M.
Heger
a,
J.
Andersen
b,
M. A.
Suhm
a and
R.
Wugt Larsen
*b
aInstitut für Physikalische Chemie, Universität Göttingen, Tammannstr. 6, D-37077 Göttingen, Germany
bDepartment of Chemistry, Technical University of Denmark, Kemitorvet 206, DK-2800 Kgs. Lyngby, Denmark. E-mail: rewl@kemi.dtu.dk
First published on 14th January 2016
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−1 and a diagonal librational anharmonicity constant of −71(5) cm−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.
The easiest way to achieve this is to observe the according combination band at s,l =
s +
l + xs,l (where s and l refer to the stretching and librational modes, respectively, and x denotes anharmonicity constants). Since the fundamental transitions
s and
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.9,11 Chances 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 scheme12–16 in its implementation by Barone10,12 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−1 suggests an anharmonic perturbation of this mode on the order of −100 cm−1, the previously found agreement with experiment may be serendipitous or misleading.8 It is thus indispensable to obtain direct experimental values for the coupling constant in order to test the predictions.
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 xs,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.†
Due to potential incompatibilities of the VPT2 implementation in Gaussian09 with Becke–Johnson damping, the results presented herein have been obtained with zero-damping.22 We have also explored the numerical sensitivity of low-frequency 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 dimer8 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.
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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.8 The absorbance scale is defined by the natural logarithm (napierian absorbance) for all the spectral regions. |
The spectra reveal some complex band patterns for the features assigned to the OH stretching fundamental of the methanol dimer.7 However, the combined concentration dependency and dedicated pre- and post-annealing measurements together with the direct comparison with previous jet observations5 unambiguously support the dimer origin of both the complex band patterns observed in the 3555–3575 cm−1 region for regular methanol and methanol-d3, and the 2625–2635 cm−1 region for methanol-d1 and methanol-d4 (see ESI†). The independent absorption spectra recorded previously for regular methanol embedded in both neon and para-H2 matrices have revealed similar spectral splittings, although smaller in the para-H2 host.7 A 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-H2 has previously revealed some complex torsional–vibrational couplings with resulting A–E splittings of the ground-state and the different fundamental states.17,23 The usual A–A and E–E gas-phase selection rules do not seem to apply in the environments of para-H2 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.17,23 The 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. CH3 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-H2 matrix cages.24
Our 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 xs,s. The results are listed in Table 1, yielding an average value of −97 cm−1 for the methanol dimer. Agreement with previous Ne, para-H2 and jet experiments is very good,7 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 xs,l further requires the librational fundamental band position, which has previously been established as 558 cm−1.8 The resulting xs,l values for the individual sub-bands are given in Table 1, yielding an average of +43 cm−1. In addition to the stretching–libration combination band, we suggest an assignment of the broad transition at 974 cm−1 to the overtone of the librational motion (see Fig. 1). Together with the fundamental band at 558 cm−1,8 this yields a diagonal anharmonicity constant xl,l = −71 cm−1. Based on the extensive band splittings, certain mismatches between the individual correlated sub-features, and residual matrix shifts even in neon, we assume an error bar of ±5 cm−1 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 CD3 species. The spectra and data are given in the ESI.† For the dimer of methanol-d3, the diagonal anharmonicity constant of −99(5) cm−1 is in good agreement with the methanol results. Likewise, a rich band structure is again observed between 4175 and 4157 cm−1, and correlating the stretching and libration fundamental bands yields a coupling constant of +42(5) cm−1. 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−1, respectively, suggests xs,l coupling elements on the order of 25(5) cm−1 in light of the general expanse of the fundamental band structures. Furthermore, we were unable to identify the librational overtones in the CD3 species due to overlapping strong monomer features. For methanol-d1, we assign a band at 766 cm−1 to the librational overtone, and together with the 420 cm−1 fundamental,8 we obtain a diagonal anharmonicity constant of xl,l = −37(5) cm−1, about half that of the non-deuterated methanol dimer.
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−1 for the position of the libration fundamental, 5 cm−1 for the donor OH stretching fundamental, and thus up to 15 cm−1 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 xs,s, xs,l and xl,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 xs,l across all methods by some 35(5)%, while xl,l is underestimated by about the same relative amount.
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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 stretching–torsion vs, vt = 1, 1 state relative to vs, vt = 0, 1. One should thus obtain two distinct values for xMs,t, depending on whether it is calculated from the A or E states. Using energy levels determined from the OH stretching fundamental25 and the first overtone26 transitions together with ground-state torsional references,27 we find average gas-phase values of xMs,t = +0.4(3) cm−1 for the A states and xMs,t = +13.5(3) cm−1 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−1 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−1.25,27 (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 gas-phase 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 vs, vt ensemble as the eigenvalues of a 3 × 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 xs,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 vs, vt states for vs = 0 to 2 is given in the ESI.† Using both the OH fundamental and overtone transitions, we find xMs,t values of +9.3 and +8.8 cm−1, respectively. Seeing the high anharmonicity content of the torsional motion, it is surprising to find the vs = 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−1 and a diagonal anharmonicity constant of xMs,s = −85.7 cm−1. Together with the 3574.5 cm−1 donor OH stretching wavenumber observed for the dimer, the overall approximate single-well dimerization shift relevant to eqn (3) is about 109 cm−1.
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−1,11 for which we assume a ±5 cm−1 uncertainty. The experimental gas-phase diagonal anharmonicity contribution in the dimer, −99.2 cm−1, together with the localized gas-phase monomer reference from above, yields −2Δxs,s = 27 cm−1.7 Meeting the overall 109 cm−1 dimerization red shift then requires an off-diagonal correction of , containing an experimental torsional/librational contribution of
(see Table 2). From an experimental perspective, the 10 remaining off-diagonal differences and 18 unique dimer coupling terms together must thus contribute −22 cm−1, but considering the cumulative errors, this residual (one half the difference of the primed sums) is only determined within about ±10 cm−1. Again, the VPT2 calculations – particularly 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.
Using a state-specific deperturbation approach to approximate tunneling-independent monomer reference values, we explain the observable 109 cm−1 gas-phase OH stretching red-shift of the methanol dimer as being comprised of about 121(5) cm−1 (theoretical) harmonic and 27(2) cm−1 (experimental) diagonal anharmonic contributions, counteracted in part by a single −17(5) cm−1 (experimental) stretching–libration contribution. This leaves a −22(10) cm−1 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.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5cp07387a |
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