Internal dynamics of cyclohexanol and the cyclohexanol–water adduct

Marcos Juanes a, Weixing Li b, Lorenzo Spada b, Luca Evangelisti *b, Alberto Lesarri *a and Walther Caminati b
aDepartamento de Química Física y Química Inorgánica – IU CINQUIMA, Facultad de Ciencias, Universidad de Valladolid, E-47011 Valladolid, Spain. E-mail:; Tel: +34-983-185895
bDipartimento di Chimica “Giacomo Ciamician” dell’Università, Via Selmi 2, I-40126 Bologna, Italy. E-mail:; Tel: +39-051-2099480

Received 14th July 2018 , Accepted 7th November 2018

First published on 7th November 2018

Two conformers of cyclohexanol and the cyclohexanol–water adduct have been characterized in a jet expansion using rotational spectroscopy. In the gas phase, cyclohexanol adopts an equatorial position for the hydroxyl group, with the two conformers differing in the orientation of the hydroxylic hydrogen, either gauche or trans with respect to the aliphatic hydrogen at C(1). Axial cyclohexanol was not detected in the jet. The transitions of the gauche conformer are split into two component lines due to the tunneling effect of the O–H internal rotation, which connects two equivalent gauche minima. The tunneling splitting in the vibrational ground state has been determined to be ΔE0+0− = 52(2) GHz. From this splitting, the inversion barriers connecting the two equivalent gauche conformers have been determined using a flexible model to be B2 = 377 cm−1. A single isomer is detected for the cyclohexanol–water dimer, in which the water molecule acts as a proton donor to the equatorial gauche ring. The presence of torsional tunneling in the adduct suggests a concerted large-amplitude-motion in which the internal rotation in the ring is accompanied by a torsion of the water molecule, to produce an equivalent enantiomer. The torsional tunneling in the adduct is reduced to ΔE0+0− = 32.7(4) GHz and the potential barrier in the complex increases to B2 = 494 cm−1.


Alcohols, R–OH, are characterized by three energy minima upon a 360° internal rotation of the hydroxyl group. Depending on the symmetry of the R group, these three minima can be: (i) energetically equivalent to each other; (ii) two of them equivalent, but different from the third one; and (iii) all of them with different energy values. In the last two cases, a conformational equilibrium is obtained, while in the first case, tunneling and mixing of wavefunctions make the pattern of rotational levels very difficult to interpret. Further conformational species can appear when R has a high flexibility. Adducts of alcohols with water are also quite important systems, with interesting motifs such as conformational equilibria, the donor/acceptor roles of water and alcohol, and puzzling internal dynamics, where the internal rotation of the hydroxyl group is often combined with the motions of water.

Rotational spectroscopy is a technique especially suitable to investigate conformational equilibria and to unveil tunneling effects in the case of equivalent minima, and it can also be extended to the formation of intermolecular clusters, in particular hydrates, when combined with molecular beam sources.

In methanol and tert-butanol, the C3 symmetry of R allows only one conformer to exist, but their rotational spectra have been found to be extremely difficult to analyze because of multiple tunneling effects.1,2 Conversely, in ethanol and iso-propanol, the Cs symmetry of R leads to the detection of the rotational spectra of the trans and gauche conformers, with a tunneling motion connecting the two equivalent gauche forms.3,4 The R chain in n-propyl alcohol is flexible and it can adopt either a trans (with Cs symmetry) or a gauche shape (with C1 symmetry). As in ethyl alcohol, trans generates, upon rotation of the hydroxyl group, a transtrans and a transgauche (tunneling) species (labelled Tt and Tg). gauche generates, upon rotation of the hydroxyl group, three distinguished non-tunneling conformers, Gt, Gg, and Gg′. All together, five conformers were assigned in the microwave spectrum.5 For the larger n-pentan-2-ol and n-hexan-2-ol, rotational spectroscopy detected 5 and 14 conformers, respectively.6

Concerning cyclic alcohols, the rotational spectra of gauche-cyclopropanol7 and of the equatorial-trans form of cyclobutanol8 were observed. The rotational spectrum of cyclopentanol has not been reported. Finally, four conformers were assigned for 1-methylcyclohexanol,9 denoted Eg, Et, Ag, and At (E is the abbreviation of equatorial, and A is axial). For cyclohexanol (C6H12O), neither the monomer nor the water dimer has been reported. For this reason, we decided to study the conformational equilibria for the bare molecule and the hydrate using supersonic jet Fourier transform microwave spectroscopy. Vibronic laser spectroscopy previously detected a single isomer for the monohydrate.10 This work complements recent investigations on other 1[thin space (1/6-em)]:[thin space (1/6-em)]1 alcohol–water adducts, like those of tert-butyl alcohol,11 iso-propyl alcohol,12n-propyl alcohol13 and ethyl alcohol.14

Cyclohexanol is an important feedstock in the polymer industry and a solvent, used as a precursor to nylons and various plasticizers. As with saturated cyclohexanes, the chair form is the most stable conformation.15 Initial Raman spectra concluded that solid ordered phases are dominated by the equatorial isomer,16 while a mixture of equatorial and axial forms is found in the glassy phase and the liquid.17 More recently, Ibberson et al.18 found that cyclohexanol molecules adopt only equatorial shapes in the crystal using high-resolution powder neutron diffraction, synchrotron X-ray powder diffraction and single-crystal X-ray diffraction. The orientation and intramolecular dynamics of the hydroxyl group can be assessed with rotational spectroscopy. Since for both equatorial or axial conformers, R has a Cs symmetry, the molecule can generate trans and gauche (doubly degenerated) species, for a total of four plausible conformers.


Samples of cyclohexanol were obtained commercially (Aldrich) and used without further purification. The rotational spectrum was measured in two different laboratories:

(a) Bologna. A COBRA-type19 Fourier-transform microwave spectrometer20 (FTMW) was used to cover the frequency range 6.5–18 GHz.21 Helium at a stagnant pressure of ∼0.3 MPa was passed over a container with C6H12O at room temperature and expanded through a solenoid valve (Parker, Series 9, nozzle diameter 0.5 mm) into a Fabry–Pérot cavity. The gas-phase expansion formed a supersonic jet, cooling the molecules in their lowest vibrational state. The spectral line positions were determined after Fourier transformation of the time-domain signal with 8k data points, recorded with 100 ns sample intervals. Each rotational transition appears as doublets due to the Doppler effect. The line positions were calculated as the arithmetic mean of the frequencies of the Doppler components. The estimated accuracy of the frequency measurements was better than 3 kHz. Lines separated by more than 7 kHz were resolvable.

(b) Valladolid. The rotational spectrum was recorded with a broadband direct-digital chirped-pulse FTMW spectrometer covering the frequency range 2–8 GHz, which follows Pate's design.22 In this spectrometer, a 5 μs chirped pulse created by an arbitrary waveform generator is amplified to 20 W and radiated perpendicular to the propagation of the jet expansion through a horn antenna. A molecular transient emission spanning 40 μs is then detected through a second horn, recorded with a digital oscilloscope and Fourier-transformed to the frequency domain. Sample preparation was similar to that in Bologna, with optimal conditions requiring backing pressures of ca. 0.4 MPa and neon as carrier gas. The accuracy of the frequency measurements was better than 5 kHz.


Theoretical calculations

The conformational equilibrium of cyclohexanol is driven by the ring inversion, which can interconvert the axial or equatorial location of the OH group, and by the internal rotation of the hydroxyl group, which can generate gauche and trans orientations of the hydroxylic hydrogen with respect to the aliphatic hydrogen at C1. These two internal motions generate six energy minima, which correspond to four different conformers, labeled as Eg, Et, Ag, and At (A, E, t and g stand for axial, equatorial, trans and gauche, respectively). Each gauche form is doubly degenerate because of the two equivalent orientations of the hydroxyl group around the C–O bond. We performed ab initio calculations (MP2/6-311++G(d,p)23) to determine the optimized structures, relative energies, rotational and centrifugal distortion constants, and the electric dipole moment components for the four conformers. Vibrational frequency analysis confirmed further that all these conformers are stable energy minima. All theoretical data are summarized in Table 1.
Table 1 Molecular structures, relative energies and spectroscopic predictions for the four conformers of cyclohexanol (MP2/6-311++G(d,p))

image file: c8cp04455d-u1.tif

image file: c8cp04455d-u2.tif

A, B, C/MHz 4309.1, 2238.5, 1617.8 4304.5, 2218.0, 1613.4
μ a, μb, μc/D 0.5, 1.5, 1.0 1.4, 0.0, 1.4
Δ(E + ZPE)/kJ mol−1 0.00 0.96
ΔG/kJ mol−1 0.00 0.82

image file: c8cp04455d-u3.tif

image file: c8cp04455d-u4.tif

A, B, C/MHz 3556.0, 2671.7, 2006.3 3581.4, 2612.8, 1972.8
μ a, μb, μc/D 0.5, 1.5, 0.2 1.2, 0.0, 1.6
Δ(E + ZPE)/kJ mol−1 1.78 5.73
ΔG/kJ mol−1 1.97 5.57

For the cyclohexanol–water dimer, we performed an initial molecular mechanics conformational search followed by re-optimization with ab initio and dispersion-corrected density-functional theory. Table 2 presents the two most stable hydrated structures, with energetic and structural predictions according to the MP2/6-311++G(d,p) level of calculation. For comparison purposes, additional calculations were performed using the B3LYP-D3 method (see ESI). In both cases, Eg-water and Et-water turned out to be the most stable isomers of the hydrate.

Table 2 Molecular structures, relative energies and spectroscopic predictions of the most stable isomers of cyclohexanol–water (MP2/6-311++G(d,p))

image file: c8cp04455d-u5.tif

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A, B, C/MHz 2553.7, 1166.6, 1139.8 3183.0, 1071.1, 889.1
μ a, μb, μc/D 1.8, 0.6, 0.9 1.4, 0.9, 1.9
Δ(E + ZPE)/kJ mol−1 0.0 1.1
ΔG/kJ mol−1 0.1 0.0
ΔEB/kJ mol−1 −22.9 −23.3

Rotational spectra

Guided by the predicted rotational constants in Table 1, a few rotational transitions for the two equatorial Eg and Et conformers were first assigned in the broadband spectrum in the range 2–8 GHz. More μa- and μc-type transitions for both conformers were then measured in the range 6–18.5 GHz using a cavity spectrometer. As illustrated in Fig. 1, all the transitions for the Eg conformer appeared as doublets because of the hydroxyl group internal rotation. These splittings led to the assignment of a pair of ground torsional states, denoted 0+ and 0. Searches for plausible axial conformers were performed unsuccessfully. We rationalized that collisional mechanisms in the jet produce an efficient conformational relaxation into the global minimum, as observed empirically when the interconversion barrier between equilibrium minima is below 2kT.24 Evidence for this argument comes from the fact that the Et/Eg population ratio should be 0.34 (intensity ratio ca. 1) according to a Boltzmann distribution, while the Et/Eg(0+) spectral intensity ratio is lower, i.e., it is just 0.1 in the transition 303 ← 202. This implies that probably a considerable conformational relaxation takes place.
image file: c8cp04455d-f1.tif
Fig. 1 A typical rotational transition (303 ← 202) of cyclohexanol recorded using a cavity spectrometer, showing two torsional tunneling components (0+/0) for the equatorial gauche conformer (Eg) but a single component for the trans species (Et). Each transition is additionally doubled by the Doppler effect.

All equatorial trans transitions were fitted with the Watson's semirigid-rotor Hamiltonian, including quartic centrifugal distortion constants (Ir representation and S reduction).25,26 For the gauche conformer, the tunneling splittings were fitted using a two-state torsion-rotation coupled Hamiltonian, including semirigid rotor terms for each torsional state (HR0, HR1), common centrifugal distortion (HCD), the torsional energy difference ΔE0+0−, and Coriolis coupling terms Fbc and Fab determined in the reduced axis system of Pickett,27 according to the equations

image file: c8cp04455d-t1.tif(1)
where the interaction term is expressed as:
Hint = Fbc(PbPc + PcPb) + Fab(PaPb + PbPa)(2)
where Pα (α = a, b, and c) represents angular momentum operators. The fitted spectroscopic constants for the two equatorial species are reported in Table 3. All experimental transition frequencies are given in Tables S1 and S2 (ESI).

Table 3 Experimental spectroscopic parameters of the two equatorial conformers of cyclohexanol
Eg Et
0+ 0
a Errors in parentheses are expressed in units of the last digit. b Standard deviation of the fit. c Number of fitted transitions.
A/MHz 4295.7884(8)a 4293.3876(7) 4288.1884(5)
B/MHz 2231.4842(4) 2231.7890(5) 2215.7086(6)
C/MHz 1612.4343(5) 1612.4672(5) 1609.2335(5)
D J/kHz 0.116(9) 0.120(12)
D JK/kHz 0.25(3) 0.312(38)
D K/kHz 0.52(9)
d 1/kHz −0.029(6) −0.0422(94)
d 2/kHz −0.006(5) −0.0171(55)
ΔE0+0−/GHz 52(2)
F ab/MHz 11.16(2)
F bc/MHz 4.57(7)
σ /kHz 1.75 2.7
N 53 27

The spectral measurements were extended to the monosubstituted 13C and 18O isotopic species in natural abundance for the most abundant Eg conformer, definitively confirming the spectral assignment. A single transition was observed for the near-symmetric 13C(2)/13C(6) and 13C(3)/13C(5) positions. The rotational parameters and transition frequencies for the minor isotopologues are given in Tables S3–S8 (ESI).

Investigation of the monohydrated cyclohexanol–water dimer started with the ab initio predictions and the broadband spectrum. The spectral signature of an asymmetric rotor was then discovered, exhibiting torsional doublings similar to the parent species. Analysis of the spectrum required a two-state Hamiltonian, with the same Coriolis coupling terms as in the monomer. The assignment of the water dimer was later confirmed by observation of the H218O cluster using an isotopically enriched water sample, as shown in Fig. 2. The spectroscopic results for the dimer are collected in Table 4 and Table S9 (ESI), while transition frequencies are presented in Tables S10 and S11 (ESI).

image file: c8cp04455d-f2.tif
Fig. 2 A section of the spectrum of cyclohexanol⋯H216O and cyclohexanol⋯H218O recorded with the broadband spectrometer, showing the isotopic shift caused by 18O-water. The torsional splitting is observed only for the most intense 20,2 ← 10,1 transition.
Table 4 Experimental spectroscopic parameters of the observed conformer Eg of cyclohexanol–water
0+ 0
a Errors in parentheses are expressed in units of the last digit. b Standard deviation of the fit. c Number of fitted transitions.
A/MHz 2555.2943(21)a 2556.2312(50)
B/MHz 1130.35883(48) 1129.94502(59)
C/MHz 1113.24155(43) 1112.60936(75)
D J/kHz −1.3293(57)
D JK/kHz 2.75(13)
D K/kHz −6.87(24)
d 1/Hz 0.1375(26)
d 2/Hz 0.0449(42)
ΔE0+0−/GHz 32.7(4)
F ab/MHz 15.4(2)
F bc/MHz 5.76(5)
σ /kHz 7.2
N 74

Molecular structure and potential energy function of the OH group internal rotation

Molecules exhibiting large-amplitude motions cannot be described by rigid structural parameters but with the potential function controlling the intramolecular dynamics. In equatorial cyclohexanol, the observation of isotopic species and the torsional energy difference ΔE0+0− allows determination of both the heavy-atom skeleton and the hydroxyl internal rotation potential function.

The skeleton of cyclohexanol was determined with substitution and effective structures. The results are presented in Tables S12 and S13 (ESI), where they are also compared with the ab initio results.

The OH internal rotation potential function was calculated with the monodimensional flexible model of Meyer,28 which allows the numerical calculation of the rotational and vibrational wave functions and eigenvalues (and then vibrational spacings). The internal rotation of the hydroxyl group, described by the dihedral angle HC–OH (τ), was first modelled using ab initio methods. The MP2/6-311++G(d,p) potential function of the equatorial conformer is represented by the red trace in Fig. 3. This function was parametrized as

V(τ) = V0 + V1(1 − cos[thin space (1/6-em)]τ) + V2(1 + cos[thin space (1/6-em)]2τ) + V3(1 + cos[thin space (1/6-em)]3τ)(3)
The values of the four parameters Vi, i = 0–3, are shown in Table 5. This table also presents the energy barriers between the two gauche forms (B2) and between the trans and the gauche form (Btg), as well as the energy difference between the two conformers (EtEg). Guided by the theoretical calculations, we took into account the main structural relaxation parameters associated with the internal rotation according to equations of the type:
Si(τ) = S0i + ΔSi(τ)(4)
For a given parameter S, S0 is the value at τ = 0 while ΔS is its variation as a function of τ. All these values were obtained from the ab initio geometries at the four critical points. Six structural relaxations were taken into account for the model calculations. The corresponding detailed expressions, according to eqn (4), are given in the supporting information as Table S14 (ESI).

image file: c8cp04455d-f3.tif
Fig. 3 Ab initio (red trace) and experimental (black trace) potential energy curves as a function of dihedral angle HC–OH (cm−1vs. degrees) when the OH group rotates around the CO bond in the equatorial conformers of cyclohexanol. The wavefunctions of the lower vibrational states are drawn on the right.
Table 5 MP2/6-311++G(d,p) values of the Vi coefficients in eqn (3) for the internal rotation potential function of the cyclohexanol monomer in Fig. 3. The energy values at the critical points, relative to the gauche energy minimum, are also given
V 0/cm−1 V 1/cm−1 V 2/cm−1 V 3/cm−1 B 2/cm−1 E tEg/cm−1 B tg/cm−1
−32.44 54.0 4.0 222.6 420.7 83.5 413.0

Meyer's model produced a reasonable reproduction of the torsional splitting by multiplying eqn (3) by a scale factor of 0.9 (the τ coordinate was considered in the 2π cyclic range and solved into 61 mesh points). The barrier to the gauchegauche pathways (B2) was found to be 377 cm−1, which is slightly larger than that in 1-methylcyclohexanol (356 cm−1, and 320 cm−1 for axial and equatorial species, respectively) but lower than the ab initio result of 420.7 cm−1. All these data are shown in Table 6. The resulting potential energy function is given in Fig. 3 (black trace), together with the wavefunctions of the lower energy levels.

Table 6 Results of the flexible model calculations for equatorial cyclohexanol
Tunneling splittings
Obs. Calc.
ΔE0+0−/GHz 52.2 52.2
Scale factor f (fitted) 0.895
Barrier B2 (extrapolated)/cm−1 377

Water dimer geometry and dynamics

As expected, a moderately strong O–H⋯O hydrogen bond will stabilize the adduct of cyclohexanol–water. However, the ab initio calculations did not offer a priori a clear structural prediction, as the two most stable dimer geometries (Eg-H2O and Et-H2O) in Table 2 were found to be practically isoenergetic (EEt-H2OEEg-H2O = 1.1 kJ mol−1) using the MP2 method in combination with the 6-311++G(d,p) basis set. Additional calculations for two more isomers obtained from the conformational search (Ag-H2O and Eg2-H2O) in Table S15 (ESI) predicted larger relative energies. These structures were reoptimized with the dispersion-corrected B3LYP-D3 method for comparison purposes in the same table.

The spectrum provided definitive experimental evidence of the geometry of the cluster and its internal dynamics. The determined rotational constants in Table 4 and Table S9 (ESI) unequivocally confirm the detection of isomer Eg-H2O, based on the most stable gauche monomer. The water molecule acts as a proton donor to the oxygen lone pair at the ring, as in other aliphatic alcohols.11–14 Interestingly, the tunneling effects in the dimer are evidence of a large-amplitude motion, which in principle could be related either to the internal rotation of the OH group of cyclohexanol or to the internal rotation of water around its C2 axis. Tunnelling splittings associated to this last motion should be very small, because it would imply the breaking and reformation of a relatively strong O–H⋯O hydrogen bond with a high barrier between the two equivalent forms. In consequence, the cluster dynamics is most probably associated with the internal rotation of the hydroxyl group. The most reasonable scenario is a concerted motion involving the internal rotation of the OH group of cyclohexanol combined with the simultaneous rearrangement of the water molecule, as observed in tert-butyl alcohol–water11 and isopropanol–water dimers.12 The decrease in the torsional energy difference in the dimer (ΔE0+0− = 32.7(4) < 52(2) GHz in the monomer) is consistent with this hypothesis.

Though only two isotopic species were detected for the cyclohexanol–water dimer, we estimated the hydrogen bond distance using an effective structure (Table S16, ESI). The resulting value of r(O–Hw) = 1.928(5) Å is slightly larger than the ab initio prediction (1.881 Å), but within the broad range observed for this interaction in crystal structures (1.40–2.18 Å).29 The substitution coordinates of the water oxygen are shown in Table S17 (ESI). A recent review offers information on other water clusters detected by rotational spectroscopy.30

Additionally, Meyer's flexible model28 was utilized to calculate the barrier to inversion between the two equivalent Eg-H2O forms of the complex. The OH internal rotation should be described by a periodic function, but in this work, we can reasonably assume that the tunneling effects are produced ‘locally’ in the range of the HO–CC dihedral angle (τ) between ca. −120 and +120°. Then, the following double minimum potential can be used:

V(τ) = B2 [1 − (τ/τ0)2]2,(5)
where B2 is the barrier at τ = 0° and τ0 is the equilibrium value of the inversion angle. Since we have only one data point, we fixed τ0 at its ab initio value (63.3°). Guided by the ab initio structural differences between the energy minimum (τ = τ0) and the transition state (τ = 0°), we took into account the main structural relaxations, those of the three structural parameters indicated below, as a function of the leading parameter τ, according to the following expressions (see Fig. 4 for labelling):
H2O2–O1C1/° = 180 − 27.9(τ/τ0)(6)
H2O2O1/° = 15.8 − 3.2(1 − cos[thin space (1/6-em)]3τ)(7)
R(O2–O1)/Å = 2.8485 + 0.0042(1 − cos[thin space (1/6-em)]3τ)(8)
The experimental splitting of 32.7 GHz was then reproduced by a B2 barrier of 494 cm−1.

image file: c8cp04455d-f4.tif
Fig. 4 The observed cyclohexanol–water dimer and labelling of the atoms involved in the flexible model analysis of Eg-W. Hf indicates the “free” (not involved in the hydrogen bond) water hydrogen.

Discussion and conclusions

We presented a rotational investigation on the internal dynamics of cyclohexanol and the adduct cyclohexanol–water. The conformational equilibria in cyclohexanol are displaced towards the two gauche and trans equatorial forms Eg and Et. This observation contrasts with the case of 1-methylcyclohexanol,9 where we succeeded in also observing the axial conformers. This fact suggests that the presence of a methyl group adjacent to the OH group decreases the energy differences between the axial and equatorial forms. The detection of tunneling doublings was instrumental for the evaluation of the potential function for the internal rotation of the hydroxyl group. The comparison of the B2 potential energy barriers hindering the motion between the equivalent Eg forms is also interesting. The ab initio values are B2 = 420 and 410 cm−1 for cyclohexanol and 1-methylcyclohexanol,9 respectively. However, the experimental data suggest quite larger B2 values in cyclohexanol (377 cm−1) than in 1-methylcyclohexanol (320 cm−1). How can this be justified? It can be argued that the presence of a methyl group in the carbon atom to which the hydroxyl is attached lowers the barrier to internal rotation of the OH group in the section connecting the two gauche forms. By comparing the tunneling splitting with the values in the case of five other alcohols, we found that the order of torsional energy difference ΔE0+0− is: cyclopropanol < iso-propanol < cyclohexanol < n-propanol < ethanol < 1-methycyclohexanol (see Table 7). All of these alcohols have both trans and gauche conformers. For the first three alcohols, the hydrogen atom is adjacent to the OH group, whereas for the latter alcohols, an alkyl group replaces the H atom.
Table 7 Comparison of the cis-inversion tunneling splitting energy ΔE0+0− of alcohols
Species ΔE0+0−/GHz
a Ref. 7. b Ref. 4. c This work. d Ref. 5. e Ref. 3. f The values are for the axial and equatorial forms, respectively. g Ref. 9.
Cyclopropanol 4.1a
Isopropanol 46.8b
Cyclohexanol 52.2c
n-Propanol 91d
Ethanol 96.7e
1-Methylcyclohexanol 102.5/103f,g

At the same time, this is one of the few cases where the torsional barrier of the hydroxyl group can be compared between the bare molecule and the monohydrated adduct. The experimental observations combined with Meyer's flexible model indicate an increase of the barrier from 377 to 494 cm−1 on water complexation, associated with the more complex concerted motion of the hydroxyl group in the dimer.

The present results confirm the advantages of rotational spectroscopy for the investigation of intra- and intermolecular dynamics in the gas phase. This work will also allow future analysis of other clusters of cyclohexanol, in particular the homodimers, species with several water molecules and larger heteroclusters, providing experimental information on the properties of more complex alcohol aggregates.

Author contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors contributed equally.

Conflicts of interest

There are no conflicts to declare.


We thank the Italian MIUR (PRIN project 2010ERFKXL_001) and the University of Bologna (RFO) for financial support. M. J. and A. L. acknowledge funding by MINECO (CTQ2015-68148-C2-2-P) and Junta de Castilla y León (VA056G18). W. L. thanks the China Scholarships Council (CSC) (201406750002) for a scholarship. L. E. was supported by the Marie Curie fellowship PIOF-GA-2012-328405. We acknowledge the CINECA award under the ISCRA initiative for the availability of high performance computing resources and support.


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Electronic supplementary information (ESI) available: Tables S1–S17 contain transition frequencies, rotational parameters of the isotopic species, ab initio calculations, structural data and description of the structural relaxations taken into account in the flexible model calculation. See DOI: 10.1039/c8cp04455d
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