Asynchronous Orthogonal Sample Design Scheme for TwoDimensional Correlation Spectroscopy (2D-COS)...

Asynchronous Orthogonal Sample Design Scheme for Two-Dimensional Correlation Spectroscopy (2D-COS) and ItsApplication in Probing Intermolecular Interactions fromOverlapping Infrared (IR) Bands

XIAOPEI LI, QINGHUA PAN, JING CHEN, SHAOXUAN LIU, ANQI HE, CUIGE LIU,YONGJU WEI,* KUN HUANG, LIMIN YANG, JUAN FENG, YING ZHAO, YIZHUANG XU,*YUKIHIRO OZAKI, ISAO NODA, and JINGUANG WUCollege of Chemistry and Material Science, Hebei Normal University, Shijiazhuang, 050016, P.R. China (X.L., C.L., Y.W.); Beijing NationalLaboratory for Molecular Sciences, State Key Laboratory for Rare Earth Materials Chemistry and Applications, College of Chemistry and

Molecular Engineering, Peking University, Beijing 100871, P.R. China (X.L., J.C., S.L., A.H., Y.X., J.W.); Institute of Process Engineering,

Chinese Academy of Sciences, 100190, P.R. China (K.H.); State Key Laboratory of Nuclear Physics and Technology, Institute of Heavy Ion

Physics, School of Physics, Peking University, Beijing 100871, P.R. China (L.Y.); School of Life Science and Technology, University of ElectronicScience and Technology of China, Chengdu, 610054, P.R. China (J.F.); Institute of Chemistry, Chinese Academy of Sciences, 100190, P.R. China

(Y.Z.); Department of Chemistry, School of Science and Technology, Kwansei-Gakuin University, Sanda 669-1337, Japan (Y.O.); and The

Procter & Gamble Company, West Chester, Ohio 45069 (I.N.)

This paper introduces a new approach to analysis of spectra called

asynchronous orthogonal sample design (AOSD). Specifically designed

concentration series are selected according to mathematical analysis of

orthogonal vectors. Based on the AOSD approach, the interfering portion

of the spectra arising strictly from the concentration effect can be

completely removed from the asynchronous spectra. Thus, two-dimen-

sional (2D) asynchronous spectra can be used as an effective tool to

characterize intermolecular interactions that lead to apparent deviations

from the Beer–Lambert law, even if the characteristic peaks of two

compounds are substantially overlapped. A model solution with two

solutes is used to investigate the behavior of the 2D asynchronous spectra

under different extents of overlap of the characteristic peaks. Simulation

results demonstrate that the resulting spectral patterns can reflect subtle

spectral variations in bandwidths, peak positions, and absorptivities

brought about by intermolecular interaction, which are barely visualized

in the conventional one-dimensional (1D) spectra. Intermolecular

interactions between butanone and dimethyl formamide (DMF) in CCl4solutions were investigated using the proposed AOSD approach to prove

the applicability of the AOSD method in real chemical systems.

Index Headings: Two-dimensional correlation spectroscopy; 2D-COS;

Intermolecular interaction; Asynchronous orthogonal sample design;

AOSD; Orthogonality.

INTRODUCTION

Intermolecular interactions have been the focus of extensiveresearch as they play an important role in many chemical,physical, and biological processes,1–5 such as assembly ofsupra-molecular architectures, molecular recognition, andmolecular catalysis.6–10 Various intermolecular interactions,such as dipole–dipole interaction, albeit quite strong, caninduce only subtle spectral changes, which are often buriedwithin complex spectral profiles. Therefore, determining howto evaluate such interactions effectively is still a bafflingquestion.

Two-dimensional (2D) spectroscopy, first proposed by Noda

in the 1980s,11 has been further developed12–20 and has gainedconsiderable popularity in various application fields, includingbiomolecules,21–25 polymers,26–28 food and agricultural prod-ucts,29–31 intermolecular interaction,32,33 inorganic materi-als,34,35 and many other chemical systems.36–39 Defined bytwo independent spectral axes, the 2D correlation spectrum isgenerated by applying correlation analysis to the dynamicfluctuations of spectral signals caused by external perturba-tions, e.g., electrical, thermal, magnetic, chemical, acoustic, ormechanical stimulations. One notable feature of 2D correlationspectroscopy (2D-COS) is that the cross-peaks can potentiallybe used to characterize intermolecular interactions, so theadvent of 2D-COS brings about a new avenue for theinvestigation of intermolecular interactions.

Although cross-peaks of the 2D correlation spectra can beused to identify intermolecular interactions, interfering cross-peaks due to other sources of correlation sometimes preventobtaining a reliable conclusion. We proposed a method calledthe ‘‘orthogonal sample design (OSD) scheme’’ to solve thisproblem.40 As a result, deviations from the Beer–Lambert lawcaused by intermolecular interaction between two solutes in thesame solution can be clearly visualized by the development ofspecific cross-peaks in the corresponding 2D synchronousspectra. The OSD approach has proved effective in character-izing intermolecular interactions in a variety of chemicalsystems. Moreover, the spectral patterns of the cross-peaksgenerated by the OSD approach can even reveal subtlevariations of peak position, bandwidth, and absorption of thecharacteristic peaks caused by intermolecular interactions.41

However, the OSD approach still suffers from the followingproblem: interfering parts of the 2D synchronous spectracannot be completely removed when the characteristic peaks ofthe solutes are substantially overlapped.

Recently, we developed a double orthogonal sample design(DOSD) method that can remove interfering cross-peaks fromboth synchronous and asynchronous spectra simultaneously.42

Thus, intermolecular interactions can be characterized by thecross-peaks in both synchronous and asynchronous spectra.

Based on the above results, and by taking advantage of themathematical properties of the Hilbert–Noda transformation

Received 7 February 2011; accepted 2 May 2011.

* Authors to whom correspondence should be sent. E-mail: [email protected], [email protected].

DOI: 10.1366/11-06250

Volume 65, Number 8, 2011 APPLIED SPECTROSCOPY 9010003-7028/11/6508-0901$2.00/0

� 2011 Society for Applied Spectroscopy

matrix, we propose a new approach called asynchronousorthogonal sample design (AOSD) in this paper. The 2Dasynchronous spectra generated by the AOSD approach can beused to characterize the apparent deviation from the Beer–Lambert law arising from intermolecular interactions, whichcan be still valid even if the characteristic peaks aresubstantially overlapped.

THEORY

The chemical system considered here is a solution with twosolutes, P and Q, whose characteristic peaks are at spectralcoordinates x and y. The spectral function of P and Q are fP(m)and fQ(m), respectively, where m is the spectral variable. Forsimplicity, we assume that the solvent has no contribution inthe spectral region studied here. Variable concentrations areused as the external perturbation to construct the 2D correlationspectra, and the initial concentrations of P and Q in a series of

solutions (i ¼1, 2, . . ., n) are denoted as

~CP ¼ C1ðinitÞP ;C

2ðinitÞP ; . . . C

nðinitÞP

n oð1aÞ

~CQ ¼ C1ðinitÞQ ;C

2ðinitÞQ ; . . . C

nðinitÞQ

n oð1bÞ

Under intermolecular interactions between P and Q, part of Pmay convert into U, whose spectral function is fU(m), and partof Q may convert into V, whose spectral function is fV(m). Thisconversion could be specified in terms of the followingequilibrium relationship, and the strength of the intermolecularinteraction can be characterized by the equilibrium constant K.

Pþ QffK

Uþ V ð2Þ

For the ith solution, the concentrations of equilibrium of P,Q, U, and V are C

iðeqÞP , C

iðeqÞQ , C

iðeqÞU , and C

iðeqÞV . The path length

of each solution is set as 1 for convenience. Therefore, thespectral function of the ith solution should be:

AiðmÞ ¼ CiðeqÞP fPðmÞ þ C

iðeqÞQ fQðmÞ þ C

iðeqÞU fUðmÞ þ C

iðeqÞV fVðmÞ

ð3Þ

Since

CiðeqÞP ¼ C

iðinitÞP � C

iðeqÞU ð4aÞ

CiðeqÞQ ¼ C

iðinitÞQ � C

iðeqÞV ð4bÞ

then Eq. 3 can also be expressed as

AiðmÞ ¼ ðCiðinitÞP � C

iðeqÞU ÞfPðmÞ þ ðCiðinitÞ

Q � CiðeqÞV ÞfQðmÞ

þ CiðeqÞU fUðmÞ þ C

iðeqÞV fVðmÞ ð5Þ

or

AiðmÞ ¼ CiðinitÞP fPðmÞ þ C

iðinitÞQ fQðmÞ þ C

iðeqÞU ½ fUðmÞ � fPðmÞ�

þ CiðeqÞV ½ fVðmÞ � fQðmÞ� ð6Þ

After removing the average value over all solution samples at

FIG. 1. 1D spectra of the first solution in Table III of the model system whenXP is set to be 280: (a) mixture of P, Q, U, and V when only bandwidthvariations are allowed due to intermolecular interaction (WU ¼ 18, WV ¼ 22);(b) no intermolecular interaction between P and Q achieved by setting theequilibrium constant K to zero.

FIG. 2. 2D asynchronous spectrum when XP is set to be 280: (a) only bandwidth variations are allowed to change due to intermolecular interaction (WU¼ 18, WV¼22); (b) there is no intermolecular interaction between P and Q.

902 Volume 65, Number 8, 2011

each wavelength, dynamic intensity can be obtained as Eq. 7:

AiðmÞ ¼ C

iPfPðmÞ þ C

iQ fQðmÞ

þ CiU½ fUðmÞ � fPðmÞ�þC

iV½ fVðmÞ � fQðmÞ� ð7Þ

where CP, CQ, CU, and CV are the dynamic concentrations of P,Q, U, and V.

CiP ¼ C

iðinitÞP � C

initðavÞP ð8aÞ

CiU ¼ C

iðinitÞU � C

initðavÞU ð8bÞ

CiQ ¼ C

iðinitÞQ � C

initðavÞQ ð8cÞ

CiV ¼ C

iðinitÞV � C

initðavÞV ð8dÞ

The corresponding synchronous and asynchronous spectrumcan be calculated according to Eqs. 9 and 10:13

Uðx; yÞ ¼ 1

n� 1~A

T

ðxÞ~AðyÞ ð9Þ

Wðx; yÞ ¼ 1

n� 1~A

T

ðxÞN~AðyÞ ð10Þ

where ‘‘T’’ stands for transposition, n is the number of solutionsused to construct the 2D asynchronous spectrum, and N is the

Hilbert–Noda transformation matrix, given by Eq. 11:

Njk ¼0 if: j ¼ k1=pðk � jÞ otherwise

�ð11Þ

First we discuss a chemical system in which the character-istic peaks of P at x and Q at y do not overlap. That is to say,the characteristic peaks of Q and V have no contribution to thecharacteristic peaks of P and U at x and vice versa. Therefore,A

iðxÞ and AiðyÞ can be simplified as Eqs. 12a and 12b.

AiðxÞ ¼ C

iPfPðxÞ þ C

iU½ fUðxÞ � fPðxÞ� ð12aÞ

AiðyÞ ¼ C

iQ fQðyÞ þ C

iV½ fVðxÞ � fQðxÞ� ð12bÞ

Because there are two items in Eqs. 12a and 12b, aftercombining Eqs. 12a and 12b with Eq. 9, the 2D asynchronouscorrelation spectrum contains four terms.

Uðx; yÞ ¼X4

i¼1

Siðx; yÞ ð13Þ

where the expressions of S1, S2, S3, and S4 are given in theAppendix.

When there is no intermolecular interaction between P and Q

to cause the conversion reaction (Eq. 2), ~CU, ~CV, ~CU, and ~CV

are all expected to become zero. Thus, S2, S3, and S4 becomezero. Because we desire cross-peaks in the 2D synchronousspectra to be strictly associated with intermolecular interaction,

FIG. 3. 1D spectrum of the first solution in Table III of the model system: idxovp is set to be (a) 7, (b) 4, (c) 2, and (d) 1.

APPLIED SPECTROSCOPY 903

U(x,y) should be zero when no intermolecular interaction

occurs between P and Q. Thus, S1 should also be zero. S1(x,y)

can be removed if special concentration series of P and Q are

adopted, and the resulting dynamic concentration vectors of P

and Q are orthogonal to each other:

~CP � ~CQ ¼ 0 ð14Þ

which is the basic idea of the orthogonal sample design (OSD)

scheme described in our previous paper.21

When the characteristic peaks of P at x and Q at y are

partially overlapped, the contributions of P, Q, U, and V

coexist at both x and y in each spectrum. Therefore, AiðxÞ and

AiðyÞ should be expressed as Eqs.15a and 15b:

AiðxÞ ¼ C

iPfPðxÞ þ C

iQ fQðxÞ þ C

iU½ fUðxÞ � fPðxÞ�

þ CiV½ fVðxÞ � fQðxÞ� ð15aÞ

AiðyÞ ¼ C

iPfPðyÞ þ C

iQ fVðyÞ þ C

iU½ fUðyÞ � fPðyÞ�

þ CiV½ fVðyÞ � fQðyÞ� ð15bÞ

Because there are four items in Eqs. 15a and 15b, aftercombining Eqs. 15a and 15b with Eq. 9, the intensities of thecross-peak at (x,y) in the corresponding synchronous spectrumcontain sixteen terms and can be expressed as in Eq. 16:

Uðx; yÞ ¼X16

i¼1

Wiðx; yÞ ð16Þ

The expressions of W1 through W16 are given in theAppendix. The assumed condition of no intermolecularinteractions affecting the population of P and Q makes CU

and CV zero, and thus W5 through W16 all take the value ofzero. Because the desired U(x,y) should be zero when nointermolecular interaction occurs between P and Q, thesummation of W1(x,y), W2(x,y), W3(x,y), and W4(x,y) should

FIG. 4. 2D asynchronous spectra of the model system obtained as a consequence of peak position variations when idxovp is set to be 7.


also be zero. W3 and W4 can be removed by using the OSDapproach. However, W1(x,y) and W2(x,y) are quadratic termsand can be zero only when the dynamic concentrations of P andQ in every solution are zero, which goes against our desiredexperimental design. Thus, interfering parts cannot becompletely removed by using the original OSD approachwhen the characteristic peaks of P and Q are partiallyoverlapped. Mathematically speaking, it is possible to find aspecial concentration series to make the summation of W1(x,y),W2(x,y), W3(x,y), and W4(x,y) zero; however, this can berealized only if fP(m) and fQ(m) are known in advance, which isnot feasible in many cases.

Based on the above analysis, it is not feasible to use the 2Dsynchronous spectra to detect intermolecular interactions in astraightforward manner when the characteristic peaks of P andQ are partially overlapped. However, the above issue can bereadily resolved if we use the cross-peaks from the 2Dasynchronous spectrum to probe the intermolecular interaction.The intensity of the cross-peaks in 2D asynchronous spectra

can be calculated if we combine Eq. 10 with Eqs. 15a and 15btogether. Because there are four items in Eqs. 15a and 15b, thecorresponding asynchronous spectrum [W(x,y)] contains six-teen terms and can be expressed as in Eq. 17.

Wðx; yÞ ¼X16

i¼1

Riðx; yÞ ð17Þ

The expressions of R1 to R16 are given in the Appendix.R1(x,y), R2(x,y), R3(x,y), and R4(x,y) are interference parts andhave to be removed. However, removal of the four interferenceterms is much easier in the 2D asynchronous spectra.

The Hilbert–Noda transformation matrix possesses thefollowing two basic properties as shown in Eqs. 18 and 19:

~ATN~A ¼ 0 ð18Þ

~ATN~B ¼ �~BT

N~A ð19Þ



where A and B are any n-dimensional vectors.Based on Eq. 18, R1(x,y) and R2(x,y) are zero and can be

naturally removed.

R1ðx; yÞ ¼ f1ðxÞf1ðyÞ~CT

PN~CP ¼ 0 ð20aÞ

R2ðx; yÞ ¼ f2ðxÞf2ðyÞ~CT

QN~CQ ¼ 0 ð20bÞ

Based on Eq. 19, R3(x,y) and R4(x,y) are opposite and can becompletely removed when

~CT

PN~CQ ¼ �~CT

QN~CP ¼ 0 ð21Þ

According to Eqs. 8a and 8b, another requirement for selectingsuitable CP and CQ is

Xm

i¼1

CiP ¼ 0 ð22aÞ

Xm

i¼1

CiQ ¼ 0 ð22bÞ

Having removed R1, R2, R3, and R4, the intensity of the

cross-peak in the asynchronous spectrum is a function of CU

and CV, the dynamic concentration of the components of the

intermolecular interaction products. Therefore, the cross-peak

does reflect intermolecular interactions.

Based upon the above analysis, the interference portion in

the 2D asynchronous spectra can be completely removed by

selecting suitable concentration series of P and Q that satisfy

Eqs. 21, 22a, and 22b. We call this new approach the

asynchronous orthogonal sample design (AOSD) scheme.

It is not difficult to find suitable dynamic concentration

series of P and Q that satisfy Eqs. 21 and 22. For example, we

can select the concentration series P and Q as in Eq. 23:

mCiðinitÞP þ nC

iðinitÞQ ¼ H ð23Þ



where m, n, and H are constants and are set arbitrarily.

Equation 23 can also be expressed by Eq. 24:

CiðinitÞQ ¼ H=n� mC

iðinitÞP =n ð24Þ

In this case, the dynamic concentration series of Q are:

~CQ ¼ �m=nC1P;�m=nC2

P; . . . ;�m=nCiP

n oð25Þ

Therefore,

~CT

PN~CQ ¼ ~CT

PNð�m=n~CPÞ¼ �m=n~CT

PN~CP ¼ 0 ð26Þ

The AOSD provides new possibilities to study intermolec-

ular interactions in many chemical systems, where the

characteristic peaks are overlapped. In the following part, we

first use simulation to study the basic property of 2D

asynchronous spectra generated by the AOSD approach. We

then apply this approach to study dipole–dipole interactions

between butanone and DMF.

EXPERIMENTAL

Materials. Butanone, dimethyl formamide (DMF), and

carbon tetrachloride were analytical reagent grade and

purchased from Beijing Chemical Company.

Instrument. Fourier transform infrared (FT-IR) spectra were

collected on a Thermo-Fischer Nicolet iN10 MX spectrometer

using a BaF2 cell with a fixed spacing (100 lm). All the spectra

were recorded at a resolution of 4 cm�1 and 32 scans were co-

added.

Programming. In the studies of the model system, the 1D

spectra, which are used as input files to construct 2D

asynchronous spectra, were generated by a program written



in our lab using Turbo C 2.0. The 2D asynchronous spectra inthe simulation study and the real chemical system were allcalculated based on the algorithm by Noda using the softwareof MATLAB.

RESULTS AND DISCUSSION

Simulated Chemical System. A solution containing twosolutes P and Q was studied as a model system. Whenintermolecular interactions between P and Q occur in thesolution, we assume that part of P and Q convert into a new setof chemical species U and V, respectively, which can beexpressed by Eq. 2. Here the equilibrium constant K isarbitrarily set as 0.01.

Each trace of the simulated 1D spectrum is thus thesummation of the peak function of each chemical species,which is represented by a Gaussian function, as shown in Eq.27:

GiðmÞ ¼X

j

ejLCije�ln2

ðm�xj Þ2

w2j ð27Þ

where i corresponds to the index of the solution and j is theindex of the chemical species, m is the spectral variable, and ej,xj, and wj are the molar absorptivity, peak position, andbandwidth (half width at half-height, HWHH) of thecharacteristic band of the jth chemical species, respectively.The path length L is set as 1 for convenience in this paper, andCi

j is the equilibrium concentration of the jth chemical speciesfor the ith solution, which can be calculated according to theequilibrium constant.

Validity of the Asynchronous Orthogonal Sample DesignApproach. Herein we use the model system described above toverify the validity of the AOSD approach. All the spectralfeatures of the characteristic bands of P and Q are listed inTable I. The concentration series shown in Table II was used to

FIG. 8. 2D asynchronous spectra of the model system obtained as a consequence of variations of bandwidth when idxovp is set to be 7.


construct the 2D synchronous spectra, which meet the

requirements of the OSD approach. We assume that there is

no intermolecular interaction between P and Q by setting the

equilibrium constant K as zero. When the characteristic peaks

of P and Q are not overlapped (XP is set to be 200), the

intensity of the cross-peak at (200, 350) is zero, and when the

characteristic peaks of P and Q are partially overlapped (XP is

set to be 280), the intensity at (280, 350) is 2.8085 3 10�4,

which is comparable with that caused by intermolecular

interactions. Thus, the 2D synchronous spectra based on the

OSD approach are not reliable to judge whether intermolecular

interaction occurs or not when the characteristic peaks ofsolutes are partially overlapped. However, the intensity at (280,350) in the 2D asynchronous spectrum is zero when theconcentration series is set as given in Table III, which meets therequirement of the AOSD approach. The above resultsdemonstrate that the AOSD approach can remove interferingparts from the asynchronous spectra successfully.

Furthermore, the 2D asynchronous correlation spectra canalso reflect subtle changes that are hardly observable in the 1D


TABLE I. Spectral variables of species P and Q in the model system.

Spectral variable Peak position (cm�1) Bandwidth (cm�1) Absorptivity

P XP 20 1.0Q 350 20 1.0

TABLE II. Initial concentrations of the chemical species P and Q in themodel system, which meet the requirement of the OSD approach.

Index of the solutions CP (mL/mL) CQ (mL/mL)

1 5.00 4.002 4.00 5.003 5.00 6.004 6.00 5.00


spectra directly. For example, when the bandwidths of P and Qare changed due to intermolecular interaction, only a smallfraction of P converts into U, and the characteristic peak of U iscompletely buried in the corresponding peak of P. Thus, theresultant spectrum of the mixture of P and U (Fig. 1a) looksalmost the same as the spectra of pure P (Fig. 1b). Similarproblems occur between Q and V. However, the cross-peaks inthe 2D asynchronous spectra generated by using the AOSDapproach manage to identify the existence of U and V caused

by the intermolecular interactions (Figs. 2a and 2b). That is tosay, the AOSD approach provides a good opportunity to studysubtle spectral variation caused by intermolecular interactionswhen the characteristic peaks of P and Q are partiallyoverlapped.

Basic Spectral Patterns in the Asynchronous Spectra.Here we examine the behaviors of the cross peaks in the 2Dasynchronous spectra generated by using the AOSD approachunder different extents of overlap of the characteristic peaks ofP and Q. We define a parameter (idxovp) to characterize theextent of band overlapping as shown in Eq. 28:

idxovp ¼XQ � XP

ðWQ þWPÞ=2ð28Þ

As idxovp is set as different values (idxovp ¼ 7, 4, 2, or 1), thecorresponding 1D spectra of the first solution in Table III areillustrated in Figs. 3a, 3b, 3c, and 3d. When idxovp is 7, there isalmost no band overlapping. When idxovp is set to be 4, slight


TABLE III. Initial concentrations of the chemical species P and Q in themodel system, which meet the requirement of the AOSD approach.

Index of the solutions CP (mL/mL) CQ (mL/mL)

1 2.40 3.002 1.60 2.203 0.80 1.404 0.00 0.60


band overlapping occurs between the characteristic peaks of P

and Q. If idxovp is 2, severe band overlapping between the two

peaks can be observed. When idxovp reaches 1, the two peaks

merge into one peak.

Spectral variations in characteristic peaks caused by

intermolecular interaction can be manifested as changes in

bandwidth, peak position, and absorptivity. First, we assume

only peak positions change due to intermolecular interaction,

and all the spectral variables for P, Q, U, and V are summarized

in Table IV. When idxovp is set as different values (idxovp¼ 7,

4, 2, or 1), the corresponding asynchronous correlation spectra

are summarized in Figs. 4, 5, 6, and 7. Second, we examine the

behaviors of the cross-peaks in the 2D asynchronous spectra

when only the bandwidths are changeable. The spectral

variables for P, Q, U, and V are summarized in Table V.

Figures 8, 9, 10, and 11 are the 2D asynchronous spectra


TABLE IV. Spectral variables of the chemical species P, Q, U, and V inthe model system where the peak positions of U and V are variable.a


P XP 20 1.0Q 350 20 1.0U XU 20 1.0V XV 20 1.0

a DXP¼ XU� XP, DXQ¼ XV� XQ.

TABLE V. Spectral variables of the chemical species P, Q, U, and V inthe model system where the bandwidths of U and V are varied.a


P XP 20 1.0Q 350 20 1.0U UP WU 1.0V 350 WV 1.0

a DWP ¼WP � WU, DWQ ¼WQ� WV.


corresponding to different values of idxovp (idxovp¼ 7, 4, 2, or

1). Additionally, only the absorptivities of U and V are allowed

to be changed and the spectral variables for P, Q, U, and V are

summarized in Table VI. The 2D asynchronous spectra

calculated for different values of idxovp (idxovp ¼ 7, 4, 2, or

1) are listed in Figs. 12, 13, 14, and 15.

When only peak positions are changeable, the variation of

the peak positions of P, Q, U, and V can be classified into nine

cases. A one-to-one correspondence relationship can beestablished between the spectral patterns in the asynchronousspectra and the type of variation of the peak positions of U andV when the value of idxovp is set to be 7 and 4 (Figs. 4 and 5).With the decreasing of idxovp, the adjacent cross-peaks mergeinto broad peaks if they have the same sign. If the adjacentpeaks have the opposite sign, the intensity of the correspondingoverlapping peaks will decrease. In some cases, overlappingpeaks even vanish from the 2D asynchronous spectrum (Figs. 6and 7). Nevertheless, even if the characteristic peaks of P and Qare severely overlapped (idxovp is set to be 1), we can stilldetect intermolecular interaction, and partial information of thevariation in peak positions can be obtained through the 2Dasynchronous spectra. In contrast, no cross-peaks appear in the2D asynchronous spectra when there are no intermolecularinteractions (Figs. 4a, 5a, 6a, and 7a). Similar results areobtained when only bandwidths change. Different from theabove results, the patterns of the cross-peaks are simple whenonly absorptivities are variable. As the value of idxovp

FIG. 12. 2D asynchronous spectra of the model system obtained as a consequence of absorptivity variations when idxovp is set to be 7.

TABLE VI. Spectral variables of the chemical species P, Q, U, and V inthe model system where the absorptivities of U and V are varied.a


P XP 20 1.0Q 350 20 1.0U XU 20 eU

V 350 20 eV

a DeP ¼ eU � eP, DeQ ¼ eV � eQ.


decreases, the adjacent peaks are just gradually approaching.However, the asynchronous correlation spectra caused by thechanges of absorptivity can also reflect intermolecularinteraction when the characteristic peaks are completelyoverlapped.

Application of the AOSD Method in a Real ChemicalSystem. We select butanone/DMF/carbon tetrachloride to testwhether the AOSD method is applicable for real chemicalsystems. Since butanone possesses a carbonyl group and DMFpossesses an amide group, dipole–dipole interactions areexpected to exist between the carbonyl group and amide group.

Dimethyl formamide and butanone can be characterizedusing the amide I band at 1686 cm�1 and the carbonyl band at1721 cm�1 in the FT-IR spectra, respectively. The selectedconcentration series of DMF and butanone are listed in TableVII, which satisfy Eq. 29:

CiðinitÞBUT � 4C

iðinitÞDMF ¼ 0:6 ð29Þ

First, we must consider that the interaction between solventand solute may also lead to interfering cross-peaks in the 2Dasynchronous spectra. Therefore, suitable concentration rangeswithin which the absorptions of the solutes satisfy the Beer–Lambert law are determined. Good linearity is observedbetween absorbance and concentrations when either DMF orbutanone alone is dissolved in carbon tetrachloride (see theSupplemental Material, available online), thereby excluding the


TABLE VII. Four solutions in which the initial concentrations of DMFand butanone satisfy the required condition for the AOSD scheme.

Index of the solutions CDMF (mL/100 mL) CBUT (mL/100 mL)

1 0.60 3.002 0.40 2.203 0.20 1.404 0.00 0.60


possibility that the cross-peaks are caused by solute–solventinteractions.

Fourier transform infrared solution spectra of DMF/butanonemixtures and their corresponding 2D asynchronous spectra areshown in Figs. 16 and 17, respectively. The carbonyl band ofbutanone and the amide I band of DMF are partiallyoverlapped. Except for changes in intensities related to thevariation of initial concentrations of DMF and butanone, nosignificant spectral changes are observed in the 1D spectra.However, the asynchronous spectrum in Fig. 17 is similar tothat in Fig. 5e obtained by setting DXP . 0 and DXQ . 0 in thesimulation study. This result suggests that dipole–dipoleinteraction brings about a blue shift of both the amide I bandof DMF and the carbonyl band of butanone.

CONCLUSION

In this paper, a new approach called asynchronousorthogonal sample design (AOSD) is proposed based on the

mathematical properties of the Hilbert–Noda transformationmatrix. Both theoretical analysis and simulation demonstratethat interfering portions in the 2D asynchronous spectra can beeffectively removed using the AOSD approach. Additionally,simulations performed on model chemical systems withdifferent extents of overlap of the solute peaks revealed thespectral characteristics of the 2D asynchronous spectra underthe influence of various forms of intermolecular interactions.The results demonstrate that distinct 2D spectral patternsproduced by the AOSD approach can reflect subtle variationsin bandwidths, peak positions, and absorptivities of character-istic bands of solutes caused by intermolecular interactionseven when the characteristic peaks of solutes are severelyoverlapped. The applicability of the AOSD approach in the realchemical system has also been proved by a DMF–butanone/carbon tetrachloride system. All the results indicate that theAOSD approach provides a new method to reveal theintermolecular interaction of two solutes when the character-istic peaks of the solutes are overlapped.




FIG. 17. 2D FT-IR asynchronous spectrum of the butanone–DMF/carbontetrachloride solutions.

FIG. 16. 1D FT-IR spectra of the butanone–DMF/carbon tetrachloridesolutions.


ACKNOWLEDGMENTS

Financial support from the National Natural Science Foundation of China(Grant No. 50673005, 50973003, 51074150, 50404004, 21001009, 20973034,20975029), National High-tech R&D Program of China (863 Program) ofMOST (No. 2010AA03A406), and Program of Advanced Technology Institute,Peking University, are gratefully acknowledged.

SUPPLEMENTAL MATERIAL

All supplemental material mentioned in the text is availablein the online version of the journal at http://www.s-a-s.org.

1. K. Sahu, D. Roy, S. K. Mondal, R. Karmakar, and K. Bhattacharyya,Chem. Phys. Lett. 404, 341 (2005).

2. M. Nakash and M. Goldvaser, J. Am. Chem. Soc. 126, 3436 (2004).3. L. F. Chi, S. Jacobi, B. Anczykowski, M. Overs, H. J. Schafer, and H.

Fuchs, Adv. Mater. 12, 25 (2000).4. W. Qian and S. Krimm, J. Phys. Chem. A 101, 5825 (1997).5. D. F. Hansen, M. A. S. Hass, H. M. Christensen, J. Ulstrup, and J. J. Led,

J. Am. Chem. Soc. 125, 6858 (2003).6. S. Dey, A. Adhikari, U. Mandal, S. Ghosh, and K. J. Bhattacharyya, J.

Phys. Chem. B 112, 5020 (2008).7. U. Mandal, A. Adhikari, S. Dey, S. Ghosh, and K. Bhattacharyya, J. Phys.

Chem. B 111, 5896 (2007).8. C. Tschierske, Angew. Chem. Int. Ed. 39, 2454 (2000).9. M. Langner and K. Kubica, Chem. Phys. Lipids 101, 3 (1999).

10. A. Bernardi, D. Arosio, D. Potenza, I. Sanchez-Medina, S. Mari, F. J.Canada, and J. Jimenez-Barbero, Chem. Eur. J. 10, 4395 (2004).

11. I. Noda, J. Am. Chem. Soc. 111, 8116 (1989).12. I. Noda, Appl. Spectrosc. 47, 1329 (1993).13. I. Noda, Appl. Spectrosc. 54, 994 (2000).14. S. Sasic, A. Muszynski, and Y. Ozaki, J. Phys. Chem. A 104, 6380 (2000).15. M. Thomas and H. Kandori, Vib. Spectrosc. 24, 225 (2000).16. Y. Q. Wu, J. H. Jiang, and Y. Ozaki, J. Phys. Chem. A 106, 2422 (2002).17. Y. Q. Wu, I. Noda, F. Meersman, and Y. Ozaki, J. Mol. Struct. 799, 121

(2006).18. I. Noda, J. Mol. Struct. 799, 34 (2006).19. Y. Q. Wu and I. Noda, Appl. Spectrosc. 60, 605 (2006).20. S. Morita, H. Shinzawa, I. Noda, and Y. Ozaki, Appl. Spectrosc. 60, 399

(2006).21. A. Ausili, A. Scire, E. Damiani, G. Zolese, E. Bertoli, and F. Tanfani,

Biochemistry 44, 15997 (2005).22. G. F. Wang, Y. Gao, and M. L. Geng, J. Phys. Chem. B 110, 8506 (2006).23. T. Lefevre, K. Arseneault, and M. Pezolet, Biopolymers 73, 705 (2004).24. L. X. Wang, Y. Q. Wu, and F. Meersman, Vib. Spectrosc. 42, 201 (2006).25. Y. B. Yan, J. Zhang, H. W. He, and H. M. Zhou, Biophys. J. 90, 2525

(2006).26. J. Yu and P. Y. Wu, Polymer 48, 3477 (2007).27. B. Zimmermann and G. Baranovic, Vib. Spectrosc. 41, 126 (2006).28. A. Padermshoke, H. Sato, Y. Katsumoto, S. Ekgasit, I. Noda, and Y.

Ozaki, Polymer 45, 7159 (2004).29. B. Muik, B. Lendl, A. M. Diaz, M. Valcarcel, and M. J. A. Canada, Anal.

Chim. Acta 593, 54 (2007).30. S. Q. Sun, C. W. Li, J. P. Wei, Q. Zhou, and I. Noda, J. Mol. Struct. 799,

72 (2006).31. R. Siuda, G. Balcerowska, and C. Sadowski, Food Addit. Contam. 23,

1201 (2006).32. J. Qi, K. Huang, X. X. Gao, H. Z. Li, S. X. Liu, Y. Zhao, Y. Z. Xu, J. G.

Wu, and I. Noda, J. Mol. Struct. 883, 116 (2008).33. L. Szyc, J. Guo, M. Yang, J. Dreyer, P. M. Tolstoy, E. T. J. Nibbering, B.

Czarnik-Matusewicz, T. Elsaesser, and H.-H. Limbach, J. Phys. Chem. A114, 7749 (2010).

34. H. Dathe, P. Haider, A. Jentys, and J. A. Lercher, J. Phys. Chem. B 110,26024 (2006).

35. J. Y. Huang and W. T. Shih, J. Phys. Condens. 18, 7593 (2006).36. E. Pechkova, P. Innocenzi, L. Malfatti, T. Kidchob, L. Gaspa, and C.

Nicolini, Langmuir 23, 1147 (2007).37. C. Matranga, L. Chen, M. Smith, E. Bittner, J. K. Johnson, and B.

Bockrath, J. Phys. Chem. B 107, 12930 (2003).38. Y. M. Jung, Y. Park, S. Sarker, J.-J. Lee, U. Dembereldorj, and S.-W. Joo,

Solar Energy Mater. Sol. Cells 95, 326 (2011).39. M. X. Han, Q. Zhou, Q. H. Li, and S. Q. Sun, Spectrosc. Spectral Anal. 29,

1851 (2009).40. J. Qi, H. Z. Li, K. Huang, H. H. Chen, S. X. Liu, L. M. Yang, Y. Zhao, C.

F. Zhang, W. H. Li, J. G. Wu, D. F. Xu, Y. Z. Xu, and I. Noda, Appl.Spectrosc. 61, 1359 (2007).

41. J. Chen, C. F. Zhang, H. Z. Li, Y. H. Liu, W. H. Li, Y. Z. Xu, J. G. Wu,and I. Noda, J. Mol. Struct. 883, 129 (2008).

42. C. F. Zhang, K. Huang, H. Z. Li, J. Chen, S. X. Liu, Y. Zhao, D. J. Wang,Y. Z. Xu, J. G. Wu, I. Noda, and Y. Ozaki, J. Phys. Chem. A 113, 12142(2009).

APPENDIX

1. The synchronous spectrum at (x,y) when the characteristicpeaks of P at x and Q at y do not overlap. After combining Eqs.12a and 12b with Eq. 9 in the main text, we obtain

S1ðx; yÞ ¼ fPðxÞfQðyÞ~CT

P~CQ ðA1Þ

S2ðx; yÞ ¼ fPðxÞ½ fVðyÞ � fQðyÞ�~CT

P~CV ðA2Þ

S3ðx; yÞ ¼ fQðxÞ½ fUðyÞ � fPðyÞ�~CT

U~CQ ðA3Þ

S4ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ�½ fVðyÞ � fQðyÞ�~CT

U~CV ðA4Þ

2. The synchronous spectrum at (x,y) when the characteristicpeaks of P at x and Q at y are partially overlapped. Thesynchronous spectrum at (x,y) is obtained by combining Eqs.15a and 15b with Eq. 9 in the main text of the manuscript.

Uðx; yÞ ¼X16

i¼1

Wiðx; yÞ ðA5Þ

where

W1ðx; yÞ ¼ fPðxÞfPðyÞ~CT

P~CP ðA6Þ

W2ðx; yÞ ¼ fQðxÞfQðyÞ~CT

Q~C ðA7Þ

W3ðx; yÞ ¼ fPðxÞfQðyÞ~CT

P~CQ ðA8Þ

W4ðx; yÞ ¼ fQðxÞfPðyÞ~CT

Q~CP ðA9Þ

W5ðx; yÞ ¼ fPðxÞ½ fUðyÞ � fPðyÞ�~CT

P~CU ðA10Þ

W6ðx; yÞ ¼ fPðxÞ½ fVðyÞ � fQðyÞ�~CT

P~CV ðA11Þ

W7ðx; yÞ ¼ fQðxÞ½ fUðyÞ � fPðyÞ�~CT

Q~CU ðA12Þ

W8ðx; yÞ ¼ fQðxÞ½ fVðyÞ � fQðyÞ�~CT

Q~CV ðA13Þ

W9ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ� fPðyÞ~CT

U~CP ðA14Þ

W10ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ� fQðyÞ~CT

U~CQ ðA15Þ

W11ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ� fPðyÞ~CT

V~CP ðA16Þ


W12ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ� fQðyÞ~CT

V~CQ ðA17Þ

W13ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ�½ fUðyÞ � fPðyÞ�~CT

U~CU ðA18Þ

W14ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ�½ fVðyÞ � fQðyÞ�~CT

V~CV ðA19Þ

W15ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ�½ fUðyÞ � fPðyÞ�~CT

V~CU ðA20Þ

W16ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ�½ fVðyÞ � fQðyÞ�~CT

U~CV ðA21Þ

3. The asynchronous spectrum at (x,y) when the character-istic peaks of P at x and Q at y are partially overlapped. Theasynchronous spectrum can be calculated if we combine Eqs.10, 15a, and 15b in the main text of the manuscript.

Wðx; yÞ ¼X16

i¼1

Riðx; yÞ ðA22Þ

where:

R1ðx; yÞ ¼ fPðxÞfPðyÞ~CT

PN~CP ðA23Þ

R2ðx; yÞ ¼ fQðxÞfQðyÞ~CT

QN~CQ ðA24Þ

R3ðx; yÞ ¼ fPðxÞfQðyÞ~CT

PN~CQ ðA25Þ

R4ðx; yÞ ¼ fQðxÞfPðyÞ~CT

QN~CP ðA26Þ

R5ðx; yÞ ¼ fPðxÞ½ fUðyÞ � fPðyÞ�~CT

PN~CU ðA27Þ

R6ðx; yÞ ¼ fPðxÞ½ fVðyÞ � fQðyÞ�~CT

PN~CV ðA28Þ

R7ðx; yÞ ¼ fQðxÞ½ fUðyÞ � fPðyÞ�~CT

QN~CU ðA29Þ

R8ðx; yÞ ¼ fQðxÞ½ fVðyÞ � fQðyÞ�~CT

QN~CV ðA30Þ

R9ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ� fPðyÞ~CT

UN~CP ðA31Þ

R10ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ� fQðyÞ~CT

UN~CQ ðA32Þ

R11ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ� fPðyÞ~CT

VN~CP ðA33Þ

R12ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ� fQðyÞ~CT

VN~CQ ðA34Þ

R13ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ�½ fUðyÞ � fPðyÞ�~CT

UN~CU ðA35Þ

R14ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ�½ fVðyÞ � fQðyÞ�~CT

V~CV ðA36Þ

R15ðx; yÞ ¼ ½ fVðxÞ � fQðxÞ�½ fUðyÞ � fPðyÞ�~CT

VN~CU ðA37Þ

R16ðx; yÞ ¼ ½ fUðxÞ � fPðxÞ�½ fVðyÞ � fQðyÞ�~CT

UN~CV ðA38Þ


Date post:	05-Oct-2016
Category:	Documents
Upload:	juan
View:	214 times
Download:	0 times

Asynchronous Orthogonal Sample Design Scheme for TwoDimensional Correlation Spectroscopy (2D-COS)...

Documents