Vibrational Dynamics of Aqueous Hydroxide Solutions Probed using. Broadband 2DIR Spectroscopy

Transcription

1 Vibrational Dynamics of Aqueous Hydroxide Solutions Probed using Broadband 2DIR Spectroscopy Aritra Mandal 1,2, and Andrei Tokmakoff 1, * 1 Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, University of Chicago, Chicago IL Department of Chemistry, Massachusetts Institute of Technology, Cambridge MA Abstract: We employed ultrafast transient absorption and broadband 2DIR spectroscopy to study the vibrational dynamics of aqueous hydroxide solutions by exciting the O H stretch vibrations of the strongly hydrogen-bonded hydroxide solvation shell water and probing the continuum absorption of the solvated ion between cm -1. We observe rapid vibrational relaxation processes on fs timescales across the entire probed spectral region as well as slower vibrational dynamics on 1 2 ps timescales. Furthermore, the O H stretch excitation loses its frequency memory in 180 fs, and vibrational energy exchange between bulk-like water vibrations and hydroxide-associated water vibrations occurs in ~200 fs. The fast dynamics in this system originate in strong nonlinear coupling between intra- and intermolecular vibrations and are explained in terms of non-adiabatic vibrational relaxation. These measurements indicate that the vibrational dynamics of the aqueous hydroxide complex are faster than the timescales reported for long-range transport of protons in aqueous hydroxide solutions. Current Address: Department of Chemistry, Boston University, Boston MA *Corresponding author. address: tokmakoff@uchicago.edu

2 I. Introduction: Aqueous proton transport (PT) is a fundamental phenomenon relevant to many chemical and biological processes. 1 4 PT in aqueous hydroxide solutions is anomalously fast because water s hydrogen bonds aid in moving a proton from a solvating water molecule to the OH ion. 5,6 This textbook picture, known as the Grotthuss mechanism, describes PT along onedimensional hydrogen-bonded wires of water molecules. However, theoretical and experimental studies increasingly point to the importance of water s dynamic three-dimensional hydrogenbonding network in the mechanism of PT. Most studies of the PT mechanism in aqueous hydroxide solutions stem from molecular dynamics (MD) simulations that describe the process in terms of interconversion between solvated structures of the OH ion with varying water coordination number. One mechanism favors a 3-coordinate stable solvated structure of OH ions (H 7 O 4 ), analogous to the Eigen cation in aqueous acid solutions. 6 9 In contrast, ab initio MD (AIMD) and empirical valence bond MD (EVB-MD) simulations point toward a 4-coordinate stable solvated structure, where the OH ion accepts four hydrogen bonds During PT, the formation of a H 3 O 2 intermediate, similar to the Zundel cation in aqueous acid solutions, is suggested. 6 9 More recently, some AIMD studies have depicted a multiscale dynamical picture of PT, in which collective changes in the hydrogen-bonding network of solvating waters over a picosecond timescale are supposedly crucial. 21 Similarly, analysis of AIMD and EVB-MD simulations indicate that PT is dictated by the collective electric fields of solvating water molecules along the PT direction. 22,23 Experimental studies to test these predictions have been challenged by the need for structurally resolved techniques with ultrafast time resolution. Since fluctuations in the hydrogen-bonding network of water take place on femtosecond to picosecond timescales, 2

3 femtosecond time resolution is required to study the impact of water dynamics on PT in aqueous hydroxide solutions. Of such methods, ultrafast infrared (IR) spectroscopy has been a valuable method since molecular vibrations in aqueous solutions, particularly O H stretches, are strongly influenced by hydrogen-bonding interactions and can be used to interrogate the dynamics of these vibrations with time resolution as low as a few tens of femtoseconds. Previous 2DIR experiments probing the O H stretch vibrations in isotope-diluted aqueous hydroxide solutions found that successful PT between hydrated OH complexes takes place on ~3 ps timescale, 24 and provided evidence that the Zundel-like H 3 O 2 species exists only fleetingly (~110 fs) during the PT event These observations are supported by AIMD and EVB-MD simulations which suggest that the proton shuttles between two OH moieties in ~180 fs before being successfully transferred within a few picoseconds Ultrafast transient absorption (TA) experiments that probe isotopically pure NaOH solutions found a 200 fs lifetime for the O H stretch vibrations as well as the growth of a thermal difference spectrum on a few picosecond timescale. 27 Linear IR spectra of aqueous hydroxide solutions show a broad continuum absorption in the cm -1 region that contains two clearly distinguishable broad and overlapping peaks These features originate in the strong interactions and fast dynamics of the OH ion and its solvating water molecules. Water molecules in the first solvation shell form significantly stronger hydrogen bonds to the oxygen of the OH ion compared to bulk water. As a result, O H stretch vibrations of the solvating water molecules red-shift significantly and H-O-H bend vibrations blue-shift. In a recent study of aqueous NaOH solutions, we found that the vibrations of the solvated OH ion are delocalized over the water molecules in the first solvation shell, and different modes of vibration can be distinguished based on their vibrational symmetry. 31 Further, 3

4 these broad resonances appear to be insensitive to the coordination number of the OH ion because they show little variation between 3- and 4-coordinate species. Given the strong interactions of the OH ion with its solvation shell and the importance of hydrogen-bonding dynamics to PT, the analysis of the vibrational motions and dynamics of the aqueous hydroxide complex has direct bearing on the mechanism of PT. In order to investigate dynamics of the vibrations arising from the solvated OH ion and bulk-like water molecules, we performed ultrafast IR TA and broadband 2DIR (BB 2DIR) experiments on aqueous NaOH solutions using a recently developed <70 fs broadband infrared (BBIR) source. In these experiments, we excite the O H stretch vibrations of aqueous hydroxide solutions and probe the response of the continuum band between 1500 and 3800 cm -1. This allows us to reveal rapid vibrational relaxation and vibrational energy transfer processes involving the solvated OH complexes that have faster timescales compared to the measured PT rates. II. Experimental Methods The experimental procedure for performing TA and BB 2DIR spectroscopy is discussed in detail elsewhere, only a brief description is given here In our experiments, we pumped the O H stretch vibrations of aqueous NaOH solutions using sub-45 fs transform-limited pulses centered around 3 μm (~0.5 µj/pulse), generated by a KNbO 3 optical parametric amplifier (OPA). 35 The time-coincident fundamental, second, and third harmonic of the sub-25 fs 800 nm pulses from a Ti:sapphire amplifier are focused in dry air to generate a plasma source that radiates <70 fs BBIR pulses used as a probe in our experiments (~10 nj/pulse). These pulses contain frequencies ranging from <400 to 4000 cm -1 and probe the entire continuum region, including the O H stretches. 36 4

5 BB 2DIR experiments reported in this work are performed in the pump probe geometry, 37 where the first two interactions of the sample have a collinearly propagating 3 μm pulse pair and the BBIR pulse acts as a probe. The 3 μm pulse pair is generated from the OPA output using a Mach-Zehnder interferometer and the time delay between them (τ ) is numerically Fourier transformed to obtain the excitation frequency axis ω. While performing the TA experiments, the moving arm of the 3 µm interferometer is blocked. The waiting time (τ ) between the pump and the probe pulses is set by a separate delay stage that introduces a time delay into the 800 nm input pulses used for BBIR generation. The BB 2DIR experiments described in this paper are performed in parallel polarization (ZZZZ) geometry. On the other hand, the TA experiments use magic angle (54.7 ) polarization geometry between pump and probe pulse for measuring the vibrational relaxation timescale. To detect BBIR pulses, we disperse the probe on a 64-element HgCdTe (MCT) array detector with a lower frequency cutoff of 1350 cm -1. Because BBIR pulses have large bandwidths and a limited numbers of array pixels, we used three grating positions to collect the entire BBIR spectrum with an overlap of at least 65 cm -1 between consecutive grating positions. A complete spectrum is obtained by taking an average of the signals in the spectral overlap regions during post-processing of the data. The TA and BB 2DIR spectra presented in this paper have been normalized to the absolute maximum peak intensity in the cm -1 region at the longest waiting time (6 ps) and in the cm -1 region of detection frequency (ω ), respectively. The TA and BB 2DIR experiments are performed in transmission mode. The sample is sandwiched without a spacer between two 1 mm thick CaF windows (pathlength ~2 μm) leading to an absorbance of for the peak of the O H stretch vibration in H 2 O as well as in aqueous NaOH solutions 5

6 of concentrations up to 10M. Aqueous solutions of NaOH are prepared by dissolving NaOH pellets (Mallinckrodt, 98% assay) in H 2 O (purified by reverse osmosis to a resistance of 18 MΩ). III. Results A. Linear IR spectra Figure 1: FTIR spectra of H 2 O and aqueous NaOH solutions of concentrations ranging from 3M to 10M. The spectra are normalized to the maximum of the O H stretch peak at 3400 cm -1. The blue and red shaded regions correspond to the spectra of the pump pulses used for different O H stretch vibrations. The orange and green bars indicate frequency regions corresponding to the asymmetric (ν a ) and symmetric (ν s ) O H stretch vibrations of the solvated OH ions, respectively. The asterisk marks the region of spectral interference by atmospheric CO 2. The distinct peaks shown in the linear IR spectrum of H 2 O include the O H stretch peak centered at 3400 cm -1, the H-O-H bend peak centered at 1650 cm -1, and a weak peak at 2150 cm -1 corresponding to the bend-libration combination band. When NaOH is added to water, a broad continuum absorption grows across the entire mid-ir region, as shown in Fig. 1. This continuum absorption has two broad but distinctive features: a shoulder to the O H stretch main band centered at 2850 cm -1 and a weak maximum centered at 2000 cm -1. Our recent study using 6

7 ultrafast IR experiments and harmonic vibrational analysis of solvated OH clusters assigned the 2850 cm -1 feature to the asymmetric O H stretch vibration of the water molecules solvating the OH ion (ν a ). 31 These O H stretch vibrations are delocalized over the first solvation shell water molecules and the symmetry is defined based on the relative phases of vibrations of the O H bonds hydrogen bonded to the oxygen atom of the ion. The symmetric O H stretch (ν s ) is blueshifted to cm -1, which overlaps with the O H stretch vibration of the bulk-like water molecules. In contrast, our assignment of the 2000 cm -1 peak was inconclusive, but it is likely that the bend vibrations of the solvating water molecules, librations, and other intermolecular vibrations significantly contribute to it. A recent study of the strong hydrogen bonds between pyridine and acetic acid concluded that a similar peak arises from strong mixing between O H stretch and R-O H bending motions. 38 B. BB 2DIR Spectra In order to study the vibrational dynamics in aqueous hydroxide solutions, we performed TA and BB 2DIR experiments in which we pumped the O H stretch vibrations and probed the response across the continuum. Figure 2 compares waiting time-dependent BB 2DIR spectra of H 2 O and 7M NaOH solutions with a pump center frequency of 3100 cm -1, as illustrated by the red shading in Fig. 1. The 100 fs spectrum is the earliest waiting time for which the pulse overlap effects are absent. At this waiting time, BB 2DIR spectra of H 2 O show a bleach of the O H stretch vibration between cm -1 along the diagonal, a corresponding broad induced absorption that peaks at ω 3 = 2950 cm -1 that has a tail that extends below ω 3 = 1500 cm -1, and a cross peak bleach of the H-O-H bend vibration at 1680 cm -1. The breadth of the induced absorption has its origin in strong anharmonic coupling between intra- and intermolecular 7

8 vibrations. 32 8

9 9

10 Figure 2: Ultrafast broadband infrared spectroscopy of (A) H 2 O and (B) 7M NaOH. BB 2DIR spectra (left) and dispersed transient absorption (right) are shown as a function of waiting time, τ 2. Contours are shaded blue for bleach and red for induced absorption. The BB 2DIR spectra are normalized to the absolute maximum peak intensity in the cm -1 region of detection frequency (ω 3 ). The TA spectra are normalized to the absolute maximum peak intensity in the cm -1 region at the longest waiting time (6 ps). The pump pulse for both measurements is centered at 3100 cm -1 (red shaded bars). FTIR spectra of the solutions are shown on the right side. Detection frequencies below 2200 cm -1 are multiplied by a factor of 15 for BB 2DIR spectra and by a factor of 3 for TA spectra to highlight spectral features. The asterisk marks the region of spectral interference by atmospheric CO 2. The blue and red arrows to the right of NaOH BB 2DIR spectra indicate the frequencies at which the ω 3 slices are taken in Fig. 7. The green arrow marks the position of the cross peak between ν a and ν s vibrations. For NaOH, we observe an additional bleach on the diagonal at 2850 cm -1 corresponding to the ν a vibration. Although the ν s vibration coincides with the O H stretch vibration of bulklike water, it manifests itself in the cross peak region at ( 1, 3 ) = (2850 cm -1, 3375 cm -1 ). Strong coupling between hydroxide-associated stretches, bends, and intermolecular vibrations results in a continuum of states with mixed character in the cm -1 region. A subsequent transition to these states following O H stretch excitation results in a qualitatively different induced absorption below ω 3 = 2200 cm -1. C. Transient Absorption Spectra Figure 2 also shows the corresponding TA spectra of H 2 O and 7M NaOH solution, illustrating the time-dependent changes to the bleaches and induced absorptions for waiting times up to 1 ps. The TA and BB 2DIR spectra show that the induced absorption for frequencies ω 3 < 3100 cm -1 relaxes within the first 300 fs in H 2 O and 200 fs in NaOH. These relaxation processes are an order of magnitude faster than the timescale for the reorganization of hydrogen bonds in 10

11 the liquid. We also observed the growth of a few positive and negative features over several hundred femtoseconds. These are particularly prominent at 3 = 3620 cm -1, 3300 cm -1, and 1640 cm -1 for both H 2 O and NaOH, and at 2800 cm -1 for just the NaOH solution. Figure 3: Pump-frequency dependence of the TA spectra of (A) H 2 O and (B) 7M NaOH. The pump-pulse center frequency is changed between 3400 cm -1 (blue) and 3100 cm -1 (red), and the waiting times are compared for τ 2 = 100 fs (solid line) and τ 2 = 6 ps (dashed line). These slices are normalized to the absolute maximum peak intensity in the cm -1 region of the spectra at 6 ps waiting time. The region of detection frequency below 2200 cm -1 is multiplied by a factor of 5 to highlight the spectral features. The asterisk marks the region of spectral interference by atmospheric CO 2. 11

12 In Fig. 3 we illustrate the dependence of the TA spectral features in H 2 O and NaOH on pump frequency. TA spectra obtained with the pump spectra shown in Fig. 1, which have center frequencies at 3400 cm -1 and 3100 cm -1, are compared. These are referred to as blue-pump and red-pump, respectively. The blue-pump and red-pump slices of H 2 O spectra at 2 = 100 fs (Fig. 3A) are similar, showing the O H stretch bleach at 3400 cm -1, the broad induced absorption that peaks at 2950 cm -1, and a cross peak bleach of the H-O-H bend vibration at 1680 cm -1. The 2 = 100 fs spectra of NaOH show a stronger dependence on pump frequency (Fig. 3B). A bleach corresponding to the ν a vibration is observed at 2700 cm -1 in the red-pump slice. This peak is 150 cm -1 red-shifted with respect to the ν a peak in the FTIR as a result of the competing contributions from bulk-like water and the hydroxide complex. The blue-pump slice, however, is dominated by the bulk-like water induced absorption. The induced absorption feature below 2200 cm -1 in NaOH is qualitatively different in both slices compared to H 2 O. Finally, there is a weak bleach at 2000 cm -1 in NaOH, which is only present in the blue-pump spectrum. This indicates a coupling of the 2000 cm -1 feature to the ν s vibrations, which also influences a bulge in the lineshape of the corresponding BB 2DIR spectrum at ( 1, 3 ) = (3300 cm -1, 2000 cm -1 ). At a 6 ps waiting time, when the vibrational relaxation is complete for H 2 O and NaOH, the TA slices are the same for both pump frequencies and they resemble a thermal difference spectrum for a small temperature rise (Fig. 4). Low frequency intermolecular vibrations are populated following vibrational relaxation, similar to increasing the temperature. 39,40 With an increase in temperature, the O H stretch vibrations blue-shift and H-O-H bend vibrations redshift. Therefore, at a 6 ps waiting time, the TA slices from both H 2 O and NaOH show an induced absorption at ω 3 = 3620 cm -1 and a bleach at ω 3 = 3300 cm -1 corresponding to the blue-shifting of the O H stretch vibrations with a prominent induced absorption at ω 3 = 1640 cm -1 12

13 corresponding to the red-shift of the H-O-H bend. A bleach at ω 3 = 2800 cm -1 corresponding to the ν a vibration is also observed for NaOH. Figure 4: Comparison of the thermal difference spectrum (T 2 T 1 = 5 C, where T 1 = 25 C and T 2 = 30 C) and TA spectrum taken at τ 2 = 6 ps for H 2 O and 7M NaOH solutions. The pump-pulse center frequency for the TA spectra is at 3100 cm -1. The asterisk marks the region of spectral interference by atmospheric CO 2. D. Vibrational Relaxation Dynamics We performed singular value decomposition (SVD) analysis on the red-pump TA spectra to identify different spectral and temporal contributions to the data (Fig. 5). SVD linearly decomposes the time-dependent TA spectra into principle spectral components and their associated time dependence. Singular values of these components determine their contribution to the overall data. We found that the data is well modeled by two spectral components. One of these components decays with waiting time ( short-time spectra) and the other rises ( long- 13

14 time spectra). We constrained the long-time spectral components to be identical to the TA spectra at 6 ps. For H 2 O, we found that the short-time spectrum decays as a single exponential with a timescale of 230 fs, and the long-time spectrum grows in with a timescale of 735 fs (Fig. 5). This observation matches a previous report with some differences in timescale that result from different excitation frequencies. 32 Figure 5: Singular value decomposition of TA spectra. (A) Spectral and (B) temporal SVD components obtained from red-pump TA spectra of H 2 O and 7M NaOH. The asterisk marks the region of spectral interference by atmospheric CO 2 in (A). For clarity in presentation, the time traces of short-time and long-time spectral components of 7M NaOH are shifted by -0.1 and units, respectively. In contrast, the temporal dependencies of the SVD components from NaOH spectra have 14

15 a bi-exponential form. The short-time spectrum decays with relaxation times of 150 fs and 1750 fs, whereas the long-time spectrum grows on 290 fs and 1650 fs timescales. The bi-exponential relaxation in NaOH could arise from different reasons. For instance, each spectral component may include relaxation contributions from both bulk-like water and water solvating the OH ion. Alternatively, both the short and long waiting time spectra of NaOH might contain intrinsically bi-exponential relaxation dynamics. Also, comparing the singular values of our analysis (See Supporting Information), it remains possible that the two component decomposition of the spectral dynamics is less satisfactory for hydroxide and does not capture fully independent processes. We present our explanation of this relaxation process in Sec. IV. Figure 6: Concentration dependence of relaxation. (A) Growth of the induced absorption feature at ω 3 = 3620 cm -1 and (B) semi-log representation decay showing bi-exponential kinetics for aqueous NaOH solutions. The traces in A are offset by 0.15 units to avoid overlap. (C) Timescale and (D) amplitude of bi-exponential growth at 3620 cm -1 obtained by fitting data in (A) to a bi-exponential of the form Afast exp( 2 / fast ) Aslow exp( 2/ slow) const where Afast Aslow 1. 15

16 We also studied the dependence of the relaxation times on NaOH concentration, which is summarized in Fig. 6. To monitor the growth of the long-time component, we fit the rise of the induced absorption at 3 = 3620 cm -1 (Fig. 6A). For H 2 O, this feature grows exponentially in 685 fs, comparable to the growth timescale of the long-time spectral component in SVD. On the other hand, 7M NaOH shows bi-exponential growth. The fast component has a rise time of ~200 fs that is concentration independent (Fig. 6C), but has an amplitude that increases monotonically with NaOH concentration (Fig. 6D). In contrast, the slow component slows with increasing concentration from 685 to 1100 fs (Fig. 6C) and decreases in amplitude by a factor of two over the same range (Fig. 6D). Similar observations are made for the decay of the TA signal at 3 = 2850 cm -1. E. Spectral Relaxation Dynamics As a point of comparison for the population relaxation decays, we measured the loss of frequency memory for the OH excitation using the decay of the center line slope (CLS) of the diagonal peaks in waiting time-dependent BB 2DIR spectra. 41 Figure 7A shows the O H stretch CLS decay for H 2 O and 7M NaOH in the cm -1 region for red pumping. The CLS decays with 165 fs and 180 fs timescales in H 2 O and 7M NaOH, respectively, which are the same within our error bars. These results depend on the excitation peak frequency. When redpumping 300 cm -1 below the peak of O H stretch vibration of H 2 O, we found that the diagonal peak appears nearly homogeneous in the cm -1 region, with a CLS of approximately zero for both H 2 O and NaOH solutions over all waiting times. In contrast, when the pump pulses are centered at 3400 cm -1, the lineshape of the same transitions appears more inhomogeneous, and the CLS decay in H 2 O was found to lengthen to 175 fs

17 Figure 7: Spectral relaxation processes. (A) Decay of the center-line slope of the O H stretch vibration in H 2 O and 7M NaOH solution. The CLS decay of NaOH is shifted up by 0.1 for clarity in presentation. (B) Time dependence of the spectral slices illustrated in C and D. (C,D) Slices through BB 2DIR spectra of 7M NaOH at two detection frequencies marked by arrows in Fig. 2: (C) ω 3 = 2850 cm -1 and (D) 3620 cm -1. Spectral relaxation involving other peaks is also apparent in the BB 2DIR spectra of 7M NaOH. As a function of waiting time, the ν a diagonal bleach peak at 2850 cm -1 appears to blueshift its center in ω 1. A similar shift is observed for the induced absorption feature at 3 = 3620 cm -1 that corresponds to the feature observed in the thermal difference IR spectrum. In order to quantify these shifts, we characterize the spectral shifts in slices from the BB 2DIR spectra for fixed ω 3. Figures 7C and 7D show spectral slices at ω 3 = 2850 cm -1 and 3620 cm -1 (marked by arrows in Fig. 2). Each slice describes the distribution of excitation frequencies that result in the detected signal at ω 3 after a waiting time τ 2. Slices at 2850 cm -1 (Fig. 7C) show a bleach of the ν a vibration at ω 1 = 2920 cm -1 and an induced absorption from bulk water at ω 1 = 3260 cm -1. For τ 2 > 500 fs, the induced absorption is absent because the vibrational relaxation of the O H stretch 17

18 of the bulk-like water molecules is complete. Fitting these slices to a sum of two Gaussians at each τ 2, we find that the peak frequency of this bleach blue-shifts by ~240 cm -1 in 210 fs (Fig. 7B). The ω 3 slices at 3620 cm -1 also show a blue-shift in the peak frequency of the induced absorption in 160 fs (Fig. 7D). In the ω 3 slices taken at the center of the main O H stretch absorption band at 3375 cm -1, we observe a single bleach with a frequency that does not change with τ 2. The spectral relaxation that we observe at all three detection frequencies converges at a longer waiting time to 3160 cm -1 the same frequency as the bleach of bulk-like O H stretch vibrations. The peak shift of these vibrational features in ω 1 can have contributions either from vibrational energy transfer or the chemical exchange processes. IV. Discussion A. Vibrational Relaxation Processes Our analysis of vibrational population relaxation and spectral diffusion reveals that the exchange of vibrational energy between bulk-like water vibrations and hydroxide-associated water vibrations occurs extremely rapidly, evolving in parallel with the fastest intermolecular motions of the liquid. These processes are observed throughout the spectrum, regardless of the type of vibration that is excited or probed. A comparison of the relaxation timescales for NaOH and H 2 O is summarized in Table 1. Although the concentration-dependent data reveal a range of femtosecond to picosecond timescales, the different experimental techniques examine the underlying dynamics through varying perspectives. The SVD analysis of TA spectrum is a pure amplitude reconstruction of the data and the TA relaxation is reflective of the vibrational lifetime, whereas the CLS measurements and peak shifts in BB 2DIR spectra are metrics for frequency shifts. 18

19 Table 1. Summary of the relaxation timescales for 7M NaOH solution and for H 2 O obtained from single or bi-exponential fits of the form A1 exp( t / 1) A2 exp( t / 2) C. Timescales are quoted in femtoseconds and the error bars for the fit are given in parenthesis. Amplitudes are quoted as a percentage of full amplitude A A 1 2. SVD: SVD analysis of TA experiments. TA: Fit to TA kinetics at single detection frequency. CLS: Decay of the O H stretch CLS in the cm -1 region for a pump center frequency of 3100 cm -1. PS: ω 1 spectral peak shift in ω 3 slices of BB 2DIR spectra. Sample Method Feature τ 1 (fs) τ 2 (fs) A 1 A 2 7M NaOH Population Relaxation SVD decay 150 (20) 1700 (990) growth 290 (35) 1650 (325) TA ω 3 = 3620 cm (30) 1100 (160) ω 3 = 2850 cm (25) 2028 (200) Spectral Relaxation CLS 180 (20) PS ω 3 = 3620 cm (20) ω 3 = 2850 cm (25) H 2 O SVD decay 230 (5) growth 735 (15) CLS 165 (20) The observed decay times in 7M NaOH are divided into fast decays with a time constant of <300 fs and slower ones with timescales varying from ps. Within 300 fs, the only intermolecular coordinates that have had an opportunity to evolve are the librations and hydrogen bond vibrations between adjacent oxygen atoms. Larger scale distortions and global changes to the liquid structure occur more slowly, corresponding to the slower experimentally observed time scales. The concentration-dependent data illustrate that the structural relaxation of the hydroxide solution is related to the picosecond relaxation timescale. This is similar to earlier findings on isotopically dilute samples in which structural relaxation of hydroxide solutions 19

20 scaled with the viscosity of the solution. 24 In the present case, we find that a two-fold increase in decay time corresponds to a four-fold increase in viscosity. Focusing on the fastest relaxation processes, our SVD analysis of TA experiments show that induced absorption signals across the entire probe frequency region ( cm -1 ) relax with a fast timescale of 150 fs. This can be compared to the 230 fs measured for the equivalent process in H 2 O. As discussed recently in the context of H 2 O spectroscopy, this massively broadened induced absorption is indicative of a continuum of O H stretching vibrations that are strongly coupled to other intra- and intermolecular degrees of freedom. 32 In H 2 O, these have been described as delocalized O H stretch vibrations. For NaOH solutions, these involve multiple O H vibrational modes of the hydroxide complex. The speed up of the relaxation in NaOH relative to H 2 O and its growing amplitude with concentration indicates that the stronger hydrogen bonds in the hydroxide complex act to more rapidly randomize and dissipate the initial OH excitation. The 2850 cm -1 slice of the TA spectra with a decay of 230 fs and spectral relaxation of the ν a vibration on 210 fs indicate that vibrational energy exchange between bulklike water and solvated hydroxide vibrations is an effective energy dissipation route. Similar concentration-independent 200 fs vibrational relaxation of the O H stretch in aqueous NaOH has been previously observed by Bakker et al., 27 and described as local heating of the hydrated hydroxide complex resulting from vibrational relaxation. Whether in the case of hydroxide solutions (2 ps) or neat H 2 O (0.7 ps), the growth of the long-time transient absorption signal results in a spectrum that is nearly identical to a thermal difference spectrum (Fig. 4), even though the system has not had enough time to fully equilibrate. The system appears as if the temperature increased, even though only intermolecular motions faster than 1-2 ps (ω> THz) have had an opportunity to significantly evolve. 20

21 These motions would include librations and hydrogen-bond configurational changes, but not lower frequency and lower wave-vector dielectric or density modes. Sub-picosecond hydrogen bond configurational changes correspond to the high wavevector density or acoustic modes of the liquid; 42 however to obtain a macroscopic density change corresponding to temperature increase would require low wavevector modes to equilibrate. The O H vibrational dynamics of the hydroxide complex are sub-picosecond, and may involve the fleeting excursion of protons from solvating water molecules to the OH ion. Shuttling of protons between two OH moieties is theoretically predicted to take place on a 180 fs timescale, duly supporting the experimentally found event on 110 fs in isotopically dilute aqueous hydroxide solutions. 19,25 It is possible that proton rattling might contribute to the loss of frequency memory of the excited O H stretch vibrations on a ~200 fs timescale; however, the actual irreversible transport of protons from one distinct hydration shell to another does not appear to contribute to the observed dynamics. An earlier estimate of the proton transfer time in isotopically dilute hydroxide solutions from 2DIR experiments set the lower limit for proton transfer at 3 ps, 24 indicating that vibrational relaxation likely precedes PT. Given that the frequency memory and vibrational population of the O H stretch vibrations are both lost within ~200 fs, our experiments do not appear to be sensitive to long range irreversible proton transfer in the system. However, these exceedingly fast vibrational relaxation dynamics indicate that intermolecular coherences beyond the delocalization of the O H stretch vibrations are not likely to contribute to the PT mechanism. B. A Model for Non-adiabatic Relaxation The observations made regarding ultrafast vibrational relaxation in strongly hydrogen 21

22 bonded systems indicate the presence of strong coupling between intra- and intermolecular motions, 31,32 governed largely by strong hydrogen-bonding interactions. Because these ultrafast processes occur on the earliest time scale of motion of the intermolecular degrees of freedom, an adiabatic separation between the fast O H stretch motion and the hydrogen bond vibration or other intermolecular vibration appears to be inappropriate. To describe our observations, we propose a model that builds on recent studies invoking strong intra- and intermolecular vibrational couplings and non-adiabatic vibrational relaxation. 46,47 We are influenced by the description of vibrational relaxation of the O D stretch in isotopically dilute ice described by Perakis and Hamm, 48,49 and connect this to our own study of vibrational relaxation in neat H 2 O. 32 To illustrate our proposal for the vibrational dynamics in our experiments, we discuss the relaxation processes as occurring on a two-dimensional potential energy surface (PES) that describes the anharmonic coupling between a high frequency O H stretch, q, and a low frequency intermolecular coordinate, Q (Fig. 8A). Unlike localized O H stretch vibrations in isotopically diluted samples, the O H coordinate in neat H 2 O or aqueous NaOH are delocalized in nature and q is an effective coordinate representing multiple degrees of freedom. The intermolecular coordinate is a single generalized coordinate taken from a multidimensional potential energy surface, which could be a local coordinate such as a hydrogen bond stretch or a collective variable such as an electric field. To illustrate the shape of the PES, Fig. 8A shows the empirical Lippincott Schroeder potential. 50,51 Eigenstates of the system described by this potential have mixed O H stretch and intermolecular vibrational character. In such situations, there are multiple eigenstates available for IR transitions with significant transition dipole moments, leading to individual excitation manifolds in the spectral density of states. The adiabatic approximation posits that q evolves much faster than Q, and therefore Q can be treated 22

23 as a fixed parameter in solving for the energy eigenvalues of q. The resulting adiabatic potential energy surfaces for the Lippincott Schroeder potential are illustrated in Fig. 8B. The spectroscopically accessible bands are seen to correspond to the ν = 0, 1, and 2 adiabatic OH stretch states in the energy level diagram in Fig. 8B. 23

24 Figure 8: Two representations of ultrafast non-adiabatic vibrational relaxation following infrared O H stretch excitation. Relaxation processes are illustrated as color coded wavepackets (orange green blue magenta). All illustrations are purely schematic proposals, and do not reflect computational results. (A) Illustration of a two-dimensional potential energy surface got the O H stretch mode, q, and intermolecular coordinate, Q, using Lippincott Schroeder potential as an example. (B) Adiabatic surfaces for the ν = 0,1,2 states of the high frequency (fast) O H stretch mode as a function of the (slow) intermolecular coordinate. (Right) Vibrational spectral density of states for the coupled OH stretch and intermolecular modes showing partitioning into bands with ν = 0, 1, and 2 excitation. The ultrafast relaxation processes in this system can be described as the evolution of coherent O H stretch excitations on these potential energy surfaces. Upon excitation of the O 24

25 H stretch, the O H bond is driven to extend, thereby strengthening the hydrogen bond. The fastest dynamics we see ( fs) reflect the fast evolution of the initial OH excitation as the hydrogen bond initially shortens and potentially vibrates, all the while dissipating energy to other intermolecular degrees of freedom. In the adiabatic picture, the coupling is strong for the compressed hydrogen bond, leading to efficient transfer from the ν = 1 to ν = 0 adiabatic states. The slower relaxation we observe ( fs) reflects the dissipation of energy that reequilibrates the excitation in the ν = 0 well. The excess intermolecular vibrational energy in the ground state leads to a net expansion of the hydrogen bond which raises the O H stretch frequency leading to the spectral features in TA and BB 2DIR experiments similar to the thermal difference spectrum. This description of relaxation can be mapped onto the energy level diagram involving continuum bands, which were also used to describe vibrational relaxation in H 2 O. 32 The excited OH excitation preferentially moves toward the lower energy, strongly hydrogen bonded states within the same O H stretch excitation manifold within a fs timescale. In the case of NaOH, the observed dynamics take on a bi-exponential form. One likely origin of such behavior is that dynamics along multiple O H stretch and/or intermolecular coordinates must be used to describe rapid non-adiabatic relaxation. In the case of a solvated OH ion, there are multiple water molecules hydrogen bonded both the ion and to the second solvation shell. As a result, an interplay of intra- and intermolecular dynamics need to be accounted for. 27 Alternatively, we note that the faster growth of the long-time spectral component in H 2 O compared to NaOH may be influenced by variations in the Fermi resonance between the O H stretch and the overtone of bend vibration of H 2 O. In the light of our description of strongly coupled intra- and intermolecular vibrations leading to fast energy relaxation, one can also speculate how this influences proton transfer in 25

26 aqueous hydroxide solution. We conclude that extended OH vibrational coherences are unlikely to play a role in the PT mechanism. The fast vibrational relaxation observed implies that proton shuttling will typically be uncorrelated with other OH motions on the 180 fs timescale of hydrogen bond vibrations. This does not exclude a description of PT based on changes in water coordination to the hydroxide ion, however we believe that such an exchange process would not involve coherent and concerted motion of multiple water molecules. V. Conclusion We have employed ultrafast TA and BB 2DIR spectroscopy on aqueous NaOH solutions to study the vibrational dynamics of the system. The use of BBIR pulses allows us to probe the continuum absorption of aqueous NaOH solutions. SVD analysis and frequency slices of the TA spectra reveal the presence of fast vibrational relaxation on fs timescales in 7M NaOH solution and also expose the presence of slower dynamics on 1 2 ps timescales. The fast vibrational relaxation is observed irrespective of the excitation or detection frequency. Analysis of spectral relaxation from BB 2DIR spectra and vibrational relaxation from TA slices indicates that vibrational energy is exchanged between bulk-like water and hydroxide-associated water vibrations on a 210 fs timescale. Measurement of spectral diffusion via O H stretch CLS decay in 7M NaOH also shows that the excited O H stretch vibration loses its frequency memory on a 180 fs timescale. In order to explain vibrational relaxation in fs, much faster than the picosecond structural relaxation of the liquid, we conclude that one needs to take into account strong nonlinear coupling between intra- and intermolecular vibrations. A vibrational relaxation mechanism is proposed to explain such observables where the fast dynamics are driven by strong 26

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31 OD (Norm.) M NaOH ν a ν s 7M NaOH 5M NaOH 3M NaOH H 2 O * ω/2πc (cm 1 )

32 (A) H 2 O BB 2DIR τ 2 =100 fs τ 2 =200 fs τ 2 =500 fs τ 2 =1000 fs TA ω 3 /2πc (cm 1 ) * * * 1600 (B) 7M NaOH ω 3 /2πc (cm 1 ) * * ω /2πc (cm 1 ) τ (fs)

33 mod (Norm.) mod (Norm.) (A) H 2 O x5 x5 (B) NaOH * * ω 3/2πc (cm 1 ) τ 2 (fs) Pump (cm -1 )

34 mod H 2 O * mod NaOH * τ 2 = 6 ps Thermal Difference ω/2πc (cm 1 )

35 mod (Norm.) Amplitude (a.u.) A H 2 O, short-time * H 2 O, long-time 7M NaOH, short-time 7M NaOH, long-time ω 3/2πc (cm 1 ) B H 2 O, short-time H 2 O, long-time 7M NaOH, short-time 7M NaOH, long-time τ 2 (fs)

36 OD (a.u.) 1.6 A H 2 O 3M NaOH 5M NaOH 7M NaOH τ 2 (fs) OD (a.u.) 10 0 B τ 2 (fs) Timescale (fs) C τ fast τ slow Concentration (M) Amplitude (a.u.) D A fast A slow Concentration (M)

37 Center Line Slope OD (Norm.) H 2 O 7M NaOH A τ 2 (fs) fs 150 fs 200 fs 250 fs 500 fs 1 ps 3 ps C ω 1 /2πc (cm 1 ) Peak Pos. in ω 1 (cm 1 ) OD (Norm.) B 0.4 D ω 3 = 3620 cm -1 ω 3 = 3375 cm -1 ω 3 = 2850 cm τ 2 (fs) ω 1 /2πc (cm 1 )

38 Intermolecular Coord. (Q) (A) O-H Stretch Coord. (q) Intermolecular Coord. (Q) (B) Adiabatic PES Spectral Density of States Energy (cm -1 ) fs fs Excitation Induced abs. ν=2 ν=1 HGS induced abs. ν=0