd(OAc) . This mixture was preheated to 60 °C and
added to the reactor to start the reaction.
Data Preprocessing and Wavenumber Selection. FT-NIR
measurements contain not only variation related to composition
change in the reaction mixture but also variation that is caused
by changing physical properties in the mixture, for example,
density, viscosity, and temperature. Some of these phenomena
(35) Xu, L. A.; Schechter, I. Anal. Chem. 1997, 69, 3722-3730.
(36) Davies, A. M. C. NIR News 1992, 3, 8-9.
(37) Release 13 version 6.5, MathWorks Inc.
(38) This toolbox can be downloaded from http://www-its.chem.uva.nl/research/
pac/.
2230 Analytical Chemistry, Vol. 77, No. 7, April 1, 2005

Table 2. Sample Composition in the Calibration Sets
for Each Model (PhI is the Analyte)
concentration/M
entry
model
A
NBA
PhI
NBC
Et3N
NMP
1
2
3
4
5
6
7
8
9
0
0.3
0
0
0
0
10.0
10.0
9.8
0.3
0
0
0
0.3
0
0
0
0
0.3
0
10.0
10.4
10.0
8.7
0
0
0
0
B
C
D
0
0.3
0
0
0
0.3
0
0.3
0.3
0
0.3
0.3
0
0
8.7
8.7
Figure 2. Pure component spectra in the Heck reaction between
PhI and NBA estimated from mixture spectra.
0
0.3
0
1
1
1
0
1
2
0
0
10.4
8.7
0.3
0.3
0
0
0
0.3
0
0.3
0.3
0
0.3
0
0.1
0
0.3
0
10.0
9.8
Table 1. Design for Studying Sample Composition on
the Calibration Modela
13
0
0.3
0
0
1
4
0
0.3
0
10.0
10.4
8.7
analyte space
15
0
0
1
1
1
1
2
6
7
8
9
0
0.3
0
0.1
0.3
0
0.3
0.3
0.3
0
interference space
single comoponent
multicomponent
8.7
0
8.7
single component
multicomponent
model A
model B
model C
model D
0
0.3
0
8.7
0
0
10.4
a
The composition of the samples in the analyte and the interference
spaces are varied systematically in models A-D.
-
5
-6
zero mean and variances of 5 × 10 (au) and 7 × 10 (au) for
the spectral and the concentration error variances, respectively.
For each model, the first samples (entries 1, 6, 11, and 16) are
the analyte samples, and the other samples are used to define
the interference space. Also note that models A and B have the
same analyte sample as have models C and D. Furthermore,
models A and C have the same interference samples as have
models B and D. For calibration, the samples are divided into
analyte and interference spaces. The validation samples, on the
other hand, always contain analyte and are made to mimic reaction
conditions. The analyte samples are as close as possible from
reaction conditions. In reaction conditions, a high concentration
of product is never present in a sample with high concentration
of reactant. This is why the analyte multicomponent sample has
a lower concentration of product with a high concentration of
analyte.
Figure 3 shows the AEP for each model in millimolar. The
analyte space in models A and B is defined using a single-
component sample, and that in models C and D using a multi-
component sample. The interference space in models A and C is
formed by single-component samples, while that in B and D is
formed by multicomponent samples. If we compare model A with
B and model C with D, we observe the effect of changing the
composition of the samples in the interference space. Clearly,
there is an improvement of the models’ predictive ability when
the interference space is formed using multicomponent samples.
To analyze the effect of the samples’ composition in the analyte
space, we should compare models A with C, and models B with
D. These models are grouped by the same interference space.
Comparing models A with C, we see an improvement when using
single-component samples in the analyte space (though the
differences are rather small). However, if we compare B with D
we see no significant change in the AEP. This indicates that
multicomponent samples are preferred in the interference space,
and in this case, the composition of the sample in the analyte space
has no effect on the prediction ability of the models.
Which Samples Should One Choose? There are five chemi-
cal components in this system (NBA, PhI, NBC, Et
3
N, and the
solvent, NMP) that have overlapping absorbencies in the 5950-
-1
6
300-cm region. Therefore, the minimum number of calibration
samples is five. What type of samples yields the lowest prediction
error? Single-component or multicomponent samples? To study
the effect of the chosen type of samples in the model, the sample’s
composition was varied in analyte and interference space as shown
in Table 1. When the spectra of blank samples are available, the
minimum number of samples defining the analyte space is one
and the analyte concentration is measured only once. As in this
paper, we use blank samples to define the interference space, four
blank samples are used to define this space, and the fifth sample
is used to define the NAS direction.
The calibration model must span the concentration of each
component. This includes the solvent (which has a higher
concentration than any other component). To observe the con-
tribution of each component, the concentration level of the
components in the calibration samples should be varied. It is then
crucial to include at least two levels in concentration of each
component. The solvent concentration is nearly constant. A high
concentration sample of solvent is only introduced in the calibra-
tion model when adding a pure solvent sample to the interference
space. Several models, with and without a sample of pure solvent
in the interference space, were tested (not shown here), and it
was found that the lowest AEP values are obtained when including
a “solvent sample”. The chosen combinations for each model
include samples with low and high concentration of all components
rather than also having intermediate concentration levels. The
models below are the combinations with the lowest AEP for each
of the groups presented in Table 1.
The composition of the samples in each of the calibration sets
is shown in Table 2. Again, note the importance of using only
one analyte concentration contribution. Each sample is simulated
according to eq 3, using normally distributed random errors with
Analytical Chemistry, Vol. 77, No. 7, April 1, 2005 2231

Figure 3. Values of averaged error in prediction, AEP, averaged out from 200 runs, for the models shown in Table 2. The error bars are the
standard deviation of the values over the 200 runs.
Figure 5. Effect of the concentration error on the interference space.
The two dimensions represented by orthogonal arrows indicate the
solvent and the NBA directions. The vectors a and a′ are two samples
of NBA in solvent.
affect the single-component case much more than the multicom-
ponent case. To understand why this happens, let us consider
the effects of each type of error on the interference space
separately.
The concentration error has no effect on the interference space.
This bold statement is best illustrated by way of an example: Let
Figure 4. Schematic representation of the interference space. The
us assume that we want to construct an interference space that
axes x, y, and z represent NBA in solvent, Et3N in solvent, and NBC
covers NBA and solvent (Figure 5). A solvent sample and sample
in solvent, respectively. Red points (â) pertain to single-component
a are used to span this space, but because of a concentration error,
samples in the interference space of models A and C, while the blue
points (γ) correspond to multicomponent samples forming the interfer-
ence space in models B and D. The bottom left point R indicates a
solvent sample.
too much NBA is weighed in. The resulting sample, a′, contains
therefore a slightly higher concentration of NBA and a slightly
lower concentration of solvent. Nevertheless, the {solvent, a}
samples still define exactly the same space as the {solvent, a′}
samples.
Why are multicomponent samples better for the interference
space than single-component samples? Figure 4 gives a schematic
If the concentration error does not affect the estimation of the
interference space, it is the spectral error that is causing the
differences between the single-component and multicomponent
interference spaces. Let us look again at Figure 4, where we now
assign the origin point as R. Assuming homoscedastic spectral
errors, an estimation of the interference space that uses the â
points (single-component sample vectors) will be more affected
by spectral error than one that uses the γ points (multicomponent
sample vectors), as the latter are further away from the origin.
The concentration error on the analyte space has a direct effect
on the calibration line and thus on the prediction error. When
too much analyte is weighed, the NAS value is overestimated. In
this case, a one-point calibration model will result in too low
concentration predictions for all samples. The effect of the spectral
error on the analyte space is partly reduced by the interference
space; i.e. the spectral error in the same direction as the
interferences space is removed.
representation of the {NBA, Et
cube represents the entire interference space, and the axes
represent NBA in solvent, Et N in solvent, and NBC in solvent,
3
N, NBC, solvent} system. The
3
respectively. The bottom left point R denotes pure solvent. Note
that the further away one goes from R, the lower the solvent
concentration. The red points â denote the single-component
samples used to construct the interference space in models A and
C, and the blue points γ denote the multicomponent samples used
to construct the interference space in B and D. Point R is present
in all models. Thus, the subspace {â, â, â, R} pertains to the range
of the interference space covered by models A and C, and the
subspace {γ, γ, γ, R} pertains to the range of the interference
space covered by models B and D.
If all interference samples were error-free, both subspaces
could be used to construct exactly the same interference space
(the cube). Measurement errors (both concentration and spectral),
however, will lead to differences. As the single-component samples
cover only a small volume of the cube, measurement errors will
Effect of Changing Error Levels. Computer simulations can
be considered as a link between theory and experimental work.
2232 Analytical Chemistry, Vol. 77, No. 7, April 1, 2005

Figure 7. Concentration profiles for the Heck reaction at 60 °C
obtained from experimental data. Legend: b, PLS model based on
32 samples; 9, model A; [, model B.
were prepared and measured using the same spectrometer. Figure
shows the concentration predictions obtained with these three
7
models: A and B built from experimental data and the PLS model.
For convenience, each point is averaged out of 10 time points.
Figure 7 gives us three important points: First, the difference
between the predictions of models A and B are close to the PLS
model predictions (the root-mean-square differences between the
PLS model and models A and B are 6.30 and 5.54 mM,
respectively). Thus, the two models, with only 5 samples, are
comparable to the PLS model that uses 32 samples. Second, the
predictions of models A and B have a small systematic deviation
from the PLS model (A is always higher, and B always lower).
This is probably due to a concentration error in the analyte
samples in these models (each model is based on a single analyte
sample). Third, the deviation from the expected monotonic
decreasing concentration curve for PhI is due to sampling and
spectral errors (less obvious here because of averaging in time).
The fact that the same spectrum (and thus the same spectral error
realization) is applied to all three models results in a similar
deviation in the concentration prediction, since the models are
similar. Repeating the reaction under the same conditions con-
firmed these results.
Cost/Information Tradeoff. Models with a minimum number
of samples are convenient, especially for HTE. Such models may
give accurate predictions as long as the assumptions on which
the models are based are valid. One may choose to test these
assumptions, but this “costs” more calibration samples. The user
must decide on this tradeoff.
Linearity in the analyte space can easily be checked by
including samples at different levels of concentration and forcing
the line through these points. This will show whether the points
all fall on a straight line or not. Until now the calibration lines for
analyte k considered are defined by one sample and therefore
forced through zero. This is a valid assumption, since a concentra-
tion of zero should give a NAS value of zero. Not forcing the line
through zero would require an additional sample to set the
calibration line. However, this extra point can also be considered
a validation step. Obtaining an offset close to zero would ensure
that the NAS direction is well chosen.
Figure 6. Effect of increasing the variances of the concentration
2
error, σR (au), and spectral error, SE (au), on the AEP of the models.
2
-6
-5
2
(
1
I) σR ) 7 × 10 and SE ) 5 × 10 (original data); (II) σR ) 7 ×
-
5
-5
2
-6
-4
0
and SE × 10 ; (III) σR ) 7 × 10 and SE ) 5 × 10 ; (IV)
-5 -4
2
σR ) 7 × 10 and SE × 10 . Note the difference in scale between
the top and bottom graphs.
They have the advantage that the experimental parameters, such
as error levels and number of components, can easily be changed
and results are obtained quickly. To study the effect of changing
the error levels in the models, the variances used to simulate the
-
5
-4
spectra were varied over the ranges 5 × 10 -5 × 10 and 7 ×
-
6
-5
1
0
-7 × 10 for the spectral and concentration errors, respec-
tively.
Figure 6 shows the results when increasing the concentration
error and the spectral error by a factor of 10. The original data
are plotted in I. Plot II shows the results obtained when the
concentration error is increased by a factor of 10 from the original
value. Plot III shows the results when the spectral error is
increased by 10 times from the original value. Finally, plot IV
shows the results when the variances of both the errors are
changed by a factor of 10.
The increase of the concentration error has almost no effect
on the models’ prediction ability. Conversely, increasing the
spectral error has a dramatic effect (note the different scales).
Thus, for this application, the contribution of the spectral error is
much larger than the contribution of the concentration error. From
Figure 2 it can be seen that PhI is almost completely overlapped
from the solvent NMP. Therefore, quantification becomes very
difficult if the spectral noise increases. As discussed before, the
concentration error affects only the analyte space. However, the
spectral error affects both spaces leading to the observed results.
We can then conclude that the investment in a HT laboratory
should be on the spectrometer rather than on the weighing robot.
Experimental Example. The Heck reaction was monitored
8
at 60 °C using FT-NIR spectroscopy. A PLS calibration model
Using the NAS approach, one has the possibility of tuning the
calibration for the application at hand. For the discovery stage in
HTE (a “go”/“no go” analysis), the calibration model does not
need to be very accurate. The main question at this stage is “Is
there any product or not?” On the other hand, the optimization
stage needs an accurate answer about the amounts of product,
(for a detailed explanation on PLS theory, see ref 39) for PhI
quantification based on GC results was built using 32 samples.
For comparison, the necessary samples to build models A and B
(
39) Wold, S.; Sjostrom, M.; Eriksson, L. Chemom. Intell. Lab. Syst. 2001, 58,
09-130.
1
Analytical Chemistry, Vol. 77, No. 7, April 1, 2005 2233

costing more analysis time. The approach applied here is flexible
and can be tuned to one situation or the other.
∂Ck
mk
mk
∂
)
) -
(9)
K
K
∂mj*k
∂mj*k
2
(
)
(
mk
)
(
mk)
∑
∑
k)1
CONCLUSIONS
k)1
By using the NAS approach for calibration, one can reduce
the minimum number of samples to the number of chemical
components in the system. In the present work, we have looked
at how these few calibration samples should be chosen to obtain
good predictions. Using blank samples (i.e., samples that contain
only interferences and no analyte) facilitates the sequential
addition of new interferences to the model, which fits well to high-
throughput environments. Our simulation results and experimen-
tal data show that the samples used to build the interference space
should be composed of several components mixed in a solvent
where j stands for one of the components except for component
k. The average number used in this study for the variance in the
2
-6
concentration, σ
Derivation of Eq 3. Let wgEr
random error in concentration of component k, and ꢀ
R
, was found to be 7 × 10
be the normal distributed
the variance
.
k
k
of the error in the mass for each component. Including these
errors in eq 2 gives
K
ꢀ
∑
k
(i.e., multicomponent samples). Choosing the right samples
m + ꢀk
ꢀ
k
k)1
k
improves the predictive ability of the model. Also, extra interfer-
ences can systematically be introduced in the model by simply
including additional calibration samples. Very high concentration
errors will of course deteriorate the analysis, and any type of
sample will yield the same results. However, the effect of the
spectral error on the prediction ability of the models is higher
than that of the concentration error. Further studies in our
laboratory will include extending the calibration model to new
situations and developing calibration-free monitoring techniques.
C + wgEr )
) C +
‚ 1 -
k
k
k
K
K
K
(
) (
)
(
m + ꢀ )
mk
mk
∑
k
k
∑
∑
k)1
k)1
k)1
(10)
The error in concentration of component k is then given by
eq 11:
K
Ck
ꢀ
∑
k
ꢀ
k
k)1
APPENDIX
wgEr
k
)
-
(11)
K
K
Derivation of the Variance in the Concentration, σ 2
. The
) is given
are independent. The
R
∑
mk
∑
mk
concentration in the weight fraction of component k (C
k
k)1
k)1
by eq 2. It is assumed that m
1
, m
2
, ..., m
K
2
variance in the concentration, σ
R
, is found by error propagation
Since the concentration is calculated as a weigh fraction,
theory as the weighted sum of the variances of the different
sources of error (masses of the different components) in the
preparation of the sample. These variances are all equal and
K
k)1
∑
C
k
) 1, the sum of all the errors in concentration is
K
K
2
2
2
ꢀ
ꢀ
k
depend only on the analytical scale, σm1 ) σ 2
m
) ..., ) σ :
∑
k
∑
K
K
k)1
k)1
wgEr )
- ( Ck) K
) 0
(12)
∑
k
∑
∂
Ck 2
∂Ck 2
∂Ck 2
∂mK
2
K
σCk2
σm12
2
σmK2
)
k)1
k)1
)
+
σm2 + ..., +
(
∂
m1
)
(∂m
)
[
(
)
∑
mk
∑
k)1
mk
2
k)1
2
2
∂
Ck
∂C
∂Ck
2
k
σ
+
+ ..., +
(
)
(
)
(
)
∂m1
∂m2
∂mK
]
In other words, the error in the solvents’ concentration, for
example, is the sum of the error of all the other components.
Therefore, the errors were included in the simulated samples as
presented in eq 3.
The partial derivatives in the previous equation lead to
∂
Ck
mk
mk
∂
1
)
)
-
(8)
Received for review October 26, 2004. Accepted January
19, 2005.
K
K
K
∂
mk
∂mk
2
(
)
(
mk
)
mk
(
mk)
∑
∑
∑
k)1
k)1
k)1
AC048421C
2234 Analytical Chemistry, Vol. 77, No. 7, April 1, 2005