Soft hydrogen bonds to alkenes: the methanol–ethene prototype under experimental and theoretical scrutiny

Theory meets experiment for the simplest model of alcohol–alkene hydrogen bonding and both support a close to harmonic description.


Introduction
Hydrogen bonds are ubiquitous in nature, governing molecular conformations and thus biochemical functionality. This holds not only for strong hydrogen bonds to heteroatoms, but also for weak OH/p interactions which have been associated with olfactory processes. 1,2 Detection of such weak interactions typically relies on the study of the sensitive vibrational signature of the donor OH bond and the spectroscopic "red shi" that usually accompanies bond formation. However, the low interaction energies in (weak) hydrogen bonds complicate the experiments in that association of the molecular constituents is eeting even at low temperatures. This demands for some sort of stabilization of the metastable clusters which is typically realized by means of supersonic expansions 3 or cryogenic matrices. 4 Embedding effects in the latter can distort the vibrational signature of weak OH/p bonds. Fixation of the donor and acceptor moieties in a common molecular frame is an alternative to increase the fraction of hydrogen-bonded structures, and O-H stretching red shis of up to 90 cm À1 have been found for various such intramolecular OH/p interactions in different environments. [5][6][7][8] However, it is difficult to elucidate the role that geometric strain and substituent effects have on the spectroscopic signatures in these cases. In contrast to aromatic OH complexes, [9][10][11][12] unconstrained olenic alcohol contacts remain surprisingly unexplored.
Quantum chemical calculations are customarily used to suggest structural motifs, dissociation energies and assignments to observed spectral features. Direct comparison between theory and experiment is typically hampered by the fact that anharmonic vibrational treatments are challenging except for small systems and rather simple methods. In addition, an experimental determination of anharmonicity via overtone bands 13,14 suffers from their low infrared intensity, which decreases as the strength of the hydrogen bond increases (conversely to the fundamental band). 15,16 Recently, we have been able to disentangle the 111 cm À1 red shi in the prototypical methanol dimer into its harmonic and anharmonic contributions, and high-level quantum chemical calculations have shown that many popular theoretical methods are inadequate for a quantitative description of the harmonic component. 17,18 In combination with FIR data, a consistent picture has emerged in which the increase in diagonal anharmonicity of the OH stretching oscillator upon bond formation is overcompensated by a large coupling to OHlibrational motion out of the bond, an effect which is absent in the free monomer. 18 Both the diagonal and off-diagonal anharmonic effects depend on the strength of the hydrogen bond itself, and it will be most interesting to contrast this model OH/O bond with a prototypical weak OH/p bond.
Such a prototypical hydrogen bond is found in the methanolethene model system, but it has so far only seen theoretical treatment in one study 19 and no explicit experimental characterization whatsoever. Here, we present for the rst time spectroscopic data on this important system (which we abbreviate "ME"), backed by high-level quantum chemical calculations. Further, the impact of the weak hydrogen bond on the anharmonicity of the OH stretching oscillator is characterized by both experiment and theory. We largely follow our earlier approach to the methanol dimer ("MM") 17,18,20 for which we also present new results from quantum chemical treatments. A specic problem that arises in methanol-ethene is the rotation of the ethene molecule around the hydrogen bond. In the equilibrium structure of the complex, the C]C bond is perpendicular to the mirror plane of the methanol molecule (see Fig. 1, le), as it has already been suggested previously. 19 We conrm that the rotation of the ethene unit around the hydrogen bond exhibits almost no barrier, which becomes problematic in the global energy minimum predictions among many quantum chemical treatments. We will address this aspect in greater detail when discussing its impact on anharmonic VPT2 calculations.

Jet-FTIR experiment
The jet-FTIR experiments were carried out using the "let" jet, which has been described in detail elsewhere. 21 Its unmatched eponymous feature is the "ne, but lengthy" 600 Â 0.2 mm 2 slit nozzle which is fed by 6 solenoid valves from a 67 L Teoncoated reservoir at typical stagnation pressures of P S ¼ 0.75 bar. The jet chamber is backed by 23 m 3 of buffer volumes and pumped continuously at 2500 m 3 h À1 pumping speed. The molecular beam is sampled by the mildly focused beam of a Bruker IFS 66v/S FTIR spectrometer at 2 cm À1 resolution, employing a 150 W tungsten lamp as the light source and CaF 2 optics. Cooled InSb and InGaAs detectors are used for fundamental and overtone measurements, respectively, in conjunction with appropriate optical lters to narrow their bandwidths. Typically, spectra are averaged from about 50 to 100 single scans for the fundamental region and about 1000 scans for overtones. Sample preparation is carried out from thermostatted liquid methanol ("M", Roth, $ 99.9%) through which a stream of helium is directed, and by admixture of ethene ("E", Linde, 99.9%) in helium stored in a gas cylinder at 50 bar.

Quantum chemical methods
Quantum chemical calculations were carried out using the MOLPRO 2012.1 (ref. 22) and GAUSSIAN09 (ref. 23) soware packages. The former features implementations of local-correlation methods (prex "L") which are advantageous in terms of computational resources while at the same time largely eliminating the basis set superposition error, 24 providing robust harmonic frequencies. 25 Specically, we rely on the explicitly correlated LCCSD(T*)-F12a method 26,27 with scaled triples ("T*"). The F12a ansatz was chosen over F12b for its fortuitous error cancellation observed when used in combination with small basis sets. 28 Inclusion of all intermolecular orbital pairs in the coupled-cluster correlation treatment, which is mandatory for correct predictions, is indicated by a suffix "(int)".
GAUSSIAN09 was used for canonical MP2 and B2PLYP-D3BJ calculations (including Grimme's empirical D3 dispersion 29 and Becke-Johnson damping 30 ). Further, anharmonic VPT2 calculations as implemented in the soware package 31,32 were carried out in order to obtain explicit estimates of anharmonicity constants, using the int ¼ ultrane grid integration option at the DFT level.
Most ab initio calculations were done using Dunning's correlation-consistent basis sets (aug-)cc-pVnZ, 33,34 which we abbreviate "(a)VnZ". For the explicitly correlated calculations, the VDZ-F12 basis set was used. 35 The use of explicit correlation in combination with the latter basis should be enough to provide results comparable to quadruple-zeta calculations or better. Density tting was employed throughout all local calculations, using the program's default aVnZ/JKFIT 36 and aVnZ/MP2FIT 37 basis sets; the F12a calculations made use of the VDZ-F12/OPTRI basis set. 38 In the current study, we refer to the LCCSD(T*)-F12a(int)/ VDZ-F12 method as our benchmark level of theory, as it has been found to be essentially converged to the basis set limit in the methanol dimer 17 while being computationally feasible even for numerical gradient and Hessian calculations.

Jet-FTIR spectra
For the jet-FTIR measurements in the fundamental region, a 2% mixture of ethene in helium was used, while the methanol concentration was controlled by cooling the liquid to À25 C. Together with the opening and closing times of the solenoid valves feeding the reservoir, we estimate a M : E ratio of about 1 : 20 in a 1300-fold excess of He, which was expanded at a stagnation pressure of P S ¼ 0.75 bar. Lower stagnation pressures down to 0.40 bar were also used to decrease the amount of larger aggregates. We identify the mixed ME dimer band at 3641 cm À1 (see Fig. 2), which corresponds to a red shi of 45 cm À1 from the methanol monomer fundamental position at 3686 cm À1 . The ME band is only 2 cm À1 higher in wavenumber than the corresponding band in the size-selected methanol-benzene complex, 11 supporting our mixed dimer assignment. Further cluster bands arise at lower wavenumber (">ME" in Fig. 2), which can be attributed to a bulk of ethene-rich structures and few distinct OH/OH stretching band pairs from methanol-rich clusters on grounds of their larger red shis. 39 This assignment is underscored by the distinct intensity evolution of these bands with respect to the 3641 cm À1 band when varying the relative Fig. 1 "Perpendicular" (left) and "parallel" (right) ME structures. Only the former is predicted to be a stable minimum, but low barriers to the torsion of the ethene unit may leave artifacts in harmonic and anharmonic approaches.
ethene concentration (Fig. 3). A more detailed analysis of these larger structures is out of scope for the current study and will be revisited later.
To facilitate the overtone measurements, a higher ME abundance in the expansion was obtained by using a richer 10% ethene mixture at a higher reservoir feeding pressure of 1.8 bar while raising the methanol temperature to À15 C, which results in a $1 : 7 M : E mixture in a 200-fold excess of He. This increases the rotational temperature and reveals the asymmetry of the ME band as being most likely due to residual rotational structure. Comparison of the fundamental and overtone spectra (Fig. 2) allows for the leading diagonal anharmonicity constant x OH,OH of the OH oscillator to be extracted from the fundamental and rst overtone band positionsñ fund OH andñ ot OH , respectively, with For the methanol monomer,ñ fund OH ¼ 3686 cm À1 andñ ot OH ¼ 7198 cm À1 yield a diagonal anharmonicity constant x OH,OH of about À86 cm À1 . 20 This anharmonicity increases to À99 cm À1 upon formation of the OH/O hydrogen bond in MM with n fund OH ¼ 3575 cm À1 andñ ot OH ¼ 6951 cm À1 . 20 Applying the same analysis to the 7105 cm À1 ME overtone band position from our spectra, we deduce a diagonal anharmonicity constant x OH,OH ¼ À89 cm À1 for the dimer, which differs only slightly from the monomer value.
In addition, anharmonic cross-terms x OH,i coupling the OH stretching motion to other vibrational modes must be considered when analyzing the fundamental band positions: In the methanol monomer, the cross-terms x OH,i were shown to be much smaller than 2x OH,OH . 20 However, the low-barrier torsional motion of the OH group becomes hindered upon formation of the hydrogen bond, and a distinct positive librational coupling term x OH,lib to the stretching mode arises; in the homodimer, it amounts to some 60 cm À1 . This value is again sensitive to the strength of the hydrogen bond, but cannot be assessed from our spectroscopic data alone without observing weak combination or hot bands. One further analysis involves the observed intensities of the fundamental and overtone bands, with the fund : ot ratio predicted to increase with stronger hydrogen bonds (i.e., the rst overtone to become weaker in comparison). 15 In our experiment, the overtone intensity has to be down-scaled by a factor of 0.83(3) to account for the change in detectors with different areas between the two measurements. From the spectra of the rich M : E mixture, we nd a fund : ot ratio of 170(70) which is signicantly lower than the 320(90) ratio found for the MM homodimer. 20 Overall, the small red shi, low increase in anharmonicity and modest overtone intensity attenuation bear witness to the weakness of this model OH/p hydrogen bond when compared to the MM case.

Harmonic wavenumbers and dissociation energies
As shown previously for the methanol dimer, 17 advancing beyond the MP2 treatment of correlation allows to improve the predictions for the harmonic red shi ÀDu of the donor O-H bond; this even holds when only this specic bond is selected for a higher correlation treatment. The latter is possible in the   Fig. 2, with all other spectra scaled to its 3641 cm À1 ME band (scaling factors annotated).
LMOMO scheme 40 which allows to single out localized electron pairs to be treated by a different method than the remainder of the system. This approach has proven to resemble full LCCSD(T)(int) closely in MM with a strongly reduced cost for numerical gradient and Hessian calculations. 17 For the donor O-H vibration, the benchmark LCCSD(T*)-F12a(int)/VDZ-F12 method predicts a harmonic red shi of À122 cm À1 which MP2/aVTZ and LMP2/aVTZ overestimate by 35 and 20%, respectively. It appears that popular MP2 approaches are at best qualitatively useful for analyzing the spectroscopic data for this important intermolecular contact. However, by applying Grimme's spin component scaling 41 approach in SCS-LMP2/aVTZ, we nd that the harmonic red shi is brought down to 113 cm À1 , in much better agreement with our benchmark value. The electronic and harmonically zero-point corrected dissociation energies are then predicted some 2-3 kJ mol À1 too low, at D e ¼ 20.1 and D h 0 ¼ 15.1 kJ mol À1 as compared to 22.9 and 16.8 kJ mol À1 at the benchmark level; this suggests that the SCS harmonic shi performance also prots from error compensation.
For the ME dimer, the F12 calculations yield a harmonic red shi of ÀDu ¼ 45 cm À1 . Again, canonical and local MP2 methods overshoot by some 33-56% (see Table 1) while SCS-LMP2/aVTZ provides a harmonic red shi that almost coincides with the benchmark data (see Table 1). For comparability with our previous MM study, we further present LMOMO calculations in which the methyl group and the adjacent C-O bond are reduced to an MP2 treatment while the rest of the system remains correlated at the CCSD(T)(int) level. We present them here only for the sake of completeness while encouraging the use of explicit correlation.
Overall, the weakness of the ME hydrogen bond becomes apparent from the $10 kJ mol À1 gap of the dissociation energies to the MM dimer with its best-estimate harmonic D h 0 of 18.3 kJ mol À1 . 17

OH stretching anharmonicity
One important contribution to the overall experimental OH red shi in the methanol homodimer is the anharmonic cross-term that couples the stretching motion and the hindered rotation (libration) in the dimer. Since the latter motion tends to weaken the hydrogen bond, x OH,lib has a positive sign, blue-shiing the stretching band from its diagonally anharmonic value. The effect on the librational motion itself was conrmed by means of matrix isolation spectra 18 which lend credibility to the F12 benchmark harmonic and VPT2 results. In this light, the predicted harmonic red shi of Du ¼ À45 cm À1 and subtle change in diagonal anharmonicity of Dx OH,OH ¼ À3 cm À1 in the ME system suggest that the stretching-libration coupling x OH,lib is only on the order of $10 cm À1 , much lower than in the homodimer ($60 cm À1 ). While this is qualitatively expected for a weak OH/p bond, it represents an interesting case where the observable red shi can be explained to a good approximation by harmonic effects alone, given that diagonal and off-diagonal anharmonic contributions are small and mutually canceling. Together with the sensitive ethene torsion preference, the ME dimer thus provides a nice accuracy test for quantum chemical methods without the need to evaluate anharmonic effects.
Perturbational anharmonic treatments are available in the GAUSSIAN program package 31,32 and have previously been applied to the methanol dimer. 18 Predictions for the anharmonic terms x OH,i of the donor OH stretching vibrations in MM and ME are given in Table 2. If the predicted anharmonic corrections are combined with benchmark LCCSD(T*)-F12a(int)/VDZ-F12 harmonic references, good agreement with the true experimental band positions is obtained. As expected, the stretching-libration coupling is markedly smaller in ME than in the homodimer and approximately cancels the diagonal anharmonic weakening of the stretching potential.
Similar MP2/aVTZ calculations were conducted (not included in Table 2) which deviate markedly from these results, with an anharmonic ME band position ofñ OH ¼ 3564 cm À1 . Closer inspection reveals that this is in part due to the difficult ethene torsion which is predicted at a harmonic wavenumber of u tors z 1 cm À1 . While the corresponding stretching-ethene torsion coupling term x OH,E-tors amounts to about 0.5 and À0.03 cm À1 in the robust B2PLYP-D3BJ/VTZ and MP2/VTZ calculations, respectively, it is À98 cm À1 at this faulty level of theory. We attribute this to a BSSE effect caused by diffuse functions on the hydrogen atoms. When neglecting this error, the overall MP2/aVTZ anharmonic correction is about À177 cm À1 , in agreement with the robust calculations (see Table 2); however, the summed cross-terms, barring the OH libration, amount to À13 cm À1 as compared to À3 to À4 cm À1 . While not drastic, this deviation cautions against taking Table 1 Dissociation energies D e and D h 0 , harmonic red shifts ÀDu with deviations to the LCCSD(T*)-F12a(int)/VDZ-F12 benchmark in parentheses, and harmonic ethene-torsion wavenumbers u tors for the ME dimer on various levels of theory contaminated VPT2 results out of context even if the error source can be identied. The VPT2 calculations further provide anharmonic infrared intensities for the fundamental and overtone bands under scrutiny. From MP2/VTZ and B2PLYP-D3BJ/VTZ, we nd predicted fund : ot ratios of about 360 to 420 for MM and 150 to 170 for ME, respectively. The MM results are in adequate agreement with the experimental value of 320(90), 20 while the ME results reproduce the experimental value of 170(70) very well. Despite the quite different character of these two model hydrogen bonds, perturbational treatments thus produce reasonable anharmonic estimates for the OH stretching mode, and combination with high-level harmonic reference wavenumbers brings them into good agreement with the absolute band positions observed in our experiments.
Estimating anharmonicity constants with our explicitly/ locally correlated benchmark method is difficult due to the lack of a comparable implementation in the MOLPRO program package. We thus calculated potential energy curves along the (donor) O-H stretching normal modes Q in the methanol monomer and the two dimers. We t a modied Morse potential of the form to the calculated energies, with C and b 1 through b 5 le free in the t. We refrain from denoting the prefactor as a dissociation energy, since the resulting potential is not strictly dissociative anymore. Solutions to the vibrational Schrödinger equation were found by numerical variational calculations with a basis set of Gaussian functions distributed along the coordinate Q, using the reduced masses from the respective normal modes.
The results are displayed in Table 3. The overtone is converged to below 10 À2 cm À1 with respect to changes in number, spacing and width of the basis functions. Harmonic wavenumbers at the equilibrium position provide a consistency check with the normal-mode calculations, showing deviations up to 3 cm À1 . We attribute these to tting errors and assume the same variations for the calculated energy levels. Among our three test cases, the most interesting system is the methanol monomer, since the torsional perturbations of the OH oscillatorwhich cannot be captured with a 1-D modelare smallest there. The experimental wavenumbers are reproduced well by the benchmark method; conversely, the MM wavenumbers are underestimated due to the lack of this specic coupling. Still, the results are compatible with the blue-shiing x OH,lib z 60 cm À1 coupling suggested by the VPT2 calculations. Overall, the diagonal anharmonicities of the OH stretching oscillator from variational and VPT2 calculations show a satisfying agreement with the experiment across our methods even when the corresponding harmonic results are unreliable. As previously noted, the computed dissociation energies for the methanol-ethene system can be found in Table 1. However, in order to obtain quantitative estimates, the electronic energy should be recomputed with a larger basis set to converge the one-particle space. We carried out LCCSD(T*)-F12a(int)/VQZ-F12 single point calculations on the optimized VDZ-F12 structures, and obtained D e ¼ 11.4 kJ mol À1 . This corresponds to a variation of only 0.5 kJ mol À1 when compared to the double-zeta result. It shows the good convergence of the value relative to the basis set. Given that these are all coupled cluster values, the error bar for D e should be around 1 kJ mol À1 . This is a rather conservative estimate. Adding the harmonic zero-point energy Table 3 Estimates of diagonal anharmonicity at the LCCSD(T*)-F12a(int)/VDZ-F12 benchmark level of theory, obtained from 1D variational calculations ("var.") for the OH stretching oscillator in the methanol monomer ("M") and the donor in the pure and mixed dimers ("MM", "ME"). Also included are harmonic wavenumbers as a consistency check with normal-mode calculations ("norm."). All data in cm À1  Table 2 Anharmonicity constants x OH,i from VPT2 calculations (all using the VTZ basis set) for the methanol (donor) OH-stretching vibrations in M, MM and ME, together with the respective harmonic wavenumbers u OH and resulting anharmonic band positionsñ OH . The primed sum over the cross-terms indicates exclusion of the stretching-libration coupling. Also given are estimates forñ OH using benchmark LCCSD(T*)-F12a(int)/ VDZ-F12 harmonic wavenumbers u OH of 3862, 3740 and 3817 cm À1 for M, MM and ME, respectively ("ñ benchm.
OH " corrections, we obtain a value of D h 0 ¼ 8.2 kJ mol À1 . In order to obtain a more reliable estimate of the spectroscopic dissociation energy, accurate anharmonic calculations for the zeropoint energy would be required. However, these are extremely challenging given the large amplitude motions present in the system.

Conclusions
We have recorded FTIR spectra of methanol : ethene mixtures in supersonic expansions, assigning the fundamental and overtone transitions of the mixed dimer. The observed OH stretching red shi ÀDñ OH ¼ 45 cm À1 from the monomer reference is reduced by about 60% from that of the homodimer. The weakness of this prototypical OH/p contact is further attested by the minute change in diagonal anharmonicity of Dx OH,OH z À3 cm À1 and moderate 170(70)-fold intensity attenuation of the overtone with respect to the fundamental.
High-level quantum chemical calculations with local and explicit electron correlation treatment predict a harmonic red shi of ÀDu OH ¼ 45 cm À1 which coincides with the experimental anharmonic value. Assuming the chosen method to be robust, the observed wavenumber shi is thus mostly a harmonic effect, indicating that diagonal and off-diagonal anharmonic corrections closely cancel each other. As in the methanol homodimer, 20 the most important contributions come from the diagonal term of the OH stretching vibration and the off-diagonal stretching-libration coupling; in the methanol-ethene dimer, the latter is predicted by VPT2 calculations at only 13-17 cm À1 , providing another measure for the weakly perturbing character of the intermolecular interaction. Likewise, the harmonic zero-point dissociation energy at our best level of theory is D h 0 ¼ 8.2 kJ mol À1 , 55% less than in the methanol dimer (D h 0 ¼ 18.3 kJ mol À1 ). 17 Allowing for possible anharmonic effects in both directions for this oppy system, a conservative estimate of 8.2 AE 2.0 kJ mol À1 for the spectroscopic dissociation energy of ME appears justied. Microwave verication of the subtle structural preference of the methanolethene complex for a perpendicular arrangement of the C-O and C]C axes would be welcome.
We reiterate our previous ndings that the MP2 method is inadequate for harmonic wavenumber predictions in alcoholic hydrogen bonds, signicantly overestimating the red shi in canonical and local correlation treatments. However, SCS-LMP2 fares well in this regard both for the weak OH/p methanolethene and stronger OH/O methanol-methanol contacts, at the well-known 42 expense of underestimating the dissociation energy. The quantitative insights into OH/p interactions obtained for methanol-ethene can help to advance our understanding of prereaction complexes in olen epoxidation, 43 hydroxyl radical reactions, 44 electric eld effects in OH/p contacts 12 and the subtle donor-acceptor balance in methanol-ethyne. 45