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Efficient Intramolecular Vibrational Excitonic Energy Transfer in Ru(CO) Cluster Revealed by Two-Dimensional Infrared Spectroscopy 3

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Xueqian Dong, Fan Yang, Juan Zhao, and Jianping Wang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b10067 • Publication Date (Web): 24 Dec 2017 Downloaded from http://pubs.acs.org on December 30, 2017

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The Journal of Physical Chemistry

Efficient Intramolecular Vibrational Excitonic Energy Transfer in Ru3(CO)12 Cluster Revealed by Two-Dimensional Infrared Spectroscopy

Xueqian Dong†‡, Fan Yang†*, Juan Zhao†‡, 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

*

Author to whom correspondence should be addressed.

Tel: (+86)-010-62563565; Fax: (+86)-010-62563167; E-mail: [email protected]; Tel: (+86)-010-62656806; Fax: (+86)-010-62563167; E-mail: [email protected].

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Abstract Trinuclear transition-metal carbonyl complex dodecacarbonyltriruthenium (Ru3(CO)12) is considered as one of the paradigms in cluster chemistry, which plays an important role in photocatalysis, photoenergy conversion and synthetic chemistry. Due to structural symmetry (D3h point group), twelve carbonyl (C≡O) groups in the Ru3(CO)12 complex contribute to mainly three excitonic carbonyl stretching modes: E' (radial), A2" (axial), and E' (axial). In this work, efficient intramolecular vibrational energy redistribution (IVR) processes among the three modes in this Ru-CO complex were observed to occur on the tens of picosecond time scale. The IVR processes were characterized in detail using a kinetic model and fitting to the waiting time dependent diagonal and off-diagonal signals of ultrafast two-dimensional infrared (2D IR) spectroscopy. In addition, the diagonal anharmonicities of the three C≡O stretching modes were determined to be quite close to one another, and the coupling-induced cross peaks were invariant because this Ru3(CO)12 cluster does not show picosecond fluxionality and hence whose contributions were neglected in modeling the IVR processes. Our results provide a benchmark for understanding the excitonic nature of the vibrational excited states of the carbonyl vibrators and the associated efficient vibrational energy-flow pathways, in such multi-centered transition-metal complexes, which are of key importance to their functions.


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I. Introduction The cluster chemistry involving transition-metal carbonyls has been developed since the discovery of metal carbonyls such as Co2(CO)8 and Fe2(CO)9.1-2 Transition-metal carbonyl clusters containing two or more metal atoms surrounded by carbonyl ligands have been widely used as solution-phase homogeneous catalysts3-4 and also synthetic precursors5-6 to other carbonyl complexes. Dodecacarbonyltriruthenium, Ru3(CO)12 is one of the representative transition-metal carbonyl clusters, which is considered as a model of trinuclear metal complex. Moreover, this trinuclear metal carbonyl cluster has been known to play an important role in photocatalysis,7 in synthetic chemistry,8 as well as in photochemistry.9-11 In condensed phases, the Ru3(CO)12 complex has twelve non-bridged C≡O groups and a D3h symmetry configuration corresponding to the most stable trinuclear core structure, which is quite typical in cluster chemistry. The overall molecular geometry and the ligand rearrangement mechanism of the Ru3(CO)12 cluster have been studied extensively. A variety of methods, such as NMR spectroscopy,12 single crystal X-ray diffraction,9, 13-15 and infrared and Raman spectroscopies,16-20 have been used to examine the molecular structure, fluxional behavior, and photolysis of this metal carbonyl cluster. In addition, theoretical insights have been obtained on Ru3(CO)12 using several density functionals, whose geometrical parameters and energetics have been predicted.21 Intuitively speaking, under a broadband ultrafast infrared laser excitation, since there are multiple C≡O stretching modes involved in Ru3(CO)12, the intramolecular vibrational relaxation (or intramolecular vibrational energy redistribution, IVR) among these C≡O modes, could have complicated pathways and/or varied time



scales, which, however, still remains unknown for this multicentered Ru-carbonyl complex. In particular, a recent IR pump-probe spectroscopic study of Os3(CO)12, which is a similar transition-metal carbonyl complex as Ru3(CO)12, showed that no vibrational energy transfer occurred among the multiple C≡O stretching modes in such trinuclear carbonyl cluster.22 An effective and comprehensive way to address these energy transfer and associated vibrational dynamics questions is to use two-dimensional infrared (2D IR) spectroscopy, as also pointed by these authors. In a specific 2D IR spectrum, a set of normal modes can be excited at the same time, including the fundamental, first overtone, and first combination transitions. These vibrational transitions are shown as diagonal and off-diagonal 2D IR signals. Waiting time (or dynamical time) between a series of 2D IR spectra, is the time window to monitor the 2D IR spectral change, in both line shape that reflects spectral diffusion that is mostly related to the evolution of solvent and neighboring chemical composition, and signal intensity that reflects either vibrational relaxation (diagonal signals) or vibrational energy transfer among different states (off-diagonal signals). Thus, by analyzing the shape and intensity changes in a series of waiting-time dependent 2D IR spectra, one obtains information about molecular structural dynamics (for both solute and solvent),23-31 and vibrational energy transfer (occurred intramolecularly and/or intermolecularly).32-35 We focus on the latter aspect in the study of the Ru3(CO)12 complex in CHCl3 solvent. This work is the first report on the IVR process among different carbonyl stretching modes of trinuclear metal carbonyl cluster. There are three IR-active C≡O stretching normal modes with large transition dipole in the Ru3(CO)12 complex, indicating their excitonic nature. Directly monitoring the time evolution of the populations of energy donor and acceptor via these exciton-like vibrational modes, as 4 ACS Paragon Plus Environment

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the intramolecular energy transfer process of Ru3(CO)12 taking place, can yield a set of kinetical (reaction rate) and dynamical (structural) insights into the vibrational energy transfer processes of these multi-centered transition-metal clusters. This article is organized as follows. Section II describes experimental and computational methods used in this work. Section III contains the detailed analysis on the vibrational properties of structurally optimized Ru3(CO)12 complex, and more importantly, on the time-dependent 2D IR experimental results of this transition metal complex. Based on which, the IVR processes and dynamics in this molecule are modeled and discussed.

II. Material and Methods A. Sample Preparation and Linear IR Experiment Ru3(CO)12 was purchased from Sigma-Aldrich and used without purification. For linear and nonlinear IR measurements, the Ru3(CO)12 cluster was dissolved in CHCl3 at a concentration of 4.6 mM. The sample solution was loaded into a home-made IR sample cell, which is consisted of two 2-mm thick CaF2 optical windows and separated by 50-m thick Teflon spacer. FTIR spectrum (linear IR) of Ru3(CO)12 cluster was collected using a Nicolet 6700 FTIR spectrometer (Thermo Electron) with 1-cm-1 resolution and 32-scan average at room temperature (22 ℃).

B. 2D IR Experiment The 2D IR experimental setup has been described in elsewhere.24, 36-37 Briefly, a 35-fs, 1-mJ pulse energy, 800-nm laser pulse was generated by a regenerative Ti : sapphire laser amplifier. The produced near-IR pulse first went into an optical 5 ACS Paragon Plus Environment


parametric amplifier (OPA) and then into a difference frequency mixer to further generate a mid-IR pulse with its frequency centered at 2020 cm-1 with a spectral width of ca. 240 cm-1 (full width at half maximum, FWHM). The mid-IR pulse was split into three excitation beams (ca. 400 nJ each) and focused together on the liquid sample to generate 2D IR signal, and a fourth weak mid-IR beam was used as a local oscillator for heterodyning amplification of the 2D IR signal. The delay time between the first and second excitation pulses (k1 and k2) is the so-called coherence time (), while that between the second and third excitation pulses (k2 and k3) is called waiting time (or dynamical time, Tw). The generated 2D IR signal is directed into an IR monochromator that is equipped with a 64-element mercury-cadmium-telluride (MCT) array detector for data acquisition along the detection time (t) using the so-called spectral interferometry. In this way, the time-domain 2D IR data are half Fourier-transformed by the MCT array detector (along the detection frequency, t). Rephasing (-k1 excites sample first) and non-rephasing (k2 excites sample first) 2D IR data were recorded as a function of at a step of 5 fs for a given Tw. A series of Tw-dependent 2D IR spectra were collected in order to characterize the IVR dynamics. The 2D IR measurement was carried out at room temperature (22 ℃) and under dark condition.

C. Density Functional Theory Computations Molecular geometry optimization and harmonic normal-mode vibrational frequency analysis for the Ru3(CO)12 complex in gas phase were carried out using 6 ACS Paragon Plus Environment

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density functional theory (DFT) at the B3LYP level. The lanl2dz pseudopotential basis was used for the transition-metal atom (Ru) and the 6-31+G* basis set was used for other atoms (C, O). The computations were performed using Gaussian.38

III. Results and Discussion A. Carbonyl Stretching Modes In order to assist peak assignment of the C≡O stretching modes in the IR spectroscopies of this work described below, we first performed the DFT calculations on the Ru3(CO)12 cluster. Four IR-active carbonyl stretching modes of the optimized Ru3(CO)12 cluster are shown in Figure 1. The detailed computed vibrational parameters are also listed in Table 1.

Figure 1. The vibrational C≡O stretching modes of Ru3(CO)12 cluster, with their symmetry coordinates arranged from low-frequency to high-frequency (from left to right). Here, “axial” and “radial” represent the symmetry coordinates which dominate in the vibrations.

The vibrational C≡O stretching modes can be grouped into two types through the linear combination of the 12 local modes: one is the axial carbonyl vibration and 7 ACS Paragon Plus Environment


the other is the radial carbonyl vibration. The carbonyl groups in the axial mode are opposite to each other spatially through the Ru atom, while those in the radial mode are opposite along the Ru-Ru bond. The difference of the intensity between the radial and axial modes is due to the π-bonding effect in the cluster.17, 39-40 The highest band (with vibrational frequency of 2122.9 cm-1) is assigned to an axially dominated E' mode, whose high intensity is due to the transition dipole strength borrowing from the local C≡O vibrators.17-18, 40 The second high-frequency band (2103.4 cm-1) represents mostly a pure axial A2" mode,39 the carbonyl groups of which vibrate in phase showing lower intensity than those vibrate out of phase (such as in the E' axial mode).39, 41 Two weak-intensity vibrations located at 2080.1 cm-1 and 2078.3 cm-1 are assigned to the E' (radial, A1) and E' (radial, B2) modes, respectively. These two modes refer to their local symmetry coordinates where an isolated Ru(CO)4 is considered as C2v symmetry.18, 39 The two bands as the consequence of factor-group splitting caused by static field effects appear to overlap,16, 18, 42 and the E' (radial, B2) mode is included together with the E' (radial, A1) in this work because of its extremely low intensity and its overlapping frequency position with the latter. Moreover, the vibrational coupling between these C≡O groups was calculated using the wave function de-mixing method43-46 and the results are shown in Table S1 of the Supporting Information (SI). How these local CO groups (labeled in Figure S1 of the SI) contribute to the three normal modes is further demonstrated in the pair-wise vibrational coupling analysis (Table S1), and also in the potential energy distributions (PEDs) analysis (Table S2 of the SI).47 These results clearly indicate the vibrational 8 ACS Paragon Plus Environment

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excitonic nature of the limited number of IR-active carbonyl stretching modes in this system.

Table 1. Calculated IR-active vibrational frequency (and intensity (I) of Ru3(CO)12 cluster in the C≡O stretching region.

/ cm-1

Assignment

I / (KM·mol-1)

2078.3

E' (radial, B2)

22.0

2080.1

E' (radial, A1)

764.0

2103.4

A2" (axial)

2939.9

2122.9

E' (axial)

4763.2

B. Linear IR Spectrum The infrared absorption spectrum and molecular structure of the Ru3(CO)12 cluster solvated in CHCl3 are shown in Figure 2. Three absorption bands are observed around 2000-2060 cm-1 region. The peaks from high- to low-frequency side are assigned to the E' (axial), A2" (axial) and E' (radial) modes, respectively. The assignment for these vibrational modes (frequency positions and intensities) is based on the DFT computations, which is in reasonable agreement with previous studies of Ru3(CO)12 cluster in solution phases and also in solid state.18-20, 48-49 In addition, it can be seen the weak peak of the E' (radial) mode overlaps to some extent with that of the A2" (axial) mode in the spectrum. The assignment of the E' (radial, B2) component in the FTIR spectrum is not reliable and hence is considered together in the E' (radial) mode. The FTIR spectrum was fitted by Voigt line shape and the fitting results were 9 ACS Paragon Plus Environment


listed in Table 2. During the fitting, peak positions of these C≡O stretching modes obtained from the projection of 2D IR spectrum (see below, Section D) were used. The peak frequencies of these modes in the FTIR are somewhat different from the DFT results because the influence of solvent was not considered in our calculation, and also because of the inaccuracy of the DFT method in predicting the vibrational frequency of molecules. The frequency-scaling factor usually applied for various density functionals was not considered either in our computation. But, the computation does agree with the experimental results in relative peak positions and peak intensities of the three more major IR bands shown in Figure 2. In addition, one sees that the highest-frequency peak (E', axial) is the narrowest among the three IR bands (listed in Table 2), suggesting more homogeneous broadening in this peak. However, the spectral line width contribution is not the major concern of this work and hence will not be discussed further.

Figure 2. Experimental linear IR spectrum of Ru3(CO)12 cluster dissolved in CHCl3 in the C≡O stretching region (solid line) and its fitting using Voigt line shape (dashed line). Inset shows the molecular structure of Ru3(CO)12. The fitting residual (dashed line) is given in the bottom panel. 10 ACS Paragon Plus Environment

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Table 2. Fitting parameters of linear IR spectrum of Ru3(CO)12 cluster in the C≡O stretching frequency region. FWHM

Area

/ cm-1

/ arb. u.

2010.6

18.6

2.9

A2" (axial)

2029.1

12.3

5.3

E' (axial)

2061.0

8.0

5.6

/ cm-1

Mode E' (radial, B2) + E' (radial, A1)

C. 2D IR Spectra of the Ru3(CO)12 Cluster The real part of the purely absorptive 2D IR spectra of Ru3(CO)12 cluster dissolved in CHCl3 at different waiting times are shown in Figure 3. In these 2D IR graphs, both diagonal and off-diagonal peaks can be clearly seen and their origins can be assigned without any ambiguity. The 2D IR signals always appear in pairs, including the 0→1 and 1→2 transition. The positive signal in red is denoted with the0→1 transition, while the negative one in blue represents the1→2 transition. Along the diagonal, three positive-negative peak pairs are observed, which correspond to the peaks in the linear IR spectrum of Ru3(CO)12 cluster. However, the diagonal peak of the E' (radial) mode shows only the negative signal because its positive signal overlaps with the negative one of peak 2 (in panel D). In the meantime, the negative signal of peak 2 appears to be smaller than its positive counterpart. The intensity of the E' (axial, E'a, labeled in panel D) mode is the strongest, while that of the E' (radial, E'r) mode is the weakest. Moreover, it is observed that all the 1→2 transitions decrease in frequency along the t axis with respect to their 0→1 transitions as a 11 ACS Paragon Plus Environment


consequence of considerable vibrational anharmonicity of the C≡O stretching normal mode.50-51 Therefore, the actual frequency differences between 0→1 and 1→2 transitions represent the diagonal anharmonicities (Δ) and more details are given in Section E.

Figure 3. Representative waiting-time dependent purely absorptive 2D IR spectra of Ru3(CO)12 cluster dissolved in CHCl3 in the C≡O stretching region. The waiting times are given in each panel. Six representative off-diagonal peak pairs are labeled with dashed squares in panel D by number 1 to 6. In panel B and C, the red dashed lines indicate 2D IR slices used to determine the anharmonicities (see Figure 5 and Figure S2 of the SI). Each 2D IR spectrum is accompanied with a color bar to show its signal intensity scale.

Six off-diagonal peak pairs are clearly shown in the purely absorptive 2D IR spectra. Peak 1 and 2 are the off-diagonal peaks between the A2" (axial) and E' (radial) modes, while peak 3 and 4 are generated from the E' (axial) and E' (radial) modes. 12 ACS Paragon Plus Environment

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Similarly, peak 5 and 6 between the E' (axial) and A2" (axial) modes are also present in Figure 3. At early Tw (2 ps), strong off-diagonal peak pairs (peak 5, 6) and weak off-diagonal peak pairs (peak 3, 4) appear. The off-diagonal peak 3 shows only its negative signal, and in the meantime the negative signal of peak 5 is weaker than its positive counterpart. However, the diagonal peak of the E' (radial) mode and the associated off-diagonal peaks (peak 1, 2) cannot be identified completely. As the waiting time increases (Tw = 10 ps), the off-diagonal peaks (peak 1, 2) become visible, but still only the negative signal of peak 1 is observable. As the waiting time further evolves, one sees that the intensities of diagonal and off-diagonal peaks generally decrease due to the vibrational relaxation. Although the off-diagonal peak signals seem to become distinct, the amplitudes generally decrease, this is particularly true for peak 6 (see Section F). The appearance of off-diagonal peaks in such metal carbonyl complexes usually has three origins. The first possibility is picosecond-time interchange of axial-equatorial C≡O groups due to the fluxional property of metal carbonyl complex.52 An early study53 indeed suggested fast fluxional dynamics for the Ru3(CO)12 cluster in solution. Later studies have shown that the activation energy for the ligand exchange process in the Ru3(CO)12 cluster is less than 5.0 kcal·mol-1.12 However, it was further shown that the ligand rearrangement occurs on the timescale of microseconds and the exchange rates are temperature-dependent.54 Thus, the fluxional origin of these picosecond-time scale cross peaks observed in Figure 3 is unlikely. The second possibility for the off-diagonal cross peaks in Figure 3 is 13 ACS Paragon Plus Environment


anharmonic vibrational coupling, which occurs inevitably for coupled modes such as a collection of carbonyl stretches studied in this case. However, for a more or less stable structure on the picosecond time scale (no fluxional dynamics yet), the coupled induced cross-peaks should have an unchanged intensity for each cross peak (with respect to the intensities of any pair of couple modes). Because the observed off-diagonal 2D IR signals change as a function of waiting time (as shown clearly in Figure 3), the coupling contribution is not dominant and can be neglected based on its nearly invariant nature on the picosecond time scale. The third possibility is the intramolecular vibrational energy redistribution, which fits the evolving feature of a network of cross peaks in the waiting-time dependent 2D IR spectra shown in Figure 3. Based on these considerations, the change of these off-diagonal peak amplitudes in purely absorptive 2D IR spectra in Figure 3 is believed to be mainly due to the intramolecular vibrational energy transfer. Recent studies have showed that picosecond IVR processes among the C≡O stretching vibrational energy levels also occur in other similar transition-metal carbonyl complexes.33, 37, 55 However, it has to be pointed out that the contribution of anharmonic coupling to the off-diagonal signals cannot be completely separated from the IVR contributions, which will be further discussed below in Section E.

D. Measuring Accurate Frequency Positions The peak of the weak E' (radial) mode overlaps with that of the A2" (axial) mode in the FTIR spectrum, so the accurate peak position of the E' (radial) mode cannot be 14 ACS Paragon Plus Environment

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read out directly from FTIR spectrum. 2D IR spectroscopy can be used to study the underlying vibrational transitions in the case of multi-vibrational modes. This is because the signal intensity in a 2D IR spectrum is proportional to the fourth power of associated transition dipole strength, while that in a FTIR spectrum is only proportional to the square of the transition dipole strength. An early study of Cp2Fe2(CO)4 and Cp2Ru2(CO)4 has revealed the precise transition frequency for the individual isomer from off-diagonal peak regions of 2D IR spectra.33 In our case, the 1→2 transitions instead of 0→1 transitions of off-diagonal peaks (peak 1 and 3) are visible in the purely absorptive 2D IR spectra of Ru3(CO)12 cluster, so it is difficult to extract the frequency position of the E' (radial) mode from the off-diagonal peaks in a straightforward way. Thus, 2D IR spectral projection along the diagonal on the t axis was used to determine the peak position of the E' (radial) mode. The diagonal projection and the FTIR spectrum are plotted together in Figure 4. As can be seen, the strong peaks of the E' (axial) and A2" (axial) modes in the diagonal projection match their FTIR bands quite well. The E' (radial) mode also forms an independent peak in the diagonal projection, even though the peak is quite small comparing to other the two high-frequency components. Based on this small peak, the peak-frequency position of the E' (radial) mode can be directly determined, which is 2010 cm-1. In addition, one has to note that the intensities of the three peaks in the 2D IR diagonal projection are not proportional to those in the FTIR spectrum because for one, the projected peaks are taken from the vibrational relaxed 2D IR diagonal signals, which may have different lifetimes, while in the FTIR spectrum the intensities are measured 15 ACS Paragon Plus Environment


under equilibrium condition; and for two, these signal intensities are proportional to the transition dipole strength differently, as mentioned above.

Figure 4. Projection of the 2D IR real-part spectrum at Tw = 10 ps on the t-axis along the diagonal (solid line) and FTIR spectrum (dot line) of Ru3(CO)12 cluster. The peak positions of these C≡O stretching modes are in dashed lines.

E. Extracting Diagonal and Off-Diagonal Anharmonicities of the Carbonyl Stretches

Figure 5. Representative slice of the 2D IR real-part spectrum (empty circle) at Tw = 10 ps at  = 2060 cm-1 and along the t-axis. The 0→1 transition is in red and 1→2 transition is in blue. Peak fitting is also shown in black solid line. 16 ACS Paragon Plus Environment

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2D IR spectroscopy is usually sensitive to three lowest vibrational transition energy levels for a given set of anharmonic oscillators (0, 1, and 2), which can hence provide a direct measure of the vibrational anharmonicity. Previous studies have extracted the anharmonicity from the slice of purely absorptive 2D IR spectra along the probe axis at a typical pump frequency.56-57 In our case, the representative 2D IR slice (Figure 5) was taken from the 2D IR real-part spectrum at Tw = 10 ps along the t axis at  = 2060 cm-1, which is indicated by the red dashed line in Figure 3, panel B. This 2D IR slice was fitted by the Voigt line shape, where the positive peaks in red represent the 0→1 transitions, and the negative ones in blue indicate the1→2 transitions. The anharmonicity for a given mode is defined as a positive value, i.e., Δ = 0→1 -1→2. During the fitting, the 0→1 transitions of these C ≡O stretching modes were taken from the results obtained in Figure 4, and the fitting results are listed in Table 3. Because the off-diagonal peaks (peak 3, peak 5) are mainly due to intramolecular energy transfer, the anharmonicity values of these off-diagonal peaks are equal to the diagonal anharmonicities of the E' (radial) and A2" (axial) modes respectively. The obtained diagonal anharmonicity of the radial E' mode (13.2 cm-1) is only slightly larger than those of the axial A2" (13.0 cm-1) and axial E' modes (12.2 cm-1). These results suggest the overall excitonic behavior of the three major IR bands observed in our linear and nonlinear IR spectroscopies. The diagonal anharmonicities of carbonyl modes are also in agreement with previous calculated and experimentally determined results for similar transition metal carbonyl stretching modes.51, 58 Moreover, 2D IR slices at other waiting times were also fitted, and 17 ACS Paragon Plus Environment


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marginal variation in the anharmonicities was observed among those diagonal and the associated off-diagonal signals that were vertically aligned (along the -axis). The results are given in Figure S2 with fitting parameters listed in Table S3, S4 an S5 of the SI for comparison. These results also indicate insignificant anharmonicity change for a given 2D IR signal, and further supporting the argument presented above for this Ru-carbonyl complex on the picosecond time scale.

Table 3. Fitting parameters and determining the diagonal and off-diagonal anharmonicities of the IR-active carbonyl stretching modes at 2060 cm-1 (see Figure 5). Mode E' (radial) A2" (axial) E' (axial)

t/ cm-1 Transition FWHM Area a / arb. u. / cm-1 1996.1

1→2

16.7

-2.4

2009.3

0→1

17.8

1.7

2015.8

1→2

12.7

-3.6

2028.8

0→1

9.9

3.9

2048.9

1→2

10.6

-15.2

2061.1

0→1

10.4

15.8

a

13.2 13.0 12.2

Voigt line shapes are used during fitting.

On the other hand, in an excitonic picture, it is known that the magnitude a mixed mode off-diagonal anharmonicity for a pair of vibrational modes will be non-negligible if the two modes are coupled.59 And, the diagonal and off-diagonal anharmonicities are molecular structural dependent. This is a generally known feature of the vibrational excitonic states consisting, for example, a group of carbonyl 18 ACS Paragon Plus Environment

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stretching vibrators. However, the fitting results mentioned above do not yield any explicit information about the mixed-mode off-diagonal anharmonicities among these modes. Because such off-diagonal anharmonicity is closely related to the anharmonic shift of the combination band, which gives rise to (coupling induced) cross peaks as mentioned in Section C. It should be pointed out that even at early waiting times, it is difficult to separate coupling-induced cross peak from IVR-induced cross peak if both exist. As one example, we examined early waiting-time 2D IR spectra. The real part of the non-rephasing 2D IR spectra at two early times (100 fs and 200 fs, Figure S3 of the SI) indeed show the presence of cross peaks, however, whose origin could still be partially vibrational coupling (that is structure dependent and hence likely to be time independent) and partially IVR (that is time dependent). These two types of cross peaks will also contribute to the transient broadband pump – broadband probe infrared spectra. The latter expectation has actually been demonstrated in a previous work22 of a similar trinuclear transition-metal carbonyl complex, namely Os3(CO)12. In addition, 2D IR spectra at Tw = 0 cannot be used to separate the coupling-induced cross peak from the IVR-induced cross peak either, because of the complication of spectral contribution when four IR pulses overlap at zero time in the 2D IR experiment. There is one way to measure coupling-induced cross-peak, that is, at a fairly long waiting time when the IVR processes finish while the vibrational relaxation does not and the signal-to-noise ratio of 2D IR signal is still reasonably good. This is beyond the scope of this work and will not discussed further. 19 ACS Paragon Plus Environment


F. Obtaining Intramolecular Vibrational Energy Redistribution Rate 2D IR spectroscopy can provide a measure for intramolecular vibrational energy transfer dynamics between two different modes. The peak amplitudes in 2D IR spectra as a function of the waiting time can be used to obtain the IVR rate. To this end, the 2D IR cross peak intensities can be taken from their positive and negative extremes.32 Previous studies have showed that the intensity ratio of cross peak and diagonal peak should be used to correct the vibrational relaxation when evaluating the IVR processes.33 In our recent study the IVR time constants in Mn(CO)5Br were obtained by fitting the waiting-time evolution of the 2D IR diagonal and off-diagonal amplitudes (or simply called intensities) simultaneously.37 To fit the IVR rate we used a series of Tw-dependent absolute non-rephasing spectra. It should be pointed out that the data collected in conventional four-wave mixing method require proper phasing of the rephasing and non-rephasing 2D IR spectra in order to obtain the purely absorptive 2D IR spectra as shown in Figure 3. It is well known that such purely absorptive 2D IR spectra have many advantages (for example, clearly showing negative and positive diagonal and off-diagonal peaks). However, one has to know that a careful phasing the time-domain rephasing and non-rephasing signals is very critical. Thus, it can be a very tedious work if a series of waiting-time dependent 2D IR spectra are needed. This problem can be circumvented by using the absolute part of the 2D IR signal, if one is only interested in evaluating the signal intensity of either a diagonal or an off-diagonal signal. In this case, the intensities of both the positive and negative parts of a 2D IR signal can be taken into 20 ACS Paragon Plus Environment

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account, if a 2D-frequncy area is properly chosen. On the other hand, if this procedure is taken, then one only has to collect either the rephasing or non-rephasing part of 2D IR spectra because the absolute-magnitude 2D IR spectra for the two types are the same. Also, because usually the coherence time for the non-rephasing 2D IR spectra is shorter than the corresponding rephasing part, it is experimentally more efficient to only collect the waiting-time dependent non-rephasing 2D IR spectra. Thus, in this work, we used a series of absolute valued non-rephasing 2D IR spectra in modeling the IVR processes illustrated in Scheme 1. Selective absolute part of 2D IR non-rephasing spectra at typical waiting time are given in Figure S4 in the SI, in which the 2D frequency regions (2 cm-1 by 2 cm-1, thus it is equivalent to peak “intensity” or proportional to the “amplitude” of the positive to negative absorptive 2D IR signal) used to evaluate the diagonal and off-diagonal peak amplitudes are shown in dashed squares.

Scheme 1. IVR kinetic model for a three-mode system in Ru3(CO)12 cluster. Here, E'r, A2", and E'a represent E' (radial), A2" (axial), and E' (axial) vibrational states respectively.



The kinetic rate equations of the IVR processes shown in Scheme 1 and the corresponding solutions are given in Scheme S1 and S2 in the SI, and parameters used in the equations are listed in Table S6. Fitting details are given in Scheme 2. For the Ru3(CO)12 cluster, the IVR process involves three major C≡O stretching normal modes as shown in Figure 3, and we assumed an equal vibrational relaxation rate for the involved modes during the fitting. This is a reasonable assumption to begin with because the C≡O stretching modes of a similar transition-metal carbonyl complex may have similar vibrational relaxation rates.22, 50 In addition, considering the excitonic nature of these C≡O normal modes that are separated by tens of wavenumbers, their lifetimes should be quite similar. On the other hand, a very complicated analytical solution would be needed to solve the kinetic model shown in Scheme 1, if one has to use different energy relaxation time constants for these three involved vibrational modes. Furthermore, our recent study showed that varying the vibrational lifetime (T1) or the relaxation rate constant (kV = 1/T1) by 10 % ~ 20 % does not significant vary the IVR time.37 In addition, because of the presence of the IVR process, traditional broadband IR pump-probe experiment under the so-called magic-angle polarization condition cannot reliably obtain the T1 values for these modes. This can be easily seen in Figure 3: the time-dependence intensity of a vibrational mode (for example, E'a) probed in the detection frequency position near t = 2061.0 cm-1 will contain the contribution of the two off-diagonal peaks (peak 4 and peak 6), because a transient pump-probe signal at a specific pump-probe delay time is the same as the vertical summation of a 2D IR spectrum at the same waiting time. 22 ACS Paragon Plus Environment

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Thus, a simplified three-mode kinetic model (Scheme 1) with the same kV parameter was used to fit the diagonal and off-diagonal 2D IR peak amplitudes. In this kinetic model, E'r, A2" and E'a represent three C≡O vibrational states, and there are seven variables including both forward and backward IVR rate constants. The forward and backward rate constants are related to each other through the equilibrium constant, Keq = kbackward / kforward. Moreover, Keq can be obtained from the transition state theory Keq = exp(-hΔ/ kBT), where h is the Planck constant, Δis the frequency splitting between the two modes involved, kB is the Boltzmann constant, and T is temperature. The frequency splitting between the E' (radial) and A2" (axial) modes, the A2" (axial) and E' (axial) modes, and the E' (radial) and E' (axial) modes is 19.5 cm-1, 32.3 cm-1 and 51.8 cm-1 respectively, which are obtained from the projection of the 2D IR spectrum in Figure 4. These integrated signals as a function of Tw were displayed in Figure 6. In Figure 6, the amplitude of the diagonal peak (the A2" (axial) mode) is given in panel B, while two off-diagonal peaks (peak 1 and peak 6) are given in panel A and panel C, respectively. As is seen, a fast decrease dominates the amplitude, and the amplitudes of these C≡O stretching modes show similarly dynamical traces. The fitting curves and residuals by applying the kinetic model shown in Scheme 1 are also shown in Figure 6. The fitting parameters and the obtained IVR rate constants among the C≡O vibrational states are list in Table 4. A faster IVR time of 11.1 ps is obtained between the E' (radial) and A2" (axial) modes, while a slightly longer IVR time of 12.7 ps exists between the E' (radial) and E' (axial) modes. These IVR processes occur 23 ACS Paragon Plus Environment


on the time scale of picosecond, as has also been shown in previous studies of other transition-metal carbonyl complexes.33, 37, 55 In addition, the vibrational relaxation rate (kV) was determined to be 0.0016 ps-1 (1/609.6 ps-1), which is in the time range similar to the reported relaxation time constant (400-600 ps) that was determined by narrowband pump - broadband probe infrared method for a similarly structured trinuclear transition-metal carbonyl clusters, i.e., Os3(CO)12.22

Figure 6. Waiting-time dependent amplitudes from the non-rephasing 2D IR spectra of Ru3(CO)12 cluster. (A) Off-diagonal signal between the A2" (axial) mode and E' (radial), i.e., peak 1 in Figure 3D); (B) Diagonal signal of the A2" axial mode; (C) Off-diagonal signal between the A2" (axial) mode and E' (axial), i.e., peak 6 in Figure 3D). Lines are the fits with functions obtained from the kinetic model shown in Scheme 1. Dashed lines are fitting residuals.

The observed long vibrational lifetime allows a broad range of time scale for the intramolecular vibrational energy transfer to occur, which turned to be quite efficient 24 ACS Paragon Plus Environment

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in this system. As already shown in the purely absorptive 2D IR spectra (Figure 3), for example, the off-diagonal signal at peak 6 become comparable in intensity to the strong diagonal signal (E'a) at 50-ps waiting time. The IVR times obtained are all on the order of tens of picosecond, indicating an indeed quite rapid and efficient vibrational energy exchange in this multi-carbonyl system. Such efficient IVR is due to several reasons. First, the energy separations among the three normal modes are quite small (the largest gap is 51.8 cm-1), which allow efficient downward and upward energy transfer. Second, these three normal modes are anharmonically coupled, in other words, they are of excitonic nature, in a sense that they are linear combination of twelve local C≡O stretching motions, as pointed out in previous Section III A. This has been shown in Table S1 for vibrational coupling and Table S2 for potential energy distributions.47 As can be seen clearly in these results, it is nearly impossible to assign the observed IR peaks to any of the local C≡O stretching mode. The efficient IVR processes among the three normal modes suggest that once one of the local C≡ O stretching mode is vibrationally excited, its neighboring C≡O stretching mode will instantaneously sense the excitation too. Under such circumstances, each C≡O group in this multi-centered transition metal complex is “equally” IR active, which is an important property of such complex when functioning as photo-catalysts, or in the processes of photoenergy conversion and chemical synthesis.



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Table 4. The peak splitting (Δ), equilibrium constant (Keq), and the forward and backward IVR rate constants (k) of the C≡O vibrational states. IVR pathway

Δ/ cm-1

Keq

kforward / ps-1

kbackward / ps-1

A2" (axial) → E' (radial)

19.5

0.910

0.090 (1/11.1 ps-1)

0.082 (1/12.2 ps-1)

E' (axial) → A2" (axial)

32.3

0.856

0.086 (1/11.6 ps-1)

0.074 (1/13.5 ps-1)

E' (axial) → E' (radial)

51.8

0.779

0.079 (1/12.7 ps-1)

0.062 (1/16.1 ps-1)

IV. Conclusions and Outlook In summary, using 2D IR spectroscopy we directly observe intramolecular vibrational energy transfer process among different C≡O stretching modes in Ru3(CO)12 cluster. This cluster with twelve C≡O groups has a non-bridged D3h configuration, forming a quite stable core structure with such a large number of ligands. The linear IR experimental measurements and DFT calculations both revealed three major C≡O stretching vibrational components, which are the E' (axial) mode, A2" (axial) mode, and E' (radial) mode. Because the latter is weak in its linear IR intensity, 2D IR projection was used to better determine its frequency position. Two major conclusions can be drawn from this work. First, these observed C≡O stretching modes are of vibrational excitonic nature. This can be seen from their unbalanced absorption intensities (due to anharmonic coupling) and frequency separations (due to both the coupling and local structural differences). Spectral fitting of the selected 2D IR slices leads to a set of diagonal and off-diagonal anharmonicities as a function of waiting time. The finding is that these C≡O modes 26 ACS Paragon Plus Environment

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in Ru3(CO)12 cluster have similar diagonal anharmonicities (13.1 cm-1 on average). The average off-diagonal anharmonicity is on the order of 12.9 cm-1, which is very close to their corresponding diagonal anharmonicities. The observed strong and intensity-increasing cross peaks, with respect to corresponding diagonal peaks, are due to the intramolecular energy transfer, which is the second most important conclusion of this work. Here, intramolecular vibrational excitonic energy redistribution occurs efficiently among these modes. This is manifested by the waiting-time dependent off-diagonal 2D IR peaks, and further characterized by a kinetic model, and from which the downhill and uphill vibrational energy transfer rates were obtained. The time scales of these energy transfer were found to be around 11-16 ps, while the lifetimes of these vibrational excited states are on the order of 400-600 ps.22 Such efficient IVR processes confirm the excitonic nature of the three linear IR absorption bands, in a sense that when some of the C≡O modes are vibrationally excited, the excitation energy will migrate to other C≡O modes very quickly. Such an excitonic nature appears to be very crucial to the chemical activity of the CO groups as they function in various ways. We have to point out that in fitting the IVR dynamics, the coupling-induced cross peaks were neglected, because this Ru3(CO)12 cluster only shows fluxional property on the timescale of microseconds.54 In addition, we have to point out that in the present work, the structural aspect of such trinuclear transition-metal complexes was not explored in detail, including equilibrium structures and their distributions, and solute-solvent interactions, which is also believed to be very important to their functions.



Acknowledgement This work was supported by the National Natural Science Foundation of China (21473212 to F.Y., 21603238 to J. Z., and 21573243 to J. W.).

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