Letter pubs.acs.org/JPCL
Differences in the Vibrational Dynamics of H2O and D2O: Observation of Symmetric and Antisymmetric Stretching Vibrations in Heavy Water Luigi De Marco,†,‡ William Carpenter,‡ Hanchao Liu,§ Rajib Biswas,‡ Joel M. Bowman,§ and Andrei Tokmakoff*,‡ †
Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States ‡ Department of Chemistry, James Frank Institute, and The Institute for Biophysical Dynamics, The University of Chicago, 929 East 57th Street, Chicago, Illinois 60637, United States § Cherry L. Emerson Center for Scientific Computation, Department of Chemistry, Emory University, 1515 Dickey Drive, Atlanta, Georgia 30322, United States S Supporting Information *
ABSTRACT: Water’s ability to donate and accept hydrogen bonds leads to unique and complex collective dynamical phenomena associated with its hydrogen-bond network. It is appreciated that the vibrations governing liquid water’s molecular dynamics are delocalized, with nuclear motion evolving coherently over the span of several molecules. Using twodimensional infrared spectroscopy, we have found that the nuclear motions of heavy water, D2O, are qualitatively different than those of H2O. The nonlinear spectrum of liquid D2O reveals distinct O−D stretching resonances, in contrast to H2O. Furthermore, our data indicates that condensed-phase O−D vibrations have a different character than those in the gas phase, which we understand in terms of weakly delocalized symmetric and antisymmetric stretching vibrations. This difference in molecular dynamics reflects the shift in the balance between intra- and intermolecular couplings upon deuteration, an effect which can be understood in terms of the anharmonicity of the nuclear potential energy surface.
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solated H2O molecules undergo symmetric and antisymmetric vibrations that result from the potential binding the three vibrational degrees of freedom and the overall molecular symmetry; however, the vibrations of liquid H2O are qualitatively different.1 Hydrogen-bonding interactions give rise to strong intermolecular coupling, which greatly influences the frequency of the O−H stretching and HOH bending modes and breaks the gas-phase symmetry. As a result, the high-frequency vibrational motions of H2O are delocalized over multiple molecules, with exciton states (eigenstates) whose form depends explicitly on the extended structure of water’s fluctuating hydrogen-bond network.2−6 We have performed broadband two-dimensional infrared (2D IR) spectroscopy of the O−D stretching vibrations of heavy water (D2O), and we observe qualitatively different molecular vibrations compared to H2O. The O−D stretch appears more localized than the O−H stretch, and the symmetric and antisymmetric forms of the O−D stretching vibrations are retained, although with a significantly different character than in the gas phase. These differences could result in significant variations in the outcome of dynamical processes and chemical reactions in heavy versus light water. The IR spectra of the O−H and O−D stretching vibrations of H2O and D2O have considerable substructure whose origins are complex and not universally agreed upon. The attenuated total reflection (ATR) spectra are compared in Figure 1, where they © XXXX American Chemical Society
Figure 1. IR ATR spectra of D2O (black) and H2O (blue). The frequency axis for H2O has been scaled by the ratio of gas-phase antisymmetric stretches, 0.742. Colored lines indicate the positions of the peaks making up the O−D stretch.
are plotted on a common frequency axis; in order to overlay the two bands, the frequency axis for H2O has been scaled by the ratio of the D2O and H2O gas-phase antisymmetric stretches, Received: March 24, 2016 Accepted: April 26, 2016
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The Journal of Physical Chemistry Letters ωa(D2O)/ωa(H2O) = 2788 cm−1/3756 cm−1 = 0.742. Contradicting proposals suggest that the vibrations are either excitonic or that the substructure comes from different hydrogen-bonding environments.3,5,7 The low-frequency shoulder has been assigned to an overtone of the bending mode, enhanced by a Fermi resonance,7,8 or alternatively, to strongly hydrogenbonded molecules in structured geometries.9−11 The differences in these spectra also indicate that there are nontrivial isotopic effects present. Fitting the linear absorption spectrum of D2O results in three distinct peaks at 2395, 2479, and 2587 cm−1 within the O−D band, which we will label δ, ν1, and ν2, respectively. (We note that these are not the usual gas-phase labels for the normal modes of the monomer.) Although the O−H stretch in H2O appears to have similar structure, the peaks are far less distinct and the high-frequency peak has essentially disappeared (though it is discernible in the Raman spectrum12). With high time resolution and structural sensitivity, 2D IR spectroscopy has proved indispensable in studying the structural dynamics of isotopically dilute13−16 and isotopically pure water.17−19 By spreading the IR spectrum over two frequency axes and revealing time-dependent spectral correlations, it is possible to garner far more information than from the linear spectrum. Although performed as a Fourier transform spectroscopy in the time-domain using ultrashort IR pulses (see the Supporting Information for experimental methods), the 2D IR spectrum is essentially the transient absorption spectrum as a function of ω3, after excitation at ω1, for a given waiting time, τ2. Cross peaks, which appear off the diagonal, are a direct indication of coupling between two vibrations, which reflects common atoms or spatial proximity between modes.20−23 Using previously described methods,18,24,25 2D IR spectra of the O−D and O−H stretches were collected at a waiting time of 100 fs for parallel (I∥, ZZZZ) and perpendicular (I⊥, ZZYY) polarizations between the excitation and probe fields (Figure 2). Both show a broad ground-state bleach (GSB, red) of the fundamental transition near the diagonal (ω1 = ω3) and an excited-state absorption (ESA, blue) that peaks several hundred wavenumbers red-shifted in ω3 because of anharmonicity of the O−xH bond. Whereas the GSB of H2O is a single peak on the diagonal, the GSB of D2O lies mainly above the diagonal and shows cross peaks between the three resonances corresponding to the δ, ν1, and ν2 frequencies. While we expect cross peaks to be present below the diagonal as well, they are not resolved because of overlap with the ESA. That the D2O modes show cross peaks between them means that there are three distinct modes of vibration with strong vibrational coupling between the atoms making up the modes.22 The three peaks must therefore come from the same molecule or group of molecules, precluding the possibility that the substructure of the O−D stretch comes from disconnected water environments. This harks back to the notion of symmetric and antisymmetric stretching vibrations of the gas phase and a Fermi resonance with the bend overtone;26 on the basis of frequencies, we assign δ to the bend overtone and ν1 and ν2 to the stretching modes. This interpretation is consistent with previous models of the anharmonic potential energy surface of liquid water.27 Given the strong intermolecular coupling in liquid water, we cannot expect that these vibrations are simply related to the symmetric and antisymmetric vibrations of individual molecules. Rather, we expect that vibrations will be delocalized over multiple molecules while retaining a particular symmetry overall. Indeed, theoretical studies5 have predicted that the collective vibrations of H2O molecules should retain some of their symmetric/
Figure 2. Comparison of 2D IR spectra for H2O (top, axes scaled by the ratio of gas-phase antisymmetric stretch frequencies, 0.742) and D2O (bottom) taken at τ2 = 100 fs for parallel (I∥, ZZZZ) and perpendicular (I⊥, ZZYY) polarizations. For D2O, gridlines indicate the positions of the δ, ν1, and ν2 peaks.
antisymmetric character though there is contention in this regard.4,6 Furthermore, collective symmetric/antisymmetric vibrations have been invoked to understand the spectrum of the solid phase.27 In any case, the vibrations of D2O are fundamentally different from those of H2O, which appear to have highly delocalized excitonic modes in which most of the oscillator strength is in one particular mode. We can gain further insight into the vibrations of D2O by calculating the depolarization ratio between vibrations i and j, ρij(θij)= I⊥(θij)/I∥(θij), because ρij depends on the angle between the transition dipoles of the coupled modes, cos θij = μî ·μĵ .28,29 Slices of the I∥ and I⊥ 2D IR spectrum taken at constant ω1 values corresponding to the frequencies of the δ, ν1, and ν2 transitions are shown in Figure 3. The enhancement of the ν2−ν1 cross peak
Figure 3. Slices of the τ2 = 100 fs D2O 2D IR spectra for I∥ (solid line) and I⊥ (dashed line) at constant ω1 values corresponding to δ, ν1, and ν2. 1770
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The Journal of Physical Chemistry Letters in I⊥ is striking (Figure 3, indicated by an arrow). Whereas parallel transition dipole moments should result in a cross peak with ρ(θ = 0) = 1/3, we observe that the bleach of the ν2−ν1 cross peak is actually more intense in I⊥ (ρ2,1 = 1.08). This indicates that the angle between the transition dipoles is close to 90°, as one would expect for isolated symmetric and antisymmetric vibrations. Furthermore, this τ2 = 100 fs measurement indicates that orientational correlations exist for delays >100 fs, which is consistent with the previously measured polarization anisotropy decay of ∼200 fs.30 This is in contrast to H2O in which angular correlations are lost on a time scale of 70 fs.18,17 In these studies, the ultrafast relaxation of the polarization anisotropy in H2O was interpreted in terms of delocalized excitonic vibrations. The persistence of such a large difference in D2O between polarizations therefore suggests more localized vibrations compared to H2O. It is tempting to extract an angle based on the measured anisotropy; however, this cannot be determined directly from the spectrum, because overlapping features, in particular those of opposite sign, skew the intensities in unpredictable ways. Nonetheless, if we consider the depolarization ratio of the ν2−ν1 cross peak of ρ2,1 = 1.08, an angle of 79° or 101° between the transition dipoles of these modes is implied;28,29 the latter is consistent with the angle of 96° which was fitted between the symmetric and antisymmetric modes for monomeric H2O in acetonitrile.31 In principle, the polarization data cannot be explained by a unique angle between the transition dipoles of the bending and stretching modes in the molecular frame. If the vibrations are delocalized over multiple molecules such that the transition dipole moments originate from molecules in a fluctuating or disordered system, the angle between the excitation and detection transition dipoles is statistical. In this case, the expressions for I∥ and I⊥ must be averaged over a suitable probability distribution; that is, the measured depolarization ratio is given by ρij [Pij(cos θ )] =
⟨I⊥ij⟩ ⟨I ij⟩
Figure 4. (A) Calculated probability density for the cosine of the angle between transition dipoles of νs and νa (black), νs and δ (blue), and νa and δ (red). Red and black curves are scaled by 5. (B) Contribution to the O−D stretching band from symmetric stretch (green), antisymmetric stretch (blue), and bend overtone (red).
phase spectrum and symmetry of the isolated molecule. However, the transition-dipole angle between the symmetric and antisymmetric stretches (and by extension between the antisymmetric stretch and bend overtone), shows a broad distribution. While it is peaked at cos θ = 0, corresponding to perpendicular dipoles, they can take on a broad range of angles, even showing nonzero probability to be parallel. It is interesting to note that a similar lack of correlation between transition dipoles, attributed to excitonic delocalization, was also observed in the spectroscopy of neat ice Ih.34 Averaging the signal with the probability distributions shown in Figure 4A as per eq 1 results in depolarization ratios of ρs,δ = 0.38, ρa,δ = 0.90, and ρs,a = 0.81 These can be compared to the theoretical values of 0.33 and 1.16 for perfectly parallel and perpendicular dipoles. The experimentally measured depolarization values (shown in Figure S10) are significantly larger than the calculated values. It is possible that the calculations overestimate the breadth of the distribution; however, it is more likely that the strong overlap between features within the O−D stretching band skews the observed depolarization ratio. While this calculation is done at the local monomer level, it is safe to assume that any delocalized mode with symmetric or antisymmetric character will result in transition dipole distributions that are broader than those shown in Figure 4 because there are a larger number of configurations. However, for a completely random distribution of angles, that is P(cos θ) = 2−1, a depolarization ratio of 0.66 is expected. This is significantly smaller than the observed depolarization in the experiment; therefore, we are led to conclude that there is necessarily residual symmetric and antisymmetric character even if the modes are delocalized. The assignment of the ν1 and ν2 modes to symmetric and antisymmetric stretches from experimental data alone is not
1
=
∫−1 d(cos θ) Pij(cos θ) I⊥ij(cos θ) 1
∫−1 d(cos θ) Pij(cos θ) I ij(cos θ) (1)
where Pij(cos θ) is the probability distribution for the cosine of the angle between dipoles i and j. We note that P(θ) sin(θ) dθ = P(cos θ) d(cos θ). The averaging in eq 1 is over an ensemble of molecules that possess different transition-dipole angles in the molecular frame, whereas I∥ and I⊥ are averaged over different orientations in the laboratory frame when calculating the thirdorder response function.28 To explore the distribution of transition-dipole angles and the effect of this distribution on the 2D IR spectrum, quantum dynamics simulations were performed and transition dipoles calculated using the local monomer method32 in which the Schrödinger equation for coupled local normal modes is solved. In the present calculations, which focus on the O−D stretching band, only the three intramolecular modes are explicitly coupled for each monomer embedded in a cluster. The details of these calculations and a recent application to the linear IR spectrum of liquid D2O is presented in ref 33; a brief recap is given in the Supporting Information. The probability density for the cosine of transition-dipole angles within one molecule is shown in Figure 4A. The distribution of angles between the symmetric stretch and bend overtone is sharply peaked at cos θ = ± 1, which shows that these transition dipoles are aligned, as expected based on the gas1771
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ESA in H2O is extremely broad compared to the fundamental GSB;18 however, in D2O the ESA has roughly the same width as the GSB one would expect for a weakly anharmonic system. In fact, similar trends were observed when studying the isotopically dilute O−D and O−H oscillators in ice Ih.35 This reflects the extreme anharmonicity in H2O vibrations, directly resulting in stronger mixing and a more excitonic character. D2O also shows a drastically different relaxation pathway (discussed in the Supporting Information) compared to our previous study on H2O. Whereas D2O shows cascaded relaxation (ν2 → ν1 → δ), characteristic of weak coupling between normal modes, such behavior is not observed in H2O. These differences can be understood in terms of the energies at which IR spectroscopy probes the nuclear potential energy surface (NPES) of the two isotopologues. Although their Hamiltonian differs only in nuclear mass, H2O’s IR vibrational transitions initiate and terminate at higher energy than D2O’s. Thus, H2O IR spectroscopy samples, on average, a significantly more anharmonic part of the NPES compared to D2O. The greater anharmonicity, in general, implies stronger coupling between modes, weakened selection rules, and faster relaxation rates.35 The enhancement of these anharmonic effects in H2O over D2O manifests itself through stronger intermolecular coupling, more delocalized vibrations, an extremely broadened ESA, and faster vibrational energy relaxation. Although the spectroscopy is quite different, our overall conclusions regarding differences between H2O and D2O are consistent with theoretical and experimental studies of ice Ih, where the difference in intermolecular coupling between H2O and D2O was found to give rise to the difference in line shape between the two.34,36,37 While these studies found that the local mode basis is, in general, more suitable for describing vibrations in the solid, the symmetric/antisymmetric basis is more appropriate in the description of D2O. Similar effects, attributed to the same physics, have been observed in the gas phase, where the line width of a hydrogen-bonded oscillator sharpens significantly upon deuteration.38 In addition, this difference in anharmonicity between H2O and D2O is also the explanation for the suppressed quantum beating observed in ice Ih, wherein the isotopically dilute O−D oscillator reaches a less anharmonic part of the NPES than the isotopically dilute O−H oscillator.35 More generally, our conclusions indicate that differences in the vibrational dynamics of H2O and D2O may have significant consequences for aqueous chemistry beyond kinetic isotope effects, viscosity, and hydrogen-bond strength. The variation in energy of vibrational states on a highly anharmonic NPES also implies that the extent to which the dynamics of an aqueous solute can be decoupled from its environment depends crucially on whether it is in H2O or D2O. This also has implications for physicochemical reactions and solvation processes in which water plays a key role, especially ones in which the translocation of atoms or dissipation of energy is important.
straightforward because the condensed-phase modes will not reflect the gas-phase ones. To investigate how intermolecular interactions in D2O influence the nature of O−D stretch vibrations, we turned to the calculation of the transmission IR spectrum using the local monomer method, briefly described above. The calculation of the O−D stretching spectrum is shown in Figure 4B. The overall peak position and width are in good agreement with the experimental spectrum shown in Figure 1. The decomposition of the band in terms of bend overtone and symmetric and antisymmetric sub-bands is also shown in Figure 4B. These are determined based on an analysis of the virtual-state configuration interaction coefficients obtained in the diagonalization of the local monomer Hamiltonian matrix. The zeroorder state with the largest coefficient is the one used to assign the molecular eigenstate to a given sub-band. This is a reasonable but somewhat blunt criterion to make these assignments. As seen, the antisymmetric stretching mode is at higher frequency than the symmetric mode, as it is in the gas phase, though there is a significant amount of overlap between the bands. The δ, νs, and νa features in the calculation peak at 2431, 2598, and 2782 cm−1, which are comparable to the frequencies measured in the linear ATR spectrum of 2395, 2479, and 2587 cm−1; however, we note that the lineshapes in transmission and ATR differ significantly. In particular, the bend overtone frequencies are in good agreement. However, the stretching bands are intense and strongly overlapped so that a direct comparison between the calculations and experiment is not easy. (A direct comparison of the experimental and simulated spectra are shown in the Supporting Information; there, the simulated spectrum is red-shifted by 40 cm−1 for better overall agreement.) The anharmonicity that gives rise to the Fermi resonance of the bend overtone is going to result in a mixing of the character of the vibrations; in particular, we expect that the mixing is strongest with the symmetric stretch based on gas-phase symmetry considerations and resonance. However, we cannot rule out mixing with the antisymmetric stretch because, by virtue of the distribution of angles between it and the symmetric stretch, it only statistically retains the same symmetry character as the gasphase modes. To further investigate the effects of vibrational delocalization, DFT-based normal modes of D2O molecules in clusters were calculated (details in the Supporting Information). Collective normal modes, delocalized over multiple molecules, were categorized by certain symmetric or antisymmetric vibrational symmetries. While no change in the ordering of antisymmetric and symmetric stretches was observed, the distribution of frequencies becomes less distinct as vibrations delocalized over more molecules are considered. Taken with the simulations above, this strongly suggests that ν1 corresponds to symmetric stretching and ν2 corresponds to antisymmetric stretching. Furthermore, this is consistent with our interpretation that vibrational modes in H2O are so delocalized that it is not possible to observe symmetric and antisymmetric stretching modes separately. In our previous H2O studies, signatures of symmetric and antisymmetric stretching modes were not observed. This is consistent with the vibrations in water being excitonic such that distinguishing vibrations based on symmetry is not possible; rather, most of the oscillator strength is in a dominant excitonic mode. While the differences in the linear spectrum are evident, the contrast between the nonlinear time-dependent spectra is even more striking. Other than the obvious differences in the structure of the GSB of the 2D IR spectra, it is observed that the
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b00668. Experimental methods; brief description of the local monomer calculations; detailed description of DFT-based cluster normal mode calculations; time dependence of the 2D IR spectrum including transient absorption spectrum; 1772
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comparison of D2O and H2O 2D IR spectra at late times; comparison of D2O and H22D IR depolarization (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail: tokmakoff@uchicago.edu. Tel.: (773) 834-7696. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was funded by a grant to A.T. from the U.S. Department of Energy (DE-SC0014305). L.D.M. thanks NSERC for a fellowship. L.D.M. thanks Joseph Fournier for useful discussions and a careful reading of the manuscript. J.M.B and H.L. thank the National Science Foundation (CHE1463552) for financial support.
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The Journal of Physical Chemistry Letters (38) Leavitt, C. M.; DeBlase, A. F.; Johnson, C. J.; Van Stipdonk, M.; McCoy, A. B.; Johnson, M. A. Hiding in Plain Sight: Unmasking the Diffuse Spectral Signatures of the Protonated N-Terminus in Isolated Dipeptides Cooled in a Cryogenic Ion Trap. J. Phys. Chem. Lett. 2013, 4, 3450−3457.
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