A Method for Determining Small Anharmonicity Values from 2DIR

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A Method for Determining Small Anharmonicity Values from 2DIR Spectra Using Thermally Induced Shifts of Frequencies of High-Frequency Modes Zhiwei Lin, Patrick Keiffer, and Igor V. Rubtsov* Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, United States ABSTRACT: The off-diagonal anharmonicity for a pair of vibrational modes, determined as a shift of their combination level, Δ12, can be linked to the molecular structure via modeling. The anharmonicity, Δ12, also determines the amplitude and shape of the cross-peak between modes 1 and 2 measured using 2DIR spectroscopy. For large anharmonicities, the anharmonicity value can be readily obtained from the shape of the cross peak. In practice, however, the anharmonicities are often small (,1 cm-1). In this case, the amplitude of the cross peak rather than its shape is sensitive to the anharmonicity value, and determination of the anharmonicity requires absolute cross-peak measurements. We proposed and tested a new approach of determining anharmonicities, which is based on sensitivity of high-frequency vibrational modes to temperature. The approach permits calibrating the cross-peak amplitude in terms of the effective anharmonicity resulting from the thermal excitation of lower-frequency vibrational modes. It relies on a series of relative 2DIR measurements. While the sensitivity of the method depends on various specific parameters of the molecular system, such as transition dipoles and temperature sensitivity of the high-frequency modes involved, we have estimated that the anharmonicities as small as 0.02 cm-1 can be determined for the cross peaks between -N3 and CdO stretching modes using this approach.

1. INTRODUCTION Multidimensional infrared spectroscopies provide a means for measuring anharmonic interactions of vibrational modes in molecules,1-16 which are structure dependent and can therefore, with proper modeling,17-22 be linked to structural features of the molecule. Anharmonic interactions cause a shift of a mode fundamental frequency, the frequency of its overtone, as well as the frequencies of the combination bands. The shift of the combination band with respect to the sum of the two respective fundamental frequencies, the off-diagonal anharmonicity, Δ12, is experimentally accessible via 2DIR spectroscopy, representing an important parameter needed for structural assessment. If the off-diagonal anharmonicity is larger than the width of the involved transition, the line shape of the cross peak reports on the anharmonicity value. However, if the anharmonicity is much smaller than the width, the line shape of the cross peak is not sensitive to the anharmonicity value; in this limit, the cross-peak amplitude is proportional to the anharmonicity value,23 and its evaluation requires absolute cross-peak measurements. The absolute cross-peak measurements are difficult, as the cross-peak amplitude depends on the excitation pulse energy and spectrum, beam diameter, and the quality of the beam overlap in the sample, efficiency of heterodyned detection, etc. Alternatively, a small off-diagonal anharmonicity value can be determined from a comparison of the cross-peak amplitude to the amplitude of the diagonal peak, for which the anharmonicity (diagonal) is known to be easily measurable.24 When the crosspeak of interest is close to the diagonal line (the frequencies of two interacting modes are similar), its comparison to the diagonal r 2010 American Chemical Society

peak(s) seems to work best for evaluating the small off-diagonal anharmonicities. If, though, the cross-peak is far from the diagonal line,25,26 a large tuning of the pulse frequencies is required to switch between the diagonal and the cross-peak measurements, which makes the comparison unreliable as many parameters of the experimental setup have to be changed. In this work, we developed a method of evaluating accurately small anharmonicities which requires only relative 2DIR measurements. The method relies on the sensitivity of vibrational frequencies to temperature. A temperature increase caused by mid-IR excitation in the sample is seen in both the diagonal and cross-peak measurements at larger waiting time delays when the thermalization is completed. At the same time, the temperature shifts of the involved transitions were measured by stationary measurements using a linear absorption FTIR spectrometer. The temperature sensitivity of both interacting modes provides the opportunity for calibrating weak cross peaks and determining their off-diagonal anharmonicity.

2. EXPERIMENTAL DETAILS 2.1. Heterodyned Dual-Frequency 2DIR Spectroscopy. Details of the dual-frequency 2DIR setup with heterodyned Special Issue: Shaul Mukamel Festschrift Received: September 30, 2010 Revised: November 16, 2010 Published: December 28, 2010 5347

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Figure 1. Linear absorption spectrum of Az-PEG4 in chloroform. Structure of the Az-PEG4 compound is shown in the inset.

detection can be found in refs 24 and 27. Briefly, the laser pulses at 806 nm, 44 fs in duration, produced by a Ti:sapphire-oscillator/ regenerative-amplifier tandem (Vitesse/USP-Legend, Coherent Inc.) were used to generate two sets of near-IR Signal and Idler pulses in two in-house built optical parametric amplifiers (OPA). The frequency difference between the Signal and Idler pulses was generated in two 2.0 mm thick AgGaS2 crystals, producing tunable mid-IR pulses. The energy of the IR pulses was ca. 3 μJ/pulse when centered at 2100 cm-1 and ca. 2 μJ/pulse when centered at 1700 cm-1. The beam centered at ca. 2100 cm-1 was split into two equal parts, which served as k1 and k2 pulses. A small portion (∼4%) was split from the beam centered at ca. 1700 cm-1 and served as the local oscillator (LO); the rest of the beam was served as k3 pulses interacting with the sample. A thirdorder signal generated in a sample was picked at the phase matching direction (-k1 þ k2 þ k3), mixed with the LO, delayed by the time delay t, and detected by an MCT detector (Infrared Associates). The delays between the first and the second and the second and the third pulses are referred to as the dephasing time, τ, and the waiting time, T, respectively. Linear-motor translation stages (PI Inc.) equipped with hollow retroreflectors were used to control the delays between the IR pulses. During the experiments, the positions of all the stages were accurately measured with an external interferometric system based on a continuouswave HeNe laser.28 The relaxation-assisted 2DIR and mid-IR pump-probe measurements were performed in a fashion similar to those described in ref 28. Both relaxation-assisted and pump-probe measurements were performed at the magic angle conditions, where for the former the τ delay time was set to zero. 2.2. Sample Preparation. The 3-(2-{2-[2-(2-azido-ethoxy)ethoxy]-ethoxy}-ethoxy)-propionic acid 2,5-dioxo-pyrrolidin-1yl ester (Az-PEG4) compound (Figure 1 inset) was purchased from Quanta BioDesign, Ltd. and was used as received. The sample, a 45 mM solution of Az-PEG4 in chloroform (Fisher Scientific, HPLC grade 99.9%), was placed in a sample cell made of two CaF2 wafers and a 50 μm thick Teflon spacer. All timeresolved experiments were performed at room temperature, 23.5 ( 0.6 °C. 2.3. FTIR Measurements at Different Temperatures. To change the temperature of the sample, the sample cell holder was placed into the sample cell assembly, a metal piece through which the cooling liquid was flowing. In addition, a thick-walled metal

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tube of ca. 2.5 in. long was attached to each side of the sample. A good thermal contact between the tubes and the metal assembly was arranged, so that the whole 5 in. long area around the sample was brought close to the designed temperature ensuring the designed temperature for the sample. The sample cell assembly and the tubes were thermally insulated from the outside. Careful temperature calibration was performed using a pair of thermocouples attached from opposite sides to the outside of the sample cell windows. The averaged temperature of the two thermocouples was taken as the sample temperature. The absolute error in temperature determination (Temp) was estimated to be 0.04*(Temp - TempRoom), which results in ca. ( 1.5 °C error bars when the temperature of the sample was -15 °C, which was the coldest temperature achieved in these measurements. The overall temperature span in the FTIR measurements was ca. 60 °C. 2.4. DFT Calculations. Density functional theory (DFT) harmonic and anharmonic calculations were performed at the Tulane's Center for Computational Science as well as with the cluster in our laboratory, using the GAUSSIAN 09 software package.29 All calculations were done using the B3LYP functional and 6-311þG(d,p) basis sets. Because of the large size of AzPEG4, the harmonic and anharmonic DFT calculations were instead performed on 4-azido-butanoic acid 2,5-dioxo-pyrrolidin1-yl ester (AzSucc), where the PEG4 moiety (Figure 1 inset) was replaced by a singe methylene group.

3. RESULTS AND DISCUSSION The proposed approach was tested using the Az-PEG4 compound (Figure 1 inset) featuring several strong peaks in the linear IR absorption spectrum (Figure 1). The covalently linked azido group has a strong asymmetric stretching mode, referred to here as the N3 stretching mode, with a peak at 2107 cm-1. The N3 peak is broad with the fwhm of ca. 49 cm-1, suggesting structural inhomogeneity for the N3 group. The DFT computed harmonic and anharmonic frequencies for the N3 peak are 2237.6 and 2159.4 cm-1, respectively, and the computed IR intensity is 688 km/mol. There are three CdO groups in Az-PEG4, one at the ester and two at the succinimide moiety, so that the site frequency of the ester CO is higher by ca. 30 cm-1 than those of the succinimide; interactions of the three groups form an interesting coupling pattern. Strong exciton coupling of the two CO modes at the succinimide forms asymmetric (1742 cm-1) and symmetric (would be at ca. 1805 cm-1) stretching modes. The symmetric stretch of the succinimide is in strong resonance with the CO stretch of the ester. Their exciton splitting results in two peaks at 1788 and 1819 cm-1, where the symmetric stretch of succinimide and the CO stretch of the ester move out-of-phase and in-phase, respectively; the DFT calculations show that the contributions of the symmetric stretch of succinimide and the CO stretch of the ester are almost equal for the two coupled states. The CO stretching normal modes computed at 1877.4 cm-1 (74.5), 1877 cm-1 (125), and 1804.9 cm-1 (781) match reasonably well the experimentally observed frequencies (Figure 1); here, the numbers in parentheses show the computed IR intensities in kilometers per mole The frequencies of anharmonically coupled states computed with DFT (1850, 1824.5, and 1775.5 cm-1) match the experiment even better. Interestingly, the lowest frequency CdO peak, which bares the largest IR intensity, has a negligible contribution from the motion of the CO group of the ester. Both the covalently linked azido groups and the CdO stretching modes of the succinimide 5348

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Figure 2. N3/CO (1742 cm-1) absolute-value cross peak amplitude for Az-PEG4 in chloroform as a function of the waiting time, T, measured at the magic angle conditions. The magenta line at T > 45 ps represents the average amplitude at the plateau.

moiety represent very attractive IR labels, mostly due to their convenient frequency range and their strong IR intensities. Note that although the N3- ion was one of the first 2DIR targets30 and was used as well more recently as an IR reporter,31-33 the organic azides to the best of our knowledge were not used as 2DIR labels. The 2DIR measurements were performed on Az-PEG4 focusing on the cross peak among N3 and CdO stretching modes. Figure 2 shows the amplitude of the cross peak as a function of the waiting time T. The dependence contains a large amount of information about the molecular system. The cross-peak amplitude at T = 0 reflects the direct coupling of the two modes, which can be linked to the mean distance between the two labels. The cross-peak growth is associated with the energy transport from the initially excited N3 stretching mode to the area where the CO groups are located, described in the framework of the relaxation-assisted 2DIR spectroscopy.34,35 The maximum is reached at ca. 4.3 ps, which is often referred to as the energy transport time between the two sites.35 The cross-peak enhancement is due to excitation of the lowto-medium-frequency modes that are local to the CO groups and strongly coupled to the CO stretching mode; this excitation occurs using the energy released from the vibrational relaxation of the N3 mode excited by the first two IR pulses. Note that the lifetime of the N3 asymmetric stretching mode has been accurately measured: the description of the N3 vibrational relaxation is complicated due to a presence of two other modes on the N3 moiety and will be reported elsewhere. The mean time for the N3 group to lose its energy was determined to be ca. 1.6 ps. After about 5 ps, the cross peak decreases (Figure 2) due to energy dissipation to the solvent. Interestingly, the cross-peak amplitude does not decay to zero: at ca. 50 ps it reaches a plateau which does not decay on the time scale of the experiment. A similar plateau has been observed for the N3/CO cross peaks in a variety of compounds as well as for cross peaks involving other modes. We assigned this plateau to the overall heating of the sample induced by the N3 mode relaxation. In analogy to the temperature-jump (T-jump) experiments often targeting water transitions in the near-IR spectral region,36 one can call the described effect a mid-IR-T-jump as it is induced by mid-IR excitation. The temperature increase of the sample by mid-IR radiation has been recently reported in D2O.37,38 It is important that the signal at T > 50 ps is spectrally narrow and bears the features of the probed (CO) transitions. The resonance character of the response at the plateau (T > 50 ps)

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indicates the sensitivity of the CO mode to temperature. Therefore, for describing the signals at the plateau, an effective anharmonicity can be introduced as a mean anharmonicity of many lowfrequency modes coupled to the probed high-frequency mode. Note that a small refractive index grating contribution to the signal,39 also observed in the experiment, has been filtered out in the time domain by eliminating points with t < 400 fs. The temperature dependence of the CO frequency can be determined experimentally using a linear absorption spectrometer. Indeed, the peak at 1742 cm-1 is found to show substantial temperature dependence (Figure 3A). Interestingly, the peak at 1788 cm-1 is about twice less sensitive to temperature (Figure 3B), while the peak at 1819 cm-1 shows very weak temperature dependence (Figure 3C). If the temperature increase caused by the N3 relaxation is known, the effective anharmonicity of the plateau can be determined, which can lead to a calibration of the ordinate of Figure 2 in terms of the effective anharmonicity values. To determine the temperature increase in the sample in the conditions of the experiment, we have measured the diagonal N3 peak dynamics using the 2DIR method. Figure 4 shows the waiting time dependence of the N3 diagonal peak magnitude. The cross-peak amplitude at T = 0 is determined by the diagonal anharmonicity value, which has been obtained by the pump-probe measurements at ca. 35 cm-1. The anharmonicity computed using DFT anharmonic calculations, 29.2 cm-1, is close to the experimentally determined value. The amplitudes of the diagonal peak at T = 0 and T > 50 ps are determined, respectively, by the diagonal anharmonicity (ΔN3) and by the effective anharmonicity, which (in the first approximation) equals the frequency shift of the N3 absorption peak due 3 to the temperature increase in the sample (ΔN pl ). In the limit of small anharmonicities, that is, when the anharmonicity is much smaller than the width of the involved transition, the peak amplitude in the 2DIR spectrum depends linearly on the anharmonicity.23 Since the diagonal anharmonicity of the N3 asymmetric stretching mode (35 cm-1) is substantially smaller than the width of the N3 peak (49 cm-1), we can assume that the diagonal-peak amplitude is proportional to the diagonal anharmonicity. At larger waiting times, the cross-peak amplitude is proportional to some effective anharmonicity, which is an average anharmonicity among the probed mode and the modes excited at that time delay.12 At the plateau, this effective anharmonicity is due to the low-frequency modes in the molecule and in the solvent that are excited excessively as a result of the mid-IR T-jump and that are coupled to the probed high-frequency mode. In this case, the diagonal peak amplitudes at T = 0 (Adiag 0 ) and at T > 50 ps ) are related via eq 1. (Adiag pl diag

A0

diag Apl

¼

ΔN3 f 3 ΔN pl

ð1Þ

Note that the signal at T = 0 is caused by only a fraction, f, of all N3 groups in the excitation region in the sample, by those excited with the excitation pulses. On the contrary, all N3 groups of the sample found in the excitation area contribute to the signal at the plateau. A linear relation between the temperature increase in the sample and 3 the shift of the N3 peak frequency, ΔN pl , can be assumed without losing generality (Figure 5) as the temperature increase in the sample is very small ΔTemp ¼ 5349

3 ΔN pl

ηN3

ð2Þ

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Figure 3. Peak frequency as a function of temperature for three CO transitions at 1742 cm-1 (A), at 1788 cm-1 (B), and at 1819 cm-1 (C).

Figure 5. N3 peak frequency as a function of temperature, measured as the peak of the first moment. Figure 4. N3 diagonal peak amplitude as a function of the waiting time, T, measured at the magic angle conditions. A fit with a single-exponential function is shown with a red line.

Note that the slope in the temperature dependence, ηN3, should be taken at room temperature, the temperature of the sample in the time-resolved measurements. Interestingly, the N3 peak frequency shifts to smaller values at higher temperatures, while the CO (1742 cm-1) peak frequency increases upon the temperature increase (vide infra). Importantly, the temperature increase generated in the sample by k1 and k2 pulses is the same in the N3 diagonal and N3/CO cross-peak measurements. This temperature increase causes a shift of the CO frequency as seen as a plateau in the N3/CO cross-peak data (Figure 2). ΔTemp ¼

ΔCO pl

ð3Þ

ηCO

By solving eqs 1-3 for the ΔCO pl , one obtains diag

ΔCO pl ¼ ΔN3 f

ηCO A0

diag

ηN3 Apl

ð4Þ

The cross-peak amplitude at T = 0 and T > 50 ps, similar to that for the N3 diagonal peak, is related, respectively, to the N3/CO anharmonicity, ΔN3/CO, and to the effective anharmonicity, ΔCO pl , that is equal to the thermally induced frequency shift of the CO peak. ΔN3 =CO f Across 0 ¼ ð5Þ Across ΔCO pl pl Note that the same excitation fraction, f, is in effect in eq 1 and eq 5, as the same excitation pulses were used in both the diagonal and the cross-peak measurements. Thus, the N3/CO anharmonicity, ΔN3/CO, can be expressed as follows 0 1 diag Apl η Across ð6Þ ΔN3 =CO ¼ @ΔN3 diag A CO 0cross ηN3 Apl A0 The ΔN3/CO anharmonicity of 0.20 cm-1 was calculated using eq 6, and the data are presented in Figures 2-5. Equations 1 and 5 rely on the assumption that the shapes of the transitions involved are the same as the shape of the respective 0-to-1 transition. For example, the N3 diagonal signal at T = 0 is characterized by v: 0 f 1 5350

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Figure 6. Absorption spectrum of Az-PEG4 at 26 °C (blue) and the scaled difference spectrum (green);the spectrum at 26 °C minus that at 22 °C.

and v: 1 f 2 transitions, and the simple model assumes their spectral shapes to be the same; here, v in the quantum number of the N3 mode. The v: 1 f 2 transition, however, is often substantially broader than the v: 0 f 1 transition, which will affect the result. Similarly, for the plateau in both dependences (Figures 2 and 4), the simple model assumes that the absorption peak does not change its shape with temperature but only shifts as a whole. This is also an approximation, as a clear broadening is observed for both N3 and CO absorption peaks at higher temperatures (Figure 6), which is especially severe for the N3 peak. In fact, the CO difference spectrum (Figure 6A) is quite symmetric with only a minor difference in the positive and negative amplitudes, which indicates that the frequency shift can describe well the response of the peak to temperature. For the N3 peak, the response to temperature is clearly much more complex (Figure 6B). To take into account the actual shapes of various transitions involved, we performed numerical modeling. We have modeled the N3 absorption peak as a set of several waveforms in the time domain (S(t) = μ2 exp(-iωt - γt- σ t2/2)) followed by the Fourier transformation of their sum into the frequency domain;18,40 here μ is the transition dipole; ω is the center frequency; and γ and σ are the homogeneous and inhomogeneous linewidths, respectively.41 To reproduce the main features of the N3 peak, at least three spectral components were necessary. The broad but asymmetric character of the N3 absorption peak at any measured temperature permitted many combinations of three different components to model the N3 spectrum. At the same time, if the spectrum at one temperature is fit, it is not possible to use those components at the same frequencies to fit well the spectrum at another temperature (by changing only the widths and contributions of the components). While the N3 absorption peaks at all temperatures are broad and almost featureless, the difference spectra (the difference of the spectra at two temperatures) are very characteristic imposing strong restrictions onto the fit. Therefore, we have employed the following procedure. First, the most resolved spectrum (the one at lowest temperature, -12.6 °C) was modeled. Second, the spectrum at higher temperature (30 °C) was fit using the components (as close as possible) obtained for the low-temperature spectrum. Note, however, that not only the amplitudes (transition dipoles) and widths but also the central frequencies of the components had to be slightly changed to reach a reasonable match with the experimental difference spectrum (Figure 7). The resulting components for the temperature of -12.6 °C (blue) and those for þ30 °C (cyan) are shown in Figure 7, top panel.

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Figure 7. (Bottom) Absorption spectra of Az-PEG4 at -12.6 °C (green) and at þ30 °C (blue) and their difference spectrum (cyan) multiplied by a factor of 10. The red lines represent the modeling. (Top) Two sets of components used to model the N3 absorption peaks at -12.6 °C (blue) and at þ30 °C (cyan) are shown.

Figure 8. N3 diagonal magnitude spectra at the waiting time T = 200 fs (blue) and at T = 100 ps (green). The red curves show the modeling.

This procedure, therefore, delivers three pairs of components, where each component is temperature dependent. Next, three components for modeling the spectrum at any temperature can be obtained by scaling linearly with temperature difference every parameter (μ, ω, γ, and σ) of the three pairs of components obtained at -12.6 and þ30 °C. This approach allowed reproducing well all the N3 absorption spectra at different temperatures. To test the quality of the modeling, we have constructed the N3 diagonal magnitude spectra for small waiting times and for the plateau. Very reasonable matches with the experimental spectra were found (Figure 8) for both spectra. Note that an additional broadening was introduced for the 1 f 2 transitions for every component, in such a way that the ratio of the 0 f 1 to 1 f 2 transition amplitudes was close to 2:1, as observed in the experiment for the overall N3 peak. The N3 diagonal anharmonicity of 32 ( 3 cm-1 was obtained from this modeling (the same value was used for all three components). The amplitude of the diagonal peak at the plateau depends on the temperature difference; the temperature difference of 0.83 °C resulted in the required ratio of the diagonal signal at T = 0 fs to that at the plateau (320fold). Thus, the value of ΔTemp*f is 0.83 °C. Using eq 3, the effective anharmonicity at the plateau of the 3 cross peak was then determined, resulting in ΔN pl = ΔTemp 3 f 3 ηN3 = 0.05 cm-1. The linear scaling with the cross-peak 5351

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The Journal of Physical Chemistry B amplitude (Figure 2) gives the N3/CO anharmonicity of 0.15 cm-1. This value is close to the estimation (0.2 cm-1) obtained without the involved numerical modeling. While the Az-PEG4 compound is too large to perform anharmonic calculations, its structure in chloroform is not expected to be extended (linear) but will likely be coiled. In this case, a broad distribution of the N3-CO distances is expected in solution. At this time, we just acknowledge the complexity of the sample structure and provide a single parameter, the effective N3/CO coupling (0.15 cm-1), which in general can be used to access the N3-CO distance distribution. It is interesting to estimate the temperature increase in the sample induced by excitation of the N3 mode. For that we need to know the fraction of the excited molecules, which requires absolute measurements of the beam size in the sample and of the IR pulse energy and spectrum. The excitation fraction in the conditions of the experiment was estimated to be ca. 7-15%, which leads to an estimate of the temperature increase of 0.060.12 °C. There is an interesting dip in the cross-peak dependence on the waiting time at ca. 40 ps (Figure 2), but there is no such dip in the N3 diagonal signal (Figure 4). We believe that the dip is caused by the difference in signs of the frequency shifts at early delay times and at later times for the cross peak. It is expected that the CO frequency shifts to the lower values when the N3 mode is excited (direct coupling) as well as when other modes at the CO site are populated via the energy transport from the N3 mode (relaxation-assisted contribution). On the contrary, the temperature increase causes a shift of the CO frequency to higher values (Figure 3A). As a result, there is a point of partial cancellation of the two contributions. The cancellation is not complete for the cross peak due to a difference in the shapes from different contributions. Note that the temperature increase causes not only a shift of the peak frequency but also some peak broadening (Figure 5A and 7). Because the N3 frequency is shifted to lower frequencies due to both direct-coupling and thermal equilibrium effects, there is no dip in the N3 diagonal signal. As expected, there is a dip in the CO diagonal peak, which confirms the hypothesis for the origin of the effect. On the basis of the signal-to-noise ratio in the cross-peak measurements, the minimal resolvable values for ΔN3/CO are estimated to be about 1 order of magnitude smaller than that obtained in the current measurement, which places it at ca. 0.02 cm-1. Of course, the ability to calibrate the small anharmonicities for another mode pair will depend on the sensitivity of mode frequencies to temperature. The temperature-induced shift of the fundamental frequency for the high-frequency transitions can have different origins. Conformational diversity in the sample is a common reason of the shift; the change in temperature causes a change in the distribution among different conformations,42,43 which is a dominant contribution to temperature sensitivity for the N3 mode in Az-PEG4. Anharmonic coupling of the high-frequency mode to the lowfrequency modes accessible by temperature can also cause a frequency shift.44 Enhanced temperature sensitivity can be found for some transitions involved in the efficient exciton coupling, as in the case of CO modes in Az-PEG4 (Figure 3A-C). Here, the temperature can not only change the site frequencies but also affect the exciton splitting by modifying the disorder in the system. Despite a large variety of different mechanisms of temperature sensitivity, it is only the value and the sign of the derivative in the temperature dependence that play a role for the described approach.

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4. CONCLUSIONS We proposed and tested a new approach for evaluating accurately small off-diagonal anharmonicities responsible for weak cross peaks in 2DIR measurements. The approach relies on temperature sensitivity of the frequencies of both modes involved and requires only relative 2DIR cross-peak and diagonal-peak measurements. The current sensitivity for determining the N3/ CO anharmonicity was estimated to be ca. 0.02 cm-1. In addition to the direct off-diagonal anharmonicity that characterizes the cross peak at T = 0, the effective anharmonicity at larger waiting times can be evaluated as well. Note that although the origin of the temperature dependence plays no role for the described approach it would work better for modes featuring stronger temperature dependences. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Support from the National Science Foundation (CHE-0750415 and CHE-0936133) is gratefully acknowledged. We thank Nan Zhang and Dr. Janarthanan Jayawickramarajah for helpful discussions on the choice of the molecular system. Computational resources were provided in part by the Center for Computational Science at Tulane University. ’ REFERENCES (1) Hamm, P.; Lim, M.; Hochstrasser, R. M. J. Phys. Chem. B 1998, 102, 6123. (2) Zhang, W. M.; Chernyak, V.; Mukamel, S. J. Chem. Phys. 1999, 110, 5011. (3) Asplund, M. C.; Zanni, M. T.; Hochstrasser, R. M. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 8219. (4) Zhao, W.; Wright, J. C. Phys. Rev. Lett. 1999, 83, 1950–1953. (5) Rubtsov, I. V.; Wang, J.; Hochstrasser, R. M. J. Chem. Phys. 2003, 118, 7733. (6) Khalil, M.; Demirdoven, N.; Tokmakoff, A. J. Chem. Phys. 2004, 121, 362. (7) Zheng, J.; Kwak, K.; Asbury, J.; Chen, X.; Piletic, I. R.; Fayer, M. D. Science 2005, 309, 1338. (8) Fulmer, E. C.; Ding, F.; Zanni, M. T. J. Chem. Phys. 2005, 122, No. 034302/1. (9) Rubtsov, I. V.; Kumar, K.; Hochstrasser, R. M. Chem. Phys. Lett. 2005, 402, 439. (10) Kozich, V.; Dreyer, J.; Ashihara, S.; Werncke, W.; Elsaesser, T. J. Chem. Phys. 2006, 125, No. 074504/1. (11) Shim, S.-H.; Strasfeld, D. B.; Zanni, M. T. Opt. Express 2006, 14, 13120. (12) Kurochkin, D. V.; Naraharisetty, S. G.; Rubtsov, I. V. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 14209. (13) Cahoon, J. F.; Sawyer, K. R.; Schlegel, J. P.; Harris, C. B. Science 2008, 319, 1820. (14) Kraemer, D.; Cowan, M. L.; Paarmann, A.; Huse, N.; Nibbering, E. T. J.; Elsaesser, T.; Miller, R. J. D. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 437. (15) Garrett-Roe, S.; Hamm, P. J. Chem. Phys. 2009, 130, 164510/1. (16) Maekawa, H.; Ballano, G.; Toniolo, C.; Ge, N.-H. J. Phys. Chem. B 2010jp105527n. (17) Scheurer, C.; Mukamel, S. J. Chem. Phys. 2001, 115, 4989. (18) Scheurer, C.; Mukamel, S. J. Chem. Phys. 2002, 116, 6803. (19) Falvo, C.; Hayashi, T.; Zhuang, W.; Mukamel, S. J. Phys. Chem. B 2008, 112, 12479. 5352

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dx.doi.org/10.1021/jp1094189 |J. Phys. Chem. B 2011, 115, 5347–5353