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Chemical Physics Letters 432 (2006) 122–127

Coupling between C–D and C@O motions using dual-frequency 2DIR photon echo spectroscopy

Keshav Kumar, Louise E. Sinks, Jianping Wang, Yung Sam Kim, Robin M. Hochstrasser *

Department of Chemistry, University of Pennsylvania, 230 South 34th Street, Philadelphia, PA 19104-6323, USA

Received 2 August 2006; in final form 6 October 2006Available online 17 October 2006

Abstract

Coupling between C–D and C@O vibrational modes of formamide has been characterized by dual-frequency 2D IR spectroscopy.The signals are consistent with those computed assuming an optically dense system at the C@O frequency. A negative off-diagonal anhar-monicity of �0.85 ± 0.20 cm�1 was obtained and the coupled modes have anticorrelated frequency distributions. Other features includ-ing relaxation times, diagonal anharmonicities for the individual C@O and C–D modes and the dephasing dynamics of the cross peakhave been determined to characterize the coupling between modes.� 2006 Elsevier B.V. All rights reserved.

1. Introduction

The two dimensional infrared (2D IR) methods intro-duced for the study of individual modes of polypeptides[1,2] have found frequent recent application in which theIR pulse sequences mimic some three pulse NMR techniques[2,3]. The dual-frequency method, akin to heteronuclearNMR, measures coupling between vibrational modes sepa-rated by more than the frequency bandwidth of the pulses. Itemploys a pair of pulses having center frequencies coincid-ing with one of the vibrators and a third pulse at the fre-quency of the other [3–5]. Previous reports explored thecoupling of C–N and amide-I [4,6], of N–H and C@O, [5]and of C–N and C@O [3] modes. The interactions betweenvibrators are interesting in both biological and non-biolog-ical contexts; in particular N–H/C@O based hydrogenbonds are ubiquitous and have substantial coupling. Othermode pairs in addition to N–H/C@O can be found in biolog-ical systems, for example S–H/C@O [7,8] and C–H/C@O.

Our focus on C–H/C@O interactions was stimulated bythe work by Senes and colleagues [9], which found thatnumerous helical dimers have multiple Ca–H. . .O contactsthat may be involved in weak hydrogen bonds, some prop-

0009-2614/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2006.10.028

* Corresponding author. Fax: +1 215 898 0590.E-mail address: hochstra@sas.upenn.edu (R.M. Hochstrasser).

erties of which have been reported using FTIR spectros-copy [10]. Recent 2D IR work on the C@O and C–Dmodes in liquid formamide have revealed that the hydro-gen bond environment is very different for the C@O andC–D modes [11] and the C–D frequency correlation func-tion decays in a manner consistent with weak hydrogenbonding with the C@O.

Formamide has structural motifs found in peptides, so isan important prototype with which to face the experimen-tal challenge of determining the C–D. . .O@C interactionthat will be essential in applying 2D IR to proteins. Theweakness of the C–D absorption peak and the necessaryhigh optical density in the C@O region make such experi-ments less straightforward than those with transitions ofnearly the same strength. Both pump-probe and the hetero-dyned dual-frequency photon echoes of the C–D, C@Oand combined C–D/C@O modes are reported here ford3-formamide in solution.

2. Experimental methods

2.1. Sample and linear IR spectroscopy

Fig. 1 shows the sample, formamide-d3, FTIR spectrum(at 60 mM in CHCl3). The FTIR of unlabeled and isotopi-cally substituted 13C@18O formamide samples indicated

Fig. 1. Amide-I (C@O) and the C–D mode FTIR of d3-formamide. Inset:DFT optimized structure discussed in the text. The arrows are transitiondipoles.

Fig. 2. Representative Liouville pathways for the dual-frequency exper-iment. C–D is the v = 1 state of C–D and C@O + C–D the combinationstate with amide-I. The pulses k1 and k2 are near the C–D frequency andk3 and ks (the signal) are near the C@O frequency. There are six morediagrams like the third row not involving a population state after k2.

K. Kumar et al. / Chemical Physics Letters 432 (2006) 122–127 123

that �90% of the formamide molecules are in a monomericform with a small fraction of a closed dimer (with N–H. . .O@C contacts) [12] that made a negligible contribu-tion to the nonlinear signals reported in this paper.

The main amide-I (C@O) peak at 1682 cm�1 (emax �708 M�1 cm�1) fits a Voigt profile with FWHM of 10–14 cm�1and equal Gaussian and Lorentzian components,which is in reasonable agreement with literature values[13]. The C–D mode at 2159 cm�1 fits to a Lorentzian(FWHM = 37.3 cm�1; emax � 40 M�1 cm�1).

2.2. Generation of dual-frequency IR pulses

A Ti:Sapphire laser (Clark MXR, CPA-2001) generates660 lJ, 130 fs pulses at 775 nm split into two parts with ener-gies of 360 lJ and 300 lJ that pump two BBO based opticalparametric amplifiers (OPA’s). The outputs of the OPA’sare 60 lJ and 45 lJ, respectively. The signal and idler pulsesfrom the OPA’s are focused into two difference frequencygeneration crystals (AgGaS2) to produce mid-IR pulses at4.6 lm (0.8 lJ) and at 6 lm (0.4 lJ). For dual-frequency2 D IR the 4.6 lm pulse is divided into beams 1 and 2 withwavevectors k1 and k2. The beam at 6 lm was split into twobeams and the higher energy portion (95%) becomes pulsethree with wavevector k3; the remainder was used to hetero-dyne the nonlinear signal. This pulse sequence (4.6 lm,4.6 lm, 6.0 lm) was chosen to provide a uniform excitationin the low absorption region. The pulses were tunable over arange of central frequencies that enabled the excitation of allthe vibrational transitions under consideration either in sin-gle or dual-frequency configurations.

2.3. 2D IR experiment

This experiment was performed in a manner similar tothat described previously [6]. The three mid-IR pulses trav-

eling in directions k1, k2 and k3 were phase matched incor-porating the frequency differences. These pulses generateda polarization with wavevector kP = k1 � k2 + k3 and a sig-nal field, ks, at �x1 + x2 + x3 in the range of the C@O fre-quency. The heterodyned signal field was measured as afunction of the intervals between the first and second (s),second and third (T), and third and the detected pulses (t).

The T interval was fixed and the signal detected as atwo-dimensional array in s and t and the 2D IR was con-structed in the (xs,xt) space by Fourier transformation.

3. Results

3.1. Pump-probe

From single frequency pump-probe experiments them = 1 populations showed bi-exponential decay of 70 fs(40%) and 820 fs (60%) for C–D, and 970 fs (27%) and6.65 ps (73%) for C@O, while the diagonal anharmonicitieswere DC–D = 51.7 cm�1and DC–O = 19 cm�1, respectively.A bi-exponential decay of the C@O anisotropy of 275 fs(44%) and 3.5 ps (56%) was observed. The dual-frequencyexperiment involved pumping the C–D mode at

Fig. 3. The cross peak pump (C–D)-probe (C@O) spectrum of d3-formamide at waiting times T = 0 (dashed) and T = 265 fs. The signal at265 fs is increased by a factor of 1.4 to match the one at T = 0.

124 K. Kumar et al. / Chemical Physics Letters 432 (2006) 122–127

2160 cm�1 and probing the C@O mode at 1680 cm�1 asshown in Fig. 3.

3.2. Dual-frequency 2D IR

The absorptive 2D IR spectrum [6] is shown in Fig. 4 attwo values of T. The partial projection of this cross peakspectrum onto the detection time axis (discrete sums ofthe signal along the frequency axes xs) generates thepump-probe measurement of the cross peak. The formam-ide cross peaks in Fig. 4 have an absolute amplitude of�3000, while the smaller peaks, <15% of the total ampli-tude, arise from the solvent response. This solvent signaldecays on the time scale of the laser pulses and is uncorre-lated, supporting its assignment as arising from solvent.Heterodyned (1D) echo signal amplitude of the solventresponse is similar with or without the addition of formam-ide for this waiting time (T = 300 fs). These contributionsare dramatically reduced by T = 600 fs, leaving a clear pic-

Fig. 4. Experimental 2D IR echo spectra of the cross peak between the C–D anshown. The ordinates and abscissas are the Fourier frequencies xs (near C–D

ture of the signal, C–D/C@O cross peak. The cross peaksignal shows two components. The blue peak correspondsto the combined transitions of the C@O and C–D funda-mentals as shown in line two of Fig. 2: in projection thisspectrum generates the bleach. The red component repre-sents the nonlinear excitation of the combination band asin the top line of Fig. 2.

4. Discussion

4.1. The vibrational states of formamide

Ab initio computations on formamide [14–23], classicalMD simulations [24,25] and ab initio MD in liquids[26,27] were reported. We performed a calculation ofCOND3 at the level of B3LYP/6-311++G** with GAUSSIAN

03 [16] that yielded frequencies xC–D = 2097.8 and xC@O

= 1742.1 cm�1, with anharmonicities 75.1 cm�1 (DC–D =2xC–D � x2(C–D)) and 19.3 cm�1, respectively and transi-tion dipoles of the amide-I and C–D modes of 0.318 Dand 0.132 D. The computed integrated IR absorption ratio(C@O/C–D) of 4.7 compares poorly with the observedratio of 10.3. The transition dipole of the amide-I modeis tilted 27.4� to the C@O bond (see Fig. 1). The C–D modeis localized (99%) on the C–D bond, but its computed tran-sition dipole is tilted by 16.8�. The computed value ofDCD/CO = xCO + xCD�xCO + CD (�0.6 cm�1) is composedof the coupling of the C–D/C@O modes (�5.2 cm�1),which establishes the sign of the anharmonicity, and contri-butions from the C–D in-plane bending (+2.9 cm�1) andamide-II (+1.5 cm�1), which tend to cancel the C–D/C@O mode coupling shift so that the sign is a sensitive bal-ance of interactions. The computation also predicts thatthe C–D and C@O mode frequencies are anticorrelatedfor fluctuations around the optimized structure.

4.2. The nonlinear spectra

The diagrams used to describe the 2D IR and pump-probe experiments are summarized in Fig. 2. The pulse lim-ited contribution to the pump-probe signal of Fig. 3 results

d C@O of formamide. The signals at T = 300 fs (left) and 600 fs (right) are) and xt (near C@O) corresponding to the delay times s and t.

K. Kumar et al. / Chemical Physics Letters 432 (2006) 122–127 125

in positive and negative peaks in the spectrum. The micro-scopic sources of these peaks can be seen by considering allthe contributing resonant Liouville pathways that can con-tribute to the signal in the pump-probe configuration. Thefirst four diagrams in Fig. 2 have populations of the C–Dmode existing during the waiting time (T): they all contrib-ute to the conventional pump-probe signal of the coupledC–D and C@O modes and they decay with the T1 lifetimeof the C–D mode. The first two diagrams correspond to theC@O mode interaction with a C–D, m = 1, frequency grat-ing. The second two correspond to the C@O absorption ofthe ground state grating obtained by coherent excitationand de-excitation of the C–D bond. In addition to thesefour pathways there are eight other diagrams [4] that con-tribute to the pump-probe spectrum when the pulses over-lap in time. Two of these eight are shown as the bottom linein Fig. 2. In the waiting period these diagrams do notinvolve populations but all eight of them involve coher-ences between the C–D and the C@O states. However,these contributions have the same magnitudes for delta-function pulses as the population terms so they cancontribute 67% of the pump probe spectrum in the pulseoverlap region. Furthermore, four of them are negative,like the first two new absorption diagrams, and four arepositive like the second two bleaching diagrams, so thatthe fast decaying coherent response has the same spectralcharacter as the new absorption and bleaching parts,respectively of the conventional pump-probe spectrum.The bleaching component of the cross peak is observedaround 1684 cm�1 in the pump-probe spectrum and thenew absorption is at higher frequency as shown in Fig. 3indicating that the off-diagonal anharmonicity (definedabove) is negative.

In the heterodyned 2D experiment k1 is used to create aC–D 01-coherence which becomes a C–D population afterk2. The third pulse creates the (C–D + C@O), C–D coher-ence (first line in Fig. 2) or the C@O coherence (second linein Fig. 2) which cause radiation at different frequencies ifthere is coupling, otherwise they will cancel one another inthe 2D IR spectrum if they relax similarly. The cross peakin the 2D spectrum (Fig. 4) confirms that these frequenciesare different. Because of absorption the frequency separationin the 2D IR does not equal the magnitude of the anharmo-nicity. The DCD/CO was estimated from relative values ofthe cross and diagonal peak intensities to be ��0.85 ±0.20 cm�1, which is in the range the computed value.

The 2D IR spectral shape shows that the C@O and C–Dmode frequency deviations have a negative correlation fac-tor: solvent–solute structures having positive deviations ofthe C@O frequency have their C–D frequencies decreased.The waiting time, T, dependence of the 2D IR signal indi-cates that the inhomogeneous distribution evolves to amore homogenous distribution during the first 600 fs. Thisis seen from the result in Fig. 4 that shows the spectrumbecoming upright as the correlation becomes lost. It is wellknown [5,28] that for uncorrelated distributions the nodeseparating the positive and negative parts of the 2D spec-

trum is parallel to the xs axis and that correlation tilts thisnode depending on the sign of the correlation.

4.3. The effects of the large C@O absorption

It is important in nonlinear experiments to keep theoptical density low enough to avoid spectral distortions[29]. This is not a problem for carbonyls where OD’s inthe range 0.01 or less can be used. In so far as the opticaldensities are considerably less than unity, the OD correc-tions can be made analytically [30]. The spectrum of thesignal for more strongly absorbing nearly collinear inputbeams can be estimated from known formulas of nonlinearoptics [31] and nonlinear spectroscopy [32]. The field at�x1 + x2 + x3 from the polarization v(3) (xs; � x1, x2,x3)e1e2e3, is given in terms of the response functions inthe usual manner [33] times the propagation factor:F ¼ 2px2

s ðe�ikpL � e�iksLÞ=c2ksDk, where ks and Dk = ks +k1 � k2 � k3 are the signal complex wavevector and mis-match of the three input wavevectors (i.e. ki = ji (xi) � iai

(xi)/2 with ji (xi) = n (xi)xi/c and ai (xi) is the absorptioncoefficient). The monochromatic input waves are decayingin amplitude and changing phase while the signal wave isgrowing through the sample. Only k3 and ks are stronglyattenuated in our example. The F factor describes the sig-nals generated by each set of three monochromatic Fouriercomponents, one taken from each of the input pulses [32].All frequency combinations that could contribute to eachsignal frequency xs were computed numerically in orderto reproduce the signal field in the frequency domain fromthree incident Gaussian pulses e1(x1) and e2(x2) in the C–Dregion and e3 (x3) at the C@O frequency. No dispersion atthe C–D frequency was incorporated. The absorptiondepletes the frequency center of the k3 pulse resulting in adistorted nonlinear spectrum, as if the k3 spectrum acquirestwo peaks having different phase [28] as it propagates.Voigt profiles were used to simulate the C@O absorption(aCO(peak) = 1.80, see Fig. 1) and dispersion n(x3). Thevalue of DCD/CO = �0.85 cm�1 gives a reasonable fit ofthe computed and measured 2D IR spectrum. Howeverthe calculation omits too many possible refinements (e.g.,non-collinearity) to be more than a demonstration of themain effects of the strong absorption on a 2D IR experi-ment. Recently an exact approach to the computation ofnonlinear signals from optically dense media was reported[34] but a more extensive experimental study is neededbefore fitting to exact solutions of Maxwell’s equations.The main features are reproduced rather well by the simpleapproach given here (Fig. 5). The large aCO alters the shapeof the 0–1 and 1�(1 + 2) components of the 2D IR spec-trum with the former becoming symmetric double peaked.The observed separation between the 0–1 and 1�(1 + 2)regions is much larger than the input off-diagonal anhar-monicity and is not a reasonable measure of this parame-ter. When the lineshapes for the 0–1 and 1�(1 + 2)response functions are similar the signal vanishes at zeroDCD/CO. The cross peak signal becomes upright when the

Fig. 5. Comparison of the 2D IR spectra for optical densities that are small (0.05) (upper three spectra) and large (0.75) (lower three spectra) at the C@Ofrequency. The columns show spectra for paths involving only v = 1 states of the C–D (first column) and the combination (second column). The thirdcolumn is a computation of the expected signal (sum of columns one and two). The negative slope arises from the anticorrelation of the frequencies.

126 K. Kumar et al. / Chemical Physics Letters 432 (2006) 122–127

correlation is zero as in optically transparent media, thusthe shapes maintain the main identifying features of spec-tral diffusion.

5. Conclusions

Pump-probe and dual-frequency 2D IR experimentsshowed coupling between C–D and C@O modes in form-amide. The diagonal anharmonicities of C–D and C@Omodes were in agreement with DFT calculations. The offdiagonal anharmonicity between C–D and C@O vibra-tional modes is estimated to be �0.85 ± 0.20 cm�1 showingthe C–D mode is highly localized. The C–D and C@Omodes have anticorrelated frequency distributions, inagreement with DFT predictions, that become uncorre-lated within 600 fs. The effects of strong sample absorptionat the C@O frequency were incorporated by assuming eachchoice of three incident Fourier components combine inde-pendently of the others to generate the signal. Reasonablerepresentations of the signals were computed. This obser-vation of C–D/C@O coupling makes more promising thegoal of utilizing these types of interactions in trackingstructural changes of proteins.

Acknowledgements

This research was supported by grants from NIH andNSF to RMH using instrumentation from the Resource

NIH RR 01348. LES was partially supported by the NIHRuth L. Kirschstein NRSA Fellowship.

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