Efficient Vibrational Energy Transfer through Covalent Bond in Indigo

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Efficient Vibrational Energy Transfer through Covalent Bond in Indigo Carmine Revealed by Nonlinear IR Spectroscopy Xuemei He, Pengyun Yu, Juan Zhao, and Jianping Wang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06766 • Publication Date (Web): 18 Sep 2017 Downloaded from http://pubs.acs.org on September 21, 2017

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The Journal of Physical Chemistry

Efficient Vibrational Energy Transfer through Covalent Bond in Indigo Carmine Revealed by Nonlinear IR Spectroscopy

Xuemei He,†,‡ Pengyun Yu,†,‡ Juan Zhao,†,‡ and Jianping Wang*,†,‡ †

Beijing National Laboratory for Molecular Sciences; Molecular Reaction Dynamics Laboratory, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China ‡

University of Chinese Academy of Sciences, Beijing 100049, P. R. China *

Corresponding author, [email protected]

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Abstract

Ultrafast vibrational relaxation and structural dynamics of indigo carmine in dimethylsulfoxide were examined using femtosecond pump-probe infrared and two-dimensional infrared (2D IR) spectroscopies. Using the intramolecularly hydrogen-bonded C=O and delocalized C=C stretching modes as infrared probes, local structural and dynamical variations of this blue dye molecule were observed. Energy relaxation of vibrationally excited C=O stretching mode was found to occur through covalent bond to the delocalized aromatic vibrational modes on the time scale of a few picoseconds or less. Vibrational quantum beating was observed in magic-angle pump-probe, anisotropy, and 2D IR cross-peak dynamics, showing an oscillation period of ca. 1010 femtoseconds, which corresponds to the energy difference between the C=O and C=C transition frequency (33 cm-1). This confirms a resonant vibrational energy transfer happened between the two vibrators. However, more efficient energy-accepting mode of the excited C=O stretching was believed to be a nearby combination and/or overtone mode that is more tightly connected to the C=O species. On the structural aspect, dynamical-time dependent 2D IR spectra reveal insignificant inhomogeneous contribution to time-correlation relaxation for both the C=O and C=C stretching modes, which is in agreement with the generally believed structural rigidity of such conjugated molecules.

Keywords

Indigo carmine; structural dynamics; vibrational energy transfer; IR pump-probe and 2D IR spectroscopies 2


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I. Introduction

Indigo carmine is one of the well-known and still one of the mostly used dyes with a broad range of applications1 because of its excellent photostability.2 Many experimental3-6 and theoretical7, 8

works have been carried out to understand the molecular mechanism of such photostability. A

commonly accepted mechanism is that indigo undergoes an ultrafast excited-state intramolecular proton transfer (ESIPT) process after photo-excitation,4, 5, 9, 10 followed by a quick recovery. The proton transfer occurs through intramolecular C=O⋅⋅⋅H−N hydrogen bond. A previous study11 showed that the intramolecular C=O⋅⋅⋅H−N hydrogen bond is strengthened in the excited-state, which may facilitate the ESIPT process. Moreover, the C=O⋅⋅⋅H−N hydrogen bond plays an essential role in the excited-state structural processes in DNA base pair.12 The excited-state proton transfer rate is influenced by the energy barrier of the C=O⋅⋅⋅H−N hydrogen bond, which is closely related to the C=O⋅⋅⋅H−N hydrogen bond dynamics. The latter can be reflected by the structural flexibility of both C=O and N−H groups and their (intramolecular) interaction, which, can be studied in the electronic ground-state using structure sensitive methods. On the other hand, vibrational energy transfer in condensed-phase molecules plays a crucial role in a variety of chemical and physical processes, including photochemical reactions such as proton transfer.13 Time-resolved nonlinear infrared spectroscopy has the advantage of being able to monitor vibrational energy dissipation pathways, as well as structural dynamics of molecular systems in condensed phases.14-16 Infrared Pump-probe experiments under the so-called magic-angle polarization condition can provide vibrational lifetime information of a given vibrational mode.17-19 How vibrational energy relaxes after excitation, whether it is through intramolecular vibrational 3



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energy redistribution channel or through intermolecular energy transfer by interacting with solvent environment, can be understood based on time-resolved vibrational measurements. Time-resolved infrared spectroscopy, in particular IR pump-IR probe and two-dimensional infrared (2D IR) spectroscopies,20-43 have the advantage of simultaneously monitoring vibrational energy dissipation channels and molecular structural dynamics. For indigo carmine, energy transfer pathways of vibrationally-excited C=O can be followed by monitoring the dynamical time (or waiting time)-dependent 2D IR cross peaks. Since in the same wavelength region of the C=O stretching vibration, i.e., 6 µm, the C=C stretching mode of the aromatic group of indigo carmine also exists, in this work, we examine the ultrafast structural dynamics of this blue dye molecule using both C=O and C=C groups as two representative vibrational probes. Linear IR and nonlinear IR methods (including pump-probe and 2D IR spectroscopies) are utilized, with the aid of quantum chemical computations. Vibrational coupling and resonant energy transfer between the C=O and C=C stretching modes are examined. Further, local structural dynamics of indigo carmine including solvent molecules are also investigated by examining the vibrational spectral diffusion process and by monitoring the evolution of 2D IR cross-peak spectra as a function of the dynamical time.

II. Material and Methods

A. Sample and FTIR

Indigo carmine was purchased from TCI (Shanghai) and used without further purification. 4


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DMSO was purchased from Sigma-Aldrich and used as received. Indigo carmine at the concentration of 10 mM in DMSO solvent was prepared and ultrasonicated for 30 min before use. Its FTIR spectrum was recorded using a commercial FTIR spectrometer (Nicolet 6700, Thermo Electron) equipped with a liquid nitrogen-cooled mercury cadmium telluride (MCT) infrared detector. To avoid the interference of water moisture and CO2, the sample compartment of the spectrometer was purged by dry air during spectral measurement. A liquid IR sample cell composed of two 2-mm thick CaF2 windows separated by a ring-shaped Teflon spacer of 100-µm thickness was used. Weak IR absorption of DMSO was subtracted. All IR measurements were carried out at room temperature (22 ºC) with 16-scan average and 1-cm-1 resolution.

B. Transient pump-probe spectroscopy and 2D IR spectroscopy

Transient IR pump-probe spectra and 2D IR spectra of indigo carmine in DMSO were collected using a mid-IR pulse-shaper based spectrometer.44 Briefly, the output IR pulse of a commercial mid-IR optical parametric amplifier (TOPAS, Light Conversion) with ca. 8-µJ pulse energy at 6-µm center wavelength was used. A CaF2 beam splitter was used to divide the output mid-IR pulse into a pump pulse and a probe pulse. An acousto-optic modulator (AOM) based pulse shaper was used to transform one pump pulse into two delay- and phase-programmable pulses. The total pump-pulse energy at the sample position is ca. 400 nJ, while that of the probe pulse is on the order of tens of nJ. Pump and probe pulses are focused on the sample using a common parabolic mirror. Parallel and perpendicular pulse polarizations were utilized separately in two pump-probe experiments in order to obtain anisotropy and relaxation dynamics. Transient spectra were measured from -3 ps to +30 ps at

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a step of 5 fs for short-time delay of -0.5 ps to 2.5 ps. Parallel polarization is used in 2D IR measurement. The coherence time delay was scanned to 4000 fs with a time step of 20 fs. A series of 2D IR spectra were collected at preselected dynamical time (i.e., time-delay between the pump pulse and the probe, also called waiting time).29, 45 IR sample cell for the pump-probe and 2D IR measurements is the same as that for the linear IR measurement. The transmitted probe beam was sent to a 100 lines/mm grating spectrometer with blazing wavelength of 6500 nm (Acton SP2150, Princeton Instruments) and detected by a 64-element MCT linear-array detector. The frequency resolution of the probe frequency axis is ca. 3 cm-1. FTIR spectra of the sample was measured before and after the pump-probe and 2D IR experiments, and insignificant spectral change was observed in the 1550-1700 cm-1 region, suggesting a stable sample condition during the experiments.

C. Computations

Structural optimizations and anharmonic vibrational-frequency calculations were carried out using the density functional theory (DFT) in the ground electronic state at the level of B3LYP using the basis set of 6-311+G**. Harmonic normal-mode frequency calculation was carried out for indigo carmine in this work. Potential energy distribution (PED) analysis was carried out for mode assignment. Anharmonic vibration frequencies and anharmonicities of the C=O stretching mode and the delocalized C=C stretching mode of indigo carmine were also calculated by using the second-order vibrational perturbative treatment,46, 47 with the same basis set at the same level of theory. Briefly, the overtone diagonal anharmonicity for the ith mode was evaluated from its anharmonic 0 → 1 and 0 →

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2 transition frequencies: ∆i = 2ωi01 - ωi02, and the off-diagonal anharmonicity for the ith and jth modes was determined from their anharmonic two 0 → 1 transitions and one 0 → 1+1 transition: ∆ij = ωi01 + ωj01- ωij0,1+1. Such calculations on peptides have been reported previously.47, 48 The obtained anharmonic frequencies are presented and compared with experimental results without using any frequency-scaling factor. Line-broadened IR spectrum of indigo carmine was obtained by applying a Lorentzian line function with full-width of half maximum (FWHM) of 11.0 cm-1 on the computed C=O and C=C stretching vibrational intensities at their respective frequency positions. Vibrational coupling between the C=O and C=C stretching modes was extracted by de-mixing the vibrational wave functions using a protocol described earlier.49, 50 Briefly, in a simplified picture, a given normal mode Qi can be expressed as a linear combination of N coupled local modes, N

Qi = ∑ q jU ji .

(1)

j =1

Here, Uij is expansion coefficient of local mode qj in the normal mode Qi, and Uij is obtained using the calculated eigenvector elements in the conventional normal-mode picture. In the frequency region shown in Figure 1, the low-frequency mode is mainly the four C=C stretching vibrations (C15=C17, C14=C16, C1=C6, C2=C3), with minor contributions from the two C=O stretching vibrations; while the high-frequency mode is mainly the two C=O stretching vibrations (C7=O27, C13=O28), with minor contributions from the four C=C stretching vibrations. Thus, a two by two U matrix can be established and then normalized. All the involved ab initio computations were carried out using Gaussian.51

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III. Results and Discussion

A. Stead-State Linear IR Spectra and Simulated IR Spectra

Figure 1. (A) FTIR spectrum in the range of 1550 - 1700 cm-1 of indigo carmine in DMSO and its fitting using Voigt function, two strong components are shown. (B) Line-broadened IR spectrum of indigo carmine with the distribution of the transition intensities at computed anharmonic normal-mode vibration frequency positions (sticks). (C) Normal mode analysis on the computed absorption components (a′, b′ and c′). Peak-a and -a′ are assigned as the asymmetric C=O stretching vibration, peak-b and -b′, -c and -c′ are assigned as the delocalized aromatic C=C vibrations.

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Shown in Figure 1 is the FTIR spectrum (A) and computed anharmonic IR spectrum (B) of indigo carmine in the frequency range of 1550 - 1700 cm-1. One asymmetric C=O stretching mode and two delocalized C=C stretching modes by computations are shown in Figure 1C, along with the optimized molecular structure of indigo carmine. In Figure 1A, there are totally four bands, two major bands with one centered at 1642.7 cm-1 (marked as peak-a) and the other centered at 1610.1 cm-1 (marked as peak-b) appear to be strong, which are assigned to the asymmetric stretching mode of two C=O groups and the delocalized C=C stretching mode of the aromatic group of this blue dye molecule, respectively. This assignment is in agreement with a previous work.52 There seems to be more inhomogeneous contribution in the spectral profile of the C=O vibration than in that of the C=C vibration. Further, there are also two minor bands centered at 1584.5 cm-1 (marked as peak-c) and 1666.6 cm-1 (marked as peak-d) respectively, where the former is also due to the C=C vibration of the aromatic ring, and the latter is due to the C=O stretching of the degeneration product (isatin sulfuric acid) of indigo carmine that appears slowly.53 In the simulated anharmonic IR spectrum of indigo carmine shown in Figure 1B, three bands centered at 1665, 1598 and 1582 cm-1 (marked as peak-a′, -b′ and -c′ respectively) are seen. The distribution of the transition frequencies and intensities is also given as sticks in Figure 1B. Two low-frequency bands (peak-b′ and -c′) are assigned to two major delocalized C=C vibrations of the aromatic ring, while the high-frequency band (peak-a′) is assigned to the asymmetric C=O stretching vibration. The normal-mode analysis of these vibrations is shown in Figure 1C. It should be noted that the stretching vibration of the C=C bond connecting the two pyrrole rings and the symmetric C=O stretching vibration are both IR inactive (see Table S1 of the Supporting Information, SI). The relative peak position and intensity of 9



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the three bands (peak-a′, -b′ and -c′, panel-B) in the simulated spectrum agree reasonably with those in the experimental results (peak-a, -b, and -c, panel-A, within 25-cm-1 variation). In this way, a one-to-one relationship between simulation and experiment can be established. Peak-fitting of the linear IR spectrum was carried out using the Voigt line shape, with fitting parameters summarized in Table 1. The observation that the C=O stretching mode is more inhomogeneous than the C=C stretching mode is confirmed by the fitting results because the former has relatively larger Gaussian component, with Gaussian / Lorentzian ratio (wG/wL) of 0.28, than the latter (with wG/wL = 0.13). In the present work, we will focus on the two strong components (peak-a and -b) because they are representative C=O and C=C stretching modes of indigo carmine, and will not further discuss the two weak components (peak-c and -d).

Table 1. Voigt fitting parameters of peak position (ω), peak value (Abs), Gaussian line width (wG), Lorentzian line width (wL), total full width at half maximum (FWHM), the ratio of Gaussian component and Lorentzian component (wG / wL), and integrated area (A) for the FTIR spectrum of indigo carmine in DMSO in the frequency range of 1550-1700 cm-1. Peak

ω / cm-1

Abs / OD

wG / cm-1

wL / cm-1

FWHM / cm-1

A / arb. u.

wG / wL

d

1666.6

0.02

--

--

13.7

0.27

--

a

1642.7

0.15

3.2

11.5

12.4

2.08

0.28

b

1610.1

0.11

1.2

9.2

9.3

2.10

0.13

c

1584.5

0.01

--

--

14.0

0.20

--

10


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B. 2D IR Spectra and Structural Dynamics

Figure 2. 2D IR spectra of the C=O and aromatic ring C=C vibrations in indigo carmine measured at different dynamical times, as indicated. The spectral window is [ωt = 1580 - 1670 cm-1 and ωτ = 1590 - 1670 cm-1]. The diagonal lines are shown in each panel and an example of the center-line slope for the 0 → 1 transition is shown in the T = 300 fs panel. Color bar is given for each individual panel.

Figure 2 displays the absorptive 2D IR spectra of indigo carmine in DMSO at selected dynamical times (T). Mainly two pairs of diagonal peaks are shown at early T, with the positive peaks arising from vibrational ground-state bleaching signals (ν = 0 → ν = 1), and the negative (blue) peaks arising from the first vibrational excitation absorption (or the first hot band) signals (ν = 1 → ν = 2). The high-frequency peaks come from the C=O stretch and the low-frequency peaks come from the delocalized C=C vibration, based on the linear IR assignment. Because the cross peaks are clearly visible at early T time, the C=O and C=C modes are anharmonically coupled. By de-mixing the wave function (i.e., the U matrix, see Section II C), one finds the inter-mode coupling between 11



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the C=O and C=C stretching vibrations to be ca. 3.1 cm-1. As T increases, the strength of the off-diagonal signals fluctuates, indicating the presence of vibrational energy transfer between the C=O and C=C vibrators. The forward and backward energy transfer time scales are on the order of a few picoseconds (see Figure S3), and can be evaluated by modeling the relative intensities of the diagonal and off-diagonal peaks,54-58 which is not the focus of this paper and is briefly discussed in Section III D. At early T values, the 2D IR spectra are elongated alone the diagonal line for both the ν = 0 → ν = 1 and ν = 1 → ν = 2 transitions; as T increases, the 2D IR spectra become more vertically tilted due to the vibrational spectral diffusion.59-61 Such diffusion dynamics can be obtained from various line-shape analysis methods59, 62, 63 that can quantify the degree of frequency correlation contained in the 2D IR signals at a specific T value. On this basis, the shape change of 2D IR signals can actually serve as a measure of the frequency-frequency time-correlation function (FTCF) of the transitions involved. Here the center-line slope (CLS) method62, 64 was used to quantitatively describe the vibrational spectral diffusion dynamics. The CLS for the ν = 0 → ν = 1 transition of each vibrational mode was extracted from the 2D IR spectra at different dynamical times, and the result was shown in Figure 3. The FTCF of the asymmetric C=O stretching mode shows a larger initial amplitude and faster relaxation process than that of the delocalized C=C stretching mode. According to the fitting results of the FTIR spectrum, the weight of Gaussian component in the C=O stretch line shape is larger than that in the delocalized C=C stretch line shape, suggesting more inhomogeneous broadening in the former than the latter and agreeing with the CLS results. 12


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Figure 3. Frequency time-correlation function evaluated using the center-line-slope method for the C=O stretching vibration (left, circles) and aromatic C=C stretching vibration (right, circles) and their mono-exponential fittings in indigo carmine. The computed normal-mode vibration is illustrated in each case.

These results can be explained on the structural basis of indigo carmine and its interaction with DMSO solvent molecules. In indigo, the C=O group is intramolecularly hydrogen-bonded to the N−H group and also forms a weak hydrogen bond with one of the CH groups of DMSO, while the N−H group can interact with a nearby DMSO molecule via intermolecular hydrogen bond, which is partially the solvation process. Here, the observed 1643-cm-1 mode is an asymmetric linear combination of the two C=O stretching vibrations, i.e., an excitonic state, instead of a local site state. However, this can still be pictured as two C=O vibrators that oscillate in an out-of-phase fashion, hence the local structural (including solvent) dynamics at the two C=O sites can be probed. In this way, the CLS dynamics are still meaningful in terms of reporting these local structural fluctuations.

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Table 2. Fitting parameters for the center-line slope dynamics by single exponential decay for the C=O stretch and delocalized C=C stretch in indigo carmine. Μode

C0 a

Coff b

τSD / fs

C=O

0.20

0.10

446.0±41.8

C=C

0.09

0.06

848.1±267.7

a

Initial amplitude. b Static offset.

The CLS of the C=O vibration shows a time constant at the level of half picosecond, which may reflect the fast CH (DMSO)…O=C (indigo carmine) hydrogen bond fluctuation on one hand, and the intramolecular NH…O=C hydrogen bond fluctuation on the other. The former is a weak hydrogen bond and there is always a possibility that a nearby polar solvent DMSO molecule would form a hydrogen bond with its one CH group facing the C=O group.65 In this case the C=O vibration senses a very limited inhomogeneous and local solvent environment (the initial CLS value is 0.2, Figure 3 left). On the other hand, the intramolecular NH…O=C hydrogen bond is relatively strong. It is known that excited-state (S1) of indigo has a very small energy barrier for intramolecular proton transfer to occur in less than half picosecond,4 thus, one can speculate that such CLS dynamics is not related to the hydrogen-bond breaking, but likely to the hydrogen-bond fluctuations that are very rapid in time. A picture of indigo carmine and DMSO interaction is illustrated in Figure 7 and further discussed in later Section. On the other hand, the CLS of the delocalized C=C stretching mode (being relatively slower in dynamics, smaller in initial amplitude, and slightly noisier than the C=O stretching mode) reflects the rigid structural aspect of the molecular frame of indigo carmine. This is because the molecular 14


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plane is less polar and has weak interaction with polar solvent such as DMSO, which explains its smaller inhomogeneity and insignificant CLS dynamics. In other words, solvent fluctuations and solvent interactions in the peripherals of the molecule are not sensitively probed by this delocalized C=C stretching mode. However, one of the CH groups of a solvent DMSO molecule on both sides of the planar molecular frame of indigo carmine may interact weakly with the π cloud of aromatic (ϕ) ring in the form of C−H⋅⋅⋅ϕ,66 which may also contribute to the frequency fluctuation of the C=C stretching mode. Further, we note that in the case of C=O stretching mode the CLS relaxation does not reflect hydrogen-bonding dynamics, because for one, the time constant is shorter than those reported in water system,60, 67, 68 and also because the intramolecular hydrogen bond mentioned above in indigo carmine does not break and reform in the observed CLS time regime, otherwise a pair of new diagonal peaks (representing free C=O) and associated off-diagonal signals (representing chemical exchange54, 69, 70 between hydrogen-bonded and free C=O groups) would appear.

C. Anharmonicities

Figure 4 shows spectral slices of 2D IR spectrum of indigo carmine at several ωτ values for either the C=O or C=C stretching mode at desired T values, and their corresponding fittings. During the spectral fitting, the peak intensities of the linear IR and 2D IR were controlled based on the well-known relationship between the optical density of the absorption band of linear IR (1D IR) and those of the 2D IR.71, 72 Briefly, the integrated peak area of a linear IR absorption band is assumed to

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be proportional to C(t)|µ|2, while that of the 2D IR signal is proportional to C(t)|µ|4, where C(t) is a coefficient associated with the dynamical-time dependent population of a given vibrator, and |µ| is the vibrational transition dipole moment magnitude of this vibration mode. Thus, the peak-area ratio of the low-frequency C=C band and the high-frequency C=O band of the 1D IR signal in this work is in proportional to [CC=C(0)|µC=C|2] / [CC=C(0)|µC=O|2], and that of 2D IR is proportional to [CC=C(t)|µC=C|4] / [CC=C(t)|µC=O|4]. This implies that the area ratio of the two diagonal bleaching signals in the 2D IR spectrum at time-zero is in proportional to square of that of the two FTIR bands. The diagonal anharmonicity of a given ith vibrational mode (∆i), is evaluated here as the magnitude of anharmonic shift of the ν = 1 → ν = 2 transition energy with respect to the ν = 0 → ν = 1 transition energy (∆i = ωi01 - ωi12), which can be estimated from the two corresponding peak positions along the ωt-axis for a given vibrational transition. The actual anharmonicity, however, can be obtained by fitting a horizontal slice of a 2D IR spectrum containing a given vibrator. Shown in Figure 4 are 2D IR slices along the ωt-axis at desired ωτ-value at two dynamical times, two at 300 fs and one at 2 ps (Figure 2). These plots can be used to extract the diagonal anharmonicity of the delocalized C=C stretching mode (Figure 4A) and the C=O stretching mode (Figure 4B), and the off-diagonal anharmonicity between the C=O and C=C modes (Figure 4C), along with a long dynamical-time evaluation of the C=O stretching mode. The diagonal anharmonicity of the delocalized C=C mode is found to be ca. 4.4 cm-1, while that of the C=O mode is found to be ca. 7.9 cm-1 at 300 fs and ca. 7.3 cm-1 at 2 ps, showing a roughly dynamical-time independent anharmonicity. The off-diagonal anharmonicity is found to be ca. 4.2 cm-1 from the upper-left cross peak at longer dynamical times (Figure 2F), which is consistent with the diagonal anharmonicity of the delocalized 16


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C=C mode evaluated at 300 fs. This indicates that cross peak is dominated by the vibrational energy transfer happened between the C=O and C=C stretching modes. On the other hand, fitting the early dynamical-time 2D IR spectra yields a much smaller off-diagonal anharmonicity (1.8 cm-1 on average, see Figure S1 and Table S2 in the SI), indicating the presence of anharmonic coupling between the two different modes.

Figure 4. Slices of 2D IR spectra of indigo carmine and their fittings along the ωt axis at dynamical time of T = 300 fs in the range of 1590 - 1630 cm-1 at ωτ = 1610 cm-1 for the C=C stretching mode (A), in the range of 1610 - 1670 cm-1 at ωτ = 1643 cm-1 for the C=O stretching mode (B) and at dynamical time of T = 2.0 ps in the range of 1590 - 1670 cm-1 at ωτ = 1643 cm-1 for both the C=C and C=O stretching modes (C). The obtained diagonal-anharmonicities are marked. The ωτ frequency positions are shown in Figure 2 as black dashed lines.

Our ab initio computations predict a diagonal anharmonicity of the C=O vibrational mode to be 8.56 cm-1, and that of the delocalized C=C vibrational mode of the aromatic ring to be 0.97 cm-1, and their off-diagonal anharmonicity to be 1.08 cm-1, showing that the computed anharmonicities are in reasonable agreement with the relative magnitudes of experimentally determined anharmonicities 17



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(7.5, 4.2, and 1.8 cm-1 respectively).

D. Vibrational Dynamics

Figure 5. Relaxation and anisotropy dynamics. (A and B) Magic-angle pump-probe transient signal at probe frequency of 1610 cm-1 and 1642 cm-1 respectively. Insert shows the early-kinetic traces in the time window of [−0.5 to 3.0 ps] in each case. (C and D) Anisotropy at the probe frequency of 1610 cm-1 and 1642 cm-1 respectively, with fittings using a damped cosinusoidal exponential decay function. See text for detail.

Linearly-polarized electric field of a pump laser pulse can be used to prepare an initial collection of orientational distribution of molecules in solution, and a linearly-polarized probe pulse can be used to track the relaxation dynamics of the “prepared” molecular orientations. The anisotropy r(t) is defined as:73

r (t ) =

∆Α|| (t ) − ∆Α⊥ (t ) ∆Α|| (t ) + 2∆Α ⊥ (t )

,

18


(2)

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where ∆Α|| and ∆Α⊥ are transient changes of absorbance obtained under parallel and perpendicular pump-probe polarization conditions. The so-called magic-angle (isotropic) signal (denoted as ∆ΑΜ) is a measure of the vibrational population relaxation, and the three signals are connected through the following equation:

1 ∆ΑM (t ) = (∆Α|| (t ) + 2∆Α⊥ (t )) . 3

(3)

Table 3. Fitting parameters for magic-angle pump-probe transient signal and anisotropic transient trace at probe frequency 1610 and 1642 cm-1.

Relaxation

Anisotropy

a

ωprobe / cm-1

Assignment

Τ1a / ps

A1 / % a

Τ1b / ps

A2 / % a

1642

C=O

1.19±0.02

79.9

5.98±0.46

20.1

1610

C=C

1.02±0.07

26.1

5.86±0.11

73.9

ω / cm-1

Assignment

τ01 / ps

A1 / % a

1642

C=O

2.54±0. 11

--

1610

C=C

1.95±0.13

--

Ai is the amplitude of the ith exponential decaying component at each probe frequency.

Shown in Figure 5 (panels A and B) are the pump-probe kinetic traces obtained under the magic-angle condition for indigo carmine in DMSO, probed at the peak position of ν = 0 → ν = 1 transition for both the C= C and C=O stretches. A biexponential fitting is shown in each case. The obtained life-time parameters in the form of double exponentials are listed in Table 3. Figure 5A shows the bleaching recovery of the delocalized aromatic C=C vibration, and Figure 5B shows that of the asymmetric C=O stretching vibration. There are two components in the relaxation process in each case, a fast component with lifetime of ∼ 1 ps and a slow component with lifetime of ∼ 5.9 ps. 19



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The fast component dominates (~ 80 % of the amplitude) in the case of C=O, while the slow component dominates (~ 74 % of the amplitude) in the case of the delocalized C=C. This suggests a relatively rapid energy dissipation process of the vibrationally excited C=O mode to certain low-frequency modes. In addition, the kinetic traces at probe frequency positions of 1610 and 1642 cm-1 at delay time of −0.5 to 3.0 ps are shown as inserts in Figures 5A and 5B. A weak quantum beating signal between the C=O and C=C modes is seen in the first few picoseconds only when probed at the C=C stretching frequency. Anisotropy measurements were carried out and the anisotropic dynamics probed at the C=C and C=O bleaching frequencies were evaluated using Eq. (2), which are displayed in Figure 5, panels C and D, and their relaxation time constants are listed in Table 3. The anisotropy of the C=O mode decays with a time constant τr of ca. 2.5 ps, demonstrating the time scale of the reorientation of this vibration. The anisotropy of the C=C mode, on the other hand, decays with a time constant τr of ca. 2.0 ps, showing roughly the same reorientation time scale as that of the C=O mode. This result is understandable if these anisotropic dynamics reflect the true reorientational motion of the indigo carmine. Further, oscillations in the anisotropy dynamics were clearly observed at both probing frequencies, which is due to vibrational quantum beating74-76 between the two coupled transitions (the C=O and C=C stretching modes). A damped cosinusoidal exponential decay function (Eq. (4)) was used to fit the oscillatory anisotropy signals:

2π T ∆Α = ∆Α0 + [Α + Β cos( T + ϕ )]exp(− ) ,

τ0

τr

(4)

where τ0 is the oscillation period, τr is the anisotropic relaxation time and ∆A is the absorbance change. ∆A0 = 0.08, A = 0.14, ϕ = −0.06 and B = 0.06 for panel-C and ∆A0 = 0.03, A = 0.29, ϕ = 6.26 20


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and B = 0.04 for panel-D. An oscillation period of ca.1010 fs was found, which corresponds reasonably to the 33 cm-1 transition-frequency difference between the two vibrators. The anisotropy starts from less than 0.4 in both cases, which is probably due to the oscillatory behaviors. The oscillation is more obvious at 1610 than at 1642 cm-1, which is due to stronger absorption intensity of the former than the latter. One sees that for the same reason an insignificant oscillatory signal is also seen in the early-time magic-angle signal at 1610 cm-1 but not at 1642 cm-1.

Figure 6. Transient cross-peak signal extracted from dynamical-time dependent absolute-value 2D IR spectra. An area of 3 cm-1 × 3 cm-1 around the off-diagonal position at [ωt = 1643 cm-1, ωτ = 1610 cm-1] was chosen. A similar damped cosinusoidal exponential decay function as in Figure 5 was used to fit the cross-peak signal, with a set of fitting parameters: ∆A0 = 0.03, A = 0.07, ϕ = 0.01, B = − 0.07 and τr = 1.40 ps, and the fitting residuals given in the lower panel.

Quantum beating between the two modes can be even clearly seen by the dynamical-time dependent intensity of the 2D IR cross peaks. As can be seen from the 2D IR spectra (Figure 2), the 21



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amplitude of the lower-right cross peak, for example, at ωt = 1643 cm-1 and ωτ = 1610 cm-1, varies from one dynamical time to another. To get a better view of the oscillatory behavior of the cross peak, we plotted the absolute amplitude of this cross peak as a function of dynamical time, which is shown in Figure 6, and is fitted using a similar damped cosinusoidal exponential decay function as in Figure 5 panel-C and -D. The oscillation period is also of ca. 1010 fs, which is in good agreement with that obtained in the anisotropy measurement.

E. Vibrational Energy Transfer

In solution phase, a vibrationally excited polyatomic system usually undergoes a “two-step relaxation process”,77-81 including a rapid intramolecular energy transfer that is usually referred to as intramolecular vibrational energy redistribution (IVR) and a slow intermolecular vibrational energy transfer process (VET). Vibrational relaxations involving multiple modes have been modeled and reported previously.82-84 In the case of indigo carmine/DMSO system, both C=O and C=C vibrators undergo the intra- and intermolecular dissipation processes. Shown in Figure 7 is the proposed energy transfer channels of the vibrationally excited C=O and delocalized C=C modes. There are several possible pathways for the C=O and C=C species to dissipate their vibrational energies. In fact, IVR from high-frequency modes to low frequency mode is generally known to be the dominant vibrational relaxation mechanism for polyatomic system,79, 80 if there are proper energy-accepting vibrational modes. For the C=O stretching mode, the results in Figure 5B suggest a relatively rapid energy

22


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dissipation process (1.19 ps) that dominates (~ 80 % in amplitude) and hence is an efficient relaxation pathway. The energy accepting mode for this fast energy relaxation process, according to the potential energy distribution analysis of all the low-frequency normal modes above 590 cm-1 (see Table S2), could be a combinational mode (902.2 cm-1 + 738.6 cm-1 = 1640.8 cm-1, unscaled harmonic frequencies), which is mainly dominated by the bending of the aromatic ring. This combination is only 57.2 cm-1 lower than the computed IR-active C=O vibration (1698.0 cm-1). Another possible energy accepting mode is likely to be the overtone of HCCC twisting motion, whose fundamental vibrational frequency is 832.1 cm-1 and its overtone is 1664.2 cm-1, which is 33.8 cm-1 lower than the computed C=O stretching frequency. This is also included in path-1.

Figure 7. Possible vibrational energy dissipation channels of the C=O and delocalized C=C of the aromatic ring of indigo carmine in solvent environment of DMSO. Left: Color code for atoms and ions: gray = carbon; light gray = hydrogen; red = oxygen; purple = sodium ion; and yellow = sulfur. Dashed lines indicate hydrogen bond. Energy transfer processes are marked by circled numbers. See text for details.

For the slow (5.98 ps) and less significant (~ 20 %) energy relaxation process, the 23



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energy-accepting mode is very likely to be the delocalized C=C vibrational mode for two reasons. One, a quantum beating between the C=O stretching and the C=C stretching modes was clearly observed in both anisotropy (Figure 5) and 2D IR cross peak (Figure 6); two, the growing processes for the downhill (C=O to C=C) and uphill (C=C to C=O) are estimated to occur with a time constant in the order of a few picoseconds (Figure S3 in the SI). The slow relaxation pathway of the excited C=O mode is illustrated as path-2 in Figure 7. Since the calculated frequency difference between the C=O and delocalized C=C stretching modes is only 54.8 cm-1, one would ask why the vibrational relaxation from the C=O mode to the C=C mode is not as efficient as that from the C=O to the combinational band and/or the overtone band. This is understandable because there is no direct chemical-bond connection between the C=O mode and the delocalized C=C mode, according to the PED analysis given in Table S1. However, the computed combinational mode (1640.8 cm-1) comes from the 902.2-cm-1 and 738.6-cm-1 modes, where the former contains contribution from (C7 and C13) that belong to the asymmetric C=O stretching mode (C7=O27 - C13=O28), and the later contains aromatic bending contribution (e.g. C6-C5-C4 and C8-N23-C2) that also appear in the former. The twisting mode (832.1 cm-1) also share a common carbon atom with the asymmetric C=O stretching mode (e.g. C7). In addition, PED analysis shows that other combination and overtone bands are unlikely to be the energy-accepting modes of the C=O mode. Further, because the C=O group is still chemically bonded to the aromatic ring of the indigo carmine molecule, the mechanic anharmonicity exists in both C=O and C=C stretching modes. This induces a mechanical vibrational coupling between the C=O and C=C stretching modes, which is 24


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predicted to be 3.1 cm-1 (as mentioned in Section B), and causes the observed very-weak early dynamical-time 2D IR cross peaks (Figure 2). From these 2D IR spectra, an averaged off-diagonal anharmonicity of 1.8 cm-1 was obtained for the early dynamical times (see Table S2), in agreement with the strength of the computed coupling constant. The presence of the coupling between the two modes, is the structural foundation of the IVR process between them to occur at longer dynamical times. Additional vibrational energy relaxation channel for the excited C=O mode may be through the intramolecular hydrogen-bonding bridge, as illustrated in Figure 7. However, the energy-accepting mode is unlikely the N−H stretching because the energy difference is relatively high and the energy-transfer efficiency will be very low. A possible energy-accepting mode is the C−N−H inplane bending, whose frequency is predicted to be ca. 1479.4 cm-1 by computation (Table S2). The large energy gap between the C=O stretching and C−N−H in-plane bending modes makes the latter unlikely an efficient energy-accepting mode, unless it is aided by a proper low-frequency solvent mode. Further additional vibrational energy relaxation channel for the excited C=O mode may be through intermolecular hydrogen bond interaction with solvent, which is also illustrated in Figure 7. The C=O group can be weakly hydrogen-bonded to the C−H group of a nearby DMSO molecule.65 However, the C−H stretching frequency is much higher than that of the C=O stretching for one, and the CH3 rocking frequency is nearly 200-cm-1 lower than that of the C=O stretching (Table S3 in the SI), thus, none of them will likely to be an efficient energy-accepting mode. Furthermore, it should be mentioned that the above discussion applies to both C=O groups because the observed C=O stretching mode is the IR-active and asymmetric combination of the two 25



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C=O stretching motions. While the C=O vibrator mainly dissipate its energy quickly through the intramolecular pathway to the combinational mode of the aromatic ring, the relaxation of the latter may involve the C=C stretching mode, which is part of the aromatic ring vibration. Here, a small portion (~ 26 %) of the excited C=C stretching mode may relax relatively fast (1.0 ps), as revealed in Figure 5A. This fast relaxation is marked as path-1′ in Figure 7. The energy accepting mode for the fast process of the delocalized C=C mode is very likely to be the other delocalized C=C stretching mode (Figure 1C, normal-mode c′), because the vibrational frequency difference of the two delocalized C=C modes is very small (1643.2-1616.8 cm-1 = 26.4 cm-1). Moreover, the PED analysis shows that these two modes share a lot of common molecular motions (Table S2). The slow relaxation process is likely due to an uphill IVR process, i.e, from the C=C stretching mode to the C=O stretching mode. Because the frequency difference of the two vibrational modes is experimentally determined to be 33 cm-1 (54.8 cm-1 computationally, unscaled), thermal fluctuation can aid such a reverse energy transfer process, which is illustrated as path-2′ in Figure 7. However, it should be mentioned that the fast and slow energy-relaxation pathways of the vibrationally excited C=C stretching may also involve some combination bands whose identity cannot be determined by our work. For example, one of the CH groups of DMSO may interact weakly with the π cloud of aromatic (ϕ) ring in the form of C−H⋅⋅⋅ϕ, which is also a possible vibrational energy dissipation pathway (not illustrated in Figure 7).

F. Further Discussions In previous transient infrared and 2D IR studies of a transition metal complex (Rh(CO)2acac)75 26


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and the well-known model peptide (N-methylacetamide),76 oscillations were clearly observed in the population relaxation dynamics as a result of the vibrational coherent energy transfer between the two vibrational modes. In this work, however, the oscillatory behavior in the relaxation dynamics is more clearly seen in the anisotropy than in the magic-angle pump-probe signal, because the essence of the anisotropy signal is the difference between the parallel and perpendicular polarization measurements, while the magic-angle signal is the sum of the two measurements, which is clearly seen in Eqs. (2 and 3). In the formal case, the contribution from the population relaxation is removed so that the oscillation can be more clearly exposed. For the same reason, the 2D IR cross-peak, which is the direct measurement of resonance energy transfer, shows more significant oscillatory characteristics (Figure 6). In addition, the oscillation in the anisotropic signal is less obvious at 1642 than at 1610 cm-1, which is due to the difference in their absorption. Concerning the cross-peak oscillation observed in our 2D IR spectra, such an oscillation pattern of cross peak has been observed previously in the two-dimensional electronic spectra of FMO,85 which was believed to be originated from coherent electronic energy transfer. However, later studies86, 87 showed that this oscillation of cross peak is due to vibronic coherent energy transfer with dominant contributions from vibrational coherence. Here, our result supports the latter explanation that the long-lived (picoseconds) coherence is resulted from vibrational coherent energy transfer. The FTCF extracted from 2D IR diagonal signal, is an autocorrelation function that is very sensitive to the structural and local environmental fluctuations of the chemical group of interest. This is also the structural basis of the 2D IR method. Our work shows a large initial amplitude and faster relaxation in the FTCF of the C=O stretching mode, which is related to the hydrogen bonding 27



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dynamics of the C=O⋅⋅⋅H−N and C=O⋅⋅⋅H−C (DMSO) complexes in the solvated indigo carmine. Such a relaxation time constant is faster than the hydrogen bond lifetime, indicating that the hydrogen bond breaking and reforming do not occur. On the contrary, the delocalized C=C stretching mode showed a small initial amplitude and a relative slow relaxation dynamics, which, is closely related to the rigid molecular frame of the conjugated system in indigo.

IV. Conclusions

In this work, structural dynamics and vibrational energy transfer in indigo carmine have been examined using linear and nonlinear IR spectroscopies. Linear FTIR and quantum chemical calculation were first used to assign the bands of indigo carmine in the 6-µm wavelength region. The high-frequency band originates from the asymmetric stretching vibration of the two intramolecularly hydrogen-bonded C=O groups, and the low-frequency band results from the delocalized C=C stretching vibration of the two aromatic rings. The obtained 2D IR spectra show a dynamical-time dependent diagonal peaks in both spectral shape and apparent spectral “orientation”, from which frequency time-correlation functions were derived using the center-line slope method. The determined spectral diffusion time constants are ca. 446 fs and 848 fs for the C=O vibrator and the delocalized C=C vibrator respectively, with the former associated with intramolecular hydrogen-bonding dynamics of C=O⋅⋅⋅H−N of indigo carmine that can be influenced by DMSO solvent, and also the hydrogen-bonding dynamics of a weak C=O⋅⋅⋅H−C (DMSO) complex, and the latter associated with the rigid aromatic structural frame of 28


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this molecule that is less affected by solvent except possible weak but direct DMSO C−H and aromatic (ϕ) ring interactions. Further, slices of 2D IR spectra were used to determine both the diagonal and off-diagonal anharmonicities associated with the C=O and C=C vibrational transitions. The average diagonal anharmonicity for the two vibrators is found to be ca. 7.6 cm-1 and ca. 4.4 cm-1 respectively, which are in reasonable trend with computational results. Early-time 2D IR cross peak showed an averaged off-diagonal anharmonicity of ca. 1.8 cm-1, which is in reasonable agreement with computed off-diagonal anharmonicity (1.08 cm-1). The strength of the off-diagonal interaction is also on the same order as the mechanical anharmonic coupling (3.1 cm-1) that was predicted by wave function de-mixing method. Furthermore, long dynamical-time 2D IR cross peak showed a relatively larger off-diagonal anharmonicity (4.2 cm-1) that is very close to the diagonal anharmonicity of the delocalized C=C stretching mode, indicating the vibrational energy transfer between the C=O and C=C stretching modes dominates the strength of the 2D IR off-diagonal signal at longer dynamical time. An oscillating off-diagonal intensity indicates the resonant vibrational energy transfer between the two modes. Finally, the vibrational energy dissipation pathways of the excited C=O and C=C modes were examined. It turns out that the IVR process from C=O to C=C is not as efficient as that from C=O to a nearby combination and/or overtone band. However, only the IVR processes between the C=O and C=C vibrations are observed by 2D IR spectroscopy because of their frequency separation. The frequency position of the above-mentioned combination and/or overtone band is believed to be very weak in intensity and may overlap with that of the C=O mode, preventing the study of their IVR 29



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processes. The quantum beating observed in magic-angle pump-probe, anisotropy, and 2D IR cross-peak dynamics show an oscillation period of ca. 1010 fs, which corresponds to the energy difference between the C=O and C=C stretching transition frequencies (33 cm-1) and confirming the resonant vibrational energy transfer happened between the two vibrators. The results also suggest other intra and inter-molecular vibrational relaxation pathways. The inefficient energy dissipation channel of the C=O and N−H hydrogen-bonding bridge is mainly because of the energy mismatch; the N−H stretching frequency is known to be nearly twice higher than that of the C=O stretching mode. However, from the opposite direction, the energy transfer is quite feasible; for example, transient proton-transfer was believed to occur between N−H and C=O groups in indigo carmine in the electronic excited state of this dye.4

Acknowledgments

This work was supported by the National Natural Science Foundation of China (21573243, 21603238, and 21327802).

References

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TOC Figure

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Efficient Vibrational Energy Transfer through Covalent Bond in Indigo

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