Hydrogen bonding in alcohol–ethylene oxide and alcohol–ethylene sulfide complexes

Abstract

The hydrogen bonds involving sulfur are generally regarded as weak hydrogen bonds in comparison with conventional ones. The O–H⋯O and O–H⋯S hydrogen bonds in the alcohol–ethylene oxide (EO) and alcohol–ethylene sulfide (ES) complexes in the gas phase have been investigated by FTIR spectroscopy. Three alcohols, methanol (MeOH), ethanol (EtOH) and 2,2,2-trifluoroethanol (TFE) were used as hydrogen bond donors, and comparable OH-stretching red shifts were observed for the complexes with EO and ES as hydrogen bond acceptors. DFT calculations were used to determine the stable structures and interaction energies of the complexes. The equilibrium constant for the complex formation was determined from the experimental integrated absorbance and the computational IR intensity of the OH-stretching transition band of the complex. The effect of CF₃ substitution on the hydrogen bond strength in alcohol–EO/ES molecular complexes was investigated and the TFE complexes form much stronger hydrogen bonds than the MeOH and EtOH complexes. Atoms-in-molecules (AIM) analysis revealed that several hydrogen bond interactions were present in the complexes. In addition, the localized molecular orbital-energy decomposition analysis (LMO-EDA) was implemented to analyze the intermolecular interactions. The O–H⋯O and O–H⋯S hydrogen bonds were found to be of similar strength, on the basis of the geometric parameters, binding energies and AIM analysis.

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1. Introduction

Heterocyclic compounds are an important group of organic molecules due to their applications in organic synthesis, as well as in industrial processes such as the production of polymers. Ethylene oxide (EO) and ethylene sulfide (ES) are the smallest heterocyclic molecules and exhibit interesting features in their molecular structure. EO is one of the most produced organic chemicals and its global production rate is expected to exceed 27 million tons per year by 2017. It is an important chemical intermediate for producing a wide range of products.¹ It has also been identified in the interstellar medium by observation in the millimeter region and in an experimental simulation of Titan's atmosphere by gas chromatography-mass spectrometry (GC-MS) and infrared spectroscopy.^2–4 ES is the smallest sulfur-containing heterocyclic compound and it is often studied as a comparison to EO.^5,6

Intermolecular interactions, such as hydrogen bonding, exist in many chemical and biological systems. Vibrational spectroscopy is an effective method to observe and characterize the hydrogen bond interactions.^7–9 The hydrogen bonded H₂O–EO complex was studied in neon matrix and with supersonic jet to obtain its FTIR spectra.¹⁰ The concentration dependence of the band at 3535.8 cm⁻¹ in neon matrix over a very wide range presents the same linear dependence with respect to either H₂O or EO, which gives confidence for assigning this absorption to the ν(OH)_b band of the H₂O–EO complex. As expected, vibrational frequencies measured in neon matrix are a few cm⁻¹ shifted with respect to the gas phase jet spectra (−6 cm⁻¹ for ν(OH)_b). The formation of 1 : 1 complex of trifluoroethene with EO has been observed in cryogenic solutions, using liquid argon and liquid krypton as solvents.¹¹ FTIR spectra and ab initio calculations show that the interaction occurs via, primarily, a hydrogen bond between the trifluoroethene C–H bond and the oxygen atom of EO. Furthermore, modification of the hydrogen bond donor can have large effect on the strength of a hydrogen bond. As reported in previous studies of methanol (MeOH), ethanol (EtOH) and 2,2,2-trifluoroethanol (TFE) complexes, the replacement of an H atom with a methyl group had limited effect on the hydrogen bond interaction, but the replacement with a CF₃ group had a significant effect.^12,13

Sulfur as a hydrogen bond acceptor is less common than oxygen and nitrogen.^14,15 The strength (weak or strong), nature (electrostatic or dispersive) and directionality (linear or non-linear) of sulfur center hydrogen bonds (SCHBs) are still debatable and need to be investigated at the molecular level.¹⁶ It is worth investigating the nature of the hydrogen bond to sulfur and comparing it to the bonding to oxygen. There are a few reports in the literature on the O–H⋯O and O–H⋯S hydrogen bonds.^17–19 Similar red shifts of the OH-stretching transition frequencies and binding energies were obtained for these two types of hydrogen bonds. Sulfur was concluded to be a weaker, but nearly equivalent hydrogen bond acceptor to oxygen. Similarly, the weak complexes of dimethylamine (DMA) with dimethylether (DME) and dimethylsulfide (DMS) were studied to compare the N–H⋯O and N–H⋯S hydrogen bonds.²⁰ The red shifts of the NH-stretching transition in both complexes were very small, 5 and 19 cm⁻¹ for the DMA–DME and DMA–DMS complexes, respectively. The calculated binding energies for the two complexes only differed by <0.5 kcal mol⁻¹, and the N–H⋯O and N–H⋯S hydrogen bonds were found to be of similar strength. Besides, the ground-state rotational spectrum of the EO–ES complex was measured by Fourier transform microwave spectroscopy,²¹ and the observed data were interpreted in terms of an antiparallel structure of Cs symmetry with the EO bound to the ES by two C–H(ES)⋯O and two S⋯H–C(EO) hydrogen bonds.

The present study was motivated by the importance of the relative strength of different types of hydrogen bonding. To focus on possible differences in the roles of the oxygen and sulfur atoms in the intermolecular interactions, we have chosen MeOH, EtOH, TFE as the hydrogen bond donors and EO and ES as the hydrogen bond acceptors to compare the hydrogen bond strength between the O–H⋯O and O–H⋯S hydrogen bonds. EO and ES have similar structure and are appropriate acceptors for investigating the relative strength of hydrogen bonding to oxygen and sulfur. The IR spectra of the alcohol–EO/ES complexes were measured in the gas phase at room temperature. We have combined the calculated intensities and the measured integrated absorbance of the fundamental OH-stretching transitions to determine the equilibrium constants of complexation. Moreover, we performed atoms-in-molecules (AIM) analysis to investigate the electronic densities and the intermolecular hydrogen bond interactions in the complexes. Natural bond orbital (NBO) analysis was used to explain the donor–acceptor charge delocalization between the lone pair of the acceptor and the antibonding orbital of the donor. In addition, the localized molecular orbital-energy decomposition analysis (LMO-EDA) was also implemented to analyze the intermolecular interactions.

2. Experimental details

MeOH (Aladdin, anhydrous, ≥99.9%), EtOH (Dengke, anhydrous, ≥99.7%), TFE (Aladdin, anhydrous, 99.5%), EO (Guoyao, ≥98%) and ES (SPC, 98%) were degassed with multiple freeze–pump–thaw cycles on a vacuum line before use. The IR spectra were recorded at 1.0 cm⁻¹ resolution and 128 scans with a Bruker Vertex 70 FTIR spectrometer fitted with KBr beam splitter and a DLaTGS (deuterated and L-alanine-doped triglycine sulfate) detector. A 20 cm glass cell equipped with CaF₂ windows was used to measure the spectra at room temperature. The cell was connected to a vacuum line with base pressure of less than 1 × 10⁻⁴ Torr. Pressures were measured with Tamagawa CDG-800 pressure gauges. Before the measurement of the mixtures, we waited for half an hour to ensure equilibrium. Spectral subtraction and analysis was performed with OPUS 7.2 software.

3. Computational details

The calculations were carried out with three functionals: B3LYP, ωB97X-D, and B3LYP-D3, as implemented in Gaussian 09,²² using aug-cc-pVTZ basis set on all atoms except for the sulfur atom. To improve the energy convergence, the recommended tight d functions were included for the sulfur atom, aug-cc-pV(T+d)Z.^23,24 The ωB97X-D and B3LYP-D3 functionals were selected due to the inclusion of an empirical dispersion correction, which has been shown to give an important contribution for noncovalent interaction.²⁵ The traditional B3LYP functional was also employed for comparison. Geometry optimizations were performed for the monomers and complexes with the “opt = verytight” and “integral = ultrafine” convergence criteria. Calculations with these two options have shown to give good frequencies and thermochemical corrections to the electronic energies for the hydrogen bonded complexes.^12,13 Several stable conformers of the complexes were obtained and frequency analysis was followed to ensure that the conformers were indeed structural minima. The binding energies (BE) were corrected with the zero-point vibrational energy (ZPVE) and basis set superposition errors (BSSE). The counterpoise (CP) procedure was applied to remove BSSE,²⁶ which has been shown to improve interaction energies of weakly bound complexes.^9,27–29

Atoms-in-molecules (AIM) analysis is widely accepted as a powerful tool that provides an understanding of both covalent and noncovalent molecular interactions, including hydrogen bonds.^30,31 Topological analysis of the charge density was carried out by utilizing the AIM2000 program (version 2) package.^32,33 The natural bond orbital (NBO) analysis is used to explain the hydrogen bonding in the X–H⋯Y system as the donor–acceptor charge delocalization takes place between the lone pair of the acceptor Y and the proximal antibonding orbital of the donor.^34,35 The NBO analysis was performed in Gaussian 09 with the three DFT functionals to compare the different hydrogen bond interactions in the complexes.

The total interaction energy of the complexes was decomposed into individual energy components at the B3LYP/aug-cc-pVTZ level (aug-cc-pV(T+d)Z basis set for sulfur) using the localized molecular orbital energy decomposition analysis (LMO-EDA), which is implemented in the GAMESS (US) program package.³⁶ The total interaction energy (E^INT) is divided into electrostatic energy (E^ES), exchange energy (E^EX), repulsion energy (E^REP), polarization energy (E^POL) and dispersion energy (E^DISP).³⁷ The interaction energy in terms of component energy terms is expressed as:

ΔE^INT = ΔE^ES + ΔE^EX + ΔE^REP + ΔE^POL + ΔE^DISP (1)

The E^ES term represents the total columbic interaction between the free monomer charge distributions. The E^EX term is the interaction caused by the exchange of electrons between the monomers satisfying Pauli's principle, and this contribution accounts for the short-range repulsion due to overlap of the electron distribution of one monomer with that of another. The E^POL term denotes the polarization interaction. The E^DISP interaction is an attractive interaction between molecules and atoms. However, to avoid misleading, it should be pointed out that the dispersion term in the LMO-EDA analysis is defined using the change in the correlation functionals on going from monomers to complexes.³⁷ Therefore, the dispersion energy is actually “correlation energy”. To be consistent with the LMO-EDA literature,^37,38 it is still called dispersion energy in this paper. The E^REP interaction is the opposing attractive force between two molecules.

4. Results and discussion

4.1. Geometry and interaction energy

The B3LYP-D3 optimized structures of the alcohol–EO and alcohol–ES complexes are shown in Fig. 1. Both the EtOH and TFE monomers have two structures, where t indicates a trans-conformer, and g a gauche-conformer. The two conformers of EtOH have very similar energy as predicted by computational methods, therefore both conformers exist in the gas phase.³⁹ The overtone bands of EtOH confirm the existence of the two conformers at room temperature.³⁹ There was also clear evidence of OH-stretching transitions for the existence of both conformers (trans 3655.5 cm⁻¹ and gauche 3660.5 cm⁻¹) in argon matrices.⁴⁰ However, only TFE (g) was observed in the infrared spectrum of TFE in the gas phase,⁴¹ and only the gauche-conformer of TFE is found to form hydrogen bonded complexes. Selected geometric parameters of the complexes are given in Tables 1 and S1.† The functionals including an empirical dispersion correction (ωB97X-D and B3LYP-D3) predict structures in good agreement with the high level CCSD(T) calculations,¹⁷ which indicates that the dispersion correction is important to describe the noncovalent interactions accurately.²⁵ TFE–EO/ES shows a much larger change in the OH bond length and a much smaller hydrogen bond distance than the other complexes, which indicates that the hydrogen bond in TFE complexes is much stronger than those in the MeOH and EtOH complexes. The intermolecular hydrogen bond angles of alcohol–EO deviate within 27° from the ideal linear orientation, and for the alcohol–ES complexes, the angles deviate within 35°.

Fig. 1 Optimized structure of the complexes with the B3LYP-D3 functional (t denotes for trans-conformers, g for gauche-conformers).

Table 1 Selected optimized geometric parameters of the complexes with the B3LYP-D3 method (angles in degrees and bond lengths in Å)^a

Conformer	r(OH)^b	Δr(OH)^c	r(HB)^d	θ(HB)^e
a aug-cc-pV(T+d)Z basis set for S and aug-cc-pVTZ basis set for the remaining atoms.b OH bond length.c Δr(OH) = rcomplex − ralcohol, is the change in the OH bond length upon complexation.d Intermolecular hydrogen bond distance.e Intermolecular hydrogen bond angle, i.e., θ(O–H⋯O) and θ(O–H⋯S).
MeOH–EO	0.9693	0.0084	1.9148	154.3
EtOH–EO (t)	0.9692	0.0082	1.9234	153.3
EtOH–EO (g)	0.9698	0.0079	1.9237	156.9
TFE–EO (g)	0.9761	0.0131	1.8027	168.7
MeOH–ES	0.9692	0.0084	2.4227	146.8
EtOH–ES (t)	0.9691	0.0081	2.4357	145.7
EtOH–ES (g)	0.9698	0.0078	2.4270	150.5
TFE–ES (g)	0.9758	0.0128	2.3038	158.6

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The calculated binding energy (BE), enthalpy of formation (ΔH^θ_298K), Gibbs free energy of formation (ΔG^θ_298K) and equilibrium constant at 298 K for all conformers are listed in Tables 2 and S2.† In general, the BSSE and ZPVE values do not vary much for the complexes studied and the three methods. The ωB97X-D and B3LYP-D3 BEs are quite similar, whereas the B3LYP BE is underestimated. The complexes formed by MeOH and EtOH have similar BEs whereas the TFE complexes have much larger BEs. There is only a little difference in BEs (with differences <2.3 kJ mol⁻¹) between the MeOH/EtOH–EO complexes and the MeOH/EtOH–ES complexes. Previously, EtOH–EO (g) was found to be more stable than EtOH–EO (t) (MP2/6-311++G(d,p): 0.57 kJ mol⁻¹).⁴² Our calculations also show that EtOH–EO (g) is slightly more stable than EtOH–EO (t) (B3LYP-D3: 0.4 kJ mol⁻¹), and for the ES complexes, EtOH–ES (g) is more stable (B3LYP-D3: 0.5 kJ mol⁻¹). Generally, both the t- and g-conformer for EtOH complex have very similar BE with the same method. In TFE complexes, the BE for TFE–EO is about 2–4 kJ mol⁻¹ larger than that of TFE–ES. Besides, the B3LYP-D3 functional predicts larger ΔH^θ_298K and smaller ΔG^θ_298K than the other methods. There is only a little difference in ΔH^θ_298K and ΔG^θ_298K between alcohol–EO and alcohol–ES, which shows that the hydrogen bond strengths of these two types of complexes are similar.

Table 2 Calculated binding energy (BE), enthalpy of formation (ΔH^θ_calc), Gibbs free energy of formation (ΔG^θ_calc) and equilibrium constant (K^calc_eq) at 298 K for the complexes with the B3LYP-D3 method^a

Conformer	BE^b	ZPVE	BSSE	ΔH^θcalc	ΔG^θcalc	K^calceq
a aug-cc-pV(T+d)Z basis set for S and aug-cc-pVTZ basis set for the remaining atoms. Energies are in kJ mol^−1.b BE corrected with ZPVE and BSSE.
MeOH–EO	−21.3	5.6	0.4	−20.7	11.0	1.2 × 10^−2
EtOH–EO (t)	−21.4	5.2	0.5	−20.4	11.3	1.1 × 10^−2
EtOH–EO (g)	−21.8	5.6	0.5	−21.1	13.6	4.1 × 10^−3
TFE–EO (g)	−30.0	5.3	0.9	−29.6	7.2	5.5 × 10^−2
MeOH–ES	−20.2	4.7	0.5	−19.3	11.5	9.5 × 10^−3
EtOH–ES (t)	−20.6	4.3	0.5	−19.3	10.9	1.2 × 10^−2
EtOH–ES (g)	−21.1	4.9	0.5	−20.3	16.8	1.1 × 10^−3
TFE–ES (g)	−27.2	4.0	0.9	−26.4	11.2	1.1 × 10^−2

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4.2. Experimental and calculated OH-stretching transitions

The gas phase spectra of the alcohol–EO and alcohol–ES complexes were measured at room temperature (298 K), and the spectra in the OH-stretching region were presented in Fig. 2 and 3 and in the ESI.† The spectra of the complexes were obtained by subtraction of the individual monomer spectra from the spectrum of their mixture.^12,13 To confirm the formation of a 1 : 1 complex, the spectra of the complexes were recorded at different combinations of monomer pressures. As seen in the Figures, stronger OH-stretching vibration bands are observed in the higher pressure measurements. In the infrared absorption spectra, the integrated intensity of the complex band is proportional to its partial pressure, p_complex. The integrated absorbance of the OH-stretching band in the complexes is plotted against the product of the pressures of the monomers, and the result fits well with a linear fit (Fig. S5†). The integration regions for MeOH–EO, EtOH–EO and TFE–EO are 3398–3674, 3397–3658 and 3219–3659 cm⁻¹, respectively. Similar measurements were performed for the alcohol–ES complex, and the integration regions for MeOH–ES, EtOH–ES and TFE–ES are 3420–3628, 3371–3629 and 3259–3626 cm⁻¹, respectively. The formation of the ES complexes in the mixture before subtraction is not as pronounced as the alcohol–EO complexes, however, the complex band was obtained by successful spectral subtraction.

Fig. 2 (A) Spectra of TFE, EO, and their mixture in the 3300–3640 cm⁻¹ region. A 20 cm path length cell was used. (B) Spectra of the TFE–EO complex in the [small nu, Greek, tilde]_OH band region. (a) 19 Torr TFE + 156 Torr EO; (b) 16 Torr TFE + 112 Torr EO.

Fig. 3 (A) Spectra of TFE, ES, and their mixture in the 3300–3635 cm⁻¹ region. A 20 cm path length cell was used. (B) Spectra of the TFE–ES complex in the [small nu, Greek, tilde]_OH band region. (a) 23 Torr TFE + 77 Torr ES; (b) 14 Torr TFE + 41 Torr ES.

The OH-stretching fundamental transition of MeOH–EO, EtOH–EO, TFE–EO, MeOH–ES, EtOH–ES and TFE–ES are measured to be 3601, 3595, 3502, 3571, 3557 and 3479 cm⁻¹, respectively. The OH-stretching transition frequency of MeOH–EO and MeOH–ES is 6 and 14 cm⁻¹ larger than those of EtOH–EO and EtOH–ES, respectively. It is interesting to compare the OH-stretching transition of the MeOH–EO and EtOH–EO complexes with their intramolecular analog glycidol. The OH-stretching wavenumber of glycidol was measured to be 3608 cm⁻¹ in supersonic jet cooled FTIR spectra.⁴³ However, the vibrational frequency could be different under different experimental conditions. The OH-stretching transition frequency of MeOH was reported to be 3681 and 3686 cm⁻¹ under room temperature and jet cooled conditions, respectively.^13,44 In the case of methyl lactate, the OH-stretching transition in the gas phase at room temperature (3574 cm⁻¹) is 9 cm⁻¹ larger than the jet cooled value.^45,46 Furthermore, the measured values were the same for the OH- and NH-stretching transitions in TFE (3657 cm⁻¹) and pyrrole (3531 cm⁻¹), respectively.^13,47–49 There might be a few wavenumbers difference between the vibrational frequencies in the room temperature and low temperature jet cooled measurements. Therefore, it is not possible in this case to indicate the ring strain in glycidol as compared to the MeOH–EO and EtOH–EO complexes. Besides, when the CH₃ group in the hydrogen bond donor is replaced with a CF₃ group, the OH-stretching transition wavenumber and bandwidth changes significantly. This phenomenon has been illustrated in previous observations in the alcohol–trimethylphosphine (TMP) and alcohol–amine complexes.^12,13

The red shifts of the OH-stretching fundamental transitions in the complexes relative to those in the corresponding monomers are calculated. The OH-stretching fundamental transitions of the alcohols in the gas phase are taken from our previously published paper,¹³ in which the measurements were performed with the same method at room temperature as we did in the current study. However, the transition wavenumber of the gauche-conformer of EtOH is taken from a higher resolution (0.35 cm⁻¹ resolution) study.³⁹ The red shifts of the OH-stretching fundamental transition of MeOH–EO and EtOH–EO (t) are measured to be 80 and 82 cm⁻¹, respectively. In a similar H₂O–EO complex, the OH-stretching fundamental transition was observed at 3542 cm⁻¹ with supersonic jet cooled FTIR spectra at low temperature, and the red shift was reported to be 115 cm⁻¹.¹⁰ The red shift of the H₂O–EtOH complex was measured to be similar (109 cm⁻¹) by supersonic jet FTIR spectra.⁵⁰ The red shift changes under different experimental conditions. For example, the red shift of the OH-stretching transition in methanol dimer was measured to be 82 cm⁻¹ in the gas phase at room temperature.¹³ The red shift measured with jet experiment at low temperature was reported to be 111 cm⁻¹.⁴⁴ A difference of about 30 cm⁻¹ also exists in the case of ethanol dimer between room temperature and jet experimental conditions.³⁹ The differences between the red shifts are larger than those between the vibrational frequencies of the monomers as discussed above, showing the large temperature effect on the vibrational transitions in the complexes. Taking this effect into consideration, the red shift of the OH-stretching transition in the H₂O–EO complex is expected to be close to those in the MeOH/EtOH–EO complexes. Besides, we carried out calculations for H₂O–EO and the binding energy is −18.8 kJ mol⁻¹ with ZPVE and BSSE corrections (B3LYP-D3/aug-cc-pVTZ), which is close to that of MeOH–EO (−21.3 kJ mol⁻¹).

The observed OH-stretching fundamental transition wavenumbers and the red shifts of the complexes are summarized in Table 3. In general, the red shifts in alcohol–ES are slightly larger (40 cm⁻¹ or less) than in alcohol–EO. The X–H⋯Y (X = O, N; Y = O, S) type of hydrogen bonded complexes has previously been studied.^18,19,51,52 The NH-stretching red shift in the N–H⋯S bonded DMA–DMS complex was found to be 19 cm⁻¹, and the red shift in the N–H⋯O bonded DMA–DME complex was only 5 cm⁻¹.⁵² In contrast, the OH-stretching red shift in O–H⋯O hydrogen bonded complexes has been found to be larger than that in O–H⋯S bonded complexes for the p-cresol·H₂O (127 cm⁻¹) and p-cresol·H₂S (102 cm⁻¹) complexes. Similarly, the OH-stretching red shift of 317 and 282 cm⁻¹ were observed for the p-cresol·tetrahydrofuran (THF) and p-cresol·tetrahydrothiophene (THT) complexes, respectively. Whether O or S is the better hydrogen bond acceptor depends on the specific system. The deconvolution of the absorption bands of the complexes have been carried out and the best fit was obtained by fitting two Lorentzian functions (see in the ESI†).

Table 3 Calculated OH-stretching wavenumbers and oscillator strengths of the alcohols and complexes with the B3LYP-D3 method^a

Conformer	[small nu, Greek, tilde]/cm^−1		Δ[small nu, Greek, tilde]^b/cm^−1		f	f/falcohol
	Calculated	Observed	Calculated	Observed
a aug-cc-pV(T+d)Z basis set for S and aug-cc-pVTZ basis set for all the remaining atoms.b Δ[small nu, Greek, tilde]OH = [small nu, Greek, tilde]alcohol − [small nu, Greek, tilde]complex.c Ref. 13.d Ref. 39.
MeOH	3828	3681^c			5.8 × 10^−6
EtOH (t)	3825	3677^c^,^d			5.3 × 10^−6
EtOH (g)	3809	3660^d			4.2 × 10^−6
TFE (g)	3804	3657^c			9.1 × 10^−6
MeOH–EO	3655	3601	173	80	8.6 × 10^−5	14.8
EtOH–EO (t)	3657	3595	168	82	8.9 × 10^−5	16.7
EtOH–EO (g)	3648	3595	161	65	7.3 × 10^−5	17.2
TFE–EO (g)	3527	3502	277	155	1.5 × 10^−4	16.7
MeOH–ES	3649	3571	179	110	7.4 × 10^−5	12.7
EtOH–ES (t)	3653	3557	172	120	7.5 × 10^−5	14.0
EtOH–ES (g)	3642	3557	168	103	6.4 × 10^−5	15.1
TFE–ES (g)	3522	3479	282	178	1.4 × 10^−4	15.2

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The OH-stretching fundamental wavenumbers of the alcohols and complexes were calculated with the B3LYP, ωB97X-D and B3LYP-D3 methods (Tables 3 and S3†). The calculated harmonic wavenumbers of the OH-stretching vibrations are larger than the experimental observations. However, as seen in Table 3, the calculated difference between the trans- and gauche-conformer of EtOH (16 cm⁻¹) agrees well with the experimental value (17 cm⁻¹). The calculated OH-stretching red shifts of the alcohol–ES complexes are larger by 20–40 cm⁻¹ than those in the alcohol–EO complexes. The oscillator strengths (f) and the relative intensities (f/f_alcohol) of the OH-stretching fundamental transition for the complexes are also listed in Tables 3 and S3.† The oscillator strengths of OH-stretching vibrations in the complexes were calculated to be about 15 times stronger than those of free alcohols. There is no significant difference in the oscillator strength between alcohol–EO and their corresponding ES complexes. The oscillator strengths of TFE complexes are larger than those of the complexes of MeOH and EtOH. In addition, the calculated oscillator strengths of different conformers of a same complex are quite close.

4.3. Thermodynamic equilibrium constant

The equilibrium constant (K_p) is determined from:where p^θ is the standard pressure (1 bar = 0.99 atm). The pressures of alcohols, EO, and ES were measured before measurement. The partial pressure of the complex in Torr was determined from the measured integrated absorbance and calculated oscillator strengths (f_calc) of the fundamental OH-stretching band, as following:⁴⁸where T is the temperature in K, is the integrated absorbance in cm⁻¹, l is the optical path length in m and f_calc is the calculated intensity (Table S3†). The method to determine the partial pressure of the complex has been used in similar studies.^7,12,53,54

With regard to the EtOH–EO/ES complexes, there are two conformers of very similar binding energy. We took the average of the calculated oscillator strengths of the gauche- and trans-conformers for the EtOH–EO and EtOH–ES complexes at the B3LYP/aug-cc-PVTZ level to determine the pressures of complexes. The f_calc used are 9.5 × 10⁻⁵, 9.3 × 10⁻⁵, 1.5 × 10⁻⁴, 8.0 × 10⁻⁵, 7.6 × 10⁻⁵ and 1.5 × 10⁻⁴ for MeOH–EO, EtOH–EO, TFE–EO, MeOH–ES, EtOH–ES and TFE–ES, respectively. The alcohol–EO complex pressure is plotted as a function of p_{MeOH/EtOH/TFE} × p_EO in Fig. 4. The K_p of the alcohol–EO complex is obtained from the slope of the least-square fitting of these data. It is clear from the slopes that the TFE–EO complex has a much larger K_p value. The measured K_p for MeOH–EO, EtOH–EO and TFE–EO are 2.7 × 10⁻², 2.9 × 10⁻² and 3.0 × 10⁻¹, respectively. A plot of the pressure of the alcohol–ES complexes p_complex as a function of p_{MeOH/EtOH/TFE} × p_ES is also shown in Fig. 4. The measured K_p for MeOH–ES, EtOH–ES and TFE–ES are 8.6 × 10⁻³, 1.1 × 10⁻² and 3.8 × 10⁻², respectively. Similar to the alcohol–EO complexes, the K_p of the TFE–ES complex is larger than EtOH–ES and MeOH–ES. The K_p of alcohol–ES is smaller than that of the corresponding alcohol–EO complex. Compared with the K^calc_eq from the DFT calculations (Tables 2 and S2†), the B3LYP-D3 method predicts the best. Most of the other calculated values are significantly underestimated as compared to the measured equilibrium constants. The measured K_p values are about an order of magnitude smaller than those for the alcohol–amine complexes.¹²

Fig. 4 (A) Plot of p_complex against p_{MeOH/EtOH/TFE} × p_EO. (B) Plot of p_complex against p_{MeOH/EtOH/TFE} × p_ES.

The Gibbs free energies of formation could be determined from the measured K_p values. The ΔG^θ_expt are measured to be 2.5, 2.3, −0.2, 2.1, 4.7 and 1.6 kJ mol⁻¹ for MeOH–EO, EtOH–EO, TFE–EO, MeOH–ES, EtOH–ES and TFE–ES, respectively. The difference between MeOH–EO and MeOH–ES is very small (0.4 kJ mol⁻¹), and the difference between TFE–DME and TFE–DMS is 1.8 kJ mol⁻¹. As compared with the computed ΔG^θ_calc values, the B3LYP-D3 results are closer to the experimental values.

4.4. AIM analysis

Topological analysis was used to obtain more information on how complexation influences the electron density of monomers. Additionally, topological analysis using AIM provides an alternative way to evaluate the hydrogen bond strength. AIM analysis was performed using the wavefunctions calculated with the DFT functionals. The electron density ρ(r) and Laplacian ∇²ρ(r) at the bond critical points (BCPs), the change in atomic energy at H atom ΔE(H), and the change in electronic charge at H atom Δq(H) should be noted. The B3LYP-D3 topological parameters are listed in Table 4, whereas the results obtained by other DFT methods are provided in ESI.†

Table 4 AIM parameters of the change in electronic charge at H atom Δq(H), the change in atomic energy at H atom ΔE(H), the electron density ρ(r) and Laplacian ∇²ρ(r) at the BCPs for the complexes obtained with the B3LYP-D3 method^a

Conformer	Δq(H)	ΔE(H)	ρ(BCP)	∇^2ρ(BCP)
a aug-cc-pV(T+d)Z basis set for S and aug-cc-pVTZ basis set for all the remaining atoms. All values are in a.u.
MeOH–EO	0.0378	0.0220	0.0285	0.0882
EtOH–EO (t)	0.0399	0.0229	0.0280	0.0876
EtOH–EO (g)	0.0143	0.0223	0.0281	0.0862
TFE–EO (g)	0.0386	0.0242	0.0369	0.0954
MeOH–ES	0.0077	0.0135	0.0191	0.0423
EtOH–ES (t)	0.0092	0.0141	0.0186	0.0418
EtOH–ES (g)	0.0118	0.0145	0.0192	0.0417
TFE–ES (g)	−0.0062	0.0075	0.0250	0.0444

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The topology of the gradient vector field could show the existence of a BCP between the donating and accepting atoms in a hydrogen bond.⁵⁵ The AIM plots of the alcohol–EO/ES complexes obtained with B3LYP-D3 method are shown in Fig. S7.† The bond critical points (BCPs) and ring critical points (RCPs) are presented by the red and yellow balls, respectively. The AIM plots show the BCPs along the lines joining the OH and Y (O, S) atoms for the alcohol–EO and alcohol–ES complexes, which clearly prove the presence of a hydrogen bond between the alcohols and EO/ES. The distance between a BCP and a RCP can also be used as a criterion to measure the structural stability of a hydrogen bond.⁵⁶ In the TFE–EO and TFE–ES complexes, the distances between the BCP of the O–H⋯O/S hydrogen bond and the RCP are 2.460 and 2.585 Å, respectively, while the distances between the BCP of the C–H⋯F hydrogen bond and the same RCP are 1.672 and 1.858 Å.

The electron density is related to bond order and, consequently, to bond strength.⁵⁶ The electron densities at the BCPs are in the ranges of 0.0280–0.0369 and 0.0186–0.0250 a.u. for the alcohol–EO and alcohol–ES complexes, respectively. The Laplacian of the electron density are 0.0862–0.0954 and 0.0417–0.0444 a.u. for alcohol–EO and alcohol–ES complexes, respectively. These values are well within the specified range for the presence of a hydrogen bond based on the criteria of electron density (0.002–0.040 a.u.) and its Laplacian (0.024–0.139 a.u.).^55,57 The electron densities of TFE complexes are higher than that of MeOH/EtOH complexes as a result of the stronger hydrogen bond, while MeOH and EtOH show similar electron density upon complexation. The Laplacian of the electron density shows the same trend as the electron density. Meanwhile, the charge density at the BCP for the O–H⋯S interaction was about two thirds of that for the O–H⋯O interaction. The Laplacian of the charge density at BCP was also smaller for the O–H⋯S interaction.

The change in atomic energy at H atom ΔE(H), is defined as the difference between the energies of the same atom in the complex and in the monomer. The atomic energy of H atom increases upon complexation (ΔE(H) > 0).⁵⁸ The ΔE(H) for the O–H⋯O hydrogen bond was 1.5–3 times larger than the O–H⋯S hydrogen bond. Similarly, Biswal et al. investigated the p-cresol·H₂O and p-cresol·H₂S complexes and found that the electron density and its Laplacian for O–H⋯S is smaller than that of the O–H⋯O interaction.¹⁸ By analyzing the loss of atomic energy on H atom, they suggested that O–H⋯O hydrogen bond is stronger than O–H⋯S.

4.5. NBO analysis

NBO analysis was carried out for the monomers and complexes, and a summary of the NBO parameters, including the changes in the natural charges on H (Δq(H)), O (Δq(O)) and S (Δq(S)) atoms, the occupancy in the p-type lone pair orbital (δ(n_pO) and δ(n_pS)) and the antibonding orbital (δ()), the second-order perturbation energy (E⁽²⁾_i→j*), the zeroth-order energy difference of the lone pair orbital and antibonding orbital (ε⁽⁰⁾_j* − ε⁽⁰⁾_i), and the Kohn–Sham matrix element between the orbitals (〈φ⁽⁰⁾_i|F̂_KS|φ⁽⁰⁾_j*〉), with the B3LYP-D3 method is listed in Tables 5 and 6. The parameters obtained by other DFT methods are provided in ESI.† The increase in the natural charges (Δq) on the H atom and decrease on the O or S atoms indicates the existence of charge transfer (electron delocalization). The delocalization of electron density takes place between lone pair of the acceptor Y (O or S) and proximal antibonding orbital of the donor, which corresponds to stabilizing interactions on donor–acceptor and is estimated by the second-order perturbation energies (E⁽²⁾_i→j*).³⁴ The overlaps of the lone pair (LP) orbitals of O atom with the OH antibonding orbital in the EtOH–EO (t) conformer (31.00 kJ mol⁻¹) is similar to that in the EtOH–EO (g) conformer (31.79 kJ mol⁻¹). For MeOH/EtOH–EO, the overlaps of the lone pair and OH antibonding orbital are greater than those in the corresponding alcohol–ES complexes. The overlap in the TFE–EO complex (55.31 kJ mol⁻¹) is greater than that in TFE–ES (51.17 kJ mol⁻¹). The results show a strong influence of the CF₃ group, and it is understandable that the values of the TFE complexes are significantly larger than those of the MeOH/EtOH complexes.

Table 5 NBO parameters for the alcohol–EO complexes with the B3LYP-D3 method^a

NBO parameters	MeOH–EO	EtOH–EO (t)	EtOH–EO (g)	TFE–EO (g)
a The values in the parentheses give the individual contribution of the nonbonding orbitals of oxygen. The δ(npO) values are for each of the two lone pairs. E^(2)i→j* is in kJ mol^−1, all other values are in a.u.
Δq(H)	0.02345	0.01748	0.01840	0.01820
Δq(O)	−0.02619	−0.02518	−0.02497	−0.03114
δ(npO)	1.987, 1.920	1.987, 1.920	1.987, 1.920	1.983, 1.916
	0.0240	0.0228	0.0250	0.0344
E^(2)i→j*	31.96	31.00	31.79	55.31
	(5.56 + 26.40)	(5.31 + 25.69)	(5.77 + 26.02)	(11.59 + 43.72)
ε^(0)j*−ε^(0)i	2.00	2.01	2.00	1.97
	(1.22 + 0.78)	(1.22 + 0.79)	(1.22 + 0.78)	(1.19 + 0.78)
〈φ^(0)i|F̂KS|φ^(0)j*〉	0.100	0.098	0.100	0.133
	(0.036 + 0.064)	(0.035 + 0.063)	(0.037 + 0.063)	(0.051 + 0.082)

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Table 6 NBO parameters for the alcohol–ES complexes with the B3LYP-D3 method^a

NBO parameters	MeOH–ES	EtOH–ES (t)	EtOH–ES (g)	TFE–ES (g)
a The values in the parentheses give the individual contribution of the nonbonding orbitals of sulfur. The δ(npS) values are for each of the two lone pairs. E^(2)i→j* is in kJ mol^−1, all other values are in a.u.
Δq(H)	0.00799	0.00700	0.00743	−0.00180
Δq(S)	−0.02598	−0.02636	−0.02217	−0.01607
δ(nS)	1.996, 1.923	1.996, 1.924	1.996, 1.923	1.995, 1.908
	0.0290	0.0267	0.0301	0.0461
E^(2)i→j*	27.82	25.86	28.28	51.17
	(1.46 + 26.36)	(1.26 + 24.60)	(1.67 + 26.61)	(3.18 + 47.99)
ε^(0)j* − ε^(0)i	1.81	1.83	1.83	1.78
	(1.13 + 0.68)	(1.14 + 0.69)	(1.14 + 0.69)	(1.11 + 0.67)
〈φ^(0)i|F̂KS|φ^(0)j*〉	0.077	0.075	0.079	0.105
	(0.018 + 0.059)	(0.017 + 0.058)	(0.019 + 0.060)	(0.026 + 0.079)

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It is remarkable that the nonbonding electron pairs (LP) on O and S atoms are not equivalent in hydrogen bonds. In the case of EO, one LP is pure p-type orbital and the other one is sp² hybrid orbital, while in the case of ES, one is pure s-type orbital and the other is pure p-type orbital. This is consistent with previous study of the p-cresol·THF and p-cresol·THT complexes.¹⁹ The extent of overlap between the oxygen LP and is greater than that between the sulfur LP and , which suggests that the sulfur LP and overlap is relatively poor upon complexation.

4.6. LMO-EDA analysis

LMO-EDA analysis can provide insights into intermolecular interactions by separating the total interaction energy into five terms including E^ES, E^EX, E^REP, E^POL and E^DISP. This method can be considered as an extension and modification of the methods developed by Kitaura and Morokuma,⁵⁹ Ziegler and Rauk,⁶⁰ and Hayes and Stone.⁶¹ It has four main features: the E^ES, E^EX and E^REP terms are isolated, therefore, it can be used for analyzing both covalent bonds and intermolecular interactions; the E^POL term arises alone; the E^DISP term is derived via a supermolecule approach using size-consistent correlation methods; and the E^EX and E^DISP terms are defined using the changes in the exchange and correlation functionals on going from monomers to supermolecule.³⁷ The LMO-EDA calculation is always affordable as long as the supermolecule calculation is affordable at the requested level of theory, with a computing time that is two to three times longer due to the interaction analysis which involves integral transformations from the basis set to the molecular orbitals.

The LMO-EDA scheme has been widely used for various weak and strong interactions because of its simplicity and robustness.^37,62,63 Su et al. developed the LMO-EDA scheme to analyze the covalent bond and nonbonding interactions, and to estimate the stability of ethane by second-order Møller–Plesset perturbation theory and coupled-cluster methods.³⁷ Ma et al. investigated the hydrogen bond interactions in HXeCCH⋯H₂O and HXeCCH⋯HF complexes by LMO-EDA analysis and found that the dominant stabilizing forces in all the complexes are exchange energies and electrostatic interactions, and the polarization and dispersion interactions play a minor role.⁶² Singh et al. studied the competition between a very weak n → π* interaction and a hydrogen bond (N–H⋯N) interaction presented in the complexes of 7-azaindole with a series of 2,6-substituted fluoropyridines by LMO-EDA analysis and reported that the increase in the dispersion component is much more rapid compared to that of the electrostatic component with an increase in fluorination of the fluoropyridine ring.⁶³

The LMO-EDA calculations were performed at the B3LYP/aug-cc-pVTZ level. The decomposition of the total interaction energy of the complexes is presented in Table 7. The ΔE^ES energy is in the range of −36.7 to −48.3 kJ mol⁻¹ for alcohol–EO complexes, with largest value for the TFE–EO complex. It is the most significant term favoring the complexation compared to the E^EX, E^POL and E^DISP terms. Generally, the individual energy terms for the TFE complexes are all larger than the corresponding MeOH/EtOH complexes, and the EO complexes are larger than the corresponding ES complexes. All the ΔE^REP energies are positive values, indicating that it is the only term favoring the dissociation of the complexes. The total interaction energy values are in the ranges of −19.2 to −27.4 kJ mol⁻¹ and −15.6 to −21.7 kJ mol⁻¹ for the alcohol–EO and alcohol–ES complexes, respectively. The interaction energy obtained from LMO-EDA is found to be comparable to the uncorrected interaction energies calculated at the B3LYP/aug-cc-pVTZ level of theory.

Table 7 Results of localized molecular orbital energy decomposition analysis (LMO-EDA) for the alcohol–EO/ES complexes at the B3LYP/aug-cc-pVTZ level (aug-cc-pV(T+d)Z basis set for sulfur, all values in kJ mol⁻¹)

Conformer	ΔE^ES	ΔE^EX	ΔE^REP	ΔE^POL	ΔE^DISP	ΔE^INT
MeOH–EO	−37.6	−17.6	63.4	−16.0	−12.1	−19.9
EtOH–EO (t)	−36.8	−17.4	62.5	−15.6	−12.0	−19.3
EtOH–EO (g)	−36.7	−17.1	62.3	−15.5	−12.1	−19.2
TFE–EO (g)	−48.3	−22.1	81.4	−23.1	−15.2	−27.4
MeOH–ES	−29.1	−14.3	53.4	−14.7	−11.7	−16.4
EtOH–ES (t)	−28.5	−14.0	52.5	−14.3	−11.6	−15.8
EtOH–ES (g)	−28.4	−13.7	52.0	−13.9	−11.7	−15.6
TFE–ES (g)	−36.4	−18.8	68.8	−21.3	−14.0	−21.7

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5. Conclusions

The alcohol–EO and alcohol–ES complexes have been investigated by gas phase FTIR and DFT calculations. The observed red shifts in the OH-stretching transition for the O–H⋯S bonded complexes were slightly larger than those for the O–H⋯O bonded complexes. The AIM analysis shows that the electron densities and the Laplacian of the electron densities for the O–H⋯S interactions are smaller than those of the O–H⋯O interactions. The NBO analysis indicates that the extent of overlap between the oxygen LP and is greater than that between the sulfur LP and . The O–H⋯O and O–H⋯S hydrogen bonds are of similar strength in the corresponding alcohol–EO and alcohol–ES complexes.

Acknowledgements

This work was supported by National Natural Science Foundation of China (21407095, 21577080) and Shandong Provincial Natural Science Foundation, China (ZR2014BQ013).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra16205c

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