Multiresonant Coherent Multidimensional Vibrational Spectroscopy of

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Multiresonant Coherent Multidimensional Vibrational Spectroscopy of Aromatic Systems: Pyridine, a Model System Kathryn M. Kornau, Mark A. Rickard, Nathan A. Mathew, Andrei V. Pakoulev, and John C. Wright* Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States ABSTRACT: Multiresonant four wave mixing has been used to measure the coherent multidimensional spectroscopy (CMDS) of representative aromatic ring modes using pyridine as a model system. This work identifies the cross-peaks that appear between several modes and measures their coherent and incoherent dynamics. The work also explores the consequences of using multiresonant CMDS for molecules with transition moments that are typical of most vibrational modes. Typically, CMDS experiments rely on using transitions with exceptionally large transition moments. To observe crosspeaks, the pyridine concentration was raised until absorption effects became very important. These effects interfere with the parametric CMDS coherence pathways, but they do not make important contributions to the nonparametric pathways.

’ INTRODUCTION Coherent multidimensional spectroscopy (CMDS) employs two different experimental strategies for obtaining multidimensional spectra.1,2 Multiresonant CMDS uses a sequence of independently tunable, coherent excitation pulses to excite a series of multiple quantum coherences (MQCs).3,4 Pairs of quantum states within the MQCs radiate output fields at the pairs’ difference frequencies. Because the excitation pulses are coherent, the radiating pairs of quantum states within the excitation volume are coherent, so their re-emission is cooperative (their intensity scales as N2) and directional. The output beam direction is defined by momentum conservation and the beam intensity is dependent on the experimental phase matching conditions. Multiresonant CMDS requires only short-term phase coherence during the excitation process so the excitation pulses can have very different frequencies. Multidimensional spectra result from measuring the output beam intensity as a function of the excitation frequencies.3 When the excitation pulses are resonant with transitions between quantum states, the output intensity is resonantly enhanced. In the steady state approximation, the resonant enhancement occurring for each excitation field interaction scales as the ratio of the Rabi frequency of the transition to its dephasing rate (Ω/Γ).3 In mixed frequency/time domain multiresonant CMDS, the excitation pulse width is comparable to the dephasing rate, so it is long enough to excite specific quantum states but short enough to resolve the dynamics.5,6 Scanning the time delay between the excitation pulses while fixing the excitation frequencies creates a multidimensional map of the coherent and incoherent dynamics for specific features in the CMDS spectrum. r 2011 American Chemical Society

Alternatively, time domain CMDS methods like 2D-IR heterodyne the output beam with a local oscillator to temporally resolve the rapid phase oscillations of the different coherences created in the excitation process.7-9 Fourier transformation of the phase oscillations creates multidimensional spectra. It is crucial to stabilize the experimental system and maintain excellent longterm phase coherence in order to avoid spectral artifacts. Typically, it is necessary to create the multiple excitation beams from a single beam to achieve long-term phase coherence. Longterm phase coherence cannot currently be established between excitation beams with very different frequencies, so fully coherent CMDS is not possible. It is possible to use different frequencies with partially coherent CMDS pathways where intermediate populations isolate the temporal oscillations of different coherences.10 Vibrational CMDS currently uses three different strategies for achieving resonance enhancement. The earliest are fully resonant coherent Raman methods that use sequential resonances with an electronic state, a vibrational state, and a vibronic state.3,11-13 Doubly vibrationally enhanced (DOVE) CMDS uses two vibrational resonances followed by an electronic resonance.14-16 Triply vibrationally enhanced (TRIVE)5,6,17 and 2D-IR7-9 methods use three vibrational resonances. The output frequency of the first two strategies occurs in the visible and is spectrally resolved from the excitation frequency. The resonant enhancements Special Issue: Graham R. Fleming Festschrift Received: November 2, 2010 Revised: February 11, 2011 Published: March 24, 2011 4054

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The Journal of Physical Chemistry A are sufficient that typical Raman and infrared active modes can be measured by these strategies.14,16,18 The output frequency from the last strategy occurs in the infrared and is not spectrally resolved from the excitation pulses. Because infrared detectors are less efficient and because the signal must be distinguished from scattering from the excitation pulses, typical experiments using this strategy rely on using infrared absorption transitions with very strong absorption coefficients. In this paper, we measure the TRIVE CMDS spectra of pyridine and its coherent and incoherent dynamics. This study has two goals. First, pyridine is representative of the broad range of molecules that do not have the very strong transition moments usually used for TRIVE and 2D-IR CMDS, and it is important to explore the challenges that these methods face in studying molecules with typical transition moments. These modes have transition dipole moments on the order of 0.01 D, much weaker than the strong carbonyl and cyano modes usually studied by 2DIR.8,9 To compensate for the weak transition moments, the experiments are performed at higher concentration to see signals from weak modes. The higher concentrations result in strong absorption effects that introduce artifacts into the CMDS spectra. The absorption effects can be described by an earlier treatment that accounts for the absorption of the excitation beams and the output beam as well as the refractive index changes that affect the phase matching conditions.19 The importance of the absorption effects depends on whether the resonance frequencies in a particular pathway occur at absorption frequencies. If a pathway involves resonance with combination band or overtone states, the resonance frequency is shifted from the absorption frequency by the anharmonicity so the absorption effects will be lessened. If the anharmonicity is large enough, some of the transitions in a pathway may not involve any appreciable absorption. We have taken advantage of these pathways to measure the coherent and incoherent dynamics of several states. Together with simulations, we then extract the dephasing and population relaxation rates of these quantum states. The second goal is to clarify the assignments of the pyridine vibrational spectra. There have been several studies detailing the mode assignments of fundamentals, overtones, and combination bands in pyridine, that sometimes offer conflicting assignment, particularly for the overtones and combination bands.20-23 As in many molecules, assigning the overtones and combination bands of pyridine is challenging because of the large number of bands in a given region and because these bands are often weak and/or broad, leading to spectral congestion. The experiments described in this paper use TRIVE CMDS to clarify the overtone and combination band assignments. Table 1 compares several of these assignments for three modes in the 1400-1600 cm-1 fundamental and 3000-3200 cm-1 overtone/combination band regions of pyridine. Results from our ab initio calculation are also included for comparison.

’ THEORY The excitation pulse widths in these experiments are wider than the coherence dephasing times so it is reasonable to approximate the resonance enhancements using steady state conditions. TRIVE CMDS involves 12 different coherence pathways for cross-peaks and 16 pathways for diagonal peaks.24 The temporal ordering of the excitation pulses and the detection frequency determine the relative importance of each pathway. As specific examples, the third order susceptibility (χ(3)) created by

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20

1

s v0 g and the parametric coherence pathway gg f gv sf gg f -2

20

1

the nonparametric coherence pathway gg f gv sf vv f s ðv þ v0 Þ, v is ! 2 2 NF μ 0 g μvg 4 1 1 v χð3Þ ¼ ð1Þ  Δgg Δv0 g Δvv Δðν þ v0 Þ, v p3 Δvg where N, F4, μba, Δba = δba - iΓba, δba, and Γba are the concentration, four wave mixing field enhancement factors, transition moment, resonance denominator, detuning factor, and dephasing rate for the ba coherence, respectively.2,3 An example detuning factor is δ(vþv0 ),v = ω(vþv0 ),v - (ω1 - ω-2 þ ω20 ). The two pathways have been labeled VR and Vβ, respectively.6 The homodyne detected output intensity is proportional to the square of the third order susceptibility’s magnitude. The output intensity is also directly related to the infrared absorption cross-section: ! εv0 g Av0 g εðv þ v0 Þ, v Aðv þ v0 Þ, v sinc2 ðΔkzÞI1 I22 Iout ¼ Cεvg εv0 g Avg jΔgg j2 jΔvv j2 ð2Þ where Aba and εba are the absorbance and peak molar absorptivity of the ba transition, respectively, the sinc function expresses the phase matching condition, Im is the excitation intensity of the mth field, and C is a constant containing fundamental constants, field enhancement factors, and transition frequencies. Note that measurement of the A(vþv0 ),v absorbance would require an initial v state population. The expression shows that the signal scales linearly with the absorbances and molar absorptivities of the two vibrational transitions. Samples with low transition moments can be compensated by using longer pathlengths and higher concentrations but the low transition moments will still limit the signal. In addition to enhancing the signal, absorption also decreases the excitation intensity as the excitation beams penetrate further into the sample and it decreases the output signal as it escapes from the sample. In addition to absorption effects, a resonant vibrational state introduces anomalous dispersion of the refractive index that can degrade phase matching. Modeling of these effects uses the M-factor to correct for the predicted intensity dependence on the excitation frequencies.19 The M-factor dependence on absorbance is defined by " #2 10-As =2 - 10-A123 =2 ð3Þ M ¼ ðAs - A123 Þ lnð10Þ=2 where A123 is the sum of the three excitation pulse absorbances and As is the absorbance of the output. For TRIVE CMDS, where only two frequencies are involved, eq 3 becomes !2 -Av0 g -Avg 1 - 10 ð4Þ M  10 Av0 g ln 10 so the observed intensity is the product of eqs 2 and 4. The enhancement resulting from increased absorption predicted by eq 2 dominates at low absorbances but the attenuation resulting from excitation and output beam absorption becomes important at high absorbances. Figure 1 shows the observed intensity as a function of the absorbances at the two excitation frequencies for a TRIVE CMDS experiment. Note that the 4055

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Table 1. Mode Assignments in Pyridinea Urenab23

Urenab23

Klotsb20

Afifib22

Wong and Colsonc21

ab initio anharmonic frequenciesd

υ22

1437

1437

1441/1438h

1441.9

1447.0

υ5

1482

1483

1482

1483.4

1486.1

υ21

1574

1574

1575

1580.5

1578.6

υ4

1581

1581

1583

1583.9g

1582.2

υ13þυ24

1597

1598

2υ22

2873 δ = 1

2872 δ = 2

υ5þυ22

2918

2υ5 υ22 þ υ21

3000 δ = 11

υ22 þ υ4

1609.0 δ = 4.4 2879.4 δ = 4.4

2889.7 δ = 4.3 2924.7 δ = 8.5

2986 δ= 25

3020 δ = -7

2963.3 δ = 3.2 3008.2 δ = 17.4

3001 δ = 17

3030f δ = -9

3013.4 δ = 15.8

υ20

3025

3000.3

υ19

3033

3014.7

υ3

3052

3045.6

υ5 þ υ21

3060.3 δ = 4.4

υ4 þ υ5

3061

υ2 2υ21

3078 3145 δ = 3

υ21 þ υ4

3157e δ = -2

2υ4

3166 δ = 4

3077.5 δ = -9.1 3145 δ = 3

3130 δ = 20

3067.2 3161.7 δ = -4.5

3159.7 δ = 1.3

3176e δ = -14

3159.7 δ = 4.7

3164.6 δ = -3.8

3159.7 δ = 8.1

3171 δ = -6.6

υ19 þ υ22

4469.7 δ = -8.0

υ2 þ υ22

4523.3 δ = -9.0

υ20 þ υ22

4469.6 δ = -22.2

υ3 þ υ22

4497.7 δ = -5.1

The δ designates the anharmoncity values. b Reported frequencies observed in liquid IR spectrum except where noted. c Reported frequencies observed in vapor IR spectrum. d Gaussian 03 -B3LYP/cc-pVTZ method and basis set. The Gaussian frequencies were calculated using unscaled harmonic frequencies. e Observed in (polarized) liquid Raman spectrum, δ calculated relative to frequencies observed in liquid IR. f Tentative assignment. g Observed triplet with bands at 1582.2 and 1583.2 cm-1, δ calculated relative to band at 1583.0 cm-1. h Splitting, δ calculated relative to 1438 cm-1. a

the population relaxation and coherence dephasing dynamics must include the actual excitation pulse widths. The modeling uses the strategy developed by Gelin et al.25,26 The electric field is the sum of the three excitation fields E¼

∑ Eoi e-ð i ¼ 1, 2, 2 0

Þ ðeiωi t þ e-iωi t Þ

t - ti 2 σ

ð5Þ

and the temporal evolution of the coherences and populations is defined by numerically integrating the Liouville equation in the rotating wave approximation   μjk E i μik E iωik t iωkj t _F ~ kj e ~ ij ¼ iðωRW - ωij þ iΓij Þ~ ~ ik e F ij þ F F 2 p p ð6Þ Figure 1. Attenuation factor as a function of the absorbance at the two excitation frequencies.

intensity reaches a peak and declines as a function of the Av0 g absorbance at ω1 because of the absorption of the excitation and output beams. It reaches an asymptote as a function of increasing Avg absorbance at ω2, where the enhancement caused by the first two interactions matches the excitation and output beam absorption. We shall see that this difference is responsible for decreased intensity at the center of the v0 g resonance that is not apparent at the center of the vg resonance. Because multiresonant CMDS methods use excitation pulse widths that are comparable to the dephasing rates, calculations of

~ije-ωRWt and ωRW is the frequency chosen for the where Fij = F rotating wave approximation. The propagation uses the superoperator approach where the ~ij form a vector and assumes the weak field limit. The individual F final coherence is integrated in time to calculate the output intensity. Because our experiments use a monochromator to spectrally resolve the free induction decay of the output coherence, the frequency dependence of the final coherence is convoluted with the monochromator instrumental function.

’ EXPERIMENTAL SECTION The experiment uses two independently tunable excitation beams labeled ω1 and ω2.6 The ω2 beam is divided to create a 4056

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Figure 2. Fourier transform infrared spectra of the pyridine sample in two spectral regions.

third beam labeled ω20 . The time delays between the beams are defined by τ21  τ2 - τ1 and by τ20 1  τ20 - τ1 . The beams are k1 - B k2 þ B k 20 angled in a boxcar geometry to create the B k out = B phase matching condition for TRIVE CMDS and focused to spot sizes of ∼100 μm. The excitation pulses have a ∼20 cm-1 bandwidth in the 1400 and 1600 cm-1 range of our experiments. A monochromator spectrally resolves the output beam frequency, ωm, and measures the intensity as a homodyne signal. Note that the monochromator measures both the driven signal created during the last excitation pulse and the free induction decay that occurs after the excitation pulse. The monochromator increases the spectral resolution of the experiment beyond the bandwidth of the excitation pulses. The typical bandpass of the monochromator was ∼4 cm-1. The signal intensity was corrected for changes in the excitation pulse intensities over the duration of each scan. Typically, the ω1 and ω2 beams have pulse energies that vary from ∼0.5 μJ at 1438 cm-1 to ∼0.75 μJ at 1581 cm-1 and this variation changes the relative intensities of the different peaks in the CMDS spectra. The sample was a 125 μm thick solution of pyridine in tetrachloroethylene. Anharmonic frequencies27,28 of pyridine were calculated using Gaussian 0329 with the B3LYP method30-32 and cc-pVTZ basis set.33

’ RESULTS Figure 2 shows the pyridine infrared spectra for a 0.63 M concentration in the ring breathing region and the C-H stretching region. The 0.63 M concentration was chosen to improve the measurement of weaker spectral features. Five peaks appear in the ring breathing region at 1438, 1481, 1573 (shoulder), 1581, and 1597 cm-1. These peaks have been assigned to the υ22, υ5, υ21, and υ4 fundamentals and the υ13þυ24 combination band, respectively.20-23 The absorbance of the strongest peak at 1438 cm-1 is 1.8, so absorption effects must be considered in the multidimensional spectra. Five peaks appear in the C-H stretching region at 3001, 3025, 3033, 3052, and 3078 cm-1. These peaks have been previously assigned to the υ21þυ22 combination band and the υ20, υ19, υ3, and υ2

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fundamentals, respectively.20-23 There is also a shoulder that is visible at 2993 cm-1 that will become important later. Figure 3 shows the 2D spectra of the diagonal peaks and crosspeaks in the ring breathing region when the excitation beams are temporally overlapped. Due to the wide frequency range and narrow excitation bandwidth, 2D scans were performed only near the different resonances. The detection conditions were optimized for each region separately, and the intensities were normalized to the most intense feature. To compare the absolute intensities, the excitation pulse intensities and detection scaling factors were combined to relate the measured peak intensities of the four features. Table 2 summarizes the relative detection sensitivities for each spectral region using the most intense feature as the reference. We did not see additional peaks in the spectral regions between the regions shown. Pathways that excite double quantum coherences are particularly valuable for defining the anharmonicities of combination bands and overtones. The region near 1580 cm-1 is complicated by the presence of the unresolved υ21 and υ4 modes. To probe this region, the excitation pulse time delays were changed to τ20 1 = 0 and τ21 = 1.25 ps delay times. This choice of delay times selects 1

20

the double quantum coherence pathways gg f s v0 g sfðv þ v0 Þ, -2

20

1

-2

g f ðv þ v0 Þ, v and gg sf vg f s ðv þ v0 Þ, g f ðv þ v0 Þ, v. The TRIVE CMDS spectrum under these conditions appears in Figure 4. There are two features. The brighter feature corresponds to the double quantum coherence transitions involving the υ21 þ υ4 combination band. The weaker feature corresponds to transitions involving the 2υ4 overtone. The interpretation of these features will be discussed later. The diagonal peak region associated with the 1438 cm-1 vibrational mode has the most intense peak at ω1 = 1434 cm-1, while the intensity at ω1 = 1438 cm-1 is 0 and τ21 > τ20 1 create double quantum coherences after the first two interactions, while the regions where τ20 1 > 0 and τ20 1 > τ21 create zero quantum coherences after the first two interactions. Figures 6b and 7b show simulations of the dynamics. It is also of interest to examine the coupling between the ring breathing and C-H stretching modes. Figures 8-10 show the cross-peaks involved in this region. Figures 8 and 9 were taken with temporally overlapped excitation pulses. They show the cross-peaks between the pyridine C-H stretching modes and the regions of the υ22 ring breathing mode (Figure 8) and the υ21 and υ4 ring breathing modes (Figure 9). Figure 10 shows the spectral changes that occur in the cross peaks between the C-H stretching modes and the υ21 and υ4 ring breathing modes when

Two Dimensional Spectroscopy. The strongest features in the CMDS spectra of Figures 3 and 8 occur for the partially coherent pathways involving intermediate populations such as -2

20

1

-2

20

1

gg f gv sf gg f s v0 g (pathway VR) and gg f gv sf vv f s 0 ðv þ v Þ, v (pathway Vβ), so two peaks are expected when ω1 is resonant with the gg f v0 g and vv f (vþv0 ),v transitions.5 The two peaks are separated by the anharmonicity of the combination band or overtone (when v0 = v). The brightest features in Figures 3 and 8 correspond to pathways like Vβ involving the combination band or overtone. Except for the 1581 cm-1 diagonal peak, the intensity is a minimum at the frequency of the fundamental vibrational transition. The peak is suppressed by the strong absorption of the excitation and output beams. The combination band and overtone transitions occur at frequencies that are offset from the absorption and are not suppressed. Note that in accordance with the predicted dependence shown in 4058

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20

-2

s v0 g sfðv þ v0 Þ, g f that define fully resonant pathways gg f 0

2

Figure 4. Coherent two-dimensional spectrum when the excitation pulse delay times are τ21 = 1.25 ps and τ20 1 = 0 ps. The lower right of the 1 20 -2 brighter peak is caused by pathways like gg f s v0 g sfðv þ v0 Þ, g f ðv þ v0 Þ, v, where (v,v0 ) = (v4,v21), while the upper left is caused by path20 1 -2 ways like gg sf vg f s ðv þ v0 Þ, g f ðv þ v0 Þ, v, where (v,v0 ) = (v21,v4). The 0 lower right of the weaker peak is caused by pathways like 2 1 -2 gg sf vg f s 2v,0 g f 2v, v, while the upper left is caused by pathways 1 2 -2 like gg f s vg sf 2v, g f 2v, v, where v = v4. The color bar scale is logarithmic.

Figure 5. The concentration dependence of one-dimensional slices of the spectra in Figure 3 when ω2 = 1438 cm-1 and ω1 is scanned. The pyridine concentration is indicated for each spectrum.

Figure 1, a comparable intensity minimum does not occur as ω2 scans across the same absorption features. The fundamental vibrational modes creating the diagonal peaks correspond to the υ22 mode at 1438 cm-1 and the υ21 and υ4 modes at 1573 and 1581 cm-1, respectively. The anharmonicities of the combination bands and overtones correspond to the peak separations in pathways VR-Vβ. The separation between the 1434 and 1438 cm-1 diagonal features in Figure 3 provides a 2υ22 overtone anharmonicity of ∼4 cm-1. The 2υ4 anharmonicity cannot be resolved from the diagonal peak at 1581 cm-1. Figure 4 shows a TRIVE CMDS spectrum for excitation pulse time delays of τ21 = 1.25 ps and τ20 1 = 0 ps

1

-2

ðv þ v0 Þ, v and gg sf vg f s ðv þ v0 Þ, g f ðv þ v0 Þ, v that have been labeled IIR and IVβ, respectively.6 These pathways create peaks with antidiagonal character, as would be expected for having ω1 þ ω2 resonant with the g f v þ v0 transition. We assign the brighter feature to a pathway involving the ν21 þ ν4 combination band at 3158 cm-1. The corresponding anharmonicity is -4 cm-1. The antidiagonal character of the features can be understood as follows. The lower right part of the brighter feature corresponds to an initial ω20 excitation of ν21 followed by an ω1 excitation of the ν4 þ ν21 combination band using pathways like IVβ. The upper left part of the feature corresponds to an initial ω1 excitation of ν21, followed by an ω20 excitation of the ν4 þ ν21 combination band using pathways like IIR. We assign the weaker feature to a pathway involving the 2υ4 overtone at 3174 cm-1. Here, the antidiagonal character results from an initial ω20 excitation of ν4 followed by an ω1 excitation of the 2ν4 overtone using pathways like IVβ for the lower right part of the feature and an initial ω1 excitation of ν4 followed by an ω20 excitation of the 2ν4 overtone using pathways like IIR for the upper left-hand part of the feature. The corresponding anharmonicity is -12 cm-1. The -4 cm-1 is in agreement with those calculated in Table 1. The -12 cm-1 is twice as large as that calculated. Note also that there is no evidence for diagonal peaks in Figure 3 at the 1481, 1573, and 1597 cm-1 frequencies observed in Figure 2. These frequencies have been assigned to υ5, υ21, and υ13 þ υ24. Urena et al. did not report an overtone for υ5 so this mode may not have sufficient anharmonicity for it to appear in the CMDS spectrum.23 In addition, the υ5 transition moment is weaker than υ22 and υ4. An overtone has been reported for the υ21 mode but the anharmonicity is small. Different calculations predict both positive and negative anharmonicities. The absence of the υ21 diagonal feature is therefore attributed to a small anharmonicity and interference from the nearby and very strong υ4 mode. The peak assigned to the υ13 þ υ24 combination band is also weak but should still appear. Its absence is attributed to a lower transition dipole for υ13 þ υ24 f 2υ13 þ 2υ24. Two cross-peaks also appear in Figure 3 at (ω1, ω2) = (1420, 1576) and (1565, 1438) cm-1. The latter is 16 times weaker when corrected for excitation intensity and measurement sensitivity (see Table 2). The ω2 value of the (1420, 1576) cm-1 cross-peak lies between the frequencies of the υ21 and υ4 modes. The peak expected at ω1 = 1438 cm-1 from the υ22 transition is absent, again because of strong absorption effects at the peak of the transition. The bright peak at ω1 = 1420 cm-1 contains contributions from both the υ21 f υ21 þ υ22 and υ4 f υ4 þ υ22 combination bands. Because the line shape is symmetrical, the two contributions must have similar anharmonicities of ∼18 cm-1. This anharmonicity agrees with previous measurements and calculations summarized in Table 1. Although the individual contributions of the υ21 and υ4 modes could not be resolved for the (1420, 1576) cm-1 cross-peak, they are resolved for the (1565, 1438) cm-1 cross-peak in Figure 3 because the monochromator resolves the free induction decay signal from both modes. The ω2 value of the (1565, 1438) cm-1 cross-peak matches the frequency of the υ22 mode. The shoulder on the cross-peak at ω1 = 1573 cm-1 is assigned to the υ21 mode. The peak expected at ω1 = 1581 cm-1 from the υ4 transitions is absent, again because of strong absorption effects at the peak of 4059

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Figure 6. Temporal scans of the excitation pulse delays between pulses 20 and 1 (x-axis) and -2 and 1 (y-axis) for fixed values of (ω1 = ωm, ω2) = (1420, 1577) cm-1. The experimental and simulated spectra are on the left and right, respectively. The color bars are logarithmic.

Figure 7. Temporal scans of the excitation pulse delays between pulses 20 and 1 (x-axis) and -2 and 1 (y-axis) for fixed values of (ω1 = ωm, ω2) = (1565, 1438) cm-1. The experimental and simulated spectra are on the left and right, respectively. The color bars are logarithmic.

the transitions. There is a bright peak at ω1 = 1565 cm-1 and a weak feature at ω1 = 1555 cm-1 that we attribute to the υ22 f υ4 þ υ22 and υ22 f υ21 þ υ22 combination band transitions, respectively. These assignments correspond to anharmonicity values of 16 and 18 cm-1 for the υ4 þ υ22 and υ21 þ υ22 combination band states, respectively. These values agree well with the Gaussian calculation values in Table 1. In addition, the relative intensity of the two features is consistent with the relative υ4 and υ21 absorbances in Figure 2 and the anharmonicities would place the two contributions to the (ω1, ω2) = (1420, 1576) cm-1 cross-peak at (1420, 1573) and (1422, 1581) cm-1 where they are not resolved. There are two strong cross-peaks in Figure 8 at ω2 = 2993 and 3025 cm-1. The first is at the position expected for the υ21 þ υ22 combination band predicted from our analysis of the (ω1, ω2) = (1555, 1438) cm-1 cross-peak in Figure 3. The 2993 cm-1 frequency matches the shoulder on the main line at 3000 cm-1 in the FTIR spectrum of Figure 2. Urena assigned the 3000 cm-1 peak to the υ21 þ υ22 combination band.23 It is also at the predicted 3003 cm-1 position of the υ4 þ υ22 combination band obtained from the analysis of Figure 3. The spectrum in Figure 8 shows there is an offset in ω2 between the bright (ω1, ω2) =

(1420, 2993) cm-1 peak and the weak (1440, 3000) cm-1 feature. The offset indicates the Figure 8 spectrum resolves the shoulder and the main peak in the Figure 2 FTIR spectrum. We therefore attribute the 2993 cm-1 shoulder in the FTIR spectrum to the υ21 þ υ22 combination band and the stronger peak near 3000 cm-1 to the υ4 þ υ22 combination band. We note that we cannot rule out that the 3000 cm-1 peak is a C-H stretching mode. Note that the peaks expected at ω1 = 1438 cm-1 are suppressed by the strong absorption feature. The peak at ω2 = 2993 cm-1 is not suppressed because of the 18 cm-1 anharmonic shift of the υ22 combination band. In this interpretation, a typical pathway is 20

-2

1

gg sf ðυ21 þ υ22 Þ, g f ðυ21 þ υ22 Þ, ðυ21 þ υ22 Þ f s ðυ21 þ υ22 Þ, υ21 . The second strong cross-peak at (ω1, ω2) = (1430, 3025) cm-1 in Figure 8 occurs when ω2 is resonant with the stretching mode. A typical pathway for this peak is υ20 C-H 20 1 -2 gg sf υ20 , g f υ20 , υ20 f s ðυ20 þ υ22 Þ, υ20 . The ω1 value of the peak is anharmonically shifted by 8 cm-1 from the 1438 cm1 frequency of the fundamental transition, which is suppressed by the strong absorption. This anharmonicity value differs from the calculated value in Table 1. 4060

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Figure 8. Coherent two-dimensional spectra of the cross-peaks between the pyridine C-H stretching modes and the υ22 mode regions. with the fundamental The cross-peaks appearing when ω1 is resonant 20 1 -2 correspond 0 to pathways like gg f gv sf gg f s v0 g. Pathways like 2 1 -2 gg f gv sf vv f s ðv þ v0 Þ, v are responsible for the peaks that are anharmonically shifted so ω1 is resonant with combination band states. The excitation pulses are temporally overlapped and the monochromator is scanned so ωm = ω1. The color bar scale is logarithmic.

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Figure 10. Coherent two-dimensional spectra of the cross-peaks between the pyridine C-H stretching modes and the υ21 and υ4 mode regions when the excitation pulse delay times are τ21 = τ20 1 = -1 ps. The monochromator is scanned so ωm = ω1 and the color bar scale is logarithmic.

some of the features near 3060 cm-1 became more important. In the Figure 2 FTIR spectrum, these lower frequency features correspond to the shoulders on the edge of the bands at 2995 and 3001 cm-1 so the populations corresponding to these shoulders decay rapidly. These features also appear at lower ω1 values, indicating that the anharmonicity associated with these states is larger than those evident from Figure 3. The most intense features in the Figures 9 and 10 spectra appears near ω2 = 2995 and 3003 cm-1, the frequencies of the υ21 þ υ22 and υ4 þ υ22 combination bands. These features would correspond to pathways such as 20

-2

1

gg sfðυ21 þ υ22 Þ, g f ðυ21 þ υ22 Þ, ðυ21 þ υ22 Þ f s ðυ21 þ υ22 Þ, υ22 2

Figure 9. Coherent two-dimensional spectra of the cross-peaks between the pyridine C-H stretching modes and the υ21 and υ4 mode regions. The excitation pulses are temporally overlapped and the monochromator is scanned so ωm = ω1. The color bar scale is logarithmic.

The same cross-peak features appear in Figures 9 and 10 at similar ω2 frequencies when ω1 is resonant with transitions involving υ21 and υ4. However, there is significant intensity at a wider range of ω2 values in the C-H stretching region. In Figure 9, the excitation pulses are temporally overlapped and all 12 fully coherent and partially coherent pathways contribute. In Figure 10, the ω1 pulse is delayed by 1 ps so the partially coherent pathways with intermediate populations contribute dominantly. The features below ω2 = 2980 cm-1 have disappeared, while

0

-2

1

or gg sfðυ4 þ υ22 Þ, g f ðυ4 þ υ22 Þ, ðυ4 þ υ22 Þ f s ðυ4 þ υ22 Þ, υ22 , respectively. The anharmonicities for these pathways matches those determined from Figure 3. Finally, the cross-peak at (ω1, ω2) = (1564, 3020) cm-1 corresponds to an anharmonic coupling between the υ20 and either the υ21 or υ4 modes. The anharmonicity for this υ21 þ υ20 or υ4 þ υ20 combination band would be 9 or 17 cm-1, respectively. Coherent and Incoherent Dynamics. The 2D delay scans in Figures 6 and 7 show the dynamics of the (ω1, ω2) = (1420, 1576) and (1565, 1438) cm-1 features, respectively, that result from pathways involving combination band states. The use of the nonparametric pathways involving combination band states simplifies the data analysis because it limits the number of populations and coherences that must be considered. In addition, the different time orderings included in the experiment isolate the individual coherence pathways. For cross-peaks, this choice 20

-2

1

s ðv þ v0 Þ, g f results in three dominant pathways: gg sf vg f -2

2

0

1

0

2

-2

ðv þ v0 Þ, v, gg f gv sf vv f s ðv þ v0 Þ, v, and gg sf vg f vv 1

s ðv þ v0 Þ, v, and these pathways are labeled IVβ, Vβ, and f VIβ, respectively. There are other pathways with different time orderings but these pathways are not fully resonant for the conditions of these experiments so they are not included in the Discussion. For diagonal peaks where v = v0 and the anharmonicity is small, all pathways can contribute. In Figure 6, the (ω1, 4061

dx.doi.org/10.1021/jp1104856 |J. Phys. Chem. A 2011, 115, 4054–4062

The Journal of Physical Chemistry A

ARTICLE

Table 3. Frequency, Anharmonicity, Dephasing Rate, and Population Relaxation Rate of Different Modes mode frequency (cm-1)

ν22

ν21

ν4

ν20

2ν22

ν21 þ ν22

ν4 þ ν22

ν21 þ ν4

1438

1573

1581

3025

2872

2993

3003

4

18

16

anharmonicity (cm-1) dephasing rate (ps-1)

1.13

2.8

population relaxation rate (ps-1)

0.15

0.27

ω2) = (1420, 1576) cm-1 cross-peak intensity decay along the negative diagonal direction reflects the population relaxation of the υ4 and υ21 states.5 The decay along the negative y-direction or negative x-direction reflects the dephasing of the coherence between the υ4 or υ21 states and the ground state, while the decay along the positive diagonal direction reflects the dephasing of the υ22 coherence with the ground state. The decay along the positive x-direction reflects the dephasing of the zero quantum coherence between υ22 and υ4 or υ21. The decay along the positive y-direction reflects the dephasing of the double quantum coherence between (υ22 þ υ4 or υ21) and the ground state. Similar logic connects Figure 7 with the different coherences and populations. The rapid decay in all directions but the negative diagonal shows the coherent dynamics is much faster than the population relaxation rate, so the partially coherent pathways involving populations dominate the spectroscopy. Nevertheless, the fully coherent pathways make important contributions in Figures 6 and 7 and allow the coherence dephasing rates to be measured. Shorter excitation pulses would allow better access to the fully coherent pathways. The simulations shown in Figures 6b and 7b result from the numerical integration of the Liouville equation using the superoperator approach. The population relaxation and dephasing rates are adjusted to match the data. The transition frequencies defined in this work are used directly. The frequencies, anharmonicities, dephasing rates, and population relaxation rates are summarized in Table 3 for each of the modes.

’ CONCLUSIONS The experiments described in this paper represent the first TRIVE CMDS on compounds with aromatic rings. Multiple strategies were used in this work to resolve the difficulties encountered in observing and resolving spectral features. Weak features were enhanced by using higher concentrations to raise weak transitions but this strategy caused absorption artifacts in the spectra. The fast dephasing rates limited the use of fully coherent pathways in these experiments. Use of excitation pulses with widths comparable to the dephasing times would allow the use of the fully coherent pathways. In some cases, it was possible to use double quantum coherence pathways to resolve spectral features and measure anharmonic shifts of combination bands and overtones. The combined use of spectral and temporal scans allowed both two-dimensional spectroscopy and measurement of the coherent and incoherent dynamics. ’ ACKNOWLEDGMENT This work was supported by the National Science Foundation under Grants CHE-0650431 and DMR-0906525.

2ν4

ν20 þ ν22

3158

3174

4455

-4

-12

8

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dx.doi.org/10.1021/jp1104856 |J. Phys. Chem. A 2011, 115, 4054–4062