Vibrational Energy Relaxation of Thiocyanate Ions ... - ACS Publications

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Vibrational Energy Relaxation of Thiocyanate Ions in Liquid-toSupercritical Light and Heavy Water. A Fermi’s Golden Rule Analysis Denis Czurlok, Jeannine Gleim, Jörg Lindner, and Peter Vöhringer* Lehrstuhl für Molekulare Physikalische Chemie, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms-Universität, Wegelerstraße 12, 53115 Bonn, Germany S Supporting Information *

ABSTRACT: The vibrational relaxation dynamics following an ultrafast nitrile stretching (ν3) excitation of thiocyanate anions dissolved in light and heavy water have been studied over a wide temperature and density range corresponding to the aqueous liquid up to the supercritical phase. In both solvents, the relaxation of the ν3 = 1 state of the anion leads to a direct recovery of the vibrational ground state and involves the resonant transfer of the excess vibrational energy onto the solvent. In light water, the energy-accepting states are provided by the bending−librational combination band (νb + νL), while in heavy water, the relaxation is thermally assisted by virtual acceptor states derived from the stretching− librational/restricted translational hot band (νS − νL,T). The relaxation rate is found to strictly obey Fermi’s Golden Rule when the density of resonant solvent states is estimated from the linear infrared spectra of the solute and the pure solvents. SECTION: Liquids; Chemical and Dynamical Processes in Solution

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spectroscopy with resonant excitation of the nitrile stretching fundamental, ν3, of the SCN− solute. The dynamics are studied over a wide range of temperatures and densities (cf. Figure 1a), thereby covering the liquid all the way up to the supercritical phase of the water solvent to obtain detailed information about the relaxation pathways for vibrational energy flow away from the solute’s ν3 fundamental (cf. Figure 1b). The intriguing questions that arise in this context are as follows: Does the relaxation of the vibrationally excited state replenish the vibrational ground state directly or are energetically intermediate vibrational states transiently populated such that the relaxation is sequential in nature? What are the degrees of freedom of the solvent (vibrational, rotational, or translational modes and combinations thereof) that can absorb the energy mismatch between the initial and final vibrational states during a relaxation transition? The ν3 mode of SCN− has predominantly nitrile stretching character, and in aqueous solutions, its MIR absorption (cf. Figure 1c) peaks at 2065 cm−1 with a full spectral width at halfmaximum of slightly less than 30 cm−1. The bandwidth and the spectral position do not change significantly upon varying the thermodynamic conditions. In light water, H 2O, the ν3 absorption band rides on top of a very broad almost continuum-like absorption band of the liquid solvent. At room temperature, the peak extinction coefficient of the ν3

ibrational energy relaxation (VER) is a central component to chemical reactions dynamics.1 Intermolecular transfer of vibrational energy enables reactants to acquire a critical internal excitation that is sufficient to overcome a barrier to chemical transformation. Intramolecular redistribution of vibrational energy may then be responsible for funneling this internal energy into the nuclear coordinates that ultimately guide a reactive system across the potential barrier. In the homogeneous gas phase, these subtle interrelations between VER and intramolecular vibrational redistribution (IVR) on the one hand and the overall rates of chemical reactions on the other are very well understood, often within the framework of the simple isolated binary collision (IBC) theory.1 In the liquid phase, however, our understanding of the VER dynamics is still rather limited because of the complexity of the solute−solvent interactions and the mixing of vibrational (V), rotational (R), and translational (T) degrees of freedom that is caused by the tight intermolecular packing of the particles.2−4 In particular, in associated liquids like water, the anisotropic nature of the hydrogen-bonding interactions between neighboring particles leads to short-range ordering phenomena that can profoundly affect the vibrational spectroscopy,5 the dynamics of VER, the molecular-level VER mechanisms and rates, as well the dependence on the thermodynamic state variables.6−18 In this context, the VER dynamics of pseudohalide anions in aqueous solutions have been investigated quite extensively in the past as they present superb model systems for studying strong dynamical solute−solvent interactions governed by charge-dipole forces in the presence of hydrogen bonding.19−36 Here, we study the vibrational relaxation dynamics of thiocyanate anions using time-resolved mid-infrared (MIR) © 2014 American Chemical Society

Received: August 13, 2014 Accepted: September 15, 2014 Published: September 15, 2014 3373

dx.doi.org/10.1021/jz501710c | J. Phys. Chem. Lett. 2014, 5, 3373−3379

The Journal of Physical Chemistry Letters

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Figure 1. (a) Phase diagram of water and distribution of state points at which experiments were carried out. (b) Vibrational manifold of thiocyanate anions. ν1 is the S−CN stretching mode, ν2 is the bending mode, and ν3 is the SCN (nitrile) stretching mode. Vibrational energy can be transferred either directly or sequentially into intramolecular vibrational (V) modes, intermolecular hindered rotational (R) modes, and/or intermolecular hindered translational modes (T) of the solvent. (c,d) Infrared absorption spectra of 0.15 M solutions of KSCN in light and heavy water (solid, dark gray), of the pure solvents (dashed, light gray) and of the pure solute (solid, white).

Figure 2. Femtosecond MIR data of thiocyanate in light water (left column) and in heavy water (right column). (a,d) Pump-induced spectra for various delays. (b,e) Transient absorption decays and bleach recoveries. (c,f) Semilogarithmic plot of the transient absorption decays.

fundamental is about 4.8 × 102 M−1 cm−1, while that of the solvent continuum band is roughly 3.5 M−1 cm−1. The solvent band involves the combined excitation of the intramolecular bending vibration, νb, of an individual water molecule and a librational mode, νL, of the liquid. The latter degree of freedom is purely intermolecular in character and arises from the rotational motion of an individual tagged water molecule about one of its three principal axes of inertia, which experiences restoring forces that are exerted by hydrogenbonded neighboring water molecules. Because of its intermolecular character, the (νb + νL) band of the solvent is exquisitely sensitive to the strength of the hydrogen bonds and hence to the thermodynamic conditions (vide infra).37 The role of the continuum of intermolecular solvent states for the dynamics of VER of the anionic thiocyanate solute is at the center of attention of this Letter. Because the individual components to a (νb + νL) combination tone involve primarily the motion of the light hydrogen atoms, its center frequency exhibits a pronounced isotope effect. As a result, the libration− bending combination band disappears completely in heavy water (D2O) solutions (cf. Figure 1d) where the SCN− band then finds itself at the extreme low-frequency edge of the OD stretching band, νs, of the solvent. Femtosecond (fs) MIR pump−probe experiments were carried out with a laser system described earlier.34,38 A pump pulse tuned to the ν3 band of SCN− was used to vibrationally excite the solute, and a delayed probe pulse was used to monitor its spectrotemporal MIR response. Representative pump-induced fs MIR spectra of a 0.15 M solution of KSCN in light water at a temperature of 453 K and a pressure of 500 bar are shown in Figure 2a for various pump−probe time delays. All spectra and kinetic traces shown in this work are raw data. A long-lived thermal contribution to the signal as is typical for equivalent fs experiments on neat water14−17,38,39 has not been observed here, and a correction for such heating effects was not

necessary. All spectra consist of a negative signal at around 2064 cm−1 and a positive signal peaking at 2039 cm−1. The former feature can be attributed to the pump-induced bleaching of the solute’s vibrational ground state and, simultaneously, to the stimulated emission from the ν3 = 1 vibrational excited state (see the dashed blue arrow in Figure 1b). The positive signal is absorptive in nature and is due to the transition from the fundamental (ν3 = 1) level populated by the pump pulse at t = 0 to the overtone (ν3 = 2) level of the stretching mode (see the dashed red arrow in Figure 1b). This excited-state absorption is shifted to lower probe wavenumbers relative to the bleaching/ emission signal because of the anharmonicity, Δ, of the mode being pumped and probed. From the spectra in Figure 2a, we extract a value for Δ of ∼30 cm−1, which is in agreement with reports from the literature.29 Within the accuracy of our experiment and within the range of thermodynamic conditions studied here, the anharmonicity varies neither with temperature nor with density. To quantify the VER dynamics, the temporal evolution of the excited-state absorption at its peak frequency is analyzed in more detail (see Figure 2b and c). Apart from the earliest delays below 500 fs at which the data are still perturbed by coherent artifacts, the transient absorption decays in a strictly singleexponential fashion over a time scale of several picoseconds. Moreover, the ground-state bleach decays also in a strictly single-exponential fashion. Hence, fitting a monoexponential decay to the data yields the excited-state (ν3 = 1) lifetime, T1. Lifetimes obtained from the transient absorption decay were identical to those obtained from the bleach recovery. These findings strongly suggest that the VER follows a direct rather than a sequential mechanism, that is, the decay of the excited state refills the vibrational ground state promptly and does not lead to an appreciable population of an energetically intermediate level (cf. Figure 1b for the vibrational manifold 3374



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of SCN−). However, it may in principle be that the energy flows transiently through such an intermediate state, like, for example, in the generalized sequence, |s,i⟩ = |1,0⟩ → |0,1⟩ → |0,0⟩, of relaxation steps, where |s,i⟩ denotes excitations in the coordinates of the nitrile stretch, |s⟩, and the intermediate mode, |i⟩. To observe single-exponential kinetics in such a sequence, the lifetime of the intermediate state, |0,1⟩, must be much shorter than the lifetime of the initially excited stretching fundamental, |1,0⟩. It may in principle also be that such intermediate states are probed at the frequency of the solute’s fundamental transition, |0,0⟩ → |1,0⟩, by virtue of anharmonic coupling to the nitrile stretch, that is, through the transition |0,1⟩ → |1,1⟩. However, the anharmonic coupling in turn inherently affects the IR cross section of the fundamental transition, that is, the cross sections, σ|0,0⟩→|1,0⟩ and σ|0,1⟩→|1,1⟩ are different, thereby precluding the observation of singleexponential kinetics. Note that once vibrational energy is dissipated from the solute into the solvent, it cannot stay for an appreciable time in the vicinity of the anion because the intermolecular couplings between the solvent molecules delocalize the excitation over many water molecules on a time scale of ∼50 fs,10 that is, the dissipated energy is redistributed over many solvent particles that are far away from the initially excited oscillator. Most intriguingly, it can be clearly seen upon inspection of Figure 1c that the excited-state depopulation decelerates upon increasing the temperature (and decreasing the density). At room temperature and a pressure of 500 bar, a relaxation rate constant of 1/(2.3 ps) is obtained, which is again in good accord with previous measurements conducted under ambient conditions.29 Upon isobarically heating the solution to 573 K, the rate goes down to 1/(3.4 ps), corresponding to an overall deceleration of the VER dynamics by about 30%. The full temperature dependence of the vibrational lifetime is compiled in Figure 3.

Complementary MIR pump−probe data for thiocyanate solutions in heavy water are shown in Figure 2d−f. The pumpinduced spectra are qualitatively very similar in shape to those obtained in light water with an anharmonic shift of 27 cm−1 between transient absorption and ground-state bleach/stimulated emission. In the time domain, there are however marked differences between the two aqueous systems. While the traces remain to obey monoexponential kinetics, the decays observed in heavy water are about an order of magnitude slower as compared to those in light water. Once again, the bleach recovery appears to be the mirror image of the absorption decay (see Figure 2e), suggesting again a direct replenishment of the ground state via depopulation of the excited state. Surprisingly, and in stark contrast to the data obtained in light water, the VER dynamics in heavy water accelerate distinctly upon raising the temperature. At 298 K and a pressure of 500 bar, the relaxation rate is about 1/(19 ps), which is in good agreement with previously reported inverse lifetimes obtained under ambient conditions.29 Upon heating to ∼600 K while keeping the pressure constant, the relaxation rate goes up to about 1/(13 ps), corresponding to an acceleration of the VER dynamics by almost 50%. The vibrational lifetimes for SCN− in D2O is again collected in Figure 3, which clearly emphasizes the opposite temperature dependencies of the VER dynamics in the two isotopologic aqueous systems. Because the solute−solvent interactions and hence the average solvation structures around the anion are essentially identical for the two solvents, the primitive local density corrected IBC model for VER must fail even at a qualitative level. The vastly different magnitude of the VER rate constants (∼3 ps for H2O versus ∼17 ps for D2O) in addition to their contradictory temperature dependencies as seen in Figure 3 present indisputable evidence that the VER mechanism must change upon isotopic substitution of the solvent. However, regardless of the solvent, the direct nature of the VER mechanism remains preserved, as indicated by the perfect mirror image relationship between excited-state absorption decay and ground-state bleach recovery for the two isotopologic solvents (cf. Figure 2b and e). A direct mechanism for VER requires the solvent to provide energy-accepting states that are fully resonant with the ν3 fundamental excitation of the solute. In the light water solvent, such acceptor states can originate from the bending−librational combination tone that appears in the MIR spectrum as a quasicontinuous pedestal under the ν3 band of the anion (see Figure 1c and ref 34). In a perturbative treatment of resonant intermolecular energy transfer, the VER rate constant can be expressed by Fermi’s Golden Rule,1,4,28 that is, k = V2ρB/h, where ρB is the density of energy-accepting states, arising from the (νb + νL) solvent background, at the energy of the relaxing ν3 = 1 state of the solute, V2 is the mean-squared coupling between the solute and the solvent states, and h is Planck’s constant. Assuming the continuously distributed bath states to have equal infrared transition moments and accounting for the energy dispersion of the solute’s ν3 = 1 state (as reflected in the finite IR bandwidth of the nitrile stretching band), the relevant density of states can be estimated from the normalized overlap integral, S(T), between the solute and the solvent absorption spectra

Figure 3. Temperature dependence of the vibrational lifetime of the ν3 = 1 vibrational level of thiocyanate ions in light water (squares) and in heavy water (circles).

A qualitatively similar deceleration of the VER dynamics with increasing temperature has previously been reported for solutions of azide anions in light water.34 This anomalous temperature dependence has been interpreted in terms of a simple IBC model that was corrected for the local density of the solvent around the relaxing anionic solute. A comparison of the VER dynamics of SCN− in H2O with the complementary dynamics in D2O demonstrates that such an interpretation oversimplifies the molecular-level mechanism of the solute-tosolvent energy transfer.

∞

ρB (T ) ∝ S(T ) = 3375

∫0 ϵsolvent(ν , T )·ϵsolute(ν , T ) dν ∞

∫0 ϵsolute(ν , T ) dν

(1)



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Here, ϵsolvent (ν,T) and ϵsolute (ν,T) represent the temperaturedependent extinction coefficients of the libration−bending combination band of the solvent and of the ν3 band of the solute, respectively. Thermally induced variations of the vibrational lifetime and, hence, of the VER rate are entirely due to modifications of the density of energy-accepting states provided by the solvent, which in turn manifest themselves as thermally induced spectral variations of the bending−librational combination band of water. A plot of the experimentally determined VER rate constants versus the spectral overlap should then yield a straight line with vanishing intercept and a slope that is proportional to the solute−solvent coupling. Figure 4a displays linear MIR absorption spectra of liquid-tosupercritical light water for various temperatures and a constant

levels of the liquid solvent and that the solute-to-solvent energy transfer rate obeys Fermi’s Golden Rule remarkably well throughout the wide thermodynamic conditions studied here. A sequential mechanism as suggested in ref 29 does not need to be invoked. Moreover, the data indicate that the solute−solvent coupling does not change appreciably upon varying the temperature from 300 K all the way up to 660 K. The thermally induced changes of the density of energyaccepting solvent states as probed through the IR spectra of Figure 4a are primarily caused by a softening of the intermolecular librational potential between neighboring particles and a weakening of their hydrogen bonds. This is because in the thermodynamic range studied here, the fundamental IR band of the intramolecular bending vibration of H2O is rather insensitive to temperature variations while the librational fundamental exhibits a pronounced shift to lower frequencies as the temperature is raised.37 Finally, we turn our attention to the VER mechanism in heavy water and ask the question how the temperature dependence can be inverted upon solvent deuteration while its direct nature is preserved. To address this issue, we briefly compare the solute’s vibrational manifold with those of the two isotopological solvents (cf. Figure 5). As was discussed above,

Figure 4. (a) Comparison of the nitrile stretching band of thiocyanate ions with temperature-dependent absorption spectra of liquid-tosupercritical light water in the ν3 region of the solute. The diminishing spectral overlap of the solute band and the solvent background with increasing temperature is evident. (b) Correlation of the temperaturedependent ν3 = 1 vibrational lifetime of thiocyanate with the temperature-dependent overlap between solute and solvent spectra. (c) Same as in (a) except for heavy water. A growing spectral overlap with increasing temperature can be seen. (d) Same as in (b) except for D2O.

Figure 5. Vibrational manifolds of the solute and the two isotopologic solvents. The solvent levels exhibit pronounced thermally induced energetic shifts. The VER mechanisms in the two isotopologic solvents are of direct nature, but in heavy water, the relaxation is thermally assisted. In both solvents, the relaxation dynamics correspond to vibration-to-vibration/rotation (V−VR) energy transfer because of the involvement of the hindered rotational (i.e., librational) modes of the solvent that are coupled to a solvent intramolecular mode.

pressure of 500 bar. It can be seen that the (νb + νL) combination band shifts to lower wavenumbers with increasing temperature. The spectral shift is accompanied by a significant reduction of overall intensity. In the same temperature interval, the solvent nitrile stretching band remains more or less unperturbed such that the overlap integral continuously decreases upon isobaric heating of the solution. Figure 4b displays the dependence of the VER rate constant on the spectral overlap integral in a more quantitative fashion. Indeed, a perfectly linear correlation between the two quantities is obtained, and the intercept vanishes as predicted. A marginally inferior correlation is obtained when the dispersion of the nitrile stretching frequency is not taken into account explicitly and instead only the extinction coefficient at the peak frequency of the azide band is taken for the solvent density of states. These observations provide very strong support in favor of a VER mechanism for thiocyanate ions in light water that involves a resonant transfer of the nitrile stretching excitation into the quasi-continuum of bending−librational combination

the solute stretching excitation is resonantly transferred to the bending−librational combination level (direct V−VR), and the energy transfer decelerates because the solvent acceptor level experiences an energetic downshift upon isobaric heating, thereby gradually lifting the solute−solvent resonance. The situation in heavy water is quite different because the complementary bending−librational combination tone (νb + νL) experiences an isotope shift and is therefore located well below the solute’s ν3 = 1 state under ambient conditions. Moreover, an increasing temperature will further lower the solvent combination level so as to widen up the ν3-to-(νb + νL) energy gap even more. In addition, the OD stretching fundamental levels, νS, of D2O are located under ambient conditions well above the nitrile stretching fundamental of SCN−, and raising the temperature 3376



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overlap of the SCN− band with the (νS − νL,T) combination band. It might seem odd that the nitrile stretching excited state couples stronger to the hot OD stretching−librational combination states than to the OD stretching states themselves. This indicates that OD oscillators that absorb in the far-lowfrequency wing of the solvent stretching band interact primarily with other D2O molecules and not with the anionic solute. In line with this notion, a pronounced shift of the stretching band of water to higher frequencies was observed31,41 upon addition of N3−, suggesting that D2O molecules that interact with the anion absorb preferentially at the high-frequency wing, that is, far away from the solute band without any significant spectral overlap. Finally, from Figure 4b and d, information about the solute− solvent couplings can be retrieved. The slope ratio between D2O and H2O turns out to be ∼60, which is about three times the ratio of the integrated absorption cross sections between the stretching and the bending fundamentals of the two isotopological liquids. Therefore, the relaxing vibrational state of the solute appears to couple stronger to the (νS − νL,T) combination tones of heavy water than to the (νb + νL) combination tones of light water. Intuitively, for an anionic solute that preferentially binds water molecules through hydrogen bonding at its terminal atoms (as expressed by the two mesomeric Lewis structures [DO−D···−S−CN···D−OD ↔ DO−D···SCN−···D−OD] and as evidenced by quantum chemical and molecular dynamics studies42), forces exerted by the OD stretching motion project nicely onto the solute stretching coordinates, while those exerted by the DOD bending motion do not. That the relaxation in D2O is nonetheless much slower than that in H2O is simply the result of the former solvent lacking the necessary acceptor states that are energetically resonant with the relaxing ν3 = 1 state of the solute. However, although this conclusion is quite intuitive, one has to emphasize that it relies on the assumption that the coupling of infrared radiation to the (νb + νL) combination tone of light water is equal to the coupling of infrared radiation to the (νs − νL) combination tone of heavy water. Only in this case is the spectral overlap ratio between D2O and H2O a reliable estimate for the ratio of the solute−solvent couplings. The role of the density of intermolecular solvent states that are resonant with a relaxing vibrational level of a solute has previously been addressed by Hamm et al.21 To this end, the relaxation dynamics of the cyanide anion’s isotopologues, 12 14 − 12 15 − C N , C N , and 13C15N−, were studied, each having a slightly different stretching frequency, thereby sampling the density of states at slightly different energies. Indeed, a correlation was found between the relaxation rate and the infrared absorbance and Raman intensities of the aqueous solvents at the frequency of the relaxing vibrator. Using the thiocyanate solutes, S12C14N−, S12C15N−, and S13C14N−, Lian and co-workers29 were unable to confirm this correlation for light and heavy water; however, for the isotopological solvents of ethanol, CH3OH, CD3OH, CH3OD, and CD3OD, the lifetimes scaled reasonably well with the solvent infrared spectrum. Recent molecular dynamics simulations43 on the relaxation of CN− in water have followed up on these ideas, but they were based on classical trajectories. Therefore, and even though they included a harmonic/Schofield factor to correct for quantum effects, they are unable to reveal a resonant decay of the solute state into a solvent combination tone because of the inherent quantum mechanical nature of the acceptor state. In

will further elevate these intramolecular solvent states37 so as to widen up the ν3-to-νS energy gap also. Thus, it appears as if there are no solvent levels available for a resonant energy transfer like in light water. However, an inspection of the linear MIR absorption spectra of neat liquid-to-supercritical heavy water in the vicinity of the ν3 band of the solvent is quite intriguing (cf. Figure 4c). It can be seen that while the onset of the νS band of D2O clearly shifts to higher wavenumbers upon isobaric heating as expected, an additional absorption onset grows in as the temperature is raised, which happens to be downshifted with respect to the solute’s ν3 band (i.e., at around 1900 cm−1). Clearly, this infrared activity cannot correspond to the (νb + νL) band of heavy water because the bending− librational combination tone should shift to lower energies with increasing temperature as it does for light water (see the absorption edge at 2300 cm−1 in Figure 4a). Interestingly, Max and Chapados40 assigned the IR activity at around 1900 cm−1 in D2O to “hot” transitions from the librational and restricted translational fundamentals to the stretching fundamentals, that is, to (νS − νL) and (νS − νT) combination tones involving an OD stretching excitation and a librational or restricted translational de-excitation. The corresponding “cold” transitions to (νS + νL) are readily identified in the IR spectra of both isotopological solvents as distinct shoulders on the high-frequency wing of the stretching fundamentals. Because they involve the de-excitation of a hindered rotation or a hindered translation, the (νS − νL,T) difference combination tone should shift to higher wavenumbers, and their intensity should increase as the temperature is raised. The IR activity of D2O at around 1900 cm−1 meets both of these expectations. Thus, we propose here that in heavy water, the nitrile stretching excitation is resonantly transferred to (virtual) solvent states that give rise to the “hot” stretching− librational/translational combination tones (we speak of a thermally assisted vibration-to-vibration/hindered-rotation/hindered-translation energy transfer or Δ-assisted V−VRT in Figure 5). By comparing Figure 4a and c, it can already be deduced that at room temperature, the spectral overlap between the solute’s ν3 band and the background absorption of the D2O solvent is much smaller than in the case of H2O. This immediately rationalizes why the vibrational lifetimes in the two isotopological solvents differ by almost an order of magnitude. Moreover, the spectral overlap in heavy water slightly increases with increasing temperature, that is, in stark contrast to the T dependence of the spectral overlap in light water, where it decreases upon heating. This finding explains quite naturally the opposite temperature dependencies of the vibrational lifetimes obtained for the two isotopological solvents. Following the above analysis based on Fermi’s Golden Rule, the rate constant for VER in heavy water is plotted in Figure 4d against the spectral overlap, S(T). The correlation is not as good as that for light water, but it is still rather satisfactory considering the limited accuracy with which the weak background absorption of neat D2O can be measured with our high-pressure equipment. There seems to be a systematic deviation from a perfectly linear correlation, in particular, at low temperatures where the IR activity of the solvent is still mostly governed by the intramolecular OD stretching band rather than the stretching−librational/translational difference tones to which the ν3 = 1 state is coupled. As a result, eq 1 systematically overestimates at low temperature the spectral 3377



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vibration of heavy water. Finally, similar 2DIR experiments on the relaxation of HN3 in methanol by Cho and co-workers46 reveal an analogous resonant transfer between solute and solvent background modes as we report here for SCN− in light water.

fact, the solvent forces acting on a cyanide anion do not reveal any signs of a bending−librational continuum as the infrared spectrum.43 Finally, Ziegler and co-workers also explored the role of the solvent density of states in the context of energy relaxation of nitrous oxide as a structural probe for interfacial aqueous and hydrophobic sites in phospholipid bilayers.44 From fs MIR spectra, a certain interfacial N2O population was identified whose vibrational lifetime was found to be hydrationdependent. Unfortunately, no attempt was made to estimate the density of intermolecular energy-accepting states as a function of the hydration level and to test Fermi’s Golden Rule as was done here by systematically correlating this quantity with the VER rate constant. In summary, we have studied the VER dynamics and their full temperature dependence of the nitrile stretching vibration of the pseudohalide, SCN−, throughout the liquid up to the supercritical phase of the two isotopologic solvents, H2O and D2O. The broad thermodynamic conditions under which the dynamics were recorded allowed us to explore in detail the molecular-level relaxation mechanism. Having experimentally verified that throughout the temperature and density range under scrutiny the VER is of direct nature leading to a prompt recovery of the vibrational ground state from the initially prepared excited state of the solute, the relaxation rate was analyzed in terms of Fermi’s Golden Rule. To this end, the density of solvent states, to which the solute’s excess vibrational energy can be resonantly transferred, was estimated from the linear MIR absorption spectra of the two isotopological solvents in the frequency range around the nitrile stretching fundamental. Our analysis provides convincing evidence for the vibrational energy being transferred either into the quasicontinuum of the bending−librational combination tones of light water or, alternatively, of the hot stretching−librational/ translational combination tones of heavy water. The striking opposite temperature dependencies of the VER rates for the two isotopological solvents is then naturally explained by thermally induced modifications of the density of acceptor states of the solvent. We note here that a striking temperature dependence has also been observed for metal carbonlys in nonpolar solvents.45 Whereas the CO stretching relaxation rate of W(CO)6 in chloroform was found to increase upon raising the temperature, the same rate was found to decrease for Cr(CO)6 in the same solvent and the same temperature interval. However, in polyatomic molecules like metal carbonyls, the intramolecular density of states can easily exceed those of triatomic ions by orders of magnitude. Therefore, an unambiguous separation of IVR processes from energy-transfer processes is difficult. The thiocyanate anion has a sparse intramolecular vibrational manifold for energies below the nitrile stretching fundamental. A closer inspection of the possible IVR pathways reveals that they are connected with quartic or higher anharmonicities, which prevent them from efficiently competing with the resonant transfers into the solvent bending/stretching−librational continua described here because these require cubic anharmonicities only. In the future, we will expand our experiments to complementary pseudohalides like azide and/or cyanide ions to explore in more detail whether or not this scenario holds more generally for solute vibrational modes with comparable frequencies. Two-color two-dimensional infrared spectra of aqueous azide recently published by Hamm and co-workers41 seem to support indeed the resonant energy-transfer mechanism involving the intramolecular OD stretching

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ASSOCIATED CONTENT

S Supporting Information *

Experimental details. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Barbara Kirchner and Michael von Domaros for helpful discussions. Financial support by the Deutsche Forschungsgemeinschaft through the Collaborative Research Center 813 “Chemistry at Spin Centers” is gratefully acknowledged.

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REFERENCES

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