Coupled proton vibrations between two weak acids: the hinge complex between formic acid and triﬂuoroethanol

When formic acid and 2,2,2-trifluoroethanol are co-expanded through a slit nozzle into vacuum, a single dominant, hinge-like 1 : 1 complex is formed in significant amounts and its two OH stretching fundamentals separated by 100 cm-1 can be unambiguously assigned by a combination of infrared absorption and Raman scattering. Quantum chemical calculations at different levels reproduce this finding in a satisfactory way and suggest that in-phase (Raman-sensitive and lower wavenumber) OH stretch excitation more or less along the concerted degenerate proton transfer coordinate in the hydrogen-bonded ring stays below the barrier for this concerted exchange. Anharmonic calculations indicate only weak intensity sharing with dark states coming into reach due to the hydrogen bond downshift of the OH stretching vibration. This well-behaved system sets the stage for acid combinations with more basic alcohols, where the in-phase OH stretching vibration is more difficult to detect, possibly due to fast intra-complex vibrational dynamics. It thus provides a benchmark point from which one can explore the evolution of vibrational resonances when the acidic proton meets a more electron-rich alcoholic oxygen.


.1 Hybrid force field VPT2 Different substituted hybrid force field approaches
It is common practice to express the higher derivatives of the potential energy ( ) that enter into the VPT2 energy formulae [1,2] as derivatives with respect to dimensionless normal coordinates (q) as opposed to the usual massweighted rectilinear normal mode coordinates (Q). This has the advantage that irrespective of the derivative order, all force constants ( ), i.e. derivatives of the potential energy, can be expressed in units of cm −1 . If the potential energy is expanded around a stationary equilibrium geometry, the Taylor series expansion (unrestricted summation) with respect to dimensionless coordinates has the form − eq = 1 2 where is the harmonic wavenumber. The conversion between the two coordinate systems equates to with the conversion factor [3] = ℎ ℏ 2 = 4 2 ℎ .
which is not a constant but proportional to the harmonic wavenumber. When constructing a substituted hybrid force field as described in the supplementary material of Ref. [4], Gaussian 16 Rev. A.03 uses the new harmonic wavenumbers to evaluate (Eq. 4) and convert the cubic and quartic force constants from Q to q (Eq. 3).

Definition of effective resonance Hamiltonians
In order to identify near-degeneracies in the VPT2 treatment of the two OH stretching fundamental energy levels of the 1:1 complex between T g and F, the well-tried Martin test is employed [5]. We use default thresholds as implemented in Gaussian 16 Rev. A.03 (harmonic energy separation ≤ 200 cm −1 and variational-perturbational difference ≥ 1 cm −1 ) and restrict the resonance treatment to Fermi resonances (VPT2+F) following the usual procedure of deperturbation (indicated by an asterisk) and subsequent diagonalisation of effective resonance Hamiltonians as described for example in Ref. [2]. Indeed, a Fermi resonance is detected between the higher-frequency alcoholic stretch ( 1 ) and a combination state which is excited along the lower-wavenumber acidic stretch ( 2 ) and a low-frequency mode ( 33 ) shown below: 33 is an intermolecular vibrational degree of freedom (or frustrated rotation) which is a mixed group vibration with partial OH libration character (and internal rotation along the CC bond) which makes 1 and 2 + 33 quite natural coupling partners. The corresponding 2 × 2 VPT2+F Hamiltonian has the following form:

Results and discussion
Differently computed energy levels of both OH stretching vibrations of the 1:1 complex between T and F are summarised in Table S1, illustrating the impact on the energy levels for different hybrid force field approximations and the explicit resonance treatment between 1 and 2 + 33 . In the limit of a single bright state, the fundamental character Table S1: Comparison of computed (harmonic and anharmonic VPT2) and experimental energy levels (in cm −1 ) of the acidic ( 2 ) and alcoholic ( 1 ) OH stretching vibrations and 33 of (T g g F). 1 is predicted to be in resonance with 2 + 33 and the squared wavefunction contribution from the deperturbed fundamental ( 2 1 ) is shown for a two-level analysis (Eq. 5). "add" and "sub" refer to the additive and substituted hybrid force field approach, respectively, where "mod" additionally indicates that the cubic and quartic force constants are scaled as described in the text. ∆ OH is the difference between the two OH stretching fundamentals and ∆ res between the two resonant levels. 2) −1 1,2,33 = 14 cm −1 at the MP2/aVTZ level. The impact of this resonance on the energy levels is negligible (deviation between VPT2 and VPT2+F is only 1-2 cm −1 ) but the mixing between both states is quite strong, as reflected in the fundamental character of the perturbed 2 + 33 state (see Table S1). The data presented in Table S1 support a speculative assignment of the weak IR band at 3441 cm −1 , which could find several possible experimental interpretations, to the combination state 2 + 33 . They also suggest that this assignment option has little impact on the theory-experiment comparison for the fundamental wavenumbers, which is most relevant for this work. We note that full CH 2 deuteration might yield further insights into the assignment of the IR band at 3441 cm −1 as the proposed resonance between 1 and 2 + 33 is not only predicted to survive but even increase in strength, as indicated by the decrease of 2 1 (Table S1). Table S2: Scaling factors ( , in %) derived for the OH stretching fundamentals ( and̃ , in cm −1 ) of the global minimum structures of formic acid F, trifluorethanol T g and their mixed 1:1 complex (T g g F). Note that at the coupled-cluster level, the anharmonic VPT2 correction is computed at the MP2/aVTZ level following the substituted hybrid force field approach, as described in Section 2.3 of the main text. Column D shows that the latter are in almost perfect agreement with experiment. Therefore, the empirical B3LYP harmonic scaling by 96% (column A) is seen to be the result of 94-95% scaling for pure anharmonicity (column C) and a 1-2% correction for the harmonic deficiency of the B3LYP approach, namely an OH bond which is somewhat too soft, both in the monomer and even more so in the complex.  Table S3: Spectroscopic properties (harmonic OH stretching wavenumber OH , downshifts relative to the respective T and F monomer ∆ OH (T/F), infrared band strength , Raman cross section Raman corrected for instrument properties and energies, relative conformational energy ∆ 0 and dissociation energies e∕0 without and with zero point energy correction into the respective monomer structures for different species optimized at the B3LYP-D3(BJ)/def2-QZVP level. Structures are shown in Figure S1 and Figure S2.

DFT minimum structures [6]
F (FF) T g T t T g T g Fig. S1: Most stable structures of the monomers and the most stable dimers of pure trifluoroethanol and formic acid, optimized at the B3LYP-D3(BJ)/def2-QZVP level. For T g the respective g+ enantiomer is shown and for its dimer, homochirality is implied.  Each spectrum was recorded with an aperture of 3.5 mm, an InSb/MCT sandwich detector, a spectral bandpass filter transparent between 2500 and 4100 cm −1 (internal reference: F13a), CaF 2 optics and a resolution of 2 cm −1 . The helium pressure in the gas pipes ( He ) and the reservoir pressure ( Res ) are listed. For each measurement, a mixed-gas bottle with defined concentrations was prepared, e.g. for the purple spectrum, 10 mbar formic acid (F) was mixed with 20 mbar of 2,2,2-trifluoroethanol (T) within 50 bar He. 'F : T in 50 bar He' shows the individual conditions. The spectra were averaged over multiple scans, with Scan as the amount of averaged scans. The date the spectra were recorded as well as the filename are listed for internal reference. The raw data for the spectra are publicly available [6].

Figure Trace
He   He' shows the individual flow meter settings for internal reference. For calibration and conversion to wavenumbers, atomic transitions of a neon and partly also a krypton discharge lamp were used ('Calib'). The date the spectra were recorded as well as the filename are listed for internal reference. Note to reviewer: the spectra will be made available as data point tables in a public repository at revision stage.   Fig. S3: Estimate of the fraction of 1:1 complexes relative to the monomer ingredients in the spectra based on computed harmonic infrared intensities and a comparison of relative experimental intensities, as reflected by the scaling factors applied to the simulated spectra (trace d) to qualitatively match experiment (trace e, obtained by subtracting the one-component spectra a and b from the spectrum c of the mixture). The 1:1 complex is seen to involve more than 1% and significantly less than 10% of the molecules in the expansion, even allowing for substantial uncertainties in the theoretical intensities.   respectively. Easy to see is the switch of the intensity pattern: While the alcoholic OH-stretching vibration at 3408/9 cm −1 has a high IR and a low Raman intensity, the pattern is changed for the acidic OH-stretching vibration at 3309 cm −1 .