The donor OH stretching–libration dynamics of hydrogen-bonded methanol dimers in cryogenic matrices

FTIR spectra of the methanol dimer trapped in neon matrices are presented. The fundamental, overtone and combination bands involving the donor OH libration and stretching motions were observed in order to extract relevant anharmonicity constants. We find a stretching–libration coupling constant of +43(5) cm (cid:2) 1 and a diagonal librational anharmonicity constant of (cid:2) 71(5) cm (cid:2) 1 . The spectra are compared to a number of VPT2 calculations and a torsionally localized monomer model in order to enhance previous explanations of the observable OH stretching red-shift upon dimerization.


Introduction
][3][4][5][6][7][8] Specifically, interest has been directed to the OH stretching motions since they provide sensitive probes for the hydrogenbonding interaction between the two constituent methanol molecules, and the 111 cm À1 red shift in the jet-cooled gas phase has recently been augmented with information on its diagonal anharmonicity. 7Together with a high-level harmonic reference for this band, it was inferred that the overall corrections from couplings to other vibrational modes should be on the order of 30 cm À1 . 7,9It can be expected that most of this ''off-diagonal'' anharmonic correction stems from the librational motion, i.e. the torsion of the donor OH group around the central C-O bond which becomes hindered in the hydrogen bond.The term ''libration'' is used for this large-amplitude intermolecular hydrogen bond motion to distinguish this mode from the much less perturbed torsion of the acceptor OH group upon complexation.The recent observation of the OH libration fundamental excitation at 560 cm À1 by matrix-and jet-FTIR spectroscopy lends credibility to a series of quantum chemical predictions which reproduce the observable band positions of the donor OH stretching and libration bands and further predict a 60 cm À1 stretching-libration coupling element. 7This would coincidentally explain almost all of the total off-diagonal shift, because each coupling element enters the correction with a factor of 1 2 . 10Overall, the emergent picture has been largely consistent so far, but lacks stringent experimental corroboration of anharmonicity data for the important stretching-libration coupling.
The easiest way to achieve this is to observe the according combination band at n s,l = n s + n l + x s,l (where s and l refer to the stretching and librational modes, respectively, and x denotes anharmonicity constants).Since the fundamental transitions n s and n l have already been characterized for the methanol dimer, 7,8 the combination band remains as the only missing link for this analysis.The usual practice of backing the experiments with predictions from quantum chemical methods can of course be helpful in providing first estimates for the band positions and coupling constants; these can then in turn be corroborated or falsified once their true values have been extracted from the observations.However, realistic estimates from quantum chemistry for the methanol dimer may be hard to come by, given that many popular theoretical methods tend to notoriously misjudge the energetics of the hydrogen-bonded OH oscillator at least at the harmonic level. 9,11Chances are that the case is even more difficult when including the librational motion due to its much shallower potential.Furthermore, the anharmonic treatments undertaken here and previously are based on a second-order perturbational scheme [12][13][14][15][16] in its implementation by Barone 10,12 in which the harmonic wavenumber assumes the role of the zeroth-order reference.As with any perturbational approach, one should be wary if the perturbation is of considerable magnitude; seeing that the best harmonic librational prediction of 660 cm À1 suggests an anharmonic perturbation of this mode on the order of À100 cm À1 , the previously found agreement with experiment may be serendipitous or misleading. 8It is thus indispensable to obtain direct experimental values for the coupling constant in order to test the predictions.
This journal is © the Owner Societies 2016 Perchard and coworkers have extensively studied methanol embedded in nitrogen, argon and neon matrices, 4,6,17 but without placing a particular focus on the stretching-libration couplings.Furthermore, only monomer transitions were assigned in the neon matrices where perturbations from the matrix environment are the smallest.We thus set out to explore the important x s,l anharmonicity constant by means of the less intense OH stretching-libration combination bands of the methanol dimer by this sensitive matrix isolation approach.Further data for the deuterated isotopologues are presented in the ESI.†

Experimental details
A pre-cooled (77 K) gas flow of neon (L'Air Liquide, 99.999%) was deposited with a flow rate of 0.02 mol h À1 on a gold-plated oxygen-free high thermal conductivity (OFHC) copper mirror at 3.6 K inside an immersion helium cryostat (IHC-3).This cryostat has been modified for matrix isolation spectroscopy 18,19 and is mounted to the Bruker IFS 120 FTIR spectrometer installed on the infrared beam-line at the MAX IV facility hosted by Lund University.The pre-cooling of neon significantly reduces the heat load on the copper mirror and enables a total deposition time of about 1 hour per experiment.The pre-cooled neon gas flow was subsequently doped with ''freeze-pump-thaw'' purified methanol (Sigma Aldrich, 99.9%) and isotopically substituted methanol-d1 (Sigma Aldrich, 99.0%D), methanol-d3 (Sigma Aldrich, 99.0%D) and methanol-d4 (Sigma Aldrich, 99.0%D) samples with mixing ratios of 1-2%.In the experiments for methanol-d1 and methanol-d4, the inner surfaces of the entire inlet system and mounted sample flasks were heavily deuterated with the enriched sample prior to the deposition procedure.A combination of resistive heaters and feedback electronics was employed to maintain a stable mirror temperature at 2.8 AE 0.1 K before and after the matrix deposition.The outer shroud of the cryostat was equipped with a CsI window to provide a viewing port and combined mid-infrared and near-infrared single-beam sample spectra were collected using a Bruker IFS 120 FTIR spectrometer employing tungsten and globar lamps as radiation sources.Liquid nitrogen cooled HgCdTe (broadband) and InSb detectors combined with Ge/KBr and CaF 2 beam splitters were employed for the 600-5000 cm À1 and 1700-11 500 cm À1 spectral region, respectively.In all experiments, the doped neon matrices were subsequently annealed to 9 K to promote the diffusion of methanol and further formation of a dimer in the soft matrices.A spectral resolution of 0.5 cm À1 was chosen as the best compromise between a high signal-to-noise ratio and a sufficiently high spectral resolution to resolve the observed sub-band spectral features assigned to the methanol dimer (see Section 4.1).The single-beam background spectra were collected using the evacuated warm cryostat.

Computational details
Quantum chemical calculations have previously been carried out for the methanol monomer and dimer at the MP2, B2PLYP-D3BJ and B3LYP-D3BJ levels of theory using the cc-pVTZ (''VTZ'') basis sets. 8We revisit these calculations herein to judge their robustness and extend the study to the deuterated isotopologues (see ESI †).All calculations were carried out using the Gaussian 09 package, 20 including Grimme's D3 dispersion for the DFT calculations. 21Tight optimization convergence criteria and, for DFT calculations, ultrafine integration grids were used throughout (opt = tight and int = ultrafine keywords, respectively).Anharmonic treatments were then carried out using the perturbational VPT2 method 10,12 implemented in this software package.
Due to potential incompatibilities of the VPT2 implementation in Gaussian09 with Becke-Johnson damping, the results presented herein have been obtained with zero-damping. 22e have also explored the numerical sensitivity of lowfrequency DFT VPT2 predictions to minute dimer structure variations, suggesting larger error bars in some of our earlier results than implied before.In particular, the off-diagonal librational anharmonicity constants calculated previously for the methanol dimer 8 will be slightly impacted by this, as we demonstrate in the ESI; † similar variations will exist in the off-diagonal coupling terms to the OH stretching wavenumbers in methanol-ethene, 9 but the impact on our previous results is likely to be small.

Neon matrix spectral data
The recorded absorption spectra of methanol are shown in Fig. 1 for the OH stretching fundamental, overtone and stretchinglibration combination bands as well as the libration overtone region.The spectra and calculations for the deuterated isotopologues are shown in the ESI.† Throughout, black and red traces show pre-and post-annealing spectra, respectively, and blue traces (annotated ''diff.'')show their difference.Due to optical saturation, the OH stretching fundamental band lacks direct intensity information, and we omit its annealing difference trace.All experiments were repeated at different methanol concentrations, and the dimer assignments we put forward below are based on the observed concentration dependence and annealing trends.
The spectra reveal some complex band patterns for the features assigned to the OH stretching fundamental of the methanol dimer. 7However, the combined concentration dependency and dedicated pre-and post-annealing measurements together with the direct comparison with previous jet observations 5 unambiguously support the dimer origin of both the complex band patterns observed in the 3555-3575 cm À1 region for regular methanol and methanol-d3, and the 2625-2635 cm À1 region for methanol-d1 and methanol-d4 (see ESI †).The independent absorption spectra recorded previously for regular methanol embedded in both neon and para-H 2 matrices have revealed similar spectral splittings, although smaller in the para-H 2 host. 7A detailed physical interpretation of the observed spectral splittings is beyond the scope of the current contribution concerned with the determination of much larger anharmonicity constants.However, the vibrational spectrum of the methanol monomer embedded in neon and para-H 2 has previously revealed some complex torsional-vibrational couplings with resulting A-E splittings of the ground-state and the different fundamental states. 17,23The usual A-A and E-E gas-phase selection rules do not seem to apply in the environments of para-H 2 and neon, and each of the fundamental bands for the methanol monomer thus gives rise to four different sub-bands with splittings determined by the size of the individual torsional-vibrational couplings. 17,23The spectral splittings observed for the OH-stretching fundamental of the methanol dimer appear to follow a similar trend, although the exact pattern is less clear.CH 3 deuteration qualitatively conserves this pattern, whereas OH deuteration does not (see ESI †).
The pronounced isotope effects rule out the presence of different random trapping sites in the solid neon matrix cages, as does the fact that the spectral splittings are also observed for the methanol dimer embedded in much larger para-H 2 matrix cages. 24ur attempts at identifying individual sub-features are marked by anchor lines in the spectra, annotated with the last two digits of the respective band origins.Accepting these features to stem from some yet unclear vibrational dynamics within the methanol dimer, we correlate them among the fundamental and overtone bands to extract the diagonal anharmonicity constants x s,s .The results are listed in Table 1, yielding an average value of À97 cm À1 for the methanol dimer.Agreement with previous Ne, para-H 2 and jet experiments is very good, 7 Fig. 1 Neon matrix spectra of the methanol dimer in the relevant spectral regions.The black and red traces show pre-and post-annealing spectra, respectively; blue traces show the difference spectra (''diff.'',omitted for the OH stretching fundamental due to saturation).Annotated are the last two digits of assigned sub-band positions.The OH libration fundamental spectrum is reproduced from a previous study at a lower methanol concentration. 8he absorbance scale is defined by the natural logarithm (napierian absorbance) for all the spectral regions.
This journal is © the Owner Societies 2016 and we assume that the desired results for the stretching-libration coupling are similarly transferable to the gas-phase situation.
Concerning the stretching-libration combination band, we are tempted to correlate the three assigned methanol dimer features with those on the lower-wavenumber side of the stretching fundamental band.Extracting the coupling constant x s,l further requires the librational fundamental band position, which has previously been established as 558 cm À1 . 8The resulting x s,l values for the individual sub-bands are given in Table 1, yielding an average of +43 cm À1 .In addition to the stretching-libration combination band, we suggest an assignment of the broad transition at 974 cm À1 to the overtone of the librational motion (see Fig. 1).Together with the fundamental band at 558 cm À1 , 8 this yields a diagonal anharmonicity constant x l,l = À71 cm À1 .Based on the extensive band splittings, certain mismatches between the individual correlated subfeatures, and residual matrix shifts even in neon, we assume an error bar of AE5 cm À1 throughout for all experimentally determined anharmonicity constants.
The analyses for the deuterated isotopologues are analogous to the methanol case and shall not be outlined here in greater detail, not least because our assignments are less complete and the annealing effects are much smaller for the CD 3 species.The spectra and data are given in the ESI.† For the dimer of methanol-d3, the diagonal anharmonicity constant of À99(5) cm À1 is in good agreement with the methanol results.Likewise, a rich band structure is again observed between 4175 and 4157 cm À1 , and correlating the stretching and libration fundamental bands yields a coupling constant of +42(5) cm À1 .This structure however vanishes in methanol-d1 and methanol-d4 upon deuteration of the hydroxy group, and we refrain from correlating individual bands.Placing their combination bands at 3075 and 3076 cm À1 , respectively, suggests x s,l coupling elements on the order of 25(5) cm À1 in light of the general expanse of the fundamental band structures.Furthermore, we were unable to identify the librational overtones in the CD 3 species due to overlapping strong monomer features.For methanol-d1, we assign a band at 766 cm À1 to the librational overtone, and together with the 420 cm À1 fundamental, 8 we obtain a diagonal anharmonicity constant of x l,l = À37(5) cm À1 , about half that of the non-deuterated methanol dimer.

Quantum chemical predictions of anharmonic coupling constants
Estimates for x s,s and x s,l in the methanol dimer have been obtained before at various levels of theory. 7,9It was established that the former anharmonicity constant is reproduced quite well by all methods, with deviations of a few cm À1 .For the stretchinglibration coupling constant, MP2 and DFT calculations yielded consistent predictions of +59 cm À1 . 7,8This consistency contrasts with substantially larger variations in the predicted vibrational transitions which are correlated by this coupling constant.The variation does not only involve different theoretical levels, but also subtly different structure optimizations at exactly the same level, when DFT methods are employed (see Section 3 of the ESI †).A particularly striking indicator for this is the harmonically second-lowest intermolecular vibration, representing the hindered rotation of the acceptor methanol molecule around an axis approximately parallel to the C-O bond (I a in the free monomer).The fundamental and overtone bands of this mode fluctuate over a large wavenumber range across all calculations, often reaching imaginary values and unreasonable anharmonicity corrections.Similar variations, albeit less drastic, persist for the librational band, and uncertainties in the fundamental band position directly impact the stretching-libration band as well.
Based on a series of DFT calculations on the methanol dimer (see Section 3 in the ESI †), we assume uncertainties of at least 10 cm À1 for the position of the libration fundamental, 5 cm À1 for the donor OH stretching fundamental, and thus up to 15 cm À1 for the stretching-libration combination band.At the same time, these instabilities are practically absent in MP2, which leads us to suspect difficulties in the numerical integration in DFT.These numerical instabilities add to the methodical inaccuracy of the perturbational approach for such large-amplitude vibrations, which is valid for any electronic structure level.However, we concentrate here on the important x s,s , x s,l and x l,l anharmonicity constants, which turn out to be robust on all employed levels of theory (see Table 1).The results show a consistent overestimation of x s,l across all methods by some 35(5)%, while x l,l is underestimated by about the same relative amount.

Analysis of the donor OH-stretching dimerization red-shift
Having established an experimental value for the stretchinglibration coupling, we can further update our previous analyses of the observable OH stretching red shift in the methanol dimer, ÀD n s . 9Since we require also anharmonicity information for the monomer, we henceforth introduce superscripts ''D'' and ''M'' for the dimer and the monomer, respectively.The OH stretching wavenumber for the dimer is given by (and likewise for the monomer), and summation in the off-diagonal terms runs over a total of 11 and 29 terms for the monomer and the dimer, respectively.Furthermore, the unconstrained counterpart to the librational motion (''l'') in the dimer is the torsion of the OH group in the monomer, which we abbreviate as ''t''.One important task in dissecting the OH dimerization red shift is to relate the two corresponding anharmonicity constants, x M s,t and x D s,l ; to this end, we separate these terms from the sums in eqn (1), which we indicate by a prime: (and analogously for the monomer, with torsion ''t'' replacing libration ''l'').Additionally, the dimerization red shift ÀD n s requires to take the difference of all terms, where we imply the different summation ranges in a common term: One fundamental error in the monomer calculations is that they do not honor the three-fold symmetry of the OH torsional motion and consequently neglect the resulting strong tunneling splittings into the A and E sub-states.Gas-phase studies by Hunt et al. 25 and Rueda et al. 26 have shown that the torsional barrier increases upon excitation of the OH stretching oscillator, thereby reducing the tunneling splittings in the stretchingtorsion v s , v t = 1, 1 state relative to v s , v t = 0, 1.One should thus obtain two distinct values for x M s,t , depending on whether it is calculated from the A or E states.Using energy levels determined from the OH stretching fundamental 25 and the first overtone 26 transitions together with ground-state torsional references, 27 we find average gas-phase values of x M s,t = +0.4(3)cm À1 for the A states and x M s,t = +13.5(3)cm À1 for the E states, with surprisingly little variation for the fundamental and overtone values.To compare these with the matrix environment, we make use of earlier monomer studies by Perchard et al. 6,17 Their band assignments suggest a coupling constant of +12.8 cm À1 for the E ' A stretching-torsion combination transition, and since the perturbations from the Ne matrix host are moderate for the fundamentals, 17 this compares quite well with the analogous gas-phase value of +10.9 cm À1 . 25,27(For details on the involved transitions, see ESI. †) We are thus confident that the experimental dimer coupling constant determined from our matrix measurements is in similarly good agreement with the gasphase situation.
Still, the ambiguities caused by the tunneling splittings prompt for some sort of localization approach in order to be directly comparable to quantum-chemical calculations.In a simple state-specific picture, we regard the A/E triplet of each v s , v t ensemble as the eigenvalues of a 3 Â 3 matrix with localized, three-fold degenerate ''single-well'' energy levels on the diagonal, and uniform inter-level couplings among the potential wells as the off-diagonal elements.From the eigenvalues of these matrices, the coupling elements amount to a third of the observable A-E splittings, and the localized energy levels represent the center of gravity of the A and E levels.We concede that this is a rather coarse approach to the problem, neglecting all interactions between the sub-levels of different torsional states.On the other hand, the moderate difference in the A and E x s,t values calculated above suggests that its errors will likely be exceeded by those of the VPT2 calculations.An energy level scheme of the delocalized (experimental) and localized v s , v t states for v s = 0 to 2 is given in the ESI.† Using both the OH fundamental and overtone transitions, we find x M s,t values of +9.3 and +8.8 cm À1 , respectively.Seeing the high anharmonicity content of the torsional motion, it is surprising to find the v s = 1 and 2 results being in such good agreement; however, we cannot rule out error compensation with the localization approach as the cause for this without further analysis.
In addition to the stretching-torsion coupling, we find a localized OH-stretching fundamental wavenumber of 3683.4 cm À1 and a diagonal anharmonicity constant of x M s,s = À85.7 cm À1 .Together with the 3574.5 cm À1 donor OH stretching wavenumber observed for the dimer, the overall approximate single-well dimerization shift relevant to eqn (3) is about 109 cm À1 .
Having established a monomer reference comparable to our calculations, we can now set out to fill in the quantities in eqn (3).The best estimate for the harmonic dimerization shift is 121 cm À1 , 11 for which we assume a AE5 cm À1 uncertainty.The experimental gas-phase diagonal anharmonicity contribution in the dimer, À99.2 cm À1 , together with the localized gas-phase monomer reference from above, yields À2Dx s,s = 27 cm À1 . 7eeting the overall 109 cm À1 dimerization red shift then requires an off-diagonal correction of À 1 2 P ias Dx s;i ¼ À39 cm À1 , containing an experimental torsional/librational contribution of À 1 2 Dx s;l=t ¼ À17 cm À1 (see Table 2).From an experimental perspective, the 10 remaining off-diagonal differences and 18 unique dimer coupling terms together must thus contribute À22 cm À1 , but considering the cumulative errors, this residual (one half the difference of the primed sums) is only determined within about AE10 cm À1 .Again, the VPT2 calculationsparticularly B3LYP -have some difficulty in predicting the quantities listed in Table 2, which we further detail in the ESI.† Given the availability of experimental values for the most important off-diagonal contributions, however, we are free of the burden to rely on these predictions alone, and can further confirm that at least a qualitative agreement between theory and experiment can be reached.

Summary
FTIR absorption spectra of the methanol dimer embedded in neon matrices have been analyzed with respect to the combination band of the donor OH stretching and libration motions, and the overtone band of the latter.A co-investigation of the stretching fundamental is necessary to correlate the complicated band patterns and extract the stretching-libration coupling constant.Together with libration fundamental band positions from previous investigations, we find a stretching-libration coupling constant of x s,l = +43(5) cm À1 for the methanol dimer.Anharmonic VPT2 calculations mostly overestimate these values by some 35(5)%, while the experimentally determined diagonal anharmonicity constant of the librational motion (x l,l = À71(5) cm À1 ) is underestimated in magnitude by a similar amount.With the new experimental finding, we are able to update previous analyses of the observable dimerization shift in the donor OH stretching band.Using a state-specific deperturbation approach to approximate tunneling-independent monomer reference values, we explain the observable 109 cm À1 gas-phase OH stretching redshift of the methanol dimer as being comprised of about 121(5) cm À1 (theoretical) harmonic and 27(2) cm À1 (experimental) diagonal anharmonic contributions, counteracted in part by a single À17(5) cm À1 (experimental) stretching-libration contribution.This leaves a À22(10) cm À1 gap to be explained by the remaining off-diagonal couplings, which VPT2 helps to do in a qualitative way.Our data support the prediction that the stretching-libration coupling is the most important contribution to the off-diagonal anharmonic shift, which is necessary to compensate for the red-shifting diagonal weakening of the OH stretching oscillator and explain the observable dimerization red-shift.A thorough variational treatment in an accurate stretching-libration potential would be desirable to gain further insight into these important dynamics.
As a bottom line, we have now characterized the two major and tendentially canceling anharmonic contributions to the overall dimerization red-shift of the methanol dimer in a direct spectroscopic manner, and the next challenge in this regard may be the influence of the torsional motion of the free OH group in the acceptor molecule.

Table 1
Predicted and observed anharmonicity constants of the methanol dimer for donor OH stretching (x s,s ), libration (x l,l ), and stretching-libration coupling (x s,l ).The neon matrix data are obtained by correlating the subbands displayed in Fig.1; also given is a diagonal donor OH anharmonicity constant from earlier jet experiments for better comparability with calculations.All data are in cm À1 a Ref. 7. b Ref. 8.This journal is © the Owner Societies 2016 Phys.Chem.Chem.Phys., 2016, 18, 3739--3745 | 3743

Table 2
VPT2 results for anharmonic couplings to the (donor) OHstretching oscillator in the localized methanol monomer and dimer.The stretching-torsion (x s,t , monomer) and stretching-libration (x s,l , dimer) couplings are separated from the remaining summed terms P 0 x s;j À Á as per eqn (2).The last line gives experimental values.All data are in cm À1