Hydrogen-Bonding-Induced Enhancement of Fermi Resonances

Article pubs.acs.org/JPCB

Hydrogen-Bonding-Induced Enhancement of Fermi Resonances: A Linear IR and Nonlinear 2D-IR Study of Aniline‑d5 Christian Greve, Erik T. J. Nibbering,* and Henk Fidder* Max Born Institut für Nichtlineare Optik und Kurzzeitspektroskopie, Max Born Strasse 2A, D-12489 Berlin, Germany S Supporting Information *

ABSTRACT: Hydrogen bonding of the amino group of aniline-d5 results in a huge enhancement of the NH2 bending overtone absorption strength, mainly attributed to the Fermi resonance effect. A quantitative analysis is presented, using a hybrid mode representation and encompassing experimental data on aniline with 0, 1, or 2 hydrogen bonds to dimethylsulfoxide (DMSO). Changes in enthalpy, hydrogen-bondinginduced frequency shifts, and the transition dipole moment increase of the local N−H stretching oscillator all demonstrate that the hydrogen bond is strongest in the single hydrogen-bonded complex. Linear IR overtone spectra show that the oscillator strength decreases upon hydrogen bonding for the N−H stretching overtones, which is opposite to the effect on the fundamental N−H stretching transitions. Polarization resolved 2DIR spectra provide detailed information on the N−H stretching overtone manifold and support the relative orientations of the various IR transitions.

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Fermi resonances14 occur when energy levels of different vibrational modes are (nearly) degenerate. The Fermi resonance phenomenon leads to mixing of these vibrational modes, producing new wave functions that are linear combinations of the uncoupled modes and, concomitantly, a transfer of oscillator strength. The latter effect makes that nearly dark overtone, or combination transitions can become prominent features in linear IR spectra. Fermi resonances are ubiquitous in vibrational spectroscopy. Fermi resonances of the hydrogen X−H stretching ν = 1 state with fingerprint overtone or combination states, as well as anharmonic coupling to lowfrequency hydrogen bond deformation modes, lead to complicated hydrogen stretching manifolds of medium strong hydrogen-bonded systems, such as acetic acid dimers,15,16 7azaindole dimers,17,18 or 2-pyridone dimers.19,20 This makes a proper assignment of O−H or N−H stretching mode spectroscopic signatures a far from trivial task.21−28 The local mode description29,30 has proven highly successful in understanding fundamental and overtone spectra of hydrogen stretching oscillators of small molecules. These theoretical studies have only recently been extended to O−H stretching overtone transitions in hydrogen-bonded water dimers and trimers.31,32 The primary goal of the investigations presented here is to obtain direct insight into the influence of hydrogen bonding upon properties of Fermi resonances. Stimulated by our

INTRODUCTION Hydrogen bonding of amine functional groups is a common feature of biological macromolecules and plays a key role in the folding of proteins and nucleobase pairing in DNA and RNA. The importance of the amino functional group is evident in fields as diverse as pharmaceutical, medicinal, agricultural, and natural product chemistry.1 Hydrogen bonding of amino groups affects the kinetics of many amine compounds in elementary reactions such as electrophilic substitution, electron transfer, and proton transfer.2−6 Infrared spectroscopy has been utilized extensively in the characterization of hydrogen bonds.7−11 Typical vibrational signatures of hydrogen bonding are a lowering of the involved hydrogen X−H stretching mode frequencies, accompanied by an increase in oscillator strength of these modes, and a broadening of the stretching infrared absorption bands. The magnitude of these effects reflects the strength of the formed hydrogen bond. Polypeptide conformations and hydrogen-bonded nucleobase pair geometries have been determined using experimental gas-phase IR spectroscopy data and calculated IR N−H stretching frequencies.12 Recently, we presented a combined NMR, FTIR, 2D-IR, and DFT study of adenosine-thymidine (A-T) base pairs in chloroform solution.13 We observed that one of the strongest A-T absorption bands (at 3188 cm−1) in the N−H stretching region essentially disappeared upon 50% H/D exchange. We ascribe this band to the Fermi resonance14 enhanced NH2 bending overtone of adenosine. This raises the question whether the Fermi resonance effect can cause intrinsically weak overtone transitions to become as strong as allowed fundamental transitions of hydrogen-bonded N−H stretching vibrations. © 2013 American Chemical Society

Special Issue: Michael D. Fayer Festschrift Received: August 22, 2013 Revised: September 3, 2013 Published: September 3, 2013 15843

dx.doi.org/10.1021/jp4084103 | J. Phys. Chem. B 2013, 117, 15843−15855

The Journal of Physical Chemistry B

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regions, whereas N−H stretching overtone spectra were measured with a Perkin-Elmer Lambda 900 spectrometer. Femtosecond 2D-IR photon-echo spectra were recorded as described before.49 Mid-IR pulses, generated by frequency down-conversion of the output of an amplified Ti:sapphire laser system, were split into two phase-locked pulse pairs using a beam splitter and reflective diffractive optics setup, providing about 500 nJ of energy for each pulse with a pulse duration of about 55 fs and a bandwidth of >250 cm−1. Three pulses were used to generate the nonlinear third-order photon-echo signal of the sample for variable time delays between the first two pulses (coherence time) and a fixed delay of 125 fs between the second and third pulses (population waiting time T). The nonzero waiting time was chosen to eliminate signals from mixed time ordering in the system−field interactions that occur during pulse overlap. The fourth pulse was attenuated by 99% to serve as a local oscillator for phase-resolved heterodyned signal detection using spectral interferometry. Applying a Fourier transformation with respect to the first coherence time interval provides the absorptive nonlinear molecular response in two frequency dimensions, correlating excitation and detection frequencies. The accuracy of the frequency positions of the peaks in the 2D spectra is mostly limited by our spectrometer resolution of 8 cm−1 and the finite signal-to-noise ratio of the recorded interference traces prior to Fourier transformation. The 2D-IR spectra were recorded for two different linear polarization geometries having all pulses with parallel polarization (ZZZZ) and having pulses 1 and 2 with orthogonal polarization to that of pulse 3 and the local oscillator (ZZXX). Aniline-2,3,4,5,6-d5 (98% atom D), DMSO (purity > 99.8%), and CCl4 (purity > 99.8%) were obtained from Sigma-Aldrich. DSMO was carefully dried using molecular sieves with pore diameters of 0.3 nm. Solutions were held between CaF2 windows with Teflon spacers, providing path lengths of 20 μm−10 mm for the FT-IR spectra and of 50−200 μm in the 2D-IR measurements and quartz cells with 12 or 50 mm path lengths for the overtone spectra.

observations on A-T base pairs, we decided on an investigation of hydrogen-bonded complexation of aniline-d5 (C6D5NH2, abbreviated as An) with dimethylsulfoxide (DMSO). We chose this deuterated compound instead of aniline-h7 because in the latter, significant mode mixing occurs between the NH2 bending fundamental at 1619 cm−1 and a ring CC stretching mode at 1602 cm−1. In An, this stretching mode is lowered to 1573 cm−1 and thereby effectively decoupled from the bending mode. Aniline is a representative model system for DNA nucleobases,33,34 which, due to its characteristic amino group, can illustrate the effect of hydrogen bonding of N−H stretching oscillators on Fermi resonances with NH2 bending overtone transitions. Moreover, as a fairly small molecule, aniline has a relatively sparse vibrational manifold in the N−H stretching region,35−41 and therefore, the number of meaningful Fermi resonances that need to be considered is still limited. By varying the DMSO concentration in ternary mixtures of An and DMSO in tetrachloromethane (CCl4), we can change the composition from only free An through predominantly single hydrogenbonded An···DMSO to almost exclusively double hydrogenbonded An···(DMSO)2 complexes. A dramatic Fermi resonance enhancement occurs as a result of the hydrogen bonding. Previous studies on the role of hydrogen bonding on Fermi resonances have only focused on the analysis of linear IR spectra of fundamental and overtone hydrogen stretching transitions. O−H stretching oscillators of hydrogen-bonded systems such as water or methanol typically show, however, substantial line broadening under room-temperature solution conditions,42 and detailed information of the vibrational structure of O−H stretching manifolds can only be obtained from low-temperature clusters in the gas phase.43,44 We show here that with a combined approach of linear IR and nonlinear ultrafast 2D-IR spectroscopy, it is possible to obtain direct insight into the anharmonicities, couplings, and relative orientations of transition dipole moments of N−H stretching oscillators of the hydrogen-bonded An complex even in roomtemperature solutions. After reporting experimental details, we first present a kinetic analysis of concentration-dependent linear IR spectra, allowing us to extract the linear fundamental and first overtone IR spectra of the An monomer, single An···DMSO, and double An···(DMSO)2 hydrogen-bonded complexes. This is followed by a quantitative analysis of the vibrational structure of the fundamental N−H stretching manifold using a hybrid mode representation consisting of two local N−H stretching and an NH2 bending degree of freedom, from which the relative strength of the hydrogen bonds in the single An···DMSO and double An···(DMSO)2 hydrogen-bonded complexes is derived. This detailed analysis is not possible for the first overtone N−H stretching manifold due to substantial spectral overlap and insufficient experimental input data. The potential of ultrafast 2D-IR spectroscopy in mapping out the level structure of overtone manifolds is demonstrated. In contrast to linear IR overtone spectroscopy, these 2D-IR assignments are unambiguous because 2D-IR peaks simultaneously reveal intermediate states related to the overtone levels.45−48 We conclude with a summary of the main findings and ponder on the potential of 2D-IR spectroscopy for studies on overtones.

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LINEAR IR SPECTROSCOPY EXPERIMENTS AND KINETIC ANALYSIS Figure 1a shows linear FT-IR spectra in the NH2 stretching spectral region of ternary An/DMSO/CCl4 mixtures. The An concentration is kept fixed at 0.4 M, and the amount of DMSO in the solution is varied. Upon hydrogen bond formation of An with DMSO, more drastic changes occur than a mere frequency downshifting of the N−H stretching modes. The symmetric and asymmetric NH2 stretching transitions of the An monomer, measured at 0 M DMSO, can be identified unambiguously at 3395 and 3480 cm−1, respectively, and a weak structure is seen at around 3200 cm−1 that is mainly ascribed to the Fermiresonance-enhanced NH2 bending overtone transition (at 3216 cm−1) (As a side note, changes from self-association of An are minor from 0.04 to 0.4 M, i.e., a ∼2 cm−1 red shift of the stretching bands and ∼2% increase of the stretching band extinction coefficients, and therefore, nearly all An is in monomeric form.) The FT-IR spectra with increasing DMSO concentration reflect a gradually changing mixture of different complexes of An with DMSO in solution, each contributing with their own vibrational manifolds to the N−H stretching spectral region. An a priori assignment of particular peaks to particular complexes cannot be made without additional analysis. Some of the key features in Figure 1a are (a) the

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EXPERIMENTAL DETAILS A Varian 640 FT-IR spectrometer equipped with a Specac variable temperature unit was used to record linear FT-IR spectra in the fundamental N−H stretching and NH2 bending 15844



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of An···DMSO in the mixture, whereas the broad band at 3402 cm−1 appearing at high DMSO concentrations is related to the An···(DMSO)2 complex. A series of IR spectra for samples with DMSO concentrations increasing from 0 to 0.6 M in steps of 0.1 M was successfully decomposed in a varying sum of the An monomer spectrum (0 M DMSO spectrum) and an additional spectrum representing the An···DMSO species IR absorption spectrum. With the knowledge that the sum of the concentrations [An], [An···DMSO], and [An···(DMSO)2] is 0.4 M, we can reconstruct all spectra in Figure 1a as a varying sum of the extracted An and An···DMSO spectra and a third component that represents the An···(DMSO)2 spectrum. We are thus able to determine the fractions of various complexes as a function of the DMSO concentration, as shown in Figure 1b, together with fits based on the above kinetic scheme (for more details see the Supporting Information (SI)). It appears that at room temperature (23 °C), the behavior for DMSO concentrations of 0−2.5 M is mainly governed by Keq1, with Keq1 = 4(±1) dm3 mol−1 (see Figure SI-1, SI), whereas at higher DMSO concentrations, Keq2 has a dominating influence on the composition. The data in Figure 1b are well-described with Keq2 = 0.18(±0.05) dm3 mol−1 for DMSO concentrations up to ∼4 M, whereas at higher DMSO concentrations, higher values of Keq2 are needed. The data suggest that Keq2 = 0.85 dm3 mol−1 is required for 0.4 M An in pure DMSO. Analysis of temperature-dependent IR spectra for samples of 0.4 M An and 4.0 M DMSO in CCl4 and for 0.4 M An in pure DMSO (13.6 M) confirm higher values of Keq2 in pure DMSO at all temperatures (see the SI for more details on temperaturedependent data and the extraction of thermodynamic parameters from these). As illustrated by Figure 1b, varying the relative amount of DMSO and CCl4 in ternary mixtures with constant 0.4 M An concentration enables us to change the composition of the sample from unassociated An monomers, through predominantly single hydrogen-bonded An···DMSO complexes, to nearly exclusively double hydrogen-bonded An··· (DMSO)2 complexes. Through the above analysis, we now have access to the isolated linear IR extinction coefficient spectra of the various species An, An···DMSO, and An···(DMSO)2. The IR spectral regions 1540−1690 and 3120−3620 cm−1, encompassing the fundamental transitions of the NH2 bending and N−H stretching vibrations, respectively, are shown in Figure 2 for the various species extracted from the DMSO concentration dependence series. The inset in Figure 2 shows in greater detail the weak and highly structured band near 3200 cm−1 for the An monomer. Comparison to the spectral region of 1540−1690 cm−1, combined with fundamental mode assignments based on ab initio calculations,50 allows for unambiguous assignment of the An 3216 cm−1 peak to the bending overtone transition δ(NH2)0→2, and the weaker maximum at 3187 cm−1 is assigned to the combination mode ν(CC) + δ(NH2). The latter mode

Figure 1. (a) Spectral changes in the N−H stretching region of 0.4 M An for a selection of different ternary mixture compositions of An/ DMSO/CCl4. These spectra have been corrected for DMSO and CCl4 absorption. Addition of 0.4 M An dilutes pure DMSO from 14.1 to 13.6 M. (b) Dependence of the fractions of An monomer (black squares), An···DMSO (red circles), and An···(DMSO)2 (blue triangles) on the DMSO concentration for 0.4 M An in mixtures of DMSO and CCl4.

rise of a new band at ∼3345 cm−1 already upon addition of small amounts of DMSO, which increases up to ∼6 M DMSO concentrations and above that decreases slightly; (b) a gradual continuous rise and slight frequency upshift of the Fermi bending overtone feature near 3200 cm−1 with increasing DMSO concentration; and (c) the rise of a broad band at ∼3402 cm−1 for DMSO concentrations of 4.57 M and higher. The composition of the mixture of free An and hydrogenbonded complexes of DMSO with An in the ternary An/ DMSO/CCl4 mixtures is governed by the “reaction” scheme shown in Scheme 1, with equilibrium constants Keq1 = (k1/k−1) and Keq2 = (k2/k−2). With this scheme at hand, it seems clear that the initial rising band at ∼3345 cm−1 marks the appearance Scheme 1

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oscillator strength does not change noticeably. Although the oscillator strength increase of the N−H stretching modes in the region of 3300−3500 cm−1 is already impressive, it nevertheless pales in comparison to the immense intensity increase of the overtone transitions near 3200 cm−1. This enormous increase has two related causes, (a) stronger Fermi resonance enhancement due to a reduction of the energy gap, which leads to stronger mixing of the overtone and N−H stretching mode wave functions, and (b) the already mentioned intrinsic enhancement of the N−H stretching oscillator strength upon hydrogen bonding. Integration of the extinction coefficient spectra from ∼3100 to 3600 cm−1 gives the following integrated intensity ratios for this region An:An···DMSO:An···(DMSO)2 = 1: 4.9: 5.7

whereas the intensity increase in the bending overtone region alone is even 3−4 times stronger

Figure 2. Extinction coefficient of An (black), single hydrogen-bonded An···DMSO (red), and double hydrogen-bonded An···(DMSO)2, obtained from a series of FT-IR absorption spectra on samples with 0.4 M An and a varying concentration of DMSO in CCl4. Panel (a) shows data in the NH2 bending fundamental region, whereas the bending overtone and N−H stretching region are seen in panel (b). The inset in panel (b) displays the bending overtone region at higher resolution. The sketch in (c) shows the NH2 vibrational transition dipole moment orientations for the normal modes (symmetric stretch νs, asymmetric stretch νas, NH2 bending δ) and the local N−H stretch modes (ν1, ν2), which make an angle θ differing from the physical H− N−H angle φ.

An:An···DMSO:An···(DMSO)2 = 1: 17: 24

Under the assumption that nearly all overtone/combination mode oscillator strength is borrowed from the N−H stretching mode, we can estimate from the intensity increase in the 3100− 3600 cm−1 region a transition dipole moment enhancement of the hydrogen-bonded local N−H stretching mode(s) by a factor of 3.0 (±0.2) for the An···DMSO species and by a factor of 2.4 (±0.2) for the double hydrogen-bonded species. This indicates that the hydrogen bond is strongest in the single hydrogen-bonded species. This conclusion was reached by others for various aniline/solvent complexes41 and water/ solvent complexes39 and is further corroborated by a thermodynamic analysis (see the SI). In terms of Gibbs free energy, both equilibria of Scheme 1 favor the single hydrogenbonded species at 23 °C. The determined enthalpy reduction per hydrogen bond (ΔH) is −32.6 kJ/mol for An···DMSO and −27.5 kJ/mol for An···(DMSO)2, again indicating that An··· DMSO has the strongest hydrogen bond. This result can easily be rationalized as in An···(DMSO)2, the two hydrogen bonds compete in increasing the negative partial charge on the nitrogen atom. It is unlikely that doubling this negative charge, compared to the An···DMSO complex, will correspond to the energetic minimum. Linear IR absorption spectra were also recorded in the NH2 stretching first overtone region for 0.4 M An in pure CCl4 or pure DMSO and for 0.4 M An in CCl4 with 0.7 or 1.75 M DMSO (see the SI for raw data). Using the knowledge of the DMSO concentration dependence of the sample composition

can still be seen as a shoulder near 3200 cm−1 in An···DMSO but is no longer identified in An···(DMSO)2, which is likely the result of less Fermi enhancement of this mode combined with the 42% broadening of the bending overtone Fermi band. Peak positions, line widths, and assignments are listed in Table 1 for the species An, An···DMSO, and An···(DMSO)2. Comparison of the three species provides relevant insight into spectral and dynamical changes with varying degrees of hydrogen bonding. The IR spectra in Figure 2b for An with 0, 1, and 2 hydrogen bonds to DMSO show the characteristic hydrogen-bonding features, notably, a significant frequency downshift of hydrogen-bonded N−H stretching oscillators, accompanied by a large increase of their oscillator strength. In the NH2 bending fundamental region, on the other hand, the bending mode frequency clearly upshifts by ∼12 cm−1 per hydrogen bond (see Figure 2a and Table 1), while simultaneously, the maximum extinction coefficient drops and the bending mode absorption band broadens. Integration suggests that the bending mode

Table 1. Vibrational Frequencies [fwhm] (both in cm−1) and Mode Assignment for the Relevant Transitions Seen in Figure 2a mode assignment

An(max) (theory)

An(max)[fwhm] (exp.)

An···DMSO(max)[fwhm] (exp.)

An···(DMSO)2(max)[fwhm] (exp.)

ν(NH2)as or ν(NH2)f ν(NH2)s or ν(NH2)b δsci0→2 δsci + νCC (sum)c νCC0→2 δsci =δ(NH2);δ(CD) νCC =ν(CC);δ(NH2)

3493 3407

3480.5(±1) [39] 3395.5(±1) [27] 3216(±1) [31] 3187(±1) (3189.5) 3142.5(±1) 1616.5(±0.5) [13] 1573(±0.5) [6]

3461(±2) [45]b 3344(±2) [56]b 3227(±1) [44]

3402(±3) [75] 3337(±2) [46] 3233(±2) [44]

1659 1580

(3202)

(3213)

1629(±1) [23] 1573(±0.5)[6]

1641(±2) [33] 1572(±0.5) [6]

a Theoretical values and related mode assignments for the aniline-d5 monomer are taken from ab initio calculations in ref 50. bThe symmetric/ asymmetric stretch normal mode description is not valid for the single hydrogen-bonded complex. Here, we use the terminology ν(NH2)f and ν(NH2)b for the (fairly local) free and hydrogen-bonded N−H stretching modes. cThis is the sum of the observed fundamental frequencies δsci (notation for bending mode in ref 50) and νCC corresponding to this combination mode. Experimentally, the position of this combination mode is only reliably determined for the free aniline-d5 monomer.

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transition, whereas a destructive interference occurs for the first overtone hydrogen stretching transition. As a result, hydrogen bonding leads to an enhancement of the fundamental hydrogen stretching transition cross section and a diminishment of the first overtone hydrogen stretching transition cross section. For free An monomers, the integrated absorbance in the N−H stretching fundamental region, reported above, is 19 times larger than the integrated absorption in the N−H stretching first overtone manifold. Again, we assume that all oscillator strength originates through mixing from the N−H stretching transitions. For the various species, we obtain in the N−H stretching first overtone manifold region the following relative integrated intensities

depicted in Figure 1b, it becomes a relatively easy task to extract from these data the overtone extinction coefficient spectra of the An monomer, An···DMSO, and An···(DMSO)2 in the NH2 stretching first overtone region (6200−7000 cm−1; these are shown in Figure 3). The number of combination and

An:An···DMSO:An···(DMSO)2 = 1.0: 0.76: 0.52

Apparently, for complexes of An and DMSO, the integrated N−H stretching first overtone intensity decreases about 24% per hydrogen bond.

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Figure 3. Overtone extinction coefficient spectra of An monomer, An···DMSO, and An···(DMSO)2 in CCl4, extracted from the measured overtone spectra with 0.4 M An and a varying concentration of DMSO. The spectrum of An in CHX is also shown, which reveals additional features due to smaller solvent-induced line broadening.

QUANTITATIVE ANALYSIS OF LINEAR IR SPECTRAL CHANGES CAUSED BY HYDROGEN BONDING

With the extracted extinction coefficient spectra of the various species (free An monomer, An···DMSO, and An···(DMSO)2 complexes) at hand, we can now attempt a quantitative analysis of the main components in the N−H stretching fundamental spectral region. By reproducing the observed hydrogenbonding-induced oscillator strength enhancements and transition frequency shifts of the stretching modes and Fermi band, we intend to extract the oscillator strength enhancements and the diagonal frequency changes caused by hydrogen bonding and the coupling strengths between the two N−H stretching oscillators and between the N−H stretching excited states and the bending overtone states. The enormous absorption enhancement of the bending overtone through Fermi resonance is captured reasonably well with a simple model Hamiltonian, involving only three vibrational states, two N−H stretching mode states with one vibrational quantum and the NH2 bending overtone state δ(NH2)2 (the superscripted number signifies the number of vibrational quanta in a mode). In modeling linear IR spectral characteristics of the various complexes, we choose to set up the coupling Hamiltonian in a hybrid representation with as basis set {|ν(NH)11⟩, |ν(NH)21⟩, |δ(NH2)2⟩}, where ν(NH)n1 are the N−H stretching local mode states with one vibrational quantum. In this basis set, the effect of hydrogen bonding is directly made clear by the required frequency downshift of the local N−H stretching frequency (E(νlocal) → E(νlocal) − ΔHB). Alternatively, the problem can be defined in the normal mode basis {|ν(NH2)s1⟩, |ν(NH2)as1⟩, |δ(NH2)2⟩}, with |ν(NH2)s1⟩ = (|ν(NH)11⟩ + |ν(NH)21⟩)/√2 and |ν(NH2)as1⟩ = (|ν(NH)11⟩ − |ν(NH)21⟩)/√2. For An and An···(DMSO)2, this transformation eliminates the couplings of |ν(NH2)as1⟩ to both |ν(NH2)s1⟩ and |δ(NH2)2⟩ because in these cases, both local N−H stretching modes have the same decoupled energy, that is

overtone bands that may lead to Fermi resonances tends to increase drastically with increasing total vibrational energy. Considering only the NH2 bending and stretching modes, we should expect three discrete energy levels in the stretching fundamental region and already six in the first stretching overtone region. Added to that, the N−H stretching overtone spectral line widths appear larger than those of the fundamental transitions (cf. Figures 2 and 3). Together, this produces a recipe for congested spectra that are difficult to resolve in individual components. Added in Figure 3 is also the overtone spectrum of 0.4 M An in cyclohexane (CHX), which exhibits less line broadening. The comparison of the An in CCl4 and CHX spectra reveals an extra peak at 6730 cm−1, ascribed to the combination mode νas + νs. The strongest peak at 6692 cm−1 is assigned to νs0→2, and νas0→2 is seen in CHX at 6899 cm−1 (6892 cm−1 in CCl4). Furthermore, the shoulder at 6579 cm−1 in CCl4 shows in CHX two local maxima, resembling the substructure of the Fermi band in the stretching fundamental region, due to the bending overtone and the combination mode ν(CC) + δ(NH2). The spectra in Figure 3 show that the integrated oscillator strength in the N−H stretching first overtone region decreases markedly upon increased hydrogen bonding. This is in stark contrast to the well-known effect for the fundamental stretching transition of an absorption cross section increase upon hydrogen bonding (illustrated in Figure 2b). It is also counterintuitive as hydrogen bonding is expected to increase the anharmonicity along the N−H stretching coordinate, thus making the harmonically forbidden overtone transitions more allowed. Our observations are, however, in accordance with previous results for hydrogen-bonded phenol complexes.51 Using a simple model Hamiltonian consisting of a Taylor expansion up to cubic order, as well as expressing the molecular dipole moment up to the quadratic expansion term as a function of the stretching coordinate, it can be shown that a constructive enhancement of the different terms results for the IR cross section of the fundamental hydrogen stretching 15847



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Table 2. Comparison of Experimental Data and Calculations Based on the Hamiltonian Equation 1 An maximum (intensitya) mode ν(NH2)as or ν(NH2)f ν(NH2)s or ν(NH2)b δsci0→2 δsci + νCC

experiment 3480.5 (0.96) 3395.5 (0.90) 3216 (0.11) 3187 (0.03)

An···DMSO maximum (intensitya)

An···(DMSO)2 maximum (intensitya)

calculated

experiment

calculated

experiment

calculated

3480.5 (0.986) 3395.4 (0.919) 3216.1 (0.095)

3461 (2.24) 3344 (5.20) 3227 (2.34)

3454.7 (2.10) 3344.2 (6.22) 3227.1 (1.49)

3402 (4.47) 3337 (3.50) 3233 (3.43)

3400.5 (5.62) 3340.0 (3.55) 3232.5 (2.23)

Parameters for the Calculations Parameters Varied for the Various Complexes δ(NH2)0→2dec. (cm−1) (3233) (=2 × δ(NH2)) ΔHB (cm−1) μ(N−H)b (1.00) Parameters Fixed by Free An Monomer Calculation ν(NH)local (cm−1) V (cm−1) J (cm−1) θ (°)

(3258) (=2 × δ(NH2))

3233 (0)

2.97

3255 88

(3282) (=2 × δ(NH2))

3274 80

2.39

3429.5 −51 −37 89.2

a Intensities are in units of the free N−H stretching local mode intensity of the An monomer. This is based on setting the integrated intensity of the monomer in the region 3100−3600 cm−1 equal to twice the free N−H stretching local mode intensity. DFT calculations on nucleobases indicate, for instance, that the oscillator strength of ν(NH2)as and ν(NH2)s for An is about twice that of the N−H stretching in thymine.13,53

⎞⎛|ν(NH)11⟩ ⎞ ⎛ E(νlocal) J V ⎟ ⎟⎜ ⎜ ⎟⎜|ν(NH)21⟩ ⎟ E(νlocal) V H |ψ ⟩ = ⎜ J ⎟ ⎟⎜ ⎜ ⎟ ⎜ V E(δ 0 → 2)⎠⎜⎝|δ(NH 2)2 ⟩⎟⎠ ⎝V 1 ⎛ E(ν ) 0 V 2 ⎞⎛|ν(NH 2)s ⟩ ⎞ ⎟ ⎟⎜ ⎜ s ⎟⎜|ν(NH ) 1⟩⎟ E(νas) 0 = ⎜0 2 as ⎟ ⎟⎜ ⎜ ⎜ ⎟ 0 → 2 ⎟⎜ V E δ 2 0 ( ) ⎠⎝|δ(NH 2)2 ⟩ ⎠ ⎝

plexes. This is motivated by DFT calculations on the adenosine monomer53 and the adenosine-thymidine base pair,13 which indicated that the coupling J, leading to the symmetric/ asymmetric stretching separation, is mainly of kinetic origin and therefore not materially changed upon hydrogen bonding. In addition, the decoupled local N−H stretching E(νlocal) and bending overtone E(δ0→2) energies are varied to best match the observed spectral band positions of the free An monomer. The absorption intensities of the selected transitions can be calculated with the obtained vibrational wave functions (see the SI). For this, we need to define the orientations of the transition dipole moment vectors (see Figure 2c). It is assumed that the NH2 bending mode overtone obtains all of its intensity from the mixing with the N−H stretching modes (this also produced the best results for the hydrogen-bonded species). For An with 0 or 2 hydrogen bonds to DMSO, the pure asymmetric stretching mode ν(NH2)as is a (fairly) proper normal mode, and as illustrated by the Hamiltonian in the normal mode basis, mixing of the bending mode with only the symmetric stretching mode is expected. Therefore, the bending overtone obtains the same transition dipole moment vector orientation as the symmetric stretching mode, and both are perpendicular to the asymmetric stretching mode transition. For the single hydrogen-bonded complex An···DMSO, the bending overtone transition dipole moment is nearly parallel to the ν(NH2)b transition dipole moment; our calculations indicate an angle of 5.9°. However, the angles both make with the transition dipole moment of ν(NH2 ) f differ significantly from 90° (calculated values: 51.7 and 45.8°). Therefore, the polarization dependence is for the most expected to be similar for the three species. Note that the θ = 89.2° angle between the local N−H transition dipoles is much smaller than the physical H−N−H angle of φ = 113° (from experiment: ref 54; theory: 110.6° in ref 50 and ∼110° in ref 33). This difference reflects the participation of the C−N stretching coordinate in the properly defined N−H stretching modes. Table 2 shows a comparison between experimental and calculated values. The magnitude of the coupling parameters was restricted in these calculations by demanding that the uncoupled bending overtone frequency of the An monomer

(1)

with E(νs) = E(νlocal) + J and E(νas) = E(νlocal) − J. This also illustrates that “coupling” is a fluid concept that needs to be defined in its specific context.52 For An···DMSO, the decoupled energy of the hydrogen-bonded N−H stretching is ΔHB lower than that of the free N−H stretching mode. This energy gap between the local N−H stretching modes has a strong localizing effect, making the local modes closer to the true vibrational wave functions than the symmetric/asymmetric stretching modes. Obviously, the underlying physics is the same, and therefore, both approaches produce equivalent results. As previously found in DFT calculations for adenosine,53 even the NH2 symmetric and asymmetric stretching modes are typically not the correct wave functions for NH2 side groups. Normal modes conserve the center of gravity, and thus, proper N−H stretching normal modes necessarily contain some C−N stretching character. From microwave spectra for a series of aniline isotopes, Lister et al.54 deduced that the NH2 group of aniline-h7 makes an angle of 37.5° with the plane of the phenyl ring and nitrogen atom (theory: ∼42° in ref 50 and ∼28° in ref 33). A nonplanar geometry was also concluded for DNA nucleobases in their isolated form.33 However, in DNA double helices, the NH2 groups lie in the plane of the purine and pyrimidine ring systems. In chemical terms, this implies a change from sp3 to sp2 hybridization, with the nitrogen lone pair perpendicular to the hydrogen-bonding plane in DNA helices. Diagonalization of the coupling matrix gives the vibrational energies and wave functions. The coupling parameters V and J are fixed by modeling the free An monomer spectral characteristics and kept identical in the calculations for the hydrogen-bonded An···(DMSO) and An···(DMSO)2 com15848



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three-pulse photon echo technique, with the signal interfering with a fourth pulse (local oscillator) in the polychromator, allowing detection of the signal amplitude and phase. These 2D-IR spectra map correlations between transition frequencies during two coherent evolution intervals. The (positive) diagonal cross section of these spectra resembles the absorption spectra, but additional information about line-broadening mechanisms and dynamical processes is accessible through the peak shapes. Moreover, positive and negative cross peak pairs between two different vibrations can be identified, the energy separation of which reflects the influence of exciting one vibration on the transition frequency of the other, revealing connectivity between different vibrations. Analysis of connectivity patterns proves which absorption peaks/2D features are related to the same species in experiments on a mixture of compounds. Emergence of new cross peaks with waiting time T (time delay between the second and third pulses) can be an indicator for interconversion of two species (e.g., An···DMSO into An). Additional negative off-diagonal peaks can be identified with (ν1 = νn0→1, ν3 = νn1→2) for a mode n that provide information about the anharmonicity of vibrational mode n and which we will loosely refer to as ESA (excited-state absorption) peaks. Finally, the dependence of the cross peak intensities on the polarization sequence of the three excitation pulses provides information about the angle between the two involved transition dipole moments and is a useful tool in the assignment of various features. The following labeling is used: D(ν1) (positive, red) for diagonal peaks at (ν1 = νn0→1, ν3 = νn0→1) for a mode n, ESA(ν1,ν3) (negative, blue) for features associated with the D(νn) vibrational mode n 0 → 1 transition during the first coherence period and 1 → 2 transition (ESA) during the last coherence period, and X−(ν1,ν3), X+(ν1,ν3) for negative (blue) and positive (red) cross peaks between the vibrational modes of D(ν1) and D(ν3). We have recorded polarization-dependent 2D-IR spectra52,56,57 for three samples, each dominated by a single species. These spectra are shown in Figure 4, normalized on the strongest peak. As one can gather from Figure 1b, An in pure CCl4 contains only free non-hydrogen-bonded An, whereas in pure DMSO, ∼90% of the An molecules form the An··· (DMSO)2 complex. For the study of the single hydrogenbonded species, we have chosen a ternary mixture with 0.4 M An and 0.7 M DMSO, which contains about 36% An, 60% An··· DMSO, and 4% An···(DMSO)2 (see Figure 1b and the SI). This combination does not maximize the An···DMSO concentration, but because hydrogen bonding enhances all oscillator strengths in the fundamental N−H stretching manifold, prevalence is given at striking the right balance of achieving a low An···(DMSO)2 concentration while still having a large fraction of An···DMSO complexes. Comparison of the diagonal peak positions in Figure 4 to the linear spectra in Figure 2 confirms that each of these 2D-IR spectra mainly reflects a single species, An monomer (panels a0, b-0), An···DMSO (c-1, d-1), or An···(DMSO)2 (e-2, f-2). The 2D-IR spectra not only confirm the oscillator strength enhancement trend of the Fermi band upon hydrogen bonding but also reveal the emergence of cross peaks between the Fermi band and both N−H stretching bands upon hydrogen bonding. Intuitively, this might not be expected for the double hydrogenbonded species because perpendicular transitions are not expected to couple electronically, and this is a further indication that the couplings are mainly mechanical. Moreover, note that all 2D-IR spectra show standard off-diagonal patterns, with

cannot exceed twice the fundamental frequency (i.e., 3233 cm−1). Table 2 shows that with J = −51 cm−1 and only a Fermi resonance coupling of V = −37 cm−1 to the bending overtone state δ(NH2)2, we already obtain roughly 2/3 of the observed Fermi band intensity. The results are very sensitive to the coupling energies, as illustrated in the SI for calculations with J = −54.5 cm−1, which accomplishes quantitative agreement between the experimental integrated intensity of the Fermi band for both An and An···DMSO. The observed similar 1/3 discrepancy can largely be attributed to contributions from other modes, primarily the combination mode ν(CC) + δ(NH2), responsible for roughly a quarter of the Fermi band intensity in free An (see Table 2). The coupling term J = −51 cm−1 between the local N−H stretching modes is significantly larger than the minimum absolute value of 42.5 cm−1, obtained as half of the energy separation of the symmetric and asymmetric stretching modes in the free monomer spectrum. For NH2 groups in free nucleobases,53,55 the latter approach gave values J = −55 to −58 cm−1, which are more in line with the value obtained in the modeling. Note that J is nearly identical to the −52 cm−1 (≈−37√2) coupling term between the bending overtone and the symmetric stretching (in normal mode basis). The extracted N−H stretching local mode frequency downshifts 88 and 80 cm−1 upon hydrogen bonding, again confirm that the hydrogen bond is strongest for the single hydrogen-bonded complex An···DMSO. In previous investigations on double hydrogen-bonded aniline−solvent complexes,40,41 it was tacitly assumed that the observed Fermi band/ν(NH2)s energy separation was entirely due to the Fermi coupling (degenerate decoupled states). This results in too large values for the coupling between these modes and the frequency downshift caused by the hydrogen bonding. Summarizing this section, the fundamental N−H stretching manifold is well-described in a hybrid mode representation consisting of two local N−H stretching modes and the NH2 bending normal mode. Using a coupling of J = −51 cm−1 between the two local N−H stretching modes and a Fermi resonance coupling V = −37 cm−1 to take into account the Fermi resonance of the local N−H stretching modes with the δ(NH2)2 overtone state, a good correspondence is obtained for the observed frequency positions and intensities of all investigated species by varying the local N−H stretching mode frequency upon hydrogen bonding from E(νlocal) = 3429.5 cm−1 for the An monomer to 3342 cm−1 for An··· DMSO and 3350 cm−1 for An···(DMSO)2. Having extracted the local N−H stretching mode frequencies, one can conclude that the hydrogen bond is slightly stronger in An···DMSO than those in An···(DMSO) 2 , as is also reflected by the thermodynamic stability estimates from temperature-dependent IR spectra. Using the hybrid mode representation, we also learn that a normal mode picture |ν(NH2)s, ν(NH2)as, δ(NH2)⟩ is appropriate for the N−H stretching manifold for the An monomer and the double hydrogen-bonded An···(DMSO)2 complex but not for the single hydrogen-bonded An···DMSO complex.

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NONLINEAR 2D-IR SPECTROSCOPY EXPERIMENTS Femtosecond two-dimensional infrared (2D-IR) spectroscopy provides a direct way to obtain insight into the connectivity of various spectroscopic transitions and can give information on such varied processes as optical dephasing, spectral diffusion, energy transfer, population decay, and interconversion of chemical species. The experiment is performed here using the 15849



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lowest signal-to-noise ratio. Comparison to the measurement with perpendicular (ZZXX) polarization (panel b-0), which enhances cross peak features between nonparallel transitions, reveals that the signal at X+(3385,3475) is, with certainty, a cross peak, namely, between ν(NH2)s and ν(NH2)as. The observed cross peak enhancement below the diagonal by roughly a factor of 3 when changing the polarization geometry from (ZZZZ) to (ZZXX) is in accordance with the expected perpendicular orientation of their transition dipoles. The corresponding cross peak X+(3465,3385) mirrored in the diagonal is weaker as it roughly coincides with the ESA peak of the asymmetric stretching mode, which dominates this location in the parallel polarization measurement. Moreover, cross peaks between the bending overtone and both the symmetric and asymmetric N−H stretching vibrations are noticeable, especially for the perpendicular polarization scheme, even though the diagonal peak of the bending overtone barely exceeds the noise level. In the 2D-IR spectra of both An···DMSO (panels c, d) and An···(DMSO)2 (panels e, f), we can identify positive cross peaks between all transitions (below the diagonal). The polarization dependence confirms for both complexes approximately parallel transition dipoles for the δ(NH2)0→2 transition, which dominate the Fermi band, and the lowest N−H stretching transition. Furthermore, the spectra illustrate that both of these transitions are more or less perpendicular to the upper N−H stretching transition, because in the ZZXX polarization scheme, the intensity of cross peaks with this transition increases about 3 times relative to the diagonal peaks. The orientations are in agreement with the outcome of our model calculations (see the SI). In the spectra with parallel polarization configuration, the positive cross peak between the two N−H stretching transitions is above the diagonal, again hidden beneath the stronger ESA peak of the upper N−H stretching mode but clearly visible in the perpendicular polarization data. In both cases, the extracted diagonal anharmonicity of the upper N−H stretching mode is ∼75 cm−1, or slightly less than that for free An. For An···(DMSO)2, the lower N−H stretching ESA peak cannot be identified, but for An···DMSO, it is found at ESA(3345,3275), implying a 70 cm−1 diagonal anharmonic shift, significantly lower than that for free An. The observed “anharmonicities” are in reality the resultant of a complex interplay of decoupled normal/local mode anharmonicities and intermode coupling strengths in both the first and second N−H stretching vibrational manifolds, as illustrated in the previous section and the SI, and thus may not show predictable trends. This caveat also holds for the energy separation of positive and negative cross peaks, which typically are interpreted in terms of off-diagonal coupling only.52 In the 2D-IR spectra of An···(DMSO)2, not only has the diagonal Fermi peak become the most intense feature, but also, the overtone “ESA”-peak ESA(ν1 = δ(NH2)0→2 = 3233, ν3 = δ(NH2)2→4 = 3125) is prominently visible, which even for the complex An···DMSO is barely noticeable. This reflects the significant additional transition dipole enhancement of the Fermi transitions caused by the formation of the second hydrogen bond, as well as the nonlinear nature of the 2D-IR experiment. A comparison of these 2D-IR spectra to the overtone spectra in Figure 3 is interesting as negative off-diagonal peaks in the 2D-IR spectra can be correlated with peak positions in these overtone spectra. Whereas the overtone spectra correspond to a direct transition from the ground state to an overtone or

Figure 4. The 2D-IR spectra in the N−H stretching mode region for parallel (ZZZZ) and perpendicular polarizations (ZZXX) of 0.7 M An in CCl4 (panels a-0, b-0), 0.4 M An and 0.7 M DMSO in CCl4 (panels c-1, d-1) composed of about 36% An, 60% An···DMSO, and 4% An··· (DMSO)2, and 0.4 M An in DMSO (panels e-2, f-2) with composition 9% An···DMSO and 91% An···(DMSO)2. The number in the panel labels indicates the number of hydrogen bonds for the dominant species. All 2D-IR spectra were recorded for a 125 fs waiting time and are normalized on the highest intensity. Above each spectrum, the linear FT-IR spectrum of the sample (solid line; y-axis scale in OD) is shown, together with the intensity profile of the used laser pulses (dashed).

positive peaks at the cross points of two diagonal peaks. This contrasts with predictions of distinct peak patterns for Fermi resonances in a recent textbook on 2D-IR,52 based on an analysis with only harmonic oscillators. At this stage, we can directly determine whether particular vibrational transitions are caused by the same molecular species as the positive cross peaks at early waiting times T, connecting various diagonal peaks, reveal which vibrational transitions are present in the same molecular species. The An 2D-IR spectrum measured with parallel polarization of the four laser pulses, that is, ZZZZ (panel a-0) shows, apart from the diagonal features, two strong ESA peaks (negative), ESA(3380,3280) and ESA(3455,3395), which suggests anharmonicities of the symmetric and asymmetric stretching modes of about 115 and 85 cm−1, respectively. Recall that the spectrometer resolution of 8 cm−1 in the 2D-IR experiments limits the accuracy along the ν3-axis. A couple of positive features seen in panel a-0 are attributable to cross peaks. Because the transition dipole moments are smallest for An monomers, their normalized 2D-IR spectra will exhibit the 15850



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Figure 5. Level scheme for An monomer, An···DMSO, and An···(DMSO)2 in CCl4, as derived from the linear IR and nonlinear 2D-IR spectra. The rectangular boxes contain the frequencies ν1 and ν3, corresponding to identified linear IR and 2D-IR peaks. In the ket definition, the label NH2 is dropped in comparison to the text.

stretching modes as |ν(NH2)b, ν(NH2)f, δ(NH2)⟩ for the An··· (DMSO) complex (see also the SI). Note that the assigned labels mainly indicate the dominant wave function component as non-negligible mixing is to be expected (see the SI for approximate Hamiltonians). For both the complexes An··· (DMSO) and An···(DMSO)2, the 2D-IR spectra identify five of the six expected states. Tentative assignments of the five levels undetected in the 2D-IR spectra can be made on the basis of the linear IR overtone spectra in Figure 3 and are shown as dashed lines in Figure 5. Within experimental accuracy (about ±10 cm−1 for each method), the linear IR overtone and 2D-IR spectra of free An in CCl4 agree on the location of the symmetric stretch (6689 vs 6678 cm−1) and asymmetric stretch (6892 vs 6875 cm−1) overtone levels. Note that the overtone transition is much stronger for the symmetric stretching than for the asymmetric stretching mode, whereas in the 2D-IR spectra (panel a) the related ESA peaks have a more comparable intensity. The combination level νs + νas, which in the 2D-IR experiment is unambiguously fixed at 6729 cm−1 through its polarization behavior, is not identifiable in Figure 3 for An in CCl4, but in CHX, which causes less line broadening, a distinct additional peak is seen at 6730 cm−1. These three bands were also identified for aniline-h7 in previous work.58 Furthermore, a significant shoulder is seen in the overtone spectrum at 6580 cm−1, and two weak local maxima (see inset Figure 3) are detected at 6445 and 6345 cm−1. Because we still need to assign three levels, it is tempting to ascribe these three levels as |ν(NH2)s, ν(NH2)as, δ(NH2)⟩ = |0,1,2⟩, |1,0,2⟩, and |0,0,4⟩, respectively. The assignment of the 6345 cm−1 peak to the δ(NH2)0→4 transition is roughly supported by the model Hamiltionian (SI) and in particular by the unambiguous 2D-IR based assignments for the hydrogen-bonded species of the level dominated by the |0,0,4⟩ basis set element. The weak maximum at 6445 cm−1, however, could also be related to a ν(CD)0→3 overtone transition. The fundamental transitions of the CD stretching modes produce a complex peak shape with a maximum at 2277 cm−1 (ε ≈ 42 dm3 mol−1 cm−1), with a band

combination state, 2D-IR experiments create amplitude on the same overtone/combination wave functions through indirect excitation pathways, and thus, signal strength patterns tend to be widely disparate. A priori, the methods can give complementary information. As we can see, 2D-IR spectra provide much more detailed and reliable information on the specific overtone states as they map different excitation pathways leading to the same end state. This information on the intermediate state results in an unambiguous assignment of overtone/combination levels, which are here even further corroborated by the polarization dependence of the cross peaks. This is particularly relevant as the number of energy levels leading to Fermi resonances rapidly increases with the total vibrational energy. As mentioned above, six combinations of NH2 bending and stretching modes are expected in the first stretching overtone region, with larger spectral line widths than the fundamental absorption lines (cf. Figures 2 and 3) and therefore more spectral overlap. As with multidimensional NMR, these 2D-IR spectra demonstrate that dispersing the data over two dimensions reveals more details, allowing reliable extraction of single-species information even for a mixture of different complexes. The energy level scheme in Figure 5 summarizes the final states (solid lines) and excitation pathway information (arrows) identified through the 2D-IR spectra in Figure 4 for all molecular species. States of the first N−H stretching manifold are most accurately determined from the linear spectra in Figure 2. For none of the species are we able to identify all six expected levels in the second N−H stretching manifold, with inclusion of the NH2 bending mode, from the 2D-IR data alone. For the free An monomer, the 2D-IR spectra only allow identification of the three “pure” stretching mode levels as limited mixing leaves the levels with bending character too weak to be identified with our current detection sensitivity in the nonlinear experiment. The states are labeled with the number of quanta in the normal modes |ν(NH2)s, ν(NH2)as, δ(NH2)⟩ for the An monomer and for the An···(DMSO)2 complex and with quanta in the bound and free N−H 15851



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at 4470 cm−1 (ε ≈ 1.4 dm3 mol−1 cm−1) potentially the first overtone absorption. Extrapolating the frequency and extinction coefficient makes the 6445 cm−1 maximum (ε ≈ 0.02 dm3 mol−1 cm−1) a candidate for the ν(CD)0→3 transition as well. The relatively strong shoulder at 6580 cm−1 for the An monomer could belong to either |1,0,2⟩ or |0,1,2⟩, or both. In normal mode representation, the |0,1,2⟩ state couples only to the state |1,1,0⟩, and this coupling should result in a minimal splitting of V2√2 ≈ 105 cm−1, and thus, with |1,1,0⟩ at 6730 cm−1, the |0,1,2⟩ state should lie at ≤6625 cm−1. On the other hand, it seems reasonable to expect the overtone transition to the combination band ν(NH2)as1 + δ(NH2)2 to be much weaker than the ν(NH2)as overtone transition, in particular because the transition dipole vectors of their fundamental transition are perpendicular. As the intensity of the 6580 cm−1 overtone band seems comparable to the asymmetric stretching overtone band, it is more likely that it relates to the combination band ν(NH2)s1 + δ(NH2)2, for which the fundamental transitions are parallel. These deliberations illustrate the difficulty in arriving at convincing assignments on the basis of overtone spectroscopy only, even for a relatively simple molecule, and thereby illustrate the power of 2D-IR spectroscopy in arriving at detailed and reliable information on the overtone manifold level structure. Continuing the analysis with the hydrogen-bonded complexes, we observe from the overtone spectra in Figure 3 a number of complications further hampering a reliable interpretation based on linear overtone spectroscopy only. First of all, the hydrogen bonding apparently leads to a significantly lower integrated cross section for the N−H stretching manifold. Furthermore, while it appears that also for the overtone manifold the hydrogen bonding leads to transfer of oscillator strength to transitions involving bending mode character, the much broader and higher number of lines makes these merge in a single broad structure with several local maxima. This problem is further exacerbated by the findings from the fundamental transitions that hydrogen bonding increases the NH2 bending frequency while simultaneously lowering the N−H stretching frequencies, together resulting in a shrinking of the energy spread of the manifold, as also reflected in Figure 5, and thus more spectral overlap. For An···DMSO, only one level of the second manifold could not be identified with our 2D-IR data, namely, the |0,1,2⟩ state. We argue that the transition |0,0,0⟩ → |0,1,2⟩ contributes to the overtone peak with a maximum at 6640 cm−1. The energy separation of the levels |0,1,2⟩ and |1,0,2⟩ should to a first approximation be comparable to that of |0,1,0⟩ and |1,0,0⟩ (i.e., 117 cm−1), and thus, the level |0,1,2⟩ is expected around 6605 cm−1. This kind of argumentation is also supported by the level scheme of An···(DMSO)2, where the separations between the two pairs of stretching mode states that differ by two bending mode quanta are 66 (3404−3338) and 58 (6525−6467) cm−1. In the 2D-IR spectra for An···(DMSO)2, the level |2,0,0⟩ cannot be identified. Although the ν(NH2)s0→2 transition is clearly strongest in the An overtone spectrum, as well as the similar transition for An···DMSO, we associate this transition for An···(DMSO)2 with the slightly weaker maximum at 6520 cm−1, rather than the strongest overtone peak at 6610 cm−1. Two arguments (at least) support this assignment. If the |2,0,0⟩ level is connected to the 6610 cm−1 overtone peak, the related 2D-IR peak (|0,0,0⟩ → |1,0,0⟩, |1,0,0⟩ → |2,0,0⟩) with negative amplitude should be clearly visible as ESA(3338,3272) in the

data with the ZZZZ polarization configuration, but we do not observe a negative peak here. Association with the 6520 cm−1 maximum predicts ESA(3338,3182), implying that two overlapping negative peaks are responsible for the (3338,3129) negative peak in the An···(DMSO)2 2D-IR spectrum. In addition, as for both An and An···(DMSO)2, the normal mode scheme is applicable, and the main interactions are comparable; the separation between the levels |2,0,0⟩ and |0,2,0⟩ should be comparable for both, that is, about 200 cm−1, which also is more in agreement with assigning the |2,0,0⟩ state to the 6520 cm−1 peak than to the 6610 cm−1 peak. Summarizing this section, using the connectivities of the vibrational transitions during the first (ν1) and third (ν3) time evolution interval in the 2D-IR spectra, it is possible to determine most frequencies of the first overtone manifolds of An, An···DMSO, and An···(DMSO)2 and, more importantly, to make an unambiguous assignment of these levels. Polarizationresolved 2D-IR data confirm the relative orientation of transition dipole moments between the ν = 0 → ν = 1 and the ν = 1 → ν = 2 transitions for all three molecular species.

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CONCLUSIONS AND PROSPECTS We have presented a combined linear IR and nonlinear 2D-IR spectroscopic study of the fundamental and first overtone N−H stretching manifolds of An and of the complexes An···DMSO and An···(DMSO)2, where An is hydrogen bonded to DMSO. Hydrogen bonding of the amino group of An to DMSO leads to a tremendous increase of the absorption cross section of the bending overtone transition via a Fermi resonance with the N− H stretching levels. For the first time, the magnitude of this Fermi resonance and the N−H stretching transition dipole enhancement have experimentally been quantified, both for single and double hydrogen-bonded complexes of An with DMSO. As is well-known, the fundamental N−H stretching oscillator strength increases upon hydrogen bonding. In contrast, hydrogen bonding apparently decreases the N−H stretching overtone absorption strength. The origin of the Fermi resonance enhancement is demonstrated with a model that contains only the two local N−H stretching and the NH2 bending degrees of freedom and reveals a coupling of −51 cm−1 between the two local N−H stretching modes and of −37 cm−1 between each of these modes and the NH2 bending overtone. The vibrational wave functions produced by the model Hamiltonian confirm the applicability of the normal mode picture to the An monomer and the double hydrogen-bonded An···(DMSO)2 complex, that is, symmetric and asymmetric N−H stretching and the NH2 bending degrees of freedom. Instead, for the complex An···DMSO complex, the single hydrogen bond leads effectively to a decoupling of the local N− H stretching modes, resulting in nearly local free and bound N−H stretching modes. Hydrogen bonding reduces the energy gap between the bending overtone and excited N−H stretching levels as it leads to a frequency upshift of the NH2 bending vibration and a downshift of the hydrogen-bonded N−H stretching vibrations. The analysis demonstrates that the resulting increased mixing of the NH2 bending and N−H stretching modes, combined with the N−H stretching transition dipole enhancement, provides a quantitative explanation for the observed strong increase of the bending overtone oscillator strength. Analyzing the spectral changes with the Hamiltonian in hybrid mode representation directly reveals the changes in local N−H stretching frequency resulting from the hydrogen 15852



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stretching first overtone manifold for ternary mixtures of An/ DMSO/CCl4 without solvent corrections, modelling of the linear IR absorption fundamental N−H stretching region, and approximate Hamiltonian for the second N−H stretching manifold of An with inclusion of the NH2 bending mode. This material is available free of charge via the Internet at http:// pubs.acs.org.

bonding, irrespective of the mode mixing effects caused by the vibrational couplings. Empirical relationships between O−H/ N−H stretching frequencies and heavy-atom distances are usually relied upon in drawing conclusions about hydrogenbonded structures.8−11 Many hydrogen-bonded molecular complexes produce more involved spectral profiles with complicated substructure from low-frequency mode progressions and Fermi resonances, and for these, often the spectrally weighted average is taken as a measure of the hydrogen-bonded O−H/N−H stretching frequency of interest. This assumption is too simplistic if several coupled vibrational modes are IRactive, as illustrated here for the hydrogen-bonded complexes An···DMSO and An···(DMSO)2. Although the An···(DMSO)2 spectrum has a lower hydrogen-bonded N−H stretching transition than An···DMSO (even more so when including the bending overtone Fermi band into a weighted average), the vibrational analysis unequivocally shows that the hydrogenbonded local N−H stretching mode has a lower frequency in An···DMSO, and An···DMSO thus has a stronger hydrogen bond than the An···(DMSO)2 complex. This finding is also confirmed by a thermodynamic analysis based on temperaturedependent steady-state IR spectra. This work also demonstrates the potential of ultrafast 2D-IR spectroscopy in analyzing the energy level structure of overtone manifolds, leading to less ambiguous assignments than with linear 1D-IR overtone spectroscopy. Ultrafast 2D-IR spectroscopy maps pathways of sequential single quantum excitations, thereby directly revealing two different intermediate states, resulting in population of the same overtone state. In principle, it can also reveal polarization differences for the consecutive single quantum transitions, thereby providing information on the relative orientation of vibrational transition dipoles. Analogous to multidimensional NMR, mapping the data into two dimensions reduces spectral overlap of various overtone states compared to standard linear 1D-IR overtone spectroscopy. In general, single quantum transitions have more oscillator strength than double quantum transitions. Therefore, extension to n-dimensional IR spectroscopy for obtaining n − 1 intermediate states leading to the nth overtone manifold energy levels is feasible. Exploration of multidimensional IR spectroscopy may provide an interesting avenue for analyzing overtone manifolds, even for larger molecules. The experimental resolution of the fundamental and first overtone N−H stretching manifolds for An and its hydrogenbonded complexes with DMSO may also stimulate advanced quantum theoretical modeling studies. The additional resolving power provided by 2D-IR spectroscopy also makes it less necessary to reduce line broadening by studying low-temperature clusters in the gas phase and perform studies on condensed-phase systems instead. Finally, we emphasize that the profound Fermi resonance enhancement in aniline-d5 of the NH2 bending overtone transition due to hydrogen bonding presents a benchmark case. Fermi resonance enhancement of bending overtone transitions upon hydrogen bonding should be a general feature of amino groups, and taking them into consideration is essential for a proper interpretation of IR spectra of hydrogen-bonded amines, including DNA/RNA base pairs or double helix strands.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (E.T.J.N.). *E-mail: fi[email protected] (H.F.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 247051.

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REFERENCES

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Kinetic analysis of hydrogen-bonded complex formation between aniline-d5 and DMSO, IR spectra of the N−H 15853



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