1. Review
Recent developments in two-dimensional (2D) correlation
spectroscopy
Isao Noda
Department of Materials Science & Engineering, University of Delaware, Newark, DE 19716, USA
1. Introduction
Two-dimensional (2D) correlation spectroscopy [1] is a
versatile analytical technique which has become popular in the
last several decades. It initially started as an obscure data sorting
technique for rheo-optical study of polymer films undergoing
small amplitude repetitive deformation [1a–1c]. With the intro-
duction of the generalized correlation concept in 1993 [1d] and
subsequent development of an efficient numerical algorithm to
compute 2D spectra [1e,1f], this technique has gained remarkable
popularity in a broad area of analytical science as one of the
mainstream spectral data analysis methods [1g].
Fig. 1 shows the general description of 2D correlation analysis
scheme. In 2D correlation spectroscopy, a sample under the
spectroscopic observation is stimulated by applying an external
perturbation, which induces systematic changes in the spectral
intensity of the sample system. The observed spectrum thus
becomes a function not only of the standard spectral variable, such
as infrared wavenumber or Raman shift, but also of other physical
variable representing the effect of the applied perturbation, such as
time, temperature, and composition. A new set of spectra defined
by two independent spectral axes are then generated by applying a
form of cross correlation analysis to the spectral intensity changes
along the perturbation variable.
Notable features of 2D correlation spectroscopy are: simpli-
fication of complex spectra consisting of many overlapped
peaks, enhancement of apparent spectral resolution by spreading
peaks over the second dimension, establishment of unambiguous
assignment through correlation of bands selectively coupled
by various interaction mechanisms, and determination of the
sequence of events represented by the variations of spectral
intensities. A wide scope of fundamental and practical spectro-
scopic research work has been conducted by taking advantages
of unique and advantageous features of 2D correlation spectra
[2]. In this review, some of the key developments in this field are
highlighted.
2. Diverse applications and opportunities
As already implied in the generic scheme depicted in Fig. 1,
there is no intrinsic limitation in 2D correlation analysis for the
selection of specific spectroscopic or analytical probes, nature of
external perturbations applied to the sample, and type and state of
the sample systems to be studied. This flexibility makes 2D
correlation spectroscopy a truly general and extremely versatile
analytical tool. A broad range of applications of 2D correlation
spectroscopy techniques have been well documented by a series of
review articles compiled in the past [2].
For example, a comprehensive review [2h] on various
perturbation methods, analytical probes and specific areas of
applications has recently been compiled. Types of perturbation
Chinese Chemical Letters xxx (2014) xxx–xxx
A R T I C L E I N F O
Article history:
Received 8 August 2014
Received in revised form 15 September 2014
Accepted 25 September 2014
Available online xxx
Keywords:
Two-dimensional correlation spectroscopy
Hetero-correlation
Multiple perturbation correlation
Orthogonal sample design
A B S T R A C T
Recent noteworthy developments in the field of two-dimensional (2D) correlation spectroscopy are
reviewed. 2D correlation spectroscopy has become a very popular tool due to its versatility and relative
ease of use. The technique utilizes a spectroscopic or other analytical probe from a number of selections
for a broad range of sample systems by employing different types of external perturbations to induce
systematic variations in intensities of spectra. Such spectral intensity variations are then converted into
2D spectra by a form of correlation analysis for subsequent interpretation. Many different types of 2D
correlation approaches have been proposed. In particular, 2D hetero-correlation and multiple
perturbation correlation analyses, including orthogonal sample design scheme, are discussed in this
review. Additional references to other important developments in the field of 2D correlation
spectroscopy, such as projection correlation and codistribution analysis, were also provided.
ß 2014 Isao Noda. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.
E-mail address: noda@udel.edu.
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Chinese Chemical Letters
journal homepage: www.elsevier.com/locate/cclet
http://dx.doi.org/10.1016/j.cclet.2014.10.006
1001-8417/ß 2014 Isao Noda. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.

2. methods found in the published literature are amazingly diverse,
encompassing both dynamic and static effects. Flexibility in the
type of analytical probes used in 2D correlation is also noted. Aside
from IR spectroscopy, which is the most commonly used tool in the
field today, many other spectroscopic and analytical probes are
used in 2D correlation analysis. Fields of applications covered by
the literature are also very broad, ranging from fundamental
research to practical applications in a number of physical, chemical
and biological systems.
Dynamic perturbations used in 2D correlation spectroscopy
may be time-dependent physical processes, such as acoustic effect
or pulsed mechanical deformation, sorption, penetration, diffusion
and evaporation of molecules, crystallization, and many other
transient physical phenomena. They also include chemical
reactions, like polymerization and crosslinking, and a number of
biological processes, as well as duration of exposure to various
stimuli, such as radiation dose. Static perturbations are much more
commonly employed today in 2D correlation spectroscopy than
dynamic counterpart. The most popular is the effect of tempera-
ture, which includes many different phenomena, such as
conformational changes of proteins, molecular associations, self-
assembly and gelation, hydrogen bonding interactions, melting,
crystallization, and glass transition, and other transition phenom-
ena, various structural changes, and various temperature-induced
chemical reactions. Aside from temperature, the influence of
concentration, such as pH effect, compositions of solution
mixtures, electrolytes and ionic liquid solutions, dissolved gasses,
blends and composites, and the use of designed concentration
series, are also reported. Other static perturbations often used
include various electro-magnetic effects, mechanical deformation,
pressure and compression, and even spatial distributions.
Analytical probes employed are currently dominated by
infrared (IR), but other probes are also used, such as Raman, near
infrared (NIR), UV–visible, THz and fluorescence, NMR, X-ray
spectroscopy and scattering techniques, and other analytical
methods, like mass spectrometry and chromatography. Combined
use of different analytical probes leads to the powerful technique
of hetero-spectral correlation analysis, such as IR-NIR correlation.
This topic will be separately discussed later. The ever expanding
depth, breadth and versatility of 2D correlation spectroscopy and
its applications all point to the robust and healthy state of the field.
Among the type of applications, polymers are most often
extensively studied, including bio-based and biodegradable
polymers, thermo-responsive polymers, water-soluble polymers,
liquid crystalline polymers, thermosetting polymers, block copo-
lymers and blends, a number of conventional polymers, as well as
polymer matrices incorporating small molecules within. Other
materials studied by 2D correlation spectroscopy include nano-
particles and nano-composites, proteins, and peptides, and other
biomolecules, bio-based materials and actual living cells, food
products, and environmental samples. 2D correlation spectroscopy
is used in medical, physiological, and pharmaceutical applications,
authentication of traditional Chinese medicines, analyses of liquids
and solution mixtures, colloids, interfaces, and electrode surfaces,
inorganic–organic hybrids and ionic species, industrial chemicals,
and various reaction systems. Specific literature citations related to
these areas are found in the recent comprehensive review [2h].
3. Noteworthy developments in 2D correlation spectroscopy
In recent years, a number of unique and different types of 2D
correlation spectroscopy techniques have been introduced. In this
review, several noteworthy forms of 2D correlation spectroscopy
techniques are highlighted. More specifically, hetero-spectral
correlation [3–5] and multiple perturbation correlation techniques
[6], including orthogonal sample design [7], will be discussed in
some detail. Other equally important and interesting forms of 2D
correction spectroscopy techniques are also briefly discussed with
pertinent literature citations [8].
3.1. Hetero-correlation analysis
Hetero-correlation analysis [3–5] is a unique and powerful
feature of generalized 2D correlation spectroscopy with a large
potential of utility for various scientific applications. In hetero-
correlation studies, 2D correlation spectra are obtained from two
distinct sets of spectral data arising from different conditions. The
degree of correlation is then examined between two different
types of spectroscopic data. There are actually three distinct types
of hetero-correlation techniques: hetero-spectral correlation, het-
ero-perturbation correlation, and hetero-sample correlation. Fig. 2
shows the schematic representations of various hetero-correlation
techniques.
By far the most commonly used form of hetero-correlation
analysis is the hetero-spectral correlation [3]. In hetero-spectral
correlation analysis, two distinct spectroscopic probes, such as IR
and Raman, are used. Systematic variations of different spectral
signals are observed for the same sample, or at least very similar
Fig. 1. Schematic representation of generalized 2D correlation spectroscopy.
Complex cross correlation analysis of the variation of spectral intensities induced by
external perturbations generates 2D correlation spectra.
Fig. 2. Three types of 2D hetero-correlation analysis. 2D spectra are generated by
comparing a pair of dynamic spectra arising from different probes (hetero-spectral
correlation), different perturbations (hetero-perturbation or hybrid correlation), or
different samples (hetero-sample correlation).
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3. samples, under the similar perturbation condition for comparison.
One of the earliest known examples of such hetero-spectral
correlation analysis was reported for the combined measurement
of IR dichroism and small-angle X-ray scattering signals of a block
copolymer sample under periodic deformation [3a]. Nowadays,
many other types of hetero-correlation studies are reported. In
contrast, hetero-sample correlation [4] utilizes dynamic spectra
collected from two different samples under a common perturba-
tion by using the same analytical probe. Finally, in hetero-
perturbation correlation [5], a sample is stimulated by two
different perturbation methods, leading to the so-called hybrid
correlation analysis. Some examples of hetero-correlation studies
are discussed below.
Hetero-spectral correlation between mid IR and NIR signals
[3b–3g] offers an interesting opportunity to combine the
advantages of the two vibrational spectroscopy techniques. The
experimental ease of NIR spectroscopy makes this technique a
preferred analytical probe for many practical applications. Mid IR
spectra, on the other hand, have much better resolved spectral
features and consequently well-established band assignments. It is
natural to combine the strength of IR and NIR spectroscopy by
using 2D correlation technique. The first 2D correlation analysis
between IR and NIR spectra was reported by Barton et al. [3b]. Since
then many other IR and NIR hetero-spectral correlation studies
have been reported. Some of the recent reports include diverse
data analyses, such as rehydration process of amylopectin starch
extracted from glutinous rice flour [3c], ethanol content determi-
nation during a fermentation process [3d], monitoring of epoxy
resin curing reaction [3e], and botanical biomass changes under
roasting process [3f].
Other types of spectroscopic probes are also combined with IR
to generate hetero-correlation spectra. For example, IR-Raman
hetero-spectral correlation [3g] to investigate thermal dynamics of
natural killer cell receptor proteins was reported. The possibility of
comparing and relating IR and CD spectra [3h] was also considered
for the hetero-spectral correlation analysis. The correlation
between XPS and IR spectra [3i] was used to study semi-crystalline
copolymers under increasing temperature by taking advantage of
the different sensitivities of the two probes to molecular
environment. 2D hetero-spectral correlation between IR and
UV–visible spectra [3j] was reported for the study of aggregate
formation process of marine mucilage as a function of incubation
period. The correlation between IR and NMR [3k] for free radical
polymerization process was also reported to gain unambiguous
band assignments.
The application of 2D hetero-spectral correlation technique is
not limited to the comparison of molecular spectra. For example,
hetero-correlation between small angle X-ray scattering (SAXS)
and wide-angle X-ray diffraction (WAXD) was reported for non-
isothermal crystallization of hydrogenated polybutadiene with
varying time and temperature [3l] and for the study of multiple-
step isothermal crystallization of a biodegradable polymer
[3m]. Hetero-correlation was applied between charge and mass
[3n] for cyclic voltammetry study. Hetero-chromatographic
correlation [3o] was reported between two detection systems
used in HPLC study of valorization of olive stones employed to
increase sugar content.
Hetero-sample or hetero-system correlation [4] is an interest-
ing variant form of hetero-correlation analysis, where the
existence or lack of correlation is examined among spectral
intensity variations of different samples by using the same
analytical probe and perturbation condition. In certain cases,
explicit constraint imposed by using the common perturbation
conditions is utilized [4a–4c]. Such a constraint makes the
technique distinct from simple covariance [4d], correlation
coefficient [3b], or conventional statistical correlation analysis
[4e] applied for spectra collected from different samples. This
technique encompasses the so-called cross spectral correlation
analysis proposed by Dai and coworkers [4a,4b], which is a clever
use of hetero-sample correlation analysis for time-resolved
emission spectra of transient radicals from different of samples.
Hetero-system correlation was recently applied for the time-
dependent evaporation of ethanol mixed with oleic acid or linoleic
acid [4c].
The concept of hybrid correlation was originally proposed by
Wu et al. [5a] to explore the implicit relationship between two
different perturbation effects influencing the sample. It can be
viewed as a form of more general class of hetero-correlation
technique called hetero-perturbation correlation analysis [5]. In
hetero-perturbation correlation, spectral intensity variations to be
correlated are induced by applying different types of external
perturbations to the same sample. Unlike the multiple perturba-
tion 2D correlation analysis to be discussed later, different
perturbations are applied one perturbation at a time. Hybrid
correlation explores the underlying similarity or differences of the
effect of applied perturbations through correlation analysis.
Recent examples include the hybrid 2D correlation study of
coil-to-globule phase transition of poly(N-isopropylacrylamide)
induced by both temperature and pressure [5b]. In another study,
time evolutions under different pH for the H/D exchange study of
immunoglobulin G were analyzed by hybrid correlation to probe
the flexibility and dynamics of different region of the protein at
different pH levels [5c]. Hybrid correlation was also used for the
study of growth process of a plant pathogen by comparing NMR
spectra obtained with and without phosphonate [5d] and for the
analysis of concentration and temperature effects on solution
mixtures [5e].
3.2. Multiple perturbation 2D correlation
2D correlation analysis is traditionally carried out under a
single perturbation applied to a system of interest. An interesting
possibility arises when more than one type of external perturba-
tions are simultaneously applied to the sample [6,7]. This situation
is different from the case for the previously mentioned hetero-
perturbation correlation study, where different type of perturba-
tion, like temperature and pressure, is applied to the system one
perturbation at a time. Fig. 3 shows the schematic representation
of a multiple perturbation experiment. Here the effect of
perturbation-1 on the response-1 may actually be influenced by
the presence of additional perturbation-2, and vice versa. The
possible existence of the interplay between two perturbation
effects will lead to nonlinear responses of the system, which can be
effectively detected by 2D correlation spectroscopy. This approach
Fig. 3. Multiple perturbation 2D correlation analysis. Two different perturbations
are simultaneously applied to the sample to induce spectral intensity changes
affected by both effects.
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4. also greatly expands the design flexibility and diversity of 2D
correlation analyses.
Shinzawa et al. [6a] studied Raman imaging data for the spatial
distribution of actives in pharmaceutical tablets by 2D correlation.
Instead of a single 2D spectrum, the evolution of a series of 2D
spectra was obtained as a function of processing time spent for
grinding. This work led to the development of multiple 2D
correlation spectra generated under multiple perturbations of
process conditions [6b]. Finely ground microcrystalline cellulose
was observed by ATR IR under different evaporation time, which
changes the water content of the sample, and also under different
grinding time, which changes the morphology, crystallinity, and
consequently the evaporation rate. A new set of formulae for
calculating a number of different types of synchronous 2D spectra
under multiple perturbation condition was proposed.
Multiple 2D correlation analysis of a system under the
simultaneous influence of different perturbations has been further
explored [6c–6e]. Self-assembly of oleic acid under the combined
double perturbation conditions consisting of both pressure and
temperature variations generated three-way dataset [6c]. To
manage the complexity of analysis, so-called partial 2D correlation
was proposed by keeping the influence of one perturbation effect
constant. In the NMR study of a nano-composite material
containing clay particles under multiple perturbation of both
temperature and clay composition, the concept of parallel factor
(PARAFAC) kernel analysis was also introduced [6d]. Multiple
perturbation 2D NIR correlation analysis was recently reported for
pressure-induced variations of cellulose affecting the packing and
crystallinity along with the effect of compositional changes by
water absorption [6e].
3.3. Orthogonal sample design
Orthogonal sample design (OSD) is an intriguing form of
multiple perturbation correlation analysis [7]. The idea was
originally forwarded by Xu of Peking University [7a–7c]. In this
scheme, a series of samples with carefully designed concentration
profiles are prepared to maximize the pertinent information
content of the resulting 2D correlation spectra. OSD utilizes a set of
mixture samples, such that the dynamic concentration variations
of two components are designed to become mathematically
orthogonal to each other. Such a sample design effectively
eliminates interfering cross peaks due exclusively to the linear
dependence on concentration variation, i.e., the Beer–Lambert law
dependence.
Since two independent concentration variations (e.g., of solutes
P and Q in a solution) are simultaneously applied as perturbations
to the system, OSD may be viewed as a form of multiple
perturbation 2D correlation spectroscopy technique. In the scheme
of Fig. 3, perturbation-1 and perturbation-2 are now designed to be
orthogonal to each other. If response-1 (spectral band intensity
change for species P) is proportional to perturbation-1 (concentra-
tion variation of species P) according to the Beer–Lambert law, and
vice versa for species Q in terms of perturbation-2 and response-2,
then the response-1 and response-2 must also become orthogonal
to each other. But do they? If there is specific intermolecular
interaction between species P and Q, their concentrations will be
modified from the initial state, and their spectral intensity
responses may no longer be strictly orthogonal.
Fig. 4 shows the graphic representation showing how an
OSD scheme with even a very simple concentration series
design can be used for the detection of subtle intermolecular
interaction. In this example, only four solution mixture samples
containing the two solutes of interest are prepared (Fig. 4a). The
concentration of solute P varies in a pattern similar to a sine
function around a fixed value along the sequence of this
solution mixture series. Meanwhile, that of the other solute Q is
designed to follow the pattern of a cosine function. Since sine
and cosine signals are mathematically orthogonal to each other,
the correlation of the spectral intensities of P and Q along the
mixture series should become zero, if the intensities are strictly
proportional to the original solute concentrations. No cross
peak should be observed in that case in synchronous 2D
correlation spectrum.
On the other hand, if there is any specific intermolecular
interaction which can modify the state of the solutes, e.g., by
association compound formation, the actual concentrations of P
and Q after mixing are no longer the same as the initial
concentrations without any interaction. In that case, the actual
solute concentrations of P and Q in the mixture are no longer
orthogonal to each other, and cross peak will be generated in the
synchronous 2D spectrum as shown in Fig. 4b. In other words, OSD
is a highly sensitive detection method for very subtle modification
of the initial concentrations of two solutes caused by specific
intermolecular interactions. Many other forms of concentration
series have been designed to suppress the appearance of
uninformative cross peaks from both synchronous and asynchro-
nous spectra.
In practice, OSD was used first for simulated and experimental
concentration-dependent UV–visible spectra of mixed solutions of
NdCl3 and PrCl3 [7a]. Portion of spectra proportional to the solute
content is effectively removed by the application of OSD scheme to
reveal the apparent deviation from the Beer–Lambert law caused
by the intermolecular interaction. Similarly, the application of OSD
to the 2D UV and UV-IR hetero-spectral correlation was reported to
detect the interaction between lanthanide (III) ions and organic
Fig. 4. (a) Orthogonal sample design (OSD) concentration series with the initial solute P concentration (before mixing with Q) varying as a sine function, while the solute Q as
cosine function. (b) Presence of cross peaks between bands for solutes P and Q indicates that spectral intensity variations for P and Q are no longer orthogonal to each other
due to intermolecular interactions.
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5. ligands [7b]. This specific work was the basis for the example used
in Fig. 4. The original OSD was modified [7c] to address the
possibility of fortuitous cancellation of cross peaks, when there is
real intermolecular interaction. The modified OSD takes advan-
tages of the effect of measurement under different path lengths to
provide unambiguous determination of an interaction. 2D UV–
visible spectra of NdCl3/PrCl3 aqueous solution mixtures show no
cross peaks under OSD regardless of path length change, indicating
the lack of interaction.
In the recent years, the concept of OSD has been further refined
to address some of the limitations of the original OSD scheme. In
double orthogonal sample design (DOSD) [7d], concentrations of
two components are set such that one series is not only simply
orthogonal to but also strictly quadrature to (i.e., 90 degrees out of
phase with) the other concentration series. In their first DOSD
study, IR and UV–visible hetero-spectral correlation of benzene/I2/
CCl4 system was analyzed, and various peak cluster patterns were
identified by an extensive simulation study reflecting the effects of
frequency shift and band width changes.
Asynchronous orthogonal sample design (AOSD) further
extends the OSD analysis to 2D asynchronous spectrum [7e].
Concentration series of butanone and dimethyl formamide in CCl4
were designed to eliminate peaks due to the uninformative effect
not related to specific intermolecular interactions. Finally, double
asynchronous orthogonal sample design (DAOSD) [7f] based on
another set of concentration series eliminate interfering peaks and
identify specific molecular interactions. It was used for 2D UV–
visible and 2D IR study of iodine-benzene/CCl4 system. AOSD
analysis based on concentration series of DMF and butanone in
CCl4 was used [7g] to find that the sequence of concentration with
four or more samples dramatically affects asynchronous spectra.
The potential of AOSD was extended in their study of acetone–
butanone interactions in CCl4 with varying concentration [7h]. A
modified reference spectrum, which was derived from average of
virtual mixture without intermolecular interactions, was used to
improve the signal-to-noise ratio and to make the detection of
weak signals possible.
3.4. Other noteworthy developments
Some of the other important new concepts [8] in the field of 2D
correlation spectroscopy are described in the recent comprehen-
sive surveys [2f,2g], so they are only briefly discussed here.
Interested readers are referred to the original publications cited
here for additional information.
Projection 2D correlation [8a] is a technique to attenuate or
amplify particular features of 2D spectra by a vector projection
operation to simplify their interpretation. Concatenated 2D
correlation [8b,8c] is a sensitive tool to detect deviation from
reversible process. Moving window analyses [8d–8f] provide the
visual representation of spectral intensity variation patterns along
the perturbation axis. They are especially useful in choosing the
region of interest along the perturbation axis for the subsequent
detailed 2D correlation analysis. Determination of sequential order
of spectral intensity variations is an important topic in the field of
2D correlation spectroscopy [8g]. 2D codistribution analysis [8h] is
a newly introduced tool useful for determining the sequential
order of presence of species in a dynamic reaction process.
Sample-sample correlation [8i] brings out the similarity of
spectra at different perturbation points. 2D correlation based on
principal component analysis (PCA) combined with eigenvalue
manipulation transformation [8j] is a powerful technique for noise
reduction and feature enhancement. Peak position shift effect in
2D correlation analysis was investigated [8g,8f]. Non-uniform
increment sampling [8k] is sometimes necessary but rather
straightforward. Pareto scaling [8l] is a useful technique to
enhance subtle feature of 2D correlation spectra obscured by
strong signals. Quadrature orthogonal signal correction [8m]
focuses on the analysis on signals pertinent only to the
perturbation variable. Coherence and global phase angles
[8n,8o] are semi-quantitative metrics generated from 2D correla-
tion analysis. Kernel analysis [8p] represents 2D correlation
spectra in terms of a compact matrix consisting of a few
parameters.
4. Concluding remarks
2D correlation spectroscopy has become a very popular tool in
the field of analytical science due to its versatility and relative ease
of use. The technique can be utilized with a number of
spectroscopic and other analytical probes for a very broad range
of sample systems by employing different types of external
perturbations to induce spectral variations. In the recent years, a
number of new types of 2D correlation spectroscopy techniques
have been introduced. In this review, 2D hetero-correlation and
multiple perturbation correlation analyses, including orthogonal
sample design scheme, were specifically discussed in detail.
References to other important developments in the field of 2D
correlation spectroscopy, such as projection correlation and
codistribution analysis, were also provided.
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I. Noda / Chinese Chemical Letters xxx (2014) xxx–xxx6
G Model
CCLET-3112; No. of Pages 6
Please cite this article in press as: I. Noda, Recent developments in two-dimensional (2D) correlation spectroscopy, Chin. Chem. Lett.
(2014), http://dx.doi.org/10.1016/j.cclet.2014.10.006