The benefits of alternation and alkylation: large amplitude hydrogen bond librational modes of alcohol trimers and tetramers

Abstract

Intermolecular hydrogen bond librational modes in cyclic trimers and tetramers of methanol and t-butyl alcohol isolated at low temperature in pulsed supersonic jet expansions are observed by direct absorption spectroscopy in the far-infrared region. The large amplitude librational modes probe the strength and directionality of the intermolecular hydrogen bonds. In addition, their frequency and intensity is very sensitive to the angle which the alkyl groups form with the hydrogen bonded ring. Theoretical predictions which fail to describe the trends in cluster size, alkylation and symmetry splitting reported in this work are likely to miss important ingredients of the underlying intermolecular interaction. Analysis of the vibrational correlation diagram between planar and puckered tetramer structures circumvents some deficiencies of approximate treatments.

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1. Introduction

The interplay between cooperative hydrogen bonding, dispersion interaction and steric repulsion is a recurrent theme in molecular recognition. While it determines the structure of many crystalline organic solids,¹ its fundamentals may be understood in more detail by characterizing simple molecular clusters.² Alcohol clusters beyond the dimer tend to be cyclic because of the simultaneous realization of hydrogen bond donor and acceptor neighbors, which lead to cooperative enhancement. The latter is particularly pronounced in alcohols because donor (H) and acceptor (O) atoms are directly linked to each other. By tuning the alkyl group, the influence of inductive effects as well as dispersion and repulsive interactions can be studied. In particular, a comparison between odd-membered and even-membered rings reveals the influence of a short alkyl group contact.³ Such a contact is enforced in the trimer or pentamer, whereas it can be circumvented in the cyclic tetramer by alternating arrangements above and below the hydrogen bond plane.⁴ To avoid complications by conformational isomerism, it is advisable to compare t-butyl alcohol⁵ to the simplest organic compound capable of classical hydrogen bonding: methanol.⁶

A sensitive infrared probe for the perturbation of a hydrogen-bonded ring arrangement by bulky alkyl group interaction is provided by the hydrogen bond librational modes.⁷ They are shifted up in frequency by a substantial amount compared to the corresponding C–O-rotational or torsional motions in the monomer⁸ because of the anisotropic hydrogen bond forces which restrain the hydrogen atoms in the hydrogen-bonded ring plane. Any strengthening of the hydrogen bonds by electronic effects of the substituent and any weakening of the hydrogen bond arrangement because of competing dispersion or steric interactions between the substituents is expected to show up in the librational mode pattern. Furthermore, the relative rigidity of the C–O–H angle translates any displacement of the alkyl group into a change in the direction of the librational motion. This has consequences for the mode splittings and intensities which show up in the vibrational spectrum. In this way, the librational manifold is substantially more sensitive than the popular O–H stretching domain^6,9,10 for the characterization of hydrogen bonds. Furthermore, its role in intermolecular energy transfer is discussed controversially^11,12 and torsional degrees of freedom are of critical importance in the systematic development of molecular force fields for flexible molecules.¹³

In the present contribution, we describe a comparative far-infrared study of methanol and t-butyl alcohol trimers and tetramers in supersonic jets. It builds on an earlier, spectrally incomplete investigation of methanol clusters⁷ and represents an elementary case study of alkylation and ring alternation effects on hydrogen bonding in organic clusters. The jet cooling is required to ensure that sufficiently many of the clusters are in their vibrational ground state, therefore giving rise to relatively sharp IR absorption bands. Dedicated size-selection techniques^6,14 are not needed in this size range, because variations in the expansion conditions can be used to discriminate between trimers and tetramers if the concentration of the alcohol in the carrier gas is not too high.¹⁵ Due to their simplicity, these systems are also free of complications from isomerism.^4,16 Existing and future computational approaches for organic hydrogen bonds should be trained on this benchmark set in order to ensure that they describe the wide range of intermolecular interactions relevant for cohesion in aliphatic matter.

The observation of librational modes in hydrogen-bonded clusters has been limited by the availability of suitable light sources. While THz and diode lasers have been employed successfully for pioneering work in small systems^17,18 and large scale light sources such as free electron lasers allow for different kinds of action spectroscopy, we have followed a straightforward FTIR direct absorption approach using conventional black body light sources in combination with sensitive detectors and intense pulsed cluster sources for the larger organic molecules.^7,15 The loss of spectral resolution is compensated by the advantage that relative intensities can be evaluated in a semi-quantitative way across a wide spectral range.

2. Experiment

In the present study, we combine a 600 mm long slit jet expansion¹⁹ with photoconductive and bolometric detection. Giant 0.13–0.27 s gas pulses (up to 2 mol) of helium seeded with methanol or t-butyl alcohol are expanded into a 23 m³ vacuum buffer chamber through a 0.2 mm wide slit. The resulting supersonic jet expansion is synchronously probed by a single 2–4 cm⁻¹ resolution scan of a rapid-scan Bruker Equinox 55 FTIR spectrometer. The collimated infrared probe beams are focused and recollimated with a set of KBr lenses of 500 and 250 mm focal length mounted to the jet chamber to achieve a better overlap with the 600 mm zone-of-silence of the expansions. The buffer chamber is evacuated by a series of high capacity roots pumps at 2500 m³ h⁻¹. The stagnation pressure is 1.0 bar with alcohol concentrations in the range of 0.1% to 1.5%. The absorption spectra in the region above 600 cm⁻¹ (upper far-infrared region) are recorded with a globar radiation source in combination with a Ge-coated KBr beam splitter and a broadband 1 mm² area HgCdTe detector. The far-infrared absorption spectra below 600 cm⁻¹ (lower far-infrared region) are obtained using a Si-bolometer (Infrared Laboratories, Inc.) operating at liquid helium temperature. The Si-bolometer is equipped with a cold internal interference filter having a cut-off at 850 cm⁻¹ (Infrared Laboratories, Inc.). The slower response of the Si-bolometer relative to the HgCdTe detector limits the FTIR scan velocity and thereby the obtainable far-infrared spectral resolution in a given scan time. The larger values for the pulse duration and resolution thus apply to the bolometric spectra. Approximately 500 to 600 scans are collected and co-added for each of the far-infrared spectra shown.

The root-mean-square displacement of a harmonic oscillator is proportional to (μν)^−1/4, where μ is the reduced mass and ν the vibrational frequency. Hence, the present hydrogen bond libration study involves particularly large amplitude motion, because the librating hydrogen atoms are light and the frequency coverage down to 15 THz is the lowest one achieved to date using size-resolved FTIR cluster spectroscopy in supersonic jets.

3. Methanol results

The upper traces of Fig. 1 show such size-resolved far-infrared absorption spectra obtained for methanol expansions in the range from 500 to 875 cm⁻¹. Expansions at higher concentration¹⁵ had only revealed a broad, structure-less, asymmetric band near 730 cm⁻¹ which is completely dominated by larger clusters and resembles the bulk spectra of condensed methanol phases.^20,21 More dilute methanol samples have previously shown at least three well-resolved bands⁷ at 613, 695 and 760 cm⁻¹ (black trace in the top part of Fig. 1). We note that these bands are two orders of magnitude sharper than those in liquid alcohols,²⁰ suggesting that the width observed in the liquid state is largely inhomogeneous. Energy flow out of the librational manifold is seen to be relatively slow in these clusters at low temperature.¹¹

Fig. 1 Upper (HgCdTe) and lower (bolometric) far-infrared absorption spectra of methanol clusters (upper far-infrared region in the upper trace taken from ref. 7) and t-butyl alcohol clusters (lower traces) isolated in pulsed supersonic jet expansions. The proposed trimer and tetramer hydrogen bond librational bands are labeled with computed minimum structures. The tetramer “antiphase” (ap) and “in-phase” (ip) hydrogen bond librational bands are marked. The 750 cm⁻¹ band is assigned to overlapping intramolecular C–C stretching modes of t-butyl alcohol monomer and clusters. The weak spectral features around 667 cm⁻¹ marked with asterisks originate from insufficiently compensated CO₂.

Based on dedicated concentration dependence studies, direct comparison with corresponding absorption spectra in the O–H stretching region⁴ and supportive quantum chemical predictions, the observed band at 613 cm⁻¹ could be assigned to a high frequency hydrogen bond libration mode of the “chair” conformation of methanol trimer, the only conformation present in such expansions⁴ (see Fig. 1). In this conformation, two methyl groups point up and one down, relative to the hydrogen bond plane. A lower-frequency trimer libration was observed near the band gap of the employed HgCdTe detector and could not be unambiguously identified. Now, with the use of the Si-bolometer detector (right trace), it is clearly visible with relatively high IR intensity at 551 cm⁻¹. The third librational band of methanol trimer is expected at higher frequency (around 730 cm⁻¹)⁷ and with little IR intensity. Attempts to identify this band by Raman jet spectroscopy²² have so far been unsuccessful.

The spectral splitting and intensity pattern of the librational modes of methanol trimer are sensitive probes for symmetry breaking due to the methyl groups above and below the hydrogen bond plane in the C₁-symmetric structure. If they were located in the hydrogen bond plane (C_3h symmetry) or all on one side of the ring (C₃ symmetry²³), the two lowest of the three librations would become degenerate (and IR-inactive in the case of C_3h symmetry). A quantitative quantum chemical analysis of the mode pattern as a function of methyl group displacement is difficult due to a lack of symmetry. It is illustrated in Fig. S1 and S2 in the ESI,† using two structural one-parameter models. The first model assumes that two methyl groups are located at a distance of ±d above and below the oxygen plane and the third one is allowed to move freely. The second model assumes that two methyl groups are located at a distance of d above the plane and the third one is allowed to move freely. The latter model should be more realistic according to predictions for the fully optimized trimer structure without any constraints on the methyl group displacements (d = 91, 92 and −106 pm). The observed frequency and approximate intensity ratios of the two librational bands are then used to determine d in the quantum-chemical diagram, but depending on the quantity and model, different results are obtained. While the frequency splitting pattern matches experiment rather nicely, the intensity pattern does not. We will see below that the analogous tetramer analysis is more conclusive because of its symmetry.

The most stable conformation of the cyclic methanol tetramer has S₄ symmetry⁴ (see Fig. 1). The methyl groups alternate between the sides of the hydrogen-bonded plane formed by the four oxygen atoms. The two observed bands at 695 and 760 cm⁻¹ have previously been assigned⁷ to the two IR-active hydrogen bond libration modes of this methanol tetramer: one doubly degenerate librational mode (E representation) at 760 cm⁻¹ where opposite methanol units move against each other with respect to the center (antiphase, denoted “ap”) and a lower frequency librational mode at 695 cm⁻¹ (B representation) where opposite units move in-phase and neighboring units move antiphase (denoted “ip”). The third and highest frequency librational mode (A representation), in which all four monomers move in-phase, is exclusively Raman active. The complete hydrogen bond librational mode assignments of methanol trimer and tetramer are listed in Table 1.

Table 1 The observed band origins (in cm⁻¹) for the most IR-active hydrogen bond librational modes of cyclic methanol (MeOH) and t-butyl alcohol (t-BuOH) trimers and tetramers isolated in supersonic jet expansions

(MeOH)3	(t-BuOH)3	(MeOH)4	(t-BuOH)4
a Ref. 7. b Tentative assignment based on the concentration dependence spectral series shown in Fig. 2.
551	564	695^a	(705)^b
613^a	614	760^a	777

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4. t-Butyl alcohol results

The lower part of Fig. 1 illustrates the spectroscopic consequence of replacing all CH₃ groups by C(CH₃)₃ groups, making the alcohol substantially more bulky. Spectroscopic and quantum chemical studies⁵ have shown that this has no qualitative effect on the trimer and tetramer structure. Indeed, the observed spectra show striking similarities to the corresponding methanol spectra with the exception of a strongly concentration dependent band at 750 cm⁻¹, which will be discussed below. The absolute intensities of the bands cannot be compared between methanol and t-butyl alcohol spectra, because monomer and cluster concentrations differ. In the lower far-infrared region the two well-resolved bands observed at 564 and 614 cm⁻¹ (red trace in the lower part of Fig. 1) can be unambiguously assigned to the two strongly IR active librational modes of the cyclic “chair” configuration of the trimer. Apart from the similarity to the methanol trimer spectrum, this also follows from the observed concentration dependence of the bands. The spectral splitting between these two hydrogen bond librational modes amounts to 50 cm⁻¹. This is smaller than the splitting of 62 cm⁻¹ observed for the corresponding bands of the methanol trimer, whereas the average position of the two librational bands is actually somewhat higher.

Several qualitative explanations may be put forward for this finding and must ultimately be verified by high-level quantum chemical calculations, which are quite challenging for such a bulky hydrogen bonded cluster.⁵ The higher average position of the librational bands points at a stronger hydrogen bond in t-butyl alcohol trimer, consistent with the inductive effect of the methyl groups, which improves the acceptor quality of the oxygen.²⁴ The reduced splitting may correspond to a change in puckering of the alkyl groups. Conceivably, the bulky t-butyl groups which sit on the same side of the hydrogen bond plane may be forced further towards the molecular plane. On the other hand, the low symmetry of the complex allows for other distortions, which may actually increase the average puckering extent. Only a theoretical approach which correctly describes the repulsion, electrostatics and dispersion attraction will be able to reproduce this trend reliably.

B3LYP calculations are unlikely to capture these driving forces for the cluster structure.⁵ One might still expect that the correlation between alkyl group displacement d and librational mode pattern is described correctly, because it is governed by geometric and electronic features of the underlying hydrogen bonds. However, the lack of symmetry in the trimer leads to an ambiguous displacement coordinate and prevents a straightforward interpretation in this case (see Fig. S1 and S2 in the ESI†).

In order to propose librational mode assignments for the cyclic tetramer of t-butyl alcohol we consult the concentration dependence series of the upper far-infrared region shown in Fig. 2. In this region at least two strong well-resolved bands are observed at 750 and 777 cm⁻¹. In addition, a weaker band may be tentatively assigned at 705 cm⁻¹ for the high concentration regime. The concentration dependence of these three bands relative to the proposed trimer librational band at 614 cm⁻¹ suggests a higher cluster size origin.

Fig. 2 Far-infrared absorption spectra in the 575–850 cm⁻¹ region of t-butyl alcohol clusters seeded in He at three different concentrations (lower trace 0.1%, center trace 0.2% and upper trace 0.5%). Important reproducible spectral features are marked by full and dashed vertical lines. The spectral features around 667 cm⁻¹ marked by asterisks originate from variations in the atmospheric CO₂ concentration.

The rather broad band observed at 750 cm⁻¹ shows the steepest concentration dependence. It is also present in the monomer, as evidenced by gas phase and matrix isolation data.²⁵ This band may be attributed to weakly clustering-sensitive overlapping intramolecular symmetric C–C stretching (or monomer breathing) modes of t-butyl alcohol. The overlap between the monomer and cluster C–C stretching bands explains the width and the strong concentration dependence of this band. Indeed, harmonic quantum chemical calculations (B3LYP/6-311+G(d,p)) indicate that this mode hardly changes in frequency with clustering, being predicted at 746 cm⁻¹ for the monomer, 744–747 cm⁻¹ for the dimer, 747–749 cm⁻¹ for the trimer and 745–748 cm⁻¹ for the tetramer. Its IR visibility is predicted to more than double upon clustering, on a per monomer basis. This explains its steep increase with concentration, because pentamers and larger clusters are also expected to contribute in the same range.

The band observed at 777 cm⁻¹ has a less pronounced concentration dependence and since the origin of this band is close to that of the doubly degenerate methanol tetramer librational mode at 760 cm⁻¹, we assign it to the corresponding doubly degenerate (E) libration mode where opposite t-butyl alcohol O–H subunits move against each other with respect to the center.

The predicted “up-down-up-down” tetramer structure with S₄ symmetry (Fig. 1) should give rise to another IR active hydrogen bond librational mode at lower frequency where opposite subunits move in-phase and neighboring subunits move antiphase (B representation). The corresponding spectral feature at 705 cm⁻¹ is surprisingly weak and only becomes visible in the jet spectrum recorded with 0.5% t-butyl alcohol (Fig. 2). We will provide an explanation for its weakness below.

At this point, we note that the proposed cluster size assignments are further supported by a combined series of infrared absorption spectra and Raman spectra in the O–H stretching region recorded for identical concentrations of t-butyl alcohol, which will be described in detail elsewhere²⁶ and which are fully consistent with cyclic minimum structures for t-butyl alcohol trimer and tetramer due to the lack of dangling O–H stretching bands and the number and intensity of the IR and Raman transitions.

Comparison between the t-butyl alcohol and methanol tetramer band positions reveals a different behavior than that for the trimers. Now, the average frequency of the librational bands and the splitting between them both increase, in line with a stronger hydrogen bond interaction in the bulkier alcohol cluster. This strengthening of the hydrogen bond upon alkylation is consistent with the expected inductive effect of the methyl group. However, the influence of ring puckering cannot be dismissed at this stage and the weakness of the B transition remains to be explained.

We have no trustworthy ab initio approach available which is able to describe the subtle balance between alkyl group attraction and repulsion across the ring in these systems involving up to 60 atoms. Note that B3LYP treatments invariably predict all discussed libration bands to be lower in frequency in the t-butyl alcohol clusters than in the methanol clusters, whereas experiment shows the opposite in all cases. Consistent with the librational frequencies, the B3LYP calculations predict hydrogen bonds to be shorter in the methanol clusters than in the t-butyl alcohol clusters. Our experimental data, although indirect in terms of structural quantities, cast doubt on this prediction. A reliable theoretical treatment would require large basis set MP2 or better CSSD(T) geometry optimizations followed by harmonic force field calculations.

However, the essence of the hydrogen bonding and electrostatics (but not of alkyl interaction) is probably captured reasonably well at B3LYP level. Therefore we adopt an approach in which we vary the extent of ring puckering for methanol tetramer at B3LYP/6-311++G(3df,2p) level, expressed by the distance d of the tertiary C atom from the hydrogen bond plane, optimizing all other degrees of freedom and calculating the librational frequencies along this distortion path. This is more rigorous in the symmetric tetramer case than in the trimer case, because one parameter fixes all alkyl group positions by symmetry.

Fig. 3 shows the result. It is seen that the vibrational B–E splitting (full triangles and circles, left scale) increases with puckering. By fitting the E/B frequency ratio to the experimental value, an effective value of d = 104 pm is extracted (upper vertical line) for the methanol tetramer. By adopting the experimental change in splitting observed in the t-butyl alcohol tetramer, one may conclude that the latter is further puckered to a value of d = 112 pm (indicated by an arrow attached to the vertical line). This frequency prediction has to be checked by the IR intensities, which are correlated in the bottom part of Fig. 3 (right scale).

Fig. 3 Predicted harmonic band origins and corresponding IR band strengths of the hydrogen bond librational modes (B,E and A S₄-point group representations) of the methanol tetramer at different restrained B3LYP/6-311++G(3df,2p) optimized geometries, fixing the methyl group carbon atoms alternatingly at a distance d/pm from the hydrogen bond (symmetry) plane. The band origin ratios and intensity ratios which match the observed spectra are indicated by solid vertical lines (d = 104 pm and 102 pm), respectively. The direction and length of the central arrow indicates how the value of d changes when going from B3LYP fully optimized methanol tetramer (d = 106 pm) to the tetramer of t-butyl alcohol (d = 124 pm). The direction and length of the upper and lower arrow indicates how the value of d changes according to the experimentally observed frequency and intensity ratios.

The IR intensity of the E-symmetric ap libration is strongly dependent on alkyl chain puckering. In a planar (C_4h) arrangement of all four COH fragments, it would correspond to an E_g vibration with vanishing IR activity. The methanol tetramer escapes this by puckering the hydrogen-bonded ring when the methyl groups are forced into the hydrogen-bonded plane, but the IR intensity still grows substantially with increasing d. In contrast, the B-symmetric in-phase vibration loses intensity with alkyl group puckering.

Fitting the approximate experimental intensity ratio of 3 : 1 (±30%) into the correlation, one obtains an effective d value of 102 pm (lower vertical line). Again, adopting the approximate experimental intensity ratio for the bulkier tetramer leads to an increased puckering, indicated by the lower arrow attached to the vertical line. It is reassuring that both frequency and intensity trends predict a more strongly puckered t-butyl alcohol tetramer, compared to methanol tetramer. Incidentally, the full optimization of these two tetramers at B3LYP/6-311++G(3df,2p) level (central arrow) also indicates a puckering enhancement when replacing the methyl hydrogens by methyl groups. It is about two times larger than estimated from the experimental data, and probably not as trustworthy. In particular, we should mention that MP2/6-31G(d,p) calculations indicate just the opposite, namely a decrease in puckering in the bulkier tetramer. It will be interesting to carry this analysis to larger basis sets.

We conclude that both the splitting and the intensity trends in our experimental IR spectra indicate that the t-butyl alcohol tetramer is about 10% more puckered than the methanol tetramer. A verification by microwave spectroscopy is difficult due to the non-polarity and the size of the system. A verification by electron diffraction is challenging due to the cluster distribution. A verification by high-level quantum chemistry predictions would be very desirable.

One aspect may interfere with this simple picture. It is conceivable that the nearby intramolecular C–C stretching modes of the subunits mix with the intermolecular hydrogen bond librational modes in the case of t-butyl alcohol clusters. Therefore, the intensity and exact position has to be viewed with some caution. However, the calculations and experimental data suggest a very weak dependence of this frequency on cluster size, vide supra. Therefore, it is likely that the splitting is dominated by vibrational coupling of the individual librational modes. The 10% magnitude of this coupling may be compared to the frequently analyzed much more subtle coupling of the OH stretching oscillators,^4–5,26 which amounts to only 2%. This confirms how sensitive the large amplitude librational modes react to cooperative enhancements along hydrogen bond sequences. The overall similarity of the coupling patterns for methanol and t-butyl alcohol underscores the liquid phase observation²¹ that hydrogen bond librational modes are effectively decoupled from the alkyl group motions. Their character is neither torsional nor C–O-rotational but rather they are genuine localized motions of the hydrogen-bonded H-atoms.

5. Conclusions

In summary, the comparison of size-resolved methanol and t-butyl alcohol trimer and in particular tetramer spectra in the librational window allows for several conclusions:

(a) Alkylation strengthens and stiffens the cooperative hydrogen bonds between alcohol molecules, as reflected in the increased average and individual frequencies of the librational modes. B3LYP calculations predict just the opposite.

(b) The energy flow out of the librational manifold remains comparatively slow, whereas the pronounced librational coupling patterns indicate fast excitonic energy flow within this manifold.

(c) Ring extension from three to four alcohol units stiffens the hydrogen bonds by a substantial amount, raising its librational frequencies by 10–30%.

(d) Bulky alkyl groups in ring clusters avoid each other either by alternation or (where this is not consistently possible in odd-membered rings) by more subtle changes in the puckering angles.

(e) The librational OH modes decouple from any motion of the alkyl groups, as soon as the molecules become engaged in a hydrogen bonded framework.

(f) From an analysis of the experimental tetramer coupling pattern as a function of puckering, it follows that t-butyl groups on the same side of the ring move closer together than methyl groups. This is possibly due to attraction by dispersion forces.

(g) On a technical level, our results show that it is possible to record size-resolved hydrogen bonded cluster FTIR spectra down to 20 μm in supersonic jets. Previous pioneering investigations either had to concentrate on larger clusters¹⁵ or shorter wavelengths.²⁷ The relative intensity information of this linear technique is crucial for the assignments.

A re-investigation of the OH stretching jet spectra of t-butyl alcohol clusters,⁵ which may serve as model systems for inverse micelle formation,²⁸ is expected to provide further insights into their structure and vibrational dynamics.

Acknowledgements

The authors would like to thank U. Schmitt for help and discussions. This work was supported by the Fonds der Chemischen Industrie and by the DFG research training group 782 (www.pcgg.de). RWL acknowledges fellowship grants from the Danish Research Council and the Carlsberg Foundation.

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Footnote

† Electronic supplementary information (ESI) available: Spectral splitting and intensity analysis for alcohol trimers. See DOI: 10.1039/b925578h

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