Ultrafast Internal Dynamics of Flexible Hydrogen-Bonded

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Ultrafast Internal Dynamics of Flexible Hydrogen-Bonded Supramolecular Complexes Martin Olschewski, Stephan Knop, Jaane Seehusen, J€org Lindner, and Peter V€ohringer* Lehrstuhl f€ur Molekulare Physikalische Chemie, Institut f€ur Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms-Universit€at, Wegelerstrasse 12, 53115 Bonn, Germany

bS Supporting Information ABSTRACT: Supramolecular chemistry is intimately linked to the dynamical interplay between intermolecular forces and intramolecular flexibility. Here, we studied the ultrafast equilibrium dynamics of a supramolecular hydrogen-bonded receptor-substrate complex, 18-crown-6 monohydrate, using Fourier transform infrared (FTIR) and two-dimensional infrared (2DIR) spectroscopy in combination with numerical simulations based on molecular mechanics, density functional theory, and transition state theory. The theoretical calculations suggest that the flexibility of the macrocyclic crown ether receptor is related to an ultrafast crankshaft isomerization occurring on a time scale of several picoseconds and that the OH stretching vibrations of the substrate can serve as internal probes for the receptor’s flexibility. The importance of population transfer among the vibrational modes of a given binding motif and of chemical exchange between spectroscopically distinguishable binding motifs for shaping the two-dimensional infrared spectrum and its temporal evolution is discussed.

1. INTRODUCTION Ever since their first discovery by Pedersen and co-workers,1 macrocyclic polyethers (commonly known as crown ethers) have served as superb model systems for chemical receptors being able to reversibly and selectively bind ionic or polar substrates. The celebrated fields of phase transfer catalysis and host-guest chemistry emerged from this class of compounds whose complexes feature all fundamental phenomena of supramolecular systems such as molecular recognition, macrocyclic flexibility, induced fit, preorganization, and self-assembly.2 A large number of supramolecular crown ether complexes involving charged or dipolar species have been prepared and their crystallographic data reported.3,4 The molecular structure of the macrocycle in such systems is conformationally highly diverse and is found to be exquisitely sensitive to the nature of the substrate. Yet, the internal supramolecular dynamics in liquid solution like conformational rearrangements within the receptor, substratereceptor couplings, and intermolecular structural fluctuations, or inter- and intramolecular transfer of energy, have so far proven too fast for conventional dynamic spectroscopies even when cryogenic temperatures were applied. The conformational flexibility of crown ethers together with their pronounced affinity to hydrophilic species in hydrophobic environments renders them highly attractive targets for studying supramolecular host-guest dynamics directly in real time using novel femtosecond nonlinear laser spectroscopy. Here, we report on the equilibrium molecular dynamics of the archetypal template-substrate complex, namely the adduct of 1,4,7,10,13,16-hexaoxacyclooctadecane (18-crown-6 or 18C6) with r 2011 American Chemical Society

a water (H2O) molecule. The crown ether monohydrate (Figure 1) is held together by hydrogen-bond interactions between the water substrate and the ether oxygens of the crown receptor.5 In principle, two binding motifs can be distinguished, a monodentate featuring a single hydrogen bond between the substrate and the receptor, and a bidentate, in which the substrate is anchored to the receptor by two hydrogen bonds. We use the hydroxyl (OH) stretching vibrations of the H2O molecule as sensitive spectroscopic probes of the supramolecular dynamics within the aggregate. The frequency of the stretching modes of hydroxyl groups that are engaged in hydrogen bonds are known to shift to significantly lower values as compared to their frequency in the absence of hydrogen bonding.6 Furthermore, this red-shift becomes larger with increasing strength and, hence, with decreasing length of the H-bond to which the stretching oscillator is coupled.7-9 It is this unique correlation between the spectral position of the OH vibrational resonance and the instantaneous hydrogen-bond geometry that could potentially be exploited for a time-resolved detection of the structural dynamics within the supramolecular crown ether monohydrate complex.

2. EXPERIMENTAL AND THEORETICAL METHODS 2.1. Spectroscopy. Stationary (i.e., linear) Fourier transform infrared absorption spectra were recorded with a spectral resolution Received: November 10, 2010 Revised: December 17, 2010 Published: January 27, 2011 1210

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Figure 1. Chemical structure of 18-crown-6 monohydrate in a bidentate (left) and a monodentate (right) binding motif. The numbers label the six oxygen atoms of the macrocyclic receptor.

of 1 cm-1 using a commercial spectrometer (Thermo Scientific, Nicolet 5700). Two-dimensional infrared spectra were recorded in the dynamic hole burning setup developed by Hamm and Hochstrasser.10 To this end, a home-built laser system consisting of two synchronously pumped and independently tunable type-I-BBO optical parametric amplifiers (OPA) that were driven by the fundamental output of a Ti: sapphire chirped pulse regenerative amplifier was used. Each OPA was equipped with a difference frequency generator based on type-IAgGaS2. One of the OPA/DFG units served as the pump source while the other was used as the probe source. The output of the pump-unit was sent through a Fabry-Perot etalon consisting of a parallel pair of dielectric flats (Laser Components) with a partial reflectance of (85 ( 5)% at normal incidence in the wavelength region between 2600 and 3150 nm. The etalon separation was controlled with a piezoelectric actuator thereby tuning the peak transmission of the etalon through the output spectral profile of the pump OPA/DFG unit. The pulses emerging from the Fabry-Perot filter had Lorentzian spectral shape with a full width at half-maximum of (22 ( 3) cm-1. The output of the second OPA/DFG-unit was split into probe and reference pulses, the first of which was sent through a computer controlled optical delay line. Pump and probe pulses were spatially and temporally overlapped in the sample with a 45 off-axis parabolic Au-mirror (OAP) having an effective focal length of 100 mm. The probe and references pulses were collimated behind the sample with an identical OAP and imaged onto the entrance slit of an 0.2 m monochromator whose exit plane was equipped with a 2 32 pixel MgCdTe array detector (Infrared Associates) for referenced frequency resolved detection of the pump induced optical density of the sample. The relative polarization between the pump and the probe pulses was set to the magic angle unless transient anisotropy measurements were carried out. In this case, the pump polarization could be rotated relative to the probe polarization by means of a half wave retardation plate. 1,4,7,10,13,16-Hexaoxacyclooctadecane, or 18-crown-6, was purchased from Sigma Aldrich (purity g99%) and was dried for several weeks over silica gel in an evacuated desiccator. Carbon tetrachloride (CCl4, IR spectroscopic grade) was also purchased from Sigma Aldrich and was thoroughly dried by refluxing over CaCl2 for several hours. Samples were prepared by saturating the CCl4 solvent with water. The solubility of H2O in carbon tetrachloride at 20 C amounts to 0.008 wt % corresponding to a molar concentration of 0.007 mol/L.11 To this well-defined binary CCl4-water solution 18crown-6 was added with concentrations of ∼0.2 mol/L, i.e., roughly a 30-fold molar excess with respect to H2O. Under these conditions, 1:1 adducts of 18-crown-6 with water are known to be formed while higher complexes such as heterotrimers are still negligible.5 This complexation behavior was also confirmed by measuring FTIR spectra as a function of the crown-ether concentration. For FTIR and femtosecond IR measurements, the samples were contained in home-built thermostatic cells that were equipped with CaF2 windows and that had an optical path length of 2 mm.

Figure 2. Experimental linear FTIR absorption spectrum (gray area) in the OH-stretching spectral region of 18-crown-6 monohydrate dissolved in liquid carbon tetrachloride at room temperature. The black curve represents a fit from a spectral decomposition into a monodentate contribution (blue) and a bidentate contribution (green). For details see text.

2.2. Computations. All molecular mechanics calculations were carried out in the Amber and Charmm classical force fields using the Hyperchem package. Nonbonded and van der Waals interactions were neither scaled nor truncated. During geometry relaxations, an rms gradient less than 10-5 kcal/(Å mol) was used to indicate convergence. Subsequent geometry postoptimizations were performed within the framework of density functional theory and employed the ORCA package developed by Neese and co-workers.12 The resolution-of-identity (RI) approximation was invoked to reduce the computational effort at negligible loss of accuracy.13 Since this approach requires a nonhybrid functional, the Becke-Perdew functional, BP86, was chosen.14,15 The Ahlrichs split valence basis sets, SVP, up to the very accurate highly polarized quadruple-ζ valence basis set, def2-QZVPP, were chosen together with the auxiliary Coulomb fitting bases, SV-J up to def2-QZV-J, required for the RI-approximation.16,17 The conductorlike screening model (COSMO) was used to account for solvation of the supramolecular complex in its van der Waals cavity by a polarizable continuum.18 A dielectric constant of 2.24 and a refractive index of 1.466 were chosen to mimic the carbon tetrachloride solvent. Structure optimizations were performed in redundant internal coordinates using analytical gradients, whose double-sided numerical differentiation yielded harmonic vibrational frequencies together with intensities for the fundamental vibronic transitions. A factor of 0.982 was used to convert from harmonic to fundamental frequencies. Such a small conversion factor complies with the recommendations given by Hess and Neugebauer19 and ascertains that the predicted “free” OH fundamental frequency of calculated monodentate structures (vide infra) is in quantitative agreement with the experiment. To further corroborate the results obtained at these levels, selected structures were also refined and vibrationally analyzed at the level B3LYP/6-311þþG**/COSMO.

3. RESULTS AND ANALYSIS 3.1. FTIR Spectroscopy. The Fourier transform infrared (FTIR) spectrum in the OH-stretching region of 18-crown-6 monohydrate in liquid carbon tetrachloride (CCl4) solution consists of three well separated peaks and an extended lowfrequency tail (Figure 2, gray area). This spectrum has previously been discussed in terms of the two distinct binding motifs between the water and the crown5 as mentioned above. In the monodentate binding motif (cf., Figure 1), the H2O uses only one of its hydroxyls to form a single, very strong hydrogen 1211

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The Journal of Physical Chemistry A bridge to the macrocycle while its other OH is left to interact mostly with the nonpolar solvent. This pattern gives rise to two OHstretching absorption bands of the water whose frequencies are very far apart. The highest frequency feature at 3684 cm-1 (labeled band c in Figure 2) is reminiscent of gas-phase-like noninteracting hydroxyls and was therefore assigned to the “free” OH of this monodentate binding pattern. The “bound” OH of the very same monodentate resonates at very low frequencies and is believed to contribute to the pronounced shoulder (denoted band d) that is located at the low-frequency edge of the 3536 cm-1 peak (band b). The second binding motif represents a bidentate (or bridged, cf., Figure 1) configuration where both water hydroxyls are engaged in hydrogen bonding to the crown ether at the same time. This pattern is also believed to result in two resonances, which are best described as the symmetric and antisymmetric stretching vibration of the substrate.5 The former was assigned to band b at 3536 cm-1 while the latter was held responsible for the peak at 3598 cm-1 (labeled band a). Both of these resonances are located in between the free and the bound OH-absorptions since the two H-bonds of the bridged binding motif are expected to be slightly longer and somewhat weaker than the one of the monodentate.5 3.2. 2DIR Spectroscopy. To observe the internal dynamics of the supramolecular complex directly in the time domain we performed two-dimensional infrared (2DIR) spectroscopy in the OH-stretching spectral region. The fundamental concept of 2DIR spectroscopy involves the projection of the system’s infrared spectral response to an initial vibrational excitation onto two frequency axes rather than one.10,20,21 In analogy to nuclear magnetic resonance (NMR), the allowed anharmonic couplings among the various molecular vibrators of the system and/or the molecular dynamical processes that convert one molecular species into another can be read off from the appearance of highly characteristic signals in the 2DIR spectrum. 2DIR spectroscopy has previously been used to successfully unravel a number of distinct ultrafast chemical processes occurring at thermodynamic equilibrium.22-26 A 2DIR spectrum of 18C6-H2O recorded at the magic angle relative pump-probe polarization for a very early pump probe (or waiting) delay, tW, of 700 fs is reproduced in Figure 3A. The spectrum represents the optical density of the sample induced by the pump-pulse as a function of the pump and probe frequencies measured in wavenumber units at the selected waiting delay, i.e., ~pump,tW = 700 fs). ΔOD (ν ~probe,ν This early time 2DIR spectrum can be read as follows: whenever the narrowband pump pulse hits an infrared resonance, the v = 1 excited state of the corresponding vibrational mode is populated and the v = 0 ground state is depleted. This causes negative pump-induced optical densities to appear along the diagonal (i.e., for ~νprobe = ~νpump). These signals are shaded in blue and are usually labeled as ground-state bleach and excited-state stimulated emission. Each of the four features that were perceptible in the FTIR spectrum now gives rise to such a diagonal signal. Furthermore, since the vibrational excited states are populated by the interaction with the pump field, strong diagonal absorptive transitions of the type v = 1 f v = 2 are now visible that are shifted to lower frequencies along the probe frequency axis due to the anharmonic character of the vibrational motion of each OHoscillator. The anharmonicities and linewidths of the vibrational modes associated with bands a and b are apparently such that their individual excited-state absorptions remain unresolved leading to a single very broad band at ~νprobe= 3380 cm-1. Apart from these diagonal signal contributions, there are also distinct absorptive and emissive off-diagonal peaks. For example,

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Figure 3. Contour representation of experimental 2DIR spectra of 18C6-H2O in liquid CCl4 at 293 K collected at a waiting delay of 700 fs (A), 1.5 ps (B), 3.0 ps (C), 4.5 ps (D), and 7.0 ps (E). Diagonal bleaches/emissions and absorptions are indicated in A by squares and circles. Prompt cross bleaches due to coupling are highlighted by triangles. The delayed growth of cross peaks is emphasized in B by the horizontal arrows. Simulated 2DIR spectra are shown in F-J for the same waiting delays. For details see text.

tuning the pump pulse to band c excites selectively the dangling hydroxyls of the monodentate binding motif. Since these water molecules also feature a hydrogen-bonded OH-oscillator, the pump pulse depletes a ground state that is common to both, the free and the bound hydroxyl stretches. Therefore, because of the coupling between these two oscillators, a weak off-diagonal bleach at ~νprobe= 3475 cm-1 and ~νpump= 3684 cm-1 is clearly present at the earliest delays. Another off-diagonal bleach that is elongated vertically is also detected upon swapping the pump and probe frequencies. These two complementary cross-peaks fully confirm the previous assignment of bands c and d belonging to the two OH-vibrations of the same monodentate binding motif. However, if the coupling between the two oscillators belonging to the monodentate gives rise to characteristic off-diagonal peaks that appear immediately upon infrared excitation, why do we not observe the complementary and prompt cross peaks between bands a and b (see Figure 3A at ~νprobe= 3536 cm-1 and ~νpump= 3598 cm-1 and vice versa)? Remember that these were believed to be due to the symmetric and antisymmetric stretching vibrations of the same water engaged in a bidendate binding motif. Furthermore, such direct cross peaks between the two OH stretching normal modes have been observed before in 2DIR spectra of monomeric water molecules dissolved in liquid acetonitrile solution.27 Further information for solving this puzzle is available from the temporal evolution of the 2DIR spectrum, four snapshots of which taken at longer waiting delays are shown in Figure 3B-E. All data are normalized to the strongest negative signal at each 1212



Figure 4. Ratio of the cross-to-diagonal bleach intensity versus waiting time for selective excitation of band a (red) and band b (blue). The dashed curve is a single-exponential fit with a time constant of 1.5 ps. The solid curve is from the nonlinear response function simulations using an a-to-b interconversion time of 4.5 ps (for details see text).

delay. A movie illustrating more clearly the full temporal evolution of the 2DIR spectrum from ∼700 fs to ∼10 ps in steps of 50 fs is provided in the Supporting Information. Apart from the vibrational population and line broadening dynamics associated with the decay of the diagonal peaks and the temporal evolution of their 2D spectral shapes (see Supporting Information for details), two important observations can be made: First, cross peaks between mondentate (c or d) and bidentate bands (a or b) that gradually appear with increasing waiting delay cannot be identified. This finding implies that hydrogen-bond breakage and formation leading to an interconversion between monodentates and bidentates must be slow on the time scale of the OH-stretching vibrational lifetimes. Apparently, the pumpinduced ground state depletions and the excited state populations have fully decayed before the two distinct binding motifs have had the chance to convert into one another. Second and most strikingly, a highly characteristic cross peak pattern in the bleaching region between bands a and b is seen to gradually emerge with increasing pump-probe delay. To reiterate, such cross peaks were actually expected to appear promptly rather than be delayed by virtue of the coupling between the symmetric and asymmetric stretching modes of the same bidentate water. A corresponding pattern in the excited state absorption region remains hidden because of the spectral fusion and the widths of the v = 1 to v = 2 transitions connected with bands a and b. To visualize the delayed nature of these cross peaks more clearly, the ratio of off-diagonal to diagonal signals is plotted in Figure 4 as a function of the pump probe delay for excitation into either of the two bands. Fitting these data to a single exponential rise yields a time constant for the underlying dynamics of 1.5 ps. 3.3. Population Transfer and Transient Anisotropy. The delayed appearance of the cross peaks between the bidentate bands a and b can originate from population transfer from the symmetric to the antisymmetric stretching mode and vice versa within the same bidentate binding motif. Such intramolecular vibrational dynamics have previously been identified for monomeric water molecules dissolved in liquid halogenated hydrocarbons.28 Figure 5 displays a sketch of the OH-stretching manifold of water when the coupling between two hydroxyl bonds is sufficiently strong such that the stretching vibrational degrees of freedom are appropriately described as symmetric and antisymmetric eigenmodes, |ss asæ. In this case, excitation of band b creates a population in the first excited state of the symmetric stretch, |1 0æ. As a result, the symmetric fundamental is bleached, and at the same time, the anharmonically shifted transient

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Figure 5. Left: Schematic of the OH-stretching normal mode manifold consisting of the common ground state, |0 0æ, the first two quanta in each, the symmetric (red) and antisymmetric (blue) stretches, and the combination quantum (|1 1æ). Pumping of the symmetric stretch can be followed by population transfer (double headed arrow), which results in delayed stimulated emission and excited state absorption signals originating from the unpumped antisymmetric stretching vibration. Right: Corresponding transient anisotropy obtained by pumping band b and probing band b (red) or pumping band b and probing band a (blue).

absorption, |1 0æ f |2 0æ, appears. Because of its coupling to the symmetric eigenmode, the asymmetric fundamental, |0 0æ f |0 1æ, should also be bleached. As pointed out above, this cross bleach is however not clearly observed at the earliest delays. Since the two fundamental quanta, |1 0æ and |0 1æ, are energetically separated by less than the thermal excitation, population can be transferred between them, i.e., |1 0æ T |0 1æ. As a result, following the excitation of the symmetric stretch, |1 0æ, a population can appear in the asymmetric fundamental at a later waiting delay, which is then detected as a stimulated emission, |0 1æ f |0 0æ, i.e., as a negative cross peak growing in with time. A complementary scenario exists where the initial excitation takes place on the antisymmetric fundamental, |0 1æ, and a delayed off-diagonal stimulated emission of the type |1 0æ f |0 0æ appears with increasing waiting delay. To test the assignment of bands a and b to the antisymmetric and symmetric OH normal modes of a bidentate water molecule and to verify whether a population transfer takes place between them, one can exploit the vectorial properties of their associated vibrational transition moments by measuring the transient anisotropy. The transition dipoles of the symmetric and antisymmetric stretching modes of water are known to be aligned orthogonally with respect to each other. The transient anisotropy, r (ν~probe, ν~pump, tW), can be calculated from the pump-induced differential optical densities, ~pump, tW), ΔODpar (ν~probe,ν~pump,tW) and ΔODperp (ν~probe, ν measured with parallel and perpendicular relative polarization between the pump and the probe pulses, according to rðtW Þ ¼

ΔODpar ðtW Þ-ΔODperp ðtW Þ ΔODpar ðtW Þþ2ΔODperp ðtW Þ

2 ¼ ÆP2 ½! μ pump ð0Þ! μ probe ðtW Þæ 5

ð1Þ

where the dependence on the pump and probe frequencies has been omitted for the sake of clarity. The quantity, r(tW), is related to the time-correlation function of the second Legendre polynomial, P2, of the scalar product formed from the transition dipole excited at time zero and the transition dipole probed at the waiting delay, tw. Neglecting for the moment any dynamic randomization of the angular distribution of dipoles, an anisotropy of 0.4 is therefore expected if the angle spanned by the pump and probe transition moments is zero. Alternatively, a 1213


The Journal of Physical Chemistry A negative anisotropy with a magnitude of 0.2 is expected if these two vectors form an angle of 90. Since the transition moments of the symmetric and antisymmetric stretching modes of water are orthogonal, an anisotropy of -0.2 is anticipated if the assignment of bands a and b is correct. Thus, by pumping band b and probing band a with parallel and perpendicular relative polarization between excitation and detection pulses, information regarding the relative orientation of the transition moments associated with the two bands can be obtained. Such a transient cross anisotropy is reproduced in Figure 5. For reference, a diagonal anisotropy obtained by pumping band b and probing band b is also reproduced. It can be seen that the cross anisotropy at early times exhibits a maximum value of about þ0.20 while at the same time the maximal diagonal anisotropy is equal to þ0.35. A diagonal anisotropy that is slightly smaller than the ideal value of 0.4 might indicate some imperfections of the polarization optics used in the experiment or, alternatively, some reorientational dynamics that cause the anisotropy to already decay on ultrafast time scales, i.e., well below 1 ps. A cross anisotropy of þ0.20 suggests an angle between the transition dipoles of the two bands of about 35, i.e., far from the 90 expected for the angle between symmetric and antisymmetric stretching vibrations of water. However, the spectral decomposition of the linear OH-stretching absorption (cf., Figure 2) showed that monodentate and bidentate contributions heavily overlap. It could well be that the cross anisotropy of þ0.20 is simply an incoherent average of a bidentate anisotropy of -0.20 and an additional anisotropy of þ0.40 resulting from the simultaneous excitation and probing of the broad underlying bound OH stretching band of the monodentate. Furthermore, bands a and b are neither entirely spectrally resolved resulting in their mixed excitation despite the narrow spectral width of the pump pulses. Therefore, because of this spectral congestion, the polarization-resolved data must remain inconclusive regarding the possibility of population transfer among the symmetric and antisymmetric stretching modes of the water molecules engaged in a bidentate binding motif. Also, a higher time-resolution might be very helpful in disentangling the individual contributions originating from the different binding patterns. Finally, we note that both diagonal and cross anisotropies display a distinct temporal decay on a time scale of a few picoseconds toward a constant nonzero value. This behavior might be attributable to an angularly restricted reorientational motion of the water molecules that are attached to the macrocycle. Indeed, the full angular randomization of the OH-stretching transition dipoles should lead to a decay of the anisotropy to zero, which requires either the complete breakage of the hydrogen bonds between the substrate and the receptor or, alternatively, the full unrestricted reorientational diffusion of the entire supramolecular complex. Obviously, both processes are rather slow and the hydrogen-bond lifetimes are long in relation to the maximum time window of our anisotropy experiments. The picosecond decay reflects only the partial loss of memory of the transition dipole orientations due to the residual small amplitude fluctuations of the H2O connected with a slight bending (rather than a fission) of the H-bonds to the crown. 3.4. Temperature Dependent FTIR Spectra. A series of temperature dependent FTIR spectra of 18-crown-6 monohydrate is reproduced in Figure 6A. All spectra have been normalized to the free OH peak at 3684 cm-1 (band c). The optical density (or absorbance) can be decomposed into four individual

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Figure 6. (A) Experimental FTIR spectra in the OH-stretching spectral region of 18-crown-6 monohydrate in liquid CCl4 as a function of temperature. (B) Simulated spectra according to eqs 2 and 3 and assuming only a single bidentate binding motif coexists at thermal equilibrium with the monodentate (---) or according to eqs 2 and 4 assuming that two bidentate species contribute to the spectrum (—).

bands as shown in Figure 1, three of which have a Lorentzian shape and the fourth is Gaussian, i.e. 2 !2 3 ~ν -~ν 0 , 1 ðTÞ 5 ODð~ν ,TÞ ¼ A1 exp4-4 ln 2 Γ1 þ

4 X i¼2

Ai

ðΓi =2Þ2 ð~ν -~ν 0,i Þ2 þðΓi =2Þ2

ð2Þ

In eq 2, the quantities Ai represent the amplitudes of the four components, ν~0,i is their center frequency, and Γi is their full width at half-maximum. The Gaussian component describes band a which exhibits a small shift to higher frequencies with increasing temperature according to (∂ν~1,i/∂T) = 0.25 cm-1/K. The parameters that yield an excellent fit to the data at the reference temperature, T = Tref = 295 K, are summarized in Table 1 (Supporting Information). Before analyzing these data, it is important to emphasize that the individual contributions spectrally overlap to a considerable extent. We deal with this complication in the following fashion. Normalizing all spectra to band c (i.e., the monodentate free OH), the temperature dependence of the relative optical density should be described to a good approximation by " _ # ΔH 1 1 ODrel ð~ ν ,TÞ ¼ ODmono ð~ ν Þ þ ODbi ð~ ν Þexp R T Tref ð3Þ provided it is composed of two species coexisting in thermodynamic equilibrium at the temperature, T. These can be the monodentate and the bidentate binding motifs as shown in Figure 1. The contribution of the former is represented by ODmono(ν~), which in turn is given by the second term of eq 3 when summing only over i = 3 and 4. In contrast, the contribution of the bidentate is then calculated from the first two terms of eq 3 (i.e., i = 1 and 2 only) multiplied by the van’t Hoff exponential carrying the molar reaction enthalpy, ΔHh, for the interconversion of a monodentate into a bidentate. Using a value of -5 kcal/mol for ΔHh, a set of temperaturedependent absorption spectra is obtained that is reproduced in Figure 6B as dashed curves. Furthermore, the ratios of the maximal absorbances (c/b, c/a, and b/a) can be plotted semilogarithmically 1214



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Figure 7. Van’t Hoff plots of the temperature dependent intensity ratios of bands a, b, and c. The curves result from simulations assuming only a single bidentate (---) or two bidentate (—) binding motifs coexists with the monodentate at thermal equilibrium.

as a function of the inverse temperature. Such simulated van’t Hoff plots for the case of two exchanging species are compared in Figure 7 (dashed) with the experimental data. It can be seen that although the simulated absorbance ratio band-c/band-a reproduces the experimental data quantitatively, there remain significant systematic deviations for the other two ratios. This finding might indicate that more species contribute to the FTIR spectrum than just a single monodentate and a single bidentate binding motif. Indeed, in the case of three interconverting species, the relative optical density must be written as "

_ # ΔH a 1 1 ODrel ð~ ν ,TÞ ¼ ODmono ð~ ν Þ þ ODbi-a ð~ ν Þexp R T Tref " _ # ΔH b 1 1 þ ODbi-b ð~ν Þexp ð4Þ R T Tref

The three interconverting species can, e.g., represent a monodentate and two spectroscopically distinguishable bidentate binding motifs, a-bidentate and b-bidentate, as suggested by the electronic structure calculations (vide infra). In general, the antisymmetric stretching vibration is more intense than the symmetric stretching vibration by at least a factor of 3-4. This is easily demonstrated by measuring the linear FTIR spectrum of monomeric water in weakly interacting solvents28 and is further supported by a normal-mode analysis using, e.g., density functional theory (vide infra). For simplicity, the vibrational spectrum of a given bidentate can then be reduced to a single absorption band representing its dominating antisymmetric stretching vibration only. The contributions of the two interconverting bidentates are then given by the terms i = 1 and i = 2 of eq 2 multiplied by their respective van’t Hoff exponential carrying the reaction enthalpy either for the monodentate T a-bidentate equilibrium, ΔH ha, or for the monodentate T b-bidentate equilibrium, ΔH hb. Using ΔH ha = -5.1 kcal/mol and ΔHhb = -3.8 kcal/mol, the solid spectra shown in Figure 6B are obtained. The simulated van’t Hoff plots are reproduced in Figure 7 also as solid curves. The agreement between experiment and simulation is much improved compared to the two-species scenario as all three ratios can now be fitted simultaneously. This quantitative agreement could be taken as an indication for a chemical exchange between two species associated with the resonances a and b. The reaction enthalpy for the equilibrium b-bidentate T a-bidentates is then given by ΔHhb - ΔHha = 1.3 kcal/mol. 3.5. Chemical Exchange between Bands a and b. The delayed growth of a cross peak pattern such as that displayed by Figures 3 and 4 might also be interpreted by invoking a dynamic

chemical exchange between two spectroscopically distinct species, each of which exhibits its own unique vibrational structure. The temperature dependent FTIR spectra presented in the previous section might lend some credence to such an interpretation. To follow up on such a notion, the experimental 2DIR spectra were simulated within the nonlinear response function formalism originally developed by Mukamel and co-workers29,30 and subsequently further refined to include chemical exchange phenomena in 2DIR spectroscopy by Fayer and co-workers.31 The simulations required the explicit treatment of three vibrators, each of which undergoes population relaxation and dynamic vibrational line broadening (spectral diffusion). Two of the three vibrators are mutually engaged in chemical exchange whereas the third relaxes independently from the other two. These three vibrators are responsible for bands a, b, and d of the FTIR spectrum of 18-crown-6 monohydrate; e.g., they represent the asymmetric stretch of the a-bidentate, the asymmetric stretch of the b-bidentate, and the bound OH-stretch of the monodentate [as implied by the electronic structure calculations (see below)]. To simplify and accelerate the numerical simulations and because of its rather small transition dipole moment as compared to the other vibrators of relevance, the free OH stretch of the monodentate was neglected. Furthermore, following v = 1 excited state depopulation, the vibrators find themselves in their vibrational ground state with the excess energy effectively distributed in a canonical fashion over all nuclear degrees of freedom of the supramolecular complex. This thermally “hot” complex gives rise to a residual diagonal bleach (even when excited state absorptions have fully decayed to zero) due to the manifold of anharmonic couplings of the OH-stretching vibrations to the low frequency modes of the crown ether hydrate. Such signatures of canonical heating are also clearly visible in previous 2DIR studies related to chemical exchange phenomena in polyatomic systems.24 Here, such heating contributions have explicitly been built into the numerical simulations. The simulations of the 2DIR spectra are compared in Figure 3F-J with the experimental data. The full temporal evolution of the simulated 2DIR spectra from 700 fs to 10 ps in increments of 50 fs is shown together with the experimental data in a movie provided in the Supporting Information. A rate constant of 1/4.5 ps for an interconversion from species a to species b results in an excellent agreement between experiment and simulation. The set of vibrational and cooling lifetimes, the line broadening parameters, as well as the chemical exchange parameters are collected in Table 2 in the Supporting Information. Note that the vibrational lifetime decreases with decreasing center frequency of the oscillator, i.e. 4.5 ps for band a, 3.5 ps for band b, and 2.5 ps for band d. The subsequent cooling of the entire supramolecular complex occurs with a time constant of 12 ps.

4. DISCUSSION At this stage, the experimental data alone are insufficient to unambiguously clarify the molecular physical process that is responsible for the delayed appearance of cross bleaches in the OH-stretching region of the 2DIR spectra of 18-crown-6 monohydrate and the peculiar temperature-dependence of its linear FTIR spectra. However, in the case of chemical exchange, an alternative assignment for the two vibrational resonances a and b in terms of two spectroscopically distinguishable species (e.g., different 18C6-H2O configurations or conformers) is required. To our knowledge, experimental data pertaining to the conformation of the macrocycle of 18-crown-6 monohydrate in 1215


The Journal of Physical Chemistry A either the monodentate or the bidentate binding motif in room temperature liquid solution do not exist. Crystal structures of 18C6-water complexes expose only a bidentate binding motif with the crown adopting a conformation with nearly D3dsymmetry.32 Questions regarding the macrocycle’s flexibility, the relative energies of monodentate versus bidentate configurations, as well as the dynamical processes interconverting the different binding motifs of 18C6-H2O at room temperature have so far only been addressed by computational methods.33,34 Experimentally, high-resolution spectroscopy has been carried out only on supersonic expansions of crown ether hydrates by Ebata and co-workers.35-38 However, their instrumental approaches of laser-induced fluorescence, hole burning, and double resonance spectroscopy always involved an ultraviolet (UV) excitation and/or probing scheme, thereby necessitating the introduction of a suitable electronic chromophore attached to the macrocycle. Consequently, they focused on studying monoand oligo-hydrates of benzo- and dibenzo-18-crown-6. Unfortunately, these systems are not really comparable to the unsubstituted 18-crown-6 investigated here, because benzo-annulated crown ethers are conformationally hindered due to the sp2 hybridization of some of the carbon atoms within the macrocycle. Hence, these molecules can be regarded as rigidified derivatives of the classical 18-crown-6 receptor with a substantially restricted conformational space. In addition, band intensities from IR-UV double resonance vibrational spectra are not comparable with those obtained from pure infrared spectra because of the unknown coupling of the electronic transition dipole moment located on the UV chromophores (here the extra-annular aromatic moieties) of the receptor with the vibrational transition moment located on the water substrate. Nonetheless, even in these rigidified crown-ether hydrates, Ebata and co-workers were able to spectroscopically isolate several energetically nearby isomers which differed significantly in their vibrational structure within the OH-stretching region of the water substrate.36-38 4.1. Conformational Search Strategy. To address the question whether or not thermally accessible conformers of 18crown-6 monohydrate exist, which are distinguishable by their OH stretching vibrational resonances, a very careful conformational search based on classical molecular mechanics and density functional theory was conducted. The conformational space of bare 18-crown-6 consists of 42 stretching, 78 bending, and 90 torsional coordinates. The conformation of the macrocycle is essentially defined by the 18 O-C-C-O and C-C-O-C dihedrals. This torsional subspace allows for a total number of 675 ideal conformations39,40 of the macrocycle, i.e., conformations that can be superimposed on an ideal diamond lattice by limiting all dihedrals to the values 60 (gauche, gþ), 180 (anti, a), or -60 (gauche, g-), by constraining all CO and CC bond lengths equal to 1.420 Å, and by restricting all bond angles to be perfectly tetrahedral (109.47). Even when dismissing all those structures having residual CH 3 3 3 CH spatial overlap, there are still 190 ideal diamond-lattice conformations, only two of which (a D3d and a Ci symmetrical) are displayed in Figure 8. Attaching a water to each of those in an arbitrary orientation results in a conformational space that is simply too large to be efficiently sampled for quantum chemical optimizations.41-45 Therefore, a conformational search strategy was conducted, whose basic strategy is as follows. First, the 18-crown-6 monohydrate was constructed in silico with the macrocycle adopting the D3d symmetry (cf., Figure 8) and the water binding to the ether oxygens 1 and 3 in a bidentate

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Figure 8. Schematic structure of the D3d (top) and Ci-symmetrical (bottom) 18-crown-6, sequence of dihedral angles defining their conformation (g = gauche, a = anti), and Newman projections along the CC and CO single bonds forming the macrocycle.

fashion. This structure was also observed in X-ray crystallography of 18-crown-6 complexes containing water.32 A classical mechanical structure optimization was then carried out in the CHARMM force field on 10 000 starting geometries derived from this D3d-1.3bidentate construct by randomly distorting along its six O-C-C-O dihedrals simultaneously. A second identical conformational search was subsequently conducted using a monohydrate construct of the Ci-symmetrical macrocycle (cf., Figure 8) and a bidentate water bridging again over the ether oxygens 1 and 3 as described in ref 33. The Ci-symmetry prevails in the crystalline phase of neat 18-crown-6. Finally, a third and a fourth conformational search were performed in the AMBER force field using both the D3d-1.3-bidentate and the Ci-1.3-bidentate constructs. The 100 energetically lowest structures identified by each of the four classical-mechanical conformational searches were subsequently preoptimized quantum-mechanically using DFT at the rather low level RI-BP86/SVP/SV-J. About 50 energetically lowest conformers were then further postoptimized up to the level RI-BP86/TZVPP/TZV-J/COSMO followed by their normal-mode analysis. A few selected structures were finally further refined and vibrationally analyzed using RI-BP86/def2-QZVPP/ def2-QZV-J/COSMO or B3LYP/6-311þþG**. This procedure identifies a number of energetically low-lying conformers, which can be systematically labeled according to the symmetry of the macrocycle conformation (e.g., Cs, D3d, Ci, boat, or mixed) and by specifying the bridging configuration (i.e., 1.3- versus 1.4bidentate). The essential results are compiled in Tables 3 and 4 (Supporting Information) without claiming to have captured all possibly existing conformers within an energy of 2000 cm-1. Yet, we do believe that we have been able to identify all structures that are relevant within the thermal energy. 4.2. Monodentate Binding Motifs. All monodentates have in common that the dangling hydroxyl group points toward the macrocycle exterior. Artificially constructed geometries having their free OH oriented toward the macrocycle interior are 1216



Figure 9. DFT-optimized structures of the D3d-single out monodentate (A) and D3d-1.3 bidentate (B) binding motifs. The numbers indicate the OH 3 3 3 O hydrogen-bond angle, as well as the O 3 3 3 H and O 3 3 3 O distances in Ångstr€oms.

intrinsically unstable and collapse into a bidentate configuration upon geometric relaxation. The only exception was a structure (Ci 1-single-in) that featured the well-known Ci-symmetrical crown ether typical for neat crystalline 18C6. The most stable monodentate was the D3d single-out which was already identified in refs 33,41. Figure 9A provides a side and a top view of this binding motif together with the structural parameters relevant to the hydrogen bonding geometry. We have used the theoretical harmonic frequency of its dangling hydroxyl oscillator as an internal reference for the conversion of harmonic to fundamental frequencies of all structures identified by the conformational search at the various DFT-levels. A common factor of 0.982 makes the free OH stretch of the D3d single-out conformer to quantitatively match the experimental value of 3684 cm-1 for the free OH-stretch (band c) of 18C6-monohydrate in CCl4 solution. There can be no doubts that this D3d-single out binding motif is responsible for the “free” and the “bound” OH resonances previously labeled bands c and d in the FTIR spectrum of 18crown-6 monohydrate 4.3. Bidentate Binding Motifs. Most other conformers represent differently bridged bidentate binding motifs. A vibrational analysis of these structures shows that each bidentate conformer exhibits its own symmetric and antisymmetric stretching frequencies as expected. Notice however that, in all instances, the symmetric mode is weaker than the asymmetric counterpart by at least a factor of 3-4 (see Tables 3 and 4, Supporting Information) as is also experimentally observed for monomeric water in weakly interacting solvents.28 Using the basis set def2-QZVPP with COSMO correction, the energtically lowest bidentate binding motif is the D3d 1.3-bidentate whose geometrical structure and H-bond parameters are reproduced in Figure 9B. In this structure, the macrocycle adopts again the D3d symmetry and the water bridges over the ether oxygens 1 and 3. The two H-bonds are fully equivalent and have a length of 2.075 Å. Both hydrogen bonds are slightly bent with an O 3 3 3 H-O angle of 164. With the exception of a strained and energetically higher lying Cs-symmetrical bidentate (Cs 2.4-bi), this D3d 1.3bidentate binding motif exhibits the longest and weakest hydrogen bonds of all bridged structures and, consequently, features the highest symmetric and asymmetric OH-stretching frequencies of

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all bidentates. Furthermore, using the internally referenced conversion factor of 0.982, its asymmetric stretching frequency of 3585 cm-1 (triple-ζ, or 3579 cm-1 with quadrupole-ζ basis set) is in near perfect agreement with the band a appearing in the FTIR of 18C6monohydrate at 3598 cm-1. Thus, there can again be no doubt that band a is brought about primarily by the antisymmetric stretching mode of the D3d 1.3-bidentate binding motif. Its internally referenced symmetric stretching frequency is 3521 cm-1 (triple-ζ, or 3518 cm-1 with quadrupole-ζ basis set); i.e., it is very close to band b, which is centered in the FTIR spectrum of 18C6-H2O at 3535 cm-1. At a first glance, it would therefore be totally consistent to assign band b to the symmetric stretching frequency of the D3d 1.3-bidentate binding motif as was done previously.5 Note, however, that the DFT calculations predict a ratio of ∼1/4 for the relative intensity of symmetric/ antisymmetric stretch whereas the spectral decomposition of the FTIR data shown in Figure 2 indicated about equal integrated intensities. Therefore, if this structure were the only existing bidentate conformer, an interpretation of the delayed appearance of the 2DIR cross peaks, which invokes a population transfer between its two OH-stretches, would be self-consistent; however, explanations for the almost equal intensities of bands a and b and, furthermore, for the peculiar temperature dependence of their amplitude ratio are still required that rely exclusively on these two eigenmodes of this unique bidentate conformer. We now return to the second interpretation of the delayed cross peaks, which invoked an additional chemical exchange equilibrium between two spectroscopically distinct bidentate receptor-substrate structures. In attempting to develop an alternative assignment of the OH stretching spectral region of 18C6-monohydrate, only energetically low-lying structures of the conformational search have to be inspected whose internally referenced antisymmetric stretching frequencies are in close agreement with the experimental center frequency of band b of 3535 cm-1. Only four binding motifs fulfill that criterion, namely, the Cs 1.4-bidentate, the boat 1.4-bidentate, the Ci 1.3bidentate, and the mixed 1.3-bidentate. The molecular structure of each of these together with the structural parameters relevant to their hydrogen-bonds is reproduced in Figure 10. The Cs-symmetrical structure shown in Figure 10A has never been reported before in crystal structures of 18C6 containing water. The Cs-symmetry of the macrocycle can however be stabilized in the crystal lattice of a Kþ-complex of dicyclohexano18-crown-6 in the presence of 2-nitrophenoxide.46 Likewise, the boat structure (cf., Figure 10B) has neither been reported nor observed experimentally before. Nonetheless, the theory identifies the boat as a low-lying conformer because it allows for additional hydrogenbonding by pairs of methylenic CH’s that are directed toward the lone pairs of the water oxygens. This totally unexpected H-bond pattern is so significant that it stabilizes the boat-1.4 bidentate binding motif even below a bridged conformer involving the well-known Cisymmetrical macrocycle (cf., Figure 10C). The Ci 1.3-bidentate has been theoretically studied before by Wipff and co-workers using density functional theory and Car-Parrinello molecular dynamics.33 Finally, the conformational search also identifies the mixed 1.3-bidentate, the structure of which is displayed in Figure 10D. The most noteworthy feature of this mixed 1.3-bidentate is that it deviates from the D3d 1.3-bidentate in only two dihedrals. The sequence of torsional angles is summarized for these binding motifs in Table 5 (Supporting Information). There exists no other bidentate structure that exhibits a similar structural conformity with the D3d 1.3-bidentate as this mixed 1.3-bidentate. 1217



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Figure 11. Overlay of the two DFT-optimized structures of the D3d-1.3 and the mixed-1.3 bidentates emphasizing their conformational similarity. The only two dihedrals in which they differ are indicated.

Figure 10. DFT-optimized structures of the Cs-1.4 bidentate (A), the boat-1.4 bidentate (B), the Ci-1.3 bidentate (C), and the mixed-1.3 bidentate (D) binding motifs. The numbers in each figure indicate the two OH 3 3 3 O hydrogen-bond angles, as well as the two sets of O 3 3 3 H and O 3 3 3 O distances for each H-bond.

The molecular similarity between these two binding motifs becomes even more apparent upon spatially overlaying their structures as shown in Figure 11. Obviously, several bidentate binding motifs are in accordance with and can contribute to the vibrational band b of 18C6-monohydrate at thermal energies. However, it is most likely that only one of these structures (the mixed 1.3-bidentate) is able to dynamically exchange on picosecond time scales with the D3d 1.3-bidentate. This is because it is the only conformer identified, which is separated from the D3d1.3-bidentate by a barrier that is thermally surmountable on such a short time scale. Furthermore, it turns out that a conversion from the D3d-1.3-bidentate to any other of the thermally populated conformers listed in Tables 3 and 4 (Supporting Information) will inevitably lead through this mixed 1.3bidentate conformation (see also the transition state theory calculation in the following section). 4.4. Transition State Theory for the Crankshaft Isomerization. In transforming the D3d-1.3-bidentate into the mixed-1.3bidentate conformer, a motion is required that involves the (concerted or sequential) motion along two nearby single bonds, the carbon-carbon single bond, O(3)-C-C-O(4), and the carbon-oxygen single bond, C-O(4)-C-C (see Table 5, Supporting Information and Figure 11). At a first glance it might appear unrealistic that such a supramolecular motion involving major conformational rearrangements around the macrocyle’s dihedrals can take place on a time scale of a few picoseconds.

Similar conformational motions such as the famous ring inversion of cyclohexane involving axial-to-equatorial hydrogen exchange occur under similar thermodynamic conditions only on microsecond time scales and slower.47,48 Only torsional isomerizations of acyclic hydrocarbons are known to occur on a time scale of tens of picoseconds.22 Pseudorotational ring puckerings of cyclic alkanes and alkenes are believed to occur on picosecond time scales but have never been time-resolved before.49,50 Therefore and to further test the tenability of chemical exchange occurring between the two macrocycle conformations, an ab initio rate constant for the conversion between the D3d 1.3bidentate and the mixed 1.3-bidentate structures was computed within the framework of canonical transition state theory (TST). To this end, a relaxed surface scan was carried out at the DFTlevel RI-BP86/TZVPP/TZV-J by varying the dihedral angle O(3)-C-C-O(4) between 74.8 (i.e., gauche, gþ, corresponding to D3d 1.3-bi) and 175.1 (i.e., anti, a, equivalent to mixed 1.3-bi). This variation was carried out in a bidirectional sense such that the optimized structure for the mixed 1.3bidentate was transformed into the D3d 1.3-bidentate and vice versa. At every fixed preset value for the dihedral angle, O(3)-C-C-O(4), the complex was structurally optimized in all other degrees of freedom, hence the term “relaxed scan”. The nuclear motions that are involved in converting the two bidentate structures into each other represent two simultaneous, i.e., concerted, single-bond isomerizations. Although the relaxed surface scan is carried out along the O(3)-C-C-O(4) dihedral, the carbon-oxygen single bond connected with the C-O(4)-C-C torsional angle rotates spontaneously from anti (a) to gauche (gþ) as the carbon-carbon single bond is externally driven by the geometry optimizer from gauche (gþ) to anti (a). An animation displaying the nuclear motions of the supramolecular complex along the reaction coordinate for the chemical exchange was produced from the DFT-relaxed surface scan and is provided in the Supporting Information. The two concerted gauche-anti isomerizations resemble very much a bicycle pedal motion or the motion of a crankshaft. Quite a similar motion has 1218



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Figure 12. Cut through the potential energy surface of 18-crown-6 monohydrate (red circles) and bare 18-crown-6 (gray circles) along the crankshaft reaction coordinate for the D3d-1.3 to mixed-1.3 conformational isomerization. The structures zoom onto the isomerizing dioxoethylenic fragment of the macrocycle undergoing a transition between gauche (D3d1.3-bidentate) and anti (mixed-1.3-bidentate) conformation, which is sensed by the intramolecular stretching vibration of the hydrogen-bonded water.

been proposed to occur in photoexcited retinal during the primary processes of vision.51 As a result of this motion, the two H-bonds >O 3 3 3 HO-H 3 3 3 O< holding the water molecule to the crown are slightly compressed (expanded) upon converting the D3d into the mixed conformer of the macrocycle (or vice versa). This in turn causes both OH-stretching vibrations of the water bidentate to shift to lower (higher) frequencies. In other words, the conformational transition within the crown ether receptor is accurately reported by the OHstretching vibrations of the water substrate. The relaxed surface scan not only provides a one-dimensional cut along the crankshaft coordinate through the potential energy surface connecting the D3d 1.3-bidentate with the mixed 1.3bidentate of 18-crown-6 monohydrate (see Figure 12) but also delivers the molecular structure of the transition state for the crankshaft isomerization. A transition state structure was identified at the potential energy maximum along the crankshaft coordinate which lies 2.5 kcal/mol above the D3d-1.3 and about 1.9 kcal/mol above the mixed-1.3 binding motif. A normal-mode analysis has then been carried out on this activated complex structure. As required, this transition state is characterized by a single imaginary frequency, which verifies its true saddle point nature on the multidimensional potential energy hypersurface. The thermal rate constant, k(T), in the high-pressure limit of a unimolecular process such as the crankshaft isomerization can be written as52 kB T Q ‡ E0 exp kðTÞ ¼ ð5Þ h 3Q 3 kB T where kB denotes Boltzmann’s constant and h is Planck’s constant. The threshold energy, E0, is calculated from the difference of the reactant and transition state internal energies whereas the quantities, Q and Q‡, represent their respective partition functions. Equation 5 is easily transformed into an Arrhenius form thereby establishing a direct connection of the threshold energy and the partition functions to the apparent activation energy and the frequency prefactor or, alternatively, upon introduction of appropriate abbreviations to the activation entropy and activation enthalpy.52 Since for the crankshaft isomerization of 18C6-H2O the translational structures of the reactants and the activated complex are identical and their rotational constants are almost equal,

Figure 13. Schematic drawing of the conformational equilibria of 18crown-6 monohydrate in liquid CCl4 solution (A) and alternative assignment of the linear FTIR absorption spectrum (B).

only the vibrational partition functions need to be known. In the harmonic approximation, these are given by Q ¼

j Y i¼1

1 1 - exp -

hνi kB T

ð6Þ

where the harmonic frequencies, νi, can be obtained directly from the DFT-calculation. Notice that the product runs over the j = 3N - 6 or the j = 3N - 7 vibrational coordinates of the N-atomic reactant and transition state, respectively. The effective chemical exchange rate constant is defined as the sum of the rate coefficients of the forward and backward processes, i.e., keff = kforward þ kbackward. At the DFT-level RI-BP86/TZVPP/TZV-J, the internal energy difference between the D3d 1.3-bidentate and the mixed 1.3-bidentate is 190 cm-1 (see also Table 3 in the Supporting Information). The threshold energy for the conversion from D3d 1.3-bi to mixed 1.3-bi at the same level of theory amounts to 875 cm-1. Together with eqs 1 and 2 in combination with the harmonic frequencies of the D3d 1.3-bidentate conformer, these energetics yield an effective exchange rate constant of keff = 1/(5.5 ps). This value is in qualitative agreement with the rate constant obtained from simulating the experimental 2DIR spectra using the nonlinear response function formalism (see above). The TST calculations demonstrate that a chemical exchange between different conformers can indeed take place on picosecond time scales. Whether or not such an exchange manifests itself in the linear FTIR spectroscopy or in the temporal evolution of the 2DIR spectrum of 18-crown-6 monohydrate as sketched in Figure 13 1219


The Journal of Physical Chemistry A remains nonetheless an unsettled issue because of the population transfer dynamics addressed in section 3.3. In this alternative “chemical exchange” scenario, the FTIR spectrum of 18-crown-6 monohydrate would have to be reassigned. Band a is then brought about by the antisymmetric stretching vibration of a D3d-1.3 bidentate. Its considerably weaker symmetric stretching vibration contributes somewhat to band b, which, in turn, arises predominantly from the antisymmetric stretching vibration of a mixed-1.3 bidentate. The weaker symmetric stretching vibration of the latter conformer merges with the bound OH resonance (band d) of the monodentate. Since no delayed cross peaks between mondentate and bidentate bands were detected, the 2DIR data seem to rule out a monodentate to bidentate interconversion on the time scale of the vibrational lifetimes. Apparently, during that time window, the water remains tightly bound during the course of any structural rearrangements within the macrocycle. The intermolecular H-bond forces are obviously strong enough to keep the supramolecular complex intact despite the intermittent structural fluctuations related to the flexibility of its macrocyclic receptor on a time scale of several picoseconds. We finally close this discussion in referring to the intriguing Car-Parrinello molecular dynamics (CPMD) simulations on 18-crown-6 monohydrate by Wipff and co-workers, which indeed revealed such crankshaft isomerization dynamics, but only for bare 18-crown-6 monohydrate. Gauche-anti isomerizations around the single bonds of the macrocycle were recorded in a dynamic trajectory of the D3d conformer during a period of less than 10 ps, i.e., exactly on the time scale of cross-peak formation in the 2DIR spectrum. However, the CPMD further implied that a hydration of the crown ether causes the macrocycle to stiffen and to freeze out the torsional isomerizations. All six OC-CO dihedrals clearly retained their gauche conformation during the entire length of the trajectory of 10 ps. The only structural fluctuations that were visible in the CPMD were related to the random hopping motion of the water from one 1.3-bidentate to another thereby transiently moving through an intrinsically unstable D3d single-in motif. We currently do not understand this stiffening effect of attaching a water molecule to the crown ether. As shown in Figure 12, a relaxed potential energy surface scan along the crankshaft isomerization of bare 18 crown-6 (calculated at exactly the same level of theory as was used before for 18C6-H2O) produces a barrier that is actually lowered upon hydration of the ether oxygens by roughly 100 cm-1. Thus, one might be tempted to conclude that the macrocycle dynamics are accelerated by the water-crown interactions. For comparative purposes, we are currently performing a careful normal-mode analysis on the transition state for the crankshaft isomerization of bare 18-crown-6 to obtain an ab initio rate in the absence of hydrogen-bonding to a water substrate.

5. CONCLUSIONS In summary, we have studied the internal dynamics of the archetypal supramolecular receptor-substrate complex consisting of 18-crown-6 and a water molecule. We have used a combination of linear FTIR and ultrafast 2DIR spectroscopy in the OH-stretching spectral region to monitor the vibrational dynamics of this hydrogen-bonded adduct in real time. The experimental data were complemented by an in-depth theoretical analysis based on classical molecular modeling and density

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functional theory, which was aimed at exploring the vast conformational space of the host-guest complex. The 2DIR spectra reveal a delayed appearance of cross peaks between OH-stretching absorption bands that are believed to reflect the symmetric and antisymmetric stretching modes of the water substrate molecule. The possibility of population transfer between these two normal modes as the molecular physical origin for these dynamic spectral features was discussed and further tested by transient anisotropy measurements using a polarization-resolved detection of the 2DIR spectrum. The peculiar temperature dependence of the stationary FTIR spectrum of 18-crown-6 monohydrate hints at the existence of more than just a single bidentate binding motif that is in thermodynamic equilibrium with the monodentate binding pattern. This idea was tested in more detail in terms of a conformational search together with a normal-mode analysis of each of the numerous conformers that are energetically sufficiently low to be thermally populated at room temperature. Calculations of an ab initio rate constant based on transition state theory imply that indeed a conformational transition within the receptor’s macrocycle can take place on a time scale of several picoseconds. These dynamics are related to a crankshaft isomerization involving the concerted motion along two torsional coordinates and result in a compression/expansion of the hydrogen-bonds that hold the water molecule to the crownether. The change in the hydrogen-bond geometry in turn translates into a modification of the OH-stretching resonance frequencies such that the OH-stretching modes of the substrate can in principle be exploited as reporters of the internal conformational dynamics within the supramolecular complex. Both interpretations for the origin of the delayed cross peaks, i.e. population transfer versus chemical exchange, are self-consistent, and the presented body of experimental data is insufficient to unambiguously rule out either of the two scenarios. We are currently expanding our experimental and theoretical efforts to the supramolecular crown ether hydrate involving the mixed isotopomer, HOD, as the substrate, which in light of the small absorption cross sections and miniscule complex concentration in nonpolar solution is not at all an easy task. Furthermore, we are currently in the process of studying the internal dynamics of the hydrates of crown ethers with varying size of the macrocycle and different substitution patterns in an effort to differentiate between vibrational relaxation dynamics from conformational structural dynamics related to the supramolecular flexibility. We close in emphasizing that the vibrational spectrum of monomeric water in medium-to-weakly interacting solvents is almost always interpreted exclusively in terms of the symmetric and antisymmetric hydroxyl stretching normal modes, their mutual couplings and internal relaxations, as well as their individual line broadening dynamics reflecting continuously distributed, stochastic frequency fluctuations.27,28,53 However, the DFT calculations and the FTIR data presented here clearly highlight the role of structurally distinct but thermally accessible configurations of the local microscopic environment in shaping the OH-stretching spectral region via additional, discretely distributed random jumps of the hydroxyl normal-mode frequencies of this apparently simple water molecule.

’ ASSOCIATED CONTENT

bS

Supporting Information. Animation displaying the temporal evolution of the experimental and simulated 2DIR spectrum of 18-crown-6 monohydrate, a table listing the parameters

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The Journal of Physical Chemistry A of the spectral decomposition of the FTIR spectrum at 298 K, a table summarizing the model parameters required for the nonlinear response function simulations of the 2DIR spectrum, two tables listing the lowest energy conformers obtained from the conformational search at the level RI-BP86/TZVPP/TZV-J/ COSM and RI-BP86/def2-QZVPP/QZV-J/COSMO, a table listing the sequence of torsional angles of the macrocycle in the D3d-1.3 bidentate, the mixed-1.3 bidentate, and the Cs-1.3 bidentate conformers, and an animation displaying the crankshaft isomerization obtained from the DFT relaxed surface scan. This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We are indebted to Prof. Georges Wipff for stimulating discussions regarding the molecular dynamics of crown ethers. Financial support by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 624 “Functional Chemical Templates” is gratefully acknowledged. ’ REFERENCES (1) Pedersen, C. J. J. Am. Chem. Soc. 1967, 89, 7017. (2) Supramolecular Chemistry: Concepts and Perspectives; Lehn, J.-M., Ed.; Wiley-VCH: Weinheim, 1995. (3) Gokel, G. W. Crown Ethers and Cryptands; The Royal Society of Chemistry: London, 1992; Vol. 3. (4) Host Guest Complex Chemistry I; V€ogtle, F., Ed.; Springer Verlag: Berlin, 1981. (5) Bryan, S. A.; Willis, R. R.; Moyer, B. A. J. Phys. Chem. 1990, 94, 5230–5233. (6) Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase; Elsaesser, T., Bakker, H. J., Eds.; Kluwer Academic Publisher: Dordrecht, 2003. (7) Novak, A. Struct. Bonding (Berlin) 1974, 18, 177–216. (8) Kandratsenka, A.; Schwarzer, D.; V€ohringer, P. J. Chem. Phys. 2008, 128, 244510–6. (9) Schwarzer, D.; Lindner, J.; V€ohringer, P. J. Phys. Chem. A 2006, 110, 2858–2867. (10) Hamm, P.; Lim, M. H.; Hochstrasser, R. M. J. Phys. Chem. B 1998, 102, 6123–6138. (11) Rosenbaum, C. K.; Walton, J. H. J. Am. Chem. Soc. 1930, 52, 3568–3573. (12) Neese, F. Orca - An ab initio, DFT and semiempirical SCF-MO package, version 2.8.0; Bonn University, 2009. (13) Neese, F. J. Comput. Chem. 2003, 24, 1740–1747. (14) Becke, A. D. Phys. Rev. A 1988, 38, 3098–3100. (15) Perdew, J. P.; Yue, W. Phys. Rev. B 1986, 33, 8800–8802. (16) Eichkorn, K.; Treutler, O.; Ohm, H.; Haser, M.; Ahlrichs, R. Chem. Phys. Lett. 1995, 240, 283–289. (17) Schafer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 2571–2577. (18) Sinnecker, S.; Rajendran, A.; Klamt, A.; Diedenhofen, M.; Neese, F. J. Phys. Chem. A 2006, 110, 2235–2245. (19) Neugebauer, J.; Hess, B. A. J. Chem. Phys. 2003, 118, 7215– 7225. (20) Khalil, M.; Demirdoven, N.; Tokmakoff, A. J. Phys. Chem. A 2003, 107, 5258–5279. (21) Asplund, M. C.; Zanni, M. T.; Hochstrasser, R. M. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 8219–8224.

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(22) Zheng, J.; Kwak, K.; Xie, J.; Fayer, M. D. Science 2006, 313, 1951–1955. (23) Zheng, J.; Kwak, K.; Asbury, J.; Chen, X.; Piletic, I. R.; Fayer, M. D. Science 2005, 309, 1338–1343. (24) Cahoon, J. F.; Sawyer, K. R.; Schlegel, J. P.; Harris, C. B. Science 2008, 319, 1820–1823. (25) Kim, Y. S.; Hochstrasser, R. M. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 11185–11190. (26) Candelaresi, M.; Pagliai, M.; Lima, M.; Righini, R. J. Phys. Chem. A 2009, 113, 12783–12790. (27) Jansen, T. L. C.; Cringus, D.; Pshenichnikov, M. S. J. Phys. Chem. A 2009, 113, 6260–6265. (28) Graener, H.; Seifert, G. J. Chem. Phys. 1993, 98, 36–45. (29) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford University Press: New York, 1995. (30) Kwac, K.; Lee, H.; Cho, M. J. Chem. Phys. 2004, 120, 1477. (31) Kwak, K.; Zheng, J.; Cang, H.; Fayer, M. D. J. Phys. Chem. B 2006, 110, 19998. (32) Mootz, D.; Albert, A.; Schaefgen, S.; Staeben, D. J. Am. Chem. Soc. 1994, 116, 12045–12046. (33) Schurhammer, R.; Vayssiere, P.; Wipff, G. J. Phys. Chem. A 2003, 107, 11128–11138. (34) Kowall, T.; Geiger, A. J. Phys. Chem. 1994, 98, 6216–6224. (35) Kokubu, S.; Kusaka, R.; Inokuchi, Y.; Haino, T.; Ebata, T. Phys. Chem. Chem. Phys. 2010, 12, 3559–3565. (36) Kusaka, R.; Inokuchi, Y.; Ebata, T. Phys. Chem. Chem. Phys. 2007, 9, 4452–4459. (37) Kusaka, R.; Inokuchi, Y.; Ebata, T. Phys. Chem. Chem. Phys. 2008, 10, 6238–6244. (38) Kusaka, R.; Inokuchi, Y.; Ebata, T. Phys. Chem. Chem. Phys. 2009, 11, 9132–9140. (39) Saunders, M. Tetrahedron 1967, 23, 2105. (40) Uiterwijk, J. W. H. M.; Harkema, S.; Vandewaal, B. W.; Gobel, F.; Nibbeling, H. T. M. J. Chem. Soc., Perkin Trans. 2 1983, 1843–1855. (41) Wipff, G.; Weiner, P.; Kollman, P. J. Am. Chem. Soc. 1982, 104, 3249–3258. (42) Leuwerink, F. T. H.; Briels, W. J. J. Chem. Phys. 1995, 103, 4637–4652. (43) Straatsma, T. P.; Mccammon, J. A. J. Chem. Phys. 1989, 91, 3631–3637. (44) Billeter, M.; Howard, A. E.; Kuntz, I. D.; Kollman, P. A. J. Am. Chem. Soc. 1988, 110, 8385–8391. (45) Uiterwijk, J. W. H. M.; Harkema, S.; Feil, D. J. Chem. Soc., Perkin Trans. 2 1987, 721–731. (46) Fronczek, F. R.; Gandour, R. D.; Gehrig, L. M. B.; Caswell, L. R.; Mcdowell, K. A.; Alam, I. J. Inclusion. Phenom. 1987, 5, 379–383. (47) Anet, F. A. L.; Bourn, A. J. R. J. Am. Chem. Soc. 1967, 89, 760– 768. (48) Hasha, D. L.; Eguchi, T.; Jonas, J. J. Am. Chem. Soc. 1982, 104, 2290–2296. (49) MacPhail, R. A.; Variyar, J. E. Chem. Phys. Lett. 1989, 161, 239– 244. (50) Strauss, H. L. Annu. Rev. Phys. Chem. 1983, 34, 301–328. (51) Warshel, A. Nature 1976, 260, 679–683. (52) Theory of Unimolecular and Recombination Reactions; Gilbert, R. G., S.C., S., Eds.; Blackwell Scientific: Oxford, 1990. (53) Seifert, G.; Patzlaff, T.; Graener, H. J. Chem. Phys. 2006, 125, 154506–7.

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Ultrafast Internal Dynamics of Flexible Hydrogen-Bonded

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