Hybridization of Nitrogen Determines Hydrogen-Bond Acceptor

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A: Molecular Structure, Quantum Chemistry, and General Theory

Hybridization of Nitrogen Determines Hydrogen Bond Acceptor Strength: Gas Phase Comparison of Redshifts and Equilibrium Constants Kristian H. Møller, Alexander Kjærsgaard, Anne Schou Hansen, Lin Du, and Henrik Grum Kjaergaard J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00541 • Publication Date (Web): 26 Mar 2018 Downloaded from http://pubs.acs.org on March 26, 2018

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The Journal of Physical Chemistry

Hybridization of Nitrogen Determines Hydrogen Bond Acceptor Strength: Gas Phase Comparison of Redshifts and Equilibrium Constants Kristian H. Møller1, Alexander Kjaersgaard1, Anne S. Hansen1, Lin Du1,† and Henrik G. Kjaergaard1,* 1

Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

ABSTRACT: Gas phase Fourier transform infrared (FTIR) spectroscopy and quantum chemical calculations are combined to illustrate the effect of hybridization on the hydrogen bond acceptor strength of nitrogen by a comparison of nine bimolecular complexes. We present gas phase results for the complexes of methanol, ethanol and 2,2,2-trifluoroethanol with acetonitrile (sphybridized N) and find that the structure of these complexes is nearly linear and dominated by the OH-N hydrogen bond with no experimental indication of an OH-π bonded structure. We compare experimental redshifts and equilibrium constants, obtained by combining experiments and theory, for these complexes to the corresponding complexes with pyridine (sp 2-hybridized N) and trimethylamine (sp3-hybridized N). The comparison clearly illustrates that increasing the s-character of the nitrogen lone pair decreases the hydrogen bond acceptor strength (sp3 > sp2 > sp). The observed trend correlates with the basicity of the acceptors and can be explained by the partial charge on the accepting nitrogen atom and the degree of localization of the nitrogen lone pair.

INTRODUCTION Hydrogen bonds are important in a wide variety of systems from biology to atmospheric science. Their strength and directionality affect the structure of a range of biological systems from DNA to proteins.1-3 In the atmosphere, hydrogen bonds affect the radiative properties by formation of molecular complexes.4-6 Furthermore, their importance has been acknowledged in the formation and growth of atmospheric aerosol influencing the radiative forcing of the Earth, cloud formation, as well as human health.7-11 In reaction kinetics, hydrogen bonding can influence overall reaction rates and affect product distributions.12 IUPAC defines the hydrogen bond as “an attractive interaction between a hydrogen atom from a molecule or a molecular fragment X–H in which X is more electronegative than H, and an atom or a group of atoms in the same or a different molecule, in which there is evidence of bond formation.”13 As such, both the donor atom (X) and the acceptor atom are important in determining the strength of the hydrogen bond. Among the hydrogen bond acceptor atoms, a number of recent studies have found that N is a significantly stronger hydrogen bond acceptor atom than O, S and P which are of comparable hydrogen bond acceptor strength.14-18 These studies, however, focus on elements in compounds with only single bonds, with the accepting atoms traditionally considered sp3-hybridized. In the liquid phase, it has been shown, that for nitrogen, the hybridization has a large effect on the hydrogen bond acceptor strength and that sp-hybridized nitrogen atoms are significantly weaker hydrogen bond acceptors than their sp2 and sp3 hybridized analogs, see e.g. 19-21 and references therein. The relative strength of sp2 and sp3 hybridized nitrogen compounds as acceptors seems to depend on the donor. For instance, redshifts of the fundamental OHstretching of 81-82, 284-300 and 427-430 cm-1 have been reported in CCl4 for methanol (MeOH)-acetonitrile (CH3–C≡N, AN, sp-

hybridized N), MeOH-pyridine (Pyr, sp2-hybridized N) and MeOH-triethylamine (TEA, sp3-hybridized N), respectively.22-26 However, for the corresponding phenol complexes, larger redshifts are reported with Pyr as the acceptor (465-492 cm-1) than with TEA as the acceptor (380-450 cm-1), also in CCl4.25, 27-28 Acetonitrile remains the inferior acceptor also with phenol, with reported redshifts of 150-178 cm-1.29-30 Here, we compare the gas phase hydrogen bond acceptor strength of nitrogen with the three different degrees of hybridization, sp, sp2 and sp3. Redshifts and equilibrium constants obtained using a combination of room-temperature gas phase Fourier transform infrared (FTIR) spectroscopy and quantum calculations are used to compare nine different complexes. The complexes consist of three different alcohol donors, methanol, ethanol (EtOH) and 2,2,2-trifluoroethanol (TFE) with three different nitrogen containing acceptors, acetonitrile (sp hybridized), pyridine (sp 2 hybridized) and trimethylamine (TMA, sp3 hybridized). The complexes with TMA as the acceptor have already been presented in the literature and especially the MeOH-TMA complex has been studied extensively in the gas phase.31-37 For these complexes, we base our comparison on the experimental data available. While experimental observations of the pyridine complexes have been presented recently, no equilibrium constants were determined.38 The gas phase AN complexes are presented here for the first time. For these new AN complexes, we compare measured spectra to calculated wavenumbers to identify the conformers that dominate the experimental gas phase spectra, more particularly whether the complexes exhibit an OH-N or OH-π hydrogen bond.

EXPERIMENTAL DETAILS MeOH (anhydrous, 99.8%), TFE (anhydrous, 99.9%), and AN (anhydrous, 99.8%) were purchased from Aldrich, and EtOH (anhydrous, 99.9%) was purchased from Kemetyl. All chemicals

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were degassed by freeze-pump-thaw cycles on a vacuum line before use. The gas phase spectra of the MeOH–AN, EtOH–AN and TFE–AN complexes were recorded using a Vertex 70 FTIR spectrometer (Bruker) in the mid-infrared (MIR) region with 1.0 cm-1 resolution (one MeOH-AN spectrum was recorded with a 0.2 cm-1 resolution). A CaF2 or KBr beam splitter and an MCT detector were fitted to the spectrometer, which was purged with dry N2 to minimize the effect of H2O and CO2 from the air surrounding the cell. The spectra were recorded at room temperature (295-298 K) using a 10 cm path length single pass gas cell and a 2.4 m path length multi-reflection White gas cell (Infrared Analysis, Inc.). The vapors of the chemicals were led into the gas cell on a vacuum line with a base pressure of ~10-4 Torr. Known pressures of the gases were mixed in the cell for at least 30 min to ensure equilibrium. To reduce the effect of condensation of AN, the gas was kept in the cell for 30 min before recording the monomer spectra, see Figure S1. Sample pressures were measured with Agilent Technologies CDG-500 capacitance diaphragm (full scale 1000 Torr and full scale 10 Torr) pressure gauges connected to the cell and vacuum line, respectively. Spectra of the complexes were obtained by subtracting reference monomer spectra of known pressures from the spectrum of the mixture of the two monomers. The pressures of the monomers in the mixtures were obtained from the reference spectra by scaling these to obtain a flat baseline in regions of only monomer absorption during the spectral subtractions. An air spectrum was also subtracted to remove the influence of absorption from water in the ambient air surrounding the cell, see Section S1.2. Section S1.3 provides a detailed explanation of the experimental procedures for determining equilibrium constants. The spectral subtraction and band integration were performed with the OPUS 6.5 (Bruker) and OriginPro 9 and 2015 software, respectively. No new spectra are recorded for the alcohol-Pyr and alcohol-TMA complexes. The experimental procedures employed for the alcohol-pyridine and alcohol-TMA complexes are very similar and described in references 37 and 38, respectively. For the alcohol-Pyr complexes, pressures were originally measured with a Varian Pirani capacitance diaphragm (PCG750) pressure gauge and have been corrected using the Agilent Technologies CDG-500 pressure gauge, see Section S1.4.38

THEORY AND CALCULATIONS The conformational space of all nine complexes was sampled manually by displacing the two monomer units relative to each other and optimizing at the ωB97X-D/6-31+G(d) level of theory in Gaussian 09, version D.01.39-43 All unique structures were subsequently optimized at the ωB97X-D/aug-cc-pVTZ level of theory using the opt=verytight and int=ultrafine keywords.44-45 The absence of imaginary frequencies in a subsequent frequency calculation was used to confirm that the stationary points located were minima on the potential energy surface. The monomers and complexes of MeOH-AN and EtOH-AN were further optimized at the higher CCSD(T)-F12a/cc-pVDZF12 (abbreviated F12) level of theory in Molpro 2012.1. 46-51 For TFE-AN and the Pyr and TMA complexes, no F12 optimizations were conducted due to computational limitations. As recommended for use with the cc-pVDZ-F12 basis set, the keyword gem_beta=0.9, which determines the geminal Slater exponent, was employed for all Molpro calculations.48 For the F12 optimizations, the following optimization thresholds were employed: energy = 10-7 au, gradient = 10-5 au and step = 10-5 au. For the individual energy calculations during the optimization, the the following thresholds were employed: energy = 10-8 au, orbital = 10-7 au and coeff = 10-7 au.

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Vibrational frequencies and intensities for the fundamental OHstretching transition in the alcohols and complexes were calculated using both a 1D and a 2D numerical local mode (LM) approach, the latter including the OH-stretching and COH-bending of the alcohols, as described elsewhere in the literature.52-54 For both of these modes, only the hydrogen atom of the OH-group is displaced, while the rest of the geometry is kept fixed at its equilibrium structure. For the complexes, the wavenumbers and intensities of the OH-stretches were further calculated using the recently developed local mode perturbation theory (LMPT) model.54-56 This model expands upon the LM model by accounting for the effect of selected intermolecular vibrational modes using perturbation theory.54-56 When used in combination with F12 ab initio calculations, the LMPT model has been found to yield good results for a number of bimolecular hydrogen bonded complexes.5456 In its current form, the mathematical definition of the intermolecular modes in the LMPT model assumes a structure with a clear near-linear hydrogen bond. It can in principle be applied to any type of hydrogen bond, but this would require a redefinition of the intermolecular modes and investigation of the associated displacements. Therefore, is employed only to conformers with a near-linear hydrogen bond. For the TFE-TMA complex, results from the 1D LMPT model (using a 1D LM basis) were employed, due to an unreasonable coupling between the redshifted fundamental OH-stretching and the first overtone of the COH-bend. The known overestimation of the redshift in the LM model shifts the fundamental OH-stretching band to closely match the first overtone of the COH-bend thus inducing an unphysically large coupling, see Section S2.54-55 The 2D LMPT model (using a 2D LM basis) was employed for all other complexes. In the LMPT model employed here, we have included the effect of two of the intermolecular vibrational modes in the perturbation theory.54 For all alcohol monomers and complexes, the vibrational models were employed using potential energy and dipole moment surfaces at the ωB97X-D/aug-cc-pVTZ level of theory. For the MeOH and EtOH monomers and their complexes with acetonitrile, the vibrational calculations were also conducted at the F12 level of theory to provide benchmark results for the smallest complexes and corroborate spectral assignments and hence structural arrangement. To visualize the interactions between the monomer units in the complexes, the non-covalent interactions (NCI) index was calculated using the program NCIPLOT Version 3.0 and imaged using VMD.57-59 Atomic polar tensor (APT) atomic charges were calculated in Gaussian 09 to determine the partial atomic charges of the monomers.60 The lone pairs of the monomers were visualized by electrostatic potential energy contours calculated in Spartan’14 at the ωB97X-D/6-31+G(d) level of theory.61 The program AIM2000 Version 2.0 was used to identify bond critical points by the theory of Atoms In Molecules (AIM) using the ωB97XD/aug-cc-pVTZ electron densities.62

RESULTS AND DISCUSSION A total of nine different complexes are included in this work to assess the hydrogen bond acceptor strength of nitrogen with various degrees of hybridization; sp, sp2 and sp3. Six of these have previously been observed in the gas phase and presented in the literature.31-38 We begin by presenting the new results obtained for the alcohol-acetonitrile complexes and discuss their conformational structure before comparing all nine complexes.

Observation and Characterization of AlcoholAcetonitrile Complexes In Figure 1, we show the conformers obtained for the complexes of the three alcohols MeOH, EtOH and TFE with acetonitrile at

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the ωB97X-D/aug-cc-pVTZ level of theory (optimized structures are available online). For the MeOH-AN complex, we find two conformers, MeOH-AN (A) and MeOH-AN (B). MeOH-AN (A) has a nearly linear hydrogen bond structure (see Table 1) suggesting a clear OH-N hydrogen bond, while the bent nature of MeOHAN (B) suggests stronger influence from dispersion interactions and an OH-π hydrogen bond. The same pattern has previously been found for the water-acetonitrile complex and both conformers have been observed using matrix-isolation IR spectroscopy.63 The assignment of the interaction in the two conformers of MeOH-AN based on their geometries is confirmed by NCI. The NCI isosurfaces show only a single interaction in the linear conformer (A) corresponding to the OH-N hydrogen bond, see Figure 2. The interaction in the other conformer (B) shows a blue region between the hydrogen atom and the C≡N triple bond indicative of an OH-π hydrogen bond as well as a larger green isosurface suggesting dispersion interactions.

bonded conformer(s) by more than 3 kJ/mol compared to the πbonded conformer(s) (see Table S3).

Table 1. OH-N angle (degrees) calculated at the ωB97XD/aug-cc-pVTZ level of theory. Complex

OH-N angle

MeOH-AN (A)

172.9

MeOH-AN (B)

140.4

t-EtOH-AN (A)

171.1

g-EtOH-AN (A)

173.6

t-EtOH-AN (B)

141.6

g-EtOH-AN (B)

138.7

TFE-AN

161.8

Figure 1. Conformers of MeOH-AN, EtOH-AN and TFE-AN optimized at the ωB97X-D/aug-cc-pVTZ level and divided into two categories by the type of hydrogen bond. The color-coding of the atoms is: gray = C, red = O, white = H and blue = N.

For the EtOH-AN complexes, conformers with both gauche (g) and trans (t) ethanol are found theoretically leading to a total of four EtOH-AN conformers. These correspond to the OH-N and OH-π conformers of MeOH-AN but with both the gauche and trans conformer of the EtOH monomer unit. For TFE-AN, only the conformer with a near-linear OH-N hydrogen bond and the gauche orientation of the TFE monomer is found. In Table 1 we show that the OH-N angle deviates about 10° more from linearity for TFE-AN compared to the other OH-N conformers. This is due to dispersion interactions of the F atoms, as shown by the NCI isosurfaces in Figure S5. The presence of only one conformer of TFE-AN can be ascribed to TFE being a very strong hydrogen bond donor favoring the clear hydrogen bond and showing a strong preference for the gauche conformer in the monomer (7 kJ/mol at the ωB97X-D/aug-cc-pVTZ level of theory, see Table S1).64-65 A single OH-N conformer has also been observed in the literature for the ethyne-acetonitrile complex.66 For both the MeOH-AN and EtOH-AN complexes, we find that all conformers have zero-point corrected electronic energies within 1.1 kJ/mol of each other at the ωB97X-D/aug-cc-pVTZ level of theory (see Table S2). Recently, the relative conformational zero-point corrected electronic energies for binding to O and π in the systems of MeOH with three different furans was compared for various computational methods.67 It was found that ωB97X-D yielded results within 1 kJ/mol compared to more elaborate methods. However, it is the Gibbs free energy that governs the conformational abundance. These Gibbs free energies are notoriously difficult to calculate due to their very strong dependence on the calculated frequency of the low frequency modes and vary very much between theoretical methods (see Table S3).68-69 However, for the MeOH-AN and EtOH-AN complexes, we find that the ωB97XD/aug-cc-pVTZ calculated Gibbs free energies favor the N-

MeOH-AN (A)

MeOH-AN (B)

Figure 2. NCI isosurfaces for MeOH-AN at the ωB97X-D/aug-ccpVTZ level of theory. The range of λ2×ρ(r) used for color-coding the NCI isosurfaces is -0.015 to 0.015 au at s = 0.5 au, where |∇𝜌(𝑟)| 1 𝑠= 4/3 . The electron density of the AIM bond critical 2 )1/3 2(3𝜋

𝜌(𝑟)

point connecting H and N is 0.0220 and 0.0109 for MeOH-AN (A) and MeOH-AN (B), respectively. Color-coding of the atoms as in Figure 1. The color-coding of the isosurfaces is blue for strong attractive interactions corresponding to the hydrogen bond and green is weaker attractive dispersion interactions.

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The OH-stretching vibration in all three alcohol-acetonitrile complexes is observed experimentally as a broad band, which is redshifted relative to the OH-stretching band in the corresponding monomer, see Figure 3 and Table 2. The redshifts (defined in Table 2) are very similar for MeOH-AN and EtOH-AN at 52 and 50 cm-1, respectively, and significantly larger for TFE-AN at 100 cm-1. This suggests similar hydrogen bond strength in MeOH-AN and EtOH-AN and a significantly stronger hydrogen bond in the TFE-AN complex, in accordance with other studies comparing these hydrogen bond donors with various other acceptors.37-38 The increased strength of the TFE donor has been ascribed to the electron withdrawing effect of the fluorine atoms and is reflected in its greater acidity.37, 70 For the MeOH-AN complex, we are unable to get a good spectral subtraction of the complete OHstretching region of the complex. This is due to the weak signal of the complex combined with the intense OH-stretching transition in the MeOH monomer, which lies close and has strong and sharp resolved rotational lines (see Figure S8 for larger spectral range). Thus, we can only determine an approximate band area and the equilibrium constant has a larger uncertainty for this complex.

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Table 2. Experimentally observed fundamental OHstretching band positions (cm-1) and redshifts (cm-1) for the alcohol monomers and their complexes with AN.

𝜈̃𝑀𝑜𝑛𝑜𝑚𝑒𝑟 𝜈̃𝐶𝑜𝑚𝑝𝑙𝑒𝑥 𝛥𝜈̃ 𝑐

𝑎

𝑏

MeOH-AN

EtOH-AN

TFE-AN

3681

3669

3657

3629

3619

3557

52

50

100

a

Defined as the Q-branch for MeOH and TFE and weighted center of the band containing both gauche and trans for EtOH. b Defined as wavenumber of maximum absorbance for EtOHAN and TFE-AN. Due to the noise in the MeOH-AN spectrum, the center of a fitted Lorentzian is used, see Figure S9. c Difference between fundamental OH-stretching wavenumber in monomers and complexes (𝛥𝜈̃ = 𝜈̃𝑀𝑜𝑛𝑜𝑚𝑒𝑟 − 𝜈̃𝐶𝑜𝑚𝑝𝑙𝑒𝑥 ), both as defined above. In Table 3 we compare the calculated wavenumbers of the fundamental OH-stretching transitions of the different conformers of MeOH-AN and EtOH-AN. We see a clear difference between the OH-N and OH-π conformers. For both complexes, the OH-N conformer(s) [MeOH-AN (A), t-EtOH-AN (A) and g-EtOHAN(A)] show(s) a redshift which is significantly larger than in the OH-π conformer(s) [MeOH-AN (B), t-EtOH-AN (B) and gEtOH-AN (B)]. This suggests that the OH-N hydrogen bond is stronger than the OH-π hydrogen bond in these complexes. The LMPT model at the F12 level of theory has previously been found to yield wavenumbers in very good agreement with experiments.54-55 We find that the wavenumbers calculated at this level for the fundamental OH-stretching of the OH-N MeOH-AN and EtOH-AN complexes (Table 3) are in excellent agreement with the experimentally observed wavenumbers. This strongly suggests that the OH-N conformers are responsible for the observed spectral bands. For the OH-N MeOH-AN and EtOH-AN complexes, the LMPT model at the ωB97X-D/aug-cc-pVTZ level overestimates the wavenumbers by 20-30 cm-1. The LMPT model is known to blueshift LM values, and by fortuitous cancellation of error, very good agreement is found between the ωB97X-D/aug-cc-pVTZ LM values and the experimentally observed and F12 LMPT calculated values. Very little difference is observed between the 1D and 2D LM values, see Section S10.2.54

Figure 3. Experimental spectra of the fundamental OH-stretching region of the three alcohol-AN complexes. Pressures and temperature for each measurement are given in Table S5. In all three, the corresponding monomer peak is located just around the right edge of the spectra.

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Table 3. Calculated and observed wavenumbers (in cm-1) of the fundamental OH-stretching vibration in the alcohol-AN complexes. H-bond

Complex

𝝂̃𝟏𝑫𝑳𝑴,𝝎𝑩𝟗𝟕𝑿−𝑫a

𝝂̃𝟐𝑫𝑳𝑴,𝝎𝑩𝟗𝟕𝑿−𝑫b

𝝂̃𝑳𝑴𝑷𝑻,𝝎𝑩𝟗𝟕𝑿−𝑫c

𝝂̃𝑳𝑴𝑷𝑻,𝑭𝟏𝟐d

𝝂̃𝒆𝒙𝒑𝒕.e

OH-N

MeOH-AN (A)

3622

3621

3651

3626

3629

OH-π

MeOH-AN (B)

3698

3688

-

-

OH-N

t-EtOH-AN (A)

3621

3619

3650

3617

OH-N

g-EtOH-AN (A)

3620

3618

3641

3610

OH-π

t-EtOH-AN (B)

3700

3695

-

-

OH-π

g-EtOH-AN (B)

3693

3680

-

-

OH-N

TFE-AN (A)

3549

3553

3579

-

3619

3557

Calculated using the 1D local mode model at the ωB97X-D/aug-cc-pVTZ level of theory. Calculated using the 2D local mode model at the ωB97X-D/aug-cc-pVTZ level of theory. c Calculated using the 2D local mode perturbation theory (LMPT) model at the ωB97X-D/aug-cc-pVTZ level of theory. d Calculated using the 2D local mode perturbation theory (LMPT) model at the F12 level of theory. e Experimental value defined as in Table 2. a

b

Using the LM model at the ωB97X-D/aug-cc-pVTZ level, we find wavenumbers for the OH-π conformers that are 60-80 cm-1 higher than the observed band maxima (application of the LMPT model would shift them to even higher frequencies). This supports our assignment of the observed band to the OH-N conformers. We see no spectral indications of the presence of the OH-π complex (see Figure S10). This means that while minor contributions from the OH-π conformers cannot be ruled out, the OH-N conformers seem to dominate the spectra. This is in spite of the relative zeropoint corrected electronic energies of the two motifs being comparable for both MeOH-AN and EtOH-AN (see Table S2). The relative Gibbs free energies of the different conformers, which actually governs their abundance, show preferential binding to N over π by at least 3 kJ/mol at the ωB97X-D/aug-cc-pVTZ level (with large variation between methods, see Table S3), in line with the experimental observations.68 Furthermore, the calculated intensity of the fundamental OH-stretching transition is about a factor of 5 higher in the N-bonded conformer compared to the πbonded conformer (see Section S10.2) further explaining why the π-bonded conformer is not observed experimentally. For the remainder of this work, we will therefore consider only the OH-N conformers. The competition between binding to a heteroatom or a π-system has previously been studied in jet cooled experiments where cluster formation is significantly more favored. Preferential binding to nitrogen over the π-system has also been observed in the complexes of pyrrole with water, methanol and ethanol.71 With oxygen as the heteroatom in the acceptor, the same preference has been observed with anisole (methoxybenzene) as the acceptor in its complexes with both water, phenol and methanol and in the complex of methanol and furan, 2-methylfuran and 2,5dimethylfuran.67, 72-76 In the complexes of 2,3-benzofuran with both water and methanol, the two binding sites (oxygen and π) are found to be in close competition.77 In a series of complexes with methanol and various substituted furans, the preferred binding site has been shown to depend on the degree of substitution.78 Calculations suggest that with furan as the acceptor, the most stable binding pattern depends on the donor.79 Finally, calculations suggest preferred binding to the heteroatom for the complexes of TFE with furan and 2-methyl furan and for MeOH with furan, 2,5-dihydrofuran and pyrrole, while the two sites are comparable in MeOH-thiophene.80-81

Comparison of Hydrogen Bond Acceptor Strength For the alcohol-Pyr and alcohol-TMA complexes, our calculations show one N-bonded conformer with MeOH and TFE as donors, and both a gauche and trans conformer for each of the EtOH complexes, see Figures S6 and S7. We do not consider the π-bonded conformers of the alcohol-Pyr complexes due to their high relative energy (Table S2). In Figure 4, we show the fundamental OH-stretching band of the complexes of TFE with AN, Pyr and TMA as hydrogen bond acceptors. The observed redshift (𝛥𝜈̃) of the fundamental OHstretching band is considered a measure of the strength of the hydrogen bond and the figure shows a very clear trend in terms of hydrogen bond acceptor strength of the three hydrogen bond acceptors: TMA (𝛥𝜈̃ = 485 cm-1) is stronger than Pyr (𝛥𝜈̃ = 370 cm-1), which is in turn significantly stronger than AN (𝛥𝜈̃ = 100 cm-1). This trend is in good agreement with the liquid phase results with MeOH as the donor presented earlier.22-26 As we show in Table 4, the same trend is observed with MeOH and EtOH as hydrogen bond donors. This shows that the strength of the hydrogen bond depends strongly on the hybridization of the acceptor nitrogen atom and increased p-character in the lone pair increases the hydrogen bond acceptor strength (sp3 > sp2 > sp). The spectrum of TFE-Pyr in Figure 4 has been truncated due to an absorption caused by CH-stretches in pyridine, which are too intense to be subtracted completely due to detector saturation. The full range can be seen in Figure S11.

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Figure 4. Fundamental OH-stretching transitions in the complexes with TFE and the three different hydrogen bond acceptors. TFEAN is from this work, while TFE-Pyr and TFE-TMA are from Lane et al.38 and Hansen et al.37, respectively. Temperature and pressures for the specific measurements are given in Table S13. While the redshift provides a measure of the strength of the hydrogen bond, the equilibrium constant (or equivalently, the Gibbs free energy) of complex formation is a measure of the total interaction strength between the monomer units in each of the complexes. The equilibrium constants are determined using the approach described in detail elsewhere.82-83 The approach combines measured monomer pressures with a complex pressure (𝑃𝑐𝑜𝑚𝑝𝑙𝑒𝑥 ) derived using the integrated absorbance of the fundamental OHstretching band (∫ 𝐴(𝜈̃)𝑑𝜈̃) and a calculated oscillator strength for that transition (𝑓𝑐𝑎𝑙𝑐 ) using the equation shown below:84-85 𝑃𝑐𝑜𝑚𝑝𝑙𝑒𝑥 = 2.6935 × 10−9 [K−1 Torr m cm]

𝑇 ∫ 𝐴(𝜈̃ )𝑑𝜈̃ 𝑓𝑐𝑎𝑙𝑐 × 𝑙

By combining results from experiments conducted at different combinations of monomer pressures, the equilibrium constant can be determined as the slope of a plot of the determined complex pressure as a function of the product of measured monomer pressures multiplied by the standard pressure, see Sections S1.3 and S14. To compare equilibrium constants, we need oscillator strengths for all complexes calculated at the same level of theory. Due to computational limitations we choose the ωB97X-D/aug-cc-pVTZ LMPT level, which is in best agreement with the F12 LMPT oscillator strengths for the AN complexes (see Tables S7 and S8). For the TMA complexes, we recalculated the equilibrium constants based on the experimental results presented in the literature but using the oscillator strengths calculated here at the ωB97XD/aug-cc-pVTZ LMPT level (see Tables S21 and S22).37 For the pyridine complexes, the equilibrium constants have not previously been determined. For these, the equilibrium constants are determined here, based on spectral integration of the experimental results already presented in the literature, while the equilibrium constants for the MeOH-AN, EtOH-AN and TFE-AN are based on the spectra recorded in this work.38 The spectra of MeOH-AN do not allow accurate integration, as the MeOH monomer band overlaps with the high-energy side of the transition from the complex. The equilibrium constant for the MeOH-AN complex is determined from only three experiments, all with very low absorbance from the complex, see Section S14.1. Thus, the uncertainty of this value is greater than that of the other complexes, and this complex will not be part of the following discussion regarding uncertainties. However, the similarity of MeOH and EtOH as hydrogen bond donors in terms of calculated and observed redshifts suggest that the equilibrium

Page 6 of 13

constant for MeOH-AN will be comparable to that of EtOH-AN, as observed for complexes of these alcohols with other acceptors.37, 64 For the three EtOH complexes, the gauche and trans conformers have similar energies and oscillator strengths (see Table S2 and Section S10.2) suggesting that they are both present in the spectrum. The calculations (Table 3) suggest that the two conformers will have transitions within 10 cm-1 of each other and with the broadness of the bands, we expect these to overlap to form a single band as observed, even in the presence of both conformers. We therefore use an average oscillator strength of the two conformers to determine the equilibrium constants. For each of the three EtOH complexes, the average oscillator strength deviates less than 15% from the oscillator strength of either conformer representing the upper limit for the error from the averaging procedure. The oscillator strengths calculated at the ωB97XD/aug-cc-pVTZ level of theory for the AN complexes are overestimated by less than 27% relative to the F12 values providing an estimate of the uncertainty introduced by calculating the oscillator strengths at this lower level of theory. Due to the scarcity of experimental intensities for molecular complexes, it is difficult to assess the uncertainty of the F12 LMPT oscillator strengths. By comparison to experimental and theoretical values for the water dimer, a previous study has suggested a maximum uncertainty of 35%, which we also adopt here.56, 86-89 The uncertainty (95% confidence interval) in the linear fits used for determining the equilibrium constants here is 20% for EtOHAN and less than 11% for the other complexes, see Table S23 and Section S14 for the linear fits. The largest uncertainty is found for the EtOH-AN complex due to its small equilibrium constant and small redshift. Similarly, we estimate the largest uncertainty in the integrated absorbance for EtOH-AN at up to 50%, while the uncertainty is below 10% for the remaining complexes. This uncertainty is estimated from the effect of a slight baseline shift based on the noise in the spectra. The uncertainty of the measured monomer pressures are assumed to be negligible. Combining the error from the integrated absorbance, the calculated oscillator strengths and the linear fits, we estimate the total uncertainty of the determined equilibrium constants to be less than a factor of two for all complexes but the EtOH-AN for which it is up to a factor of three. Again, the uncertainty for the MeOH-AN complex is larger. However, as shown previously, the uncertainty in these combined experimental and theoretical equilibrium constants is significantly smaller than purely theoretical equilibrium constants obtained using various electronic structure methods which vary more than two orders of magnitude between methods, see Table S4.68 The use of the fundamental OH-stretching band for determining equilibrium constants has been tested for the MeOHdimethylamine (DMA) complex, for which the equilibrium constant could also be determined from the first overtone of the NHstretching transition.36, 54 Using high level oscillator strengths and correcting for slight differences in temperature, the same value is obtained using both transitions, which suggests that the OHstretching band is a valid choice provided that an accurate oscillator strength can be calculated for this transition. 36, 54 Furthermore, this suggests that the uncertainty of the calculated equilibrium constants is smaller than reported above.13, 90

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Table 4. Observed wavenumbers, 𝝂̃ (cm-1), redshifts, 𝜟𝝂̃ (cm-1) and determined equilibrium constants, KP, (and corresponding standard Gibbs free energies, ΔG⦵, kJ/mol) at room temperature (295-300 K). Oscillator strengths used for the determination of each equilibrium constant are summarized in Table S22. MeOH

𝜈̃ b

AN

Pyr

f

TMAg

𝛥𝜈̃ 𝑎

EtOH

KP (ΔG⦵)

𝜈̃

52

~0.017c (~10 c)

3472

209

0.086e

3355

326

0.16e (4.6)

3629

(6.0)

𝛥𝜈̃ 𝑎

TFE

KP (ΔG⦵)

𝜈̃

𝛥𝜈̃ 𝑎

KP (ΔG⦵)

50

0.035d (8.3)

3557

100

0.26e (3.4)

3462

207

0.096e

3289

368

2.5e (-2.3)

3345

324

0.19e (4.1)

3174

483

3.9e,h (-3.4)

3619

(5.8)

aDefined

as in Table 2. Calculated from the wavenumbers of the complexes presented in the original literature but with the monomer wavenumbers in Table 2 for consistency. b The temperatures for the three equilibrium constants are 295 K (MeOH), 297 K (EtOH) and 296 K (TFE). c Estimated uncertainty larger than for EtOH-AN by about 50 % due to integrated band intensity and only three experiments. d Estimated uncertainty less than a factor of three. See text. e Estimated uncertainty less than a factor of two. See text. f Wavenumbers from 38. The temperatures for the three equilibrium constants are 296 K (MeOH), 298 K (EtOH), and 299 K (TFE). g Wavenumbers for MeOH-TMA from 36. Remaining wavenumbers and experimental results for determination of equilibrium constants from 37. The temperatures for the three equilibrium constants are 297 K (MeOH), 296 K (EtOH), and 297 K (TFE). h Based on a 1D LMPT oscillator strength, see “Theory and Calculations”. The remaining equilibrium constants are based on 2D LMPT oscillator strengths. In Table 4, we show the equilibrium constants (KP) and corresponding standard Gibbs free energies of complex formation (ΔG⦵) that have been obtained for the complexes using the combined experimental and theoretical procedure described above. The equilibrium constants are determined at slightly different temperatures, but remain qualitatively comparable. The trend found for the equilibrium constants matches that observed for the redshifts of the complexes: For the donors, we find again that TFE is a stronger donor than MeOH and EtOH, which are comparable. TMA is the strongest acceptor followed by Pyr followed again by AN. As observed for the redshifts, the difference between Pyr and AN is larger than that between TMA and Pyr. Again this indicates that the interaction strength of complexes depends strongly on the hybridization of the acceptor nitrogen with the order sp3 > sp2 > sp. The same trend in hydrogen bond acceptor strength is observed for equilibrium constants in the liquid phase, as shown for instance by a hydrogen-bond basicity scale.21 The trend observed with hydrogen bond acceptor strength (TMA > Pyr > AN) is reflected in the basicity of the three hydrogen bond acceptors, as shown by the pKa values of their corresponding acids as shown in Table 5.91-93 The higher the pKa value of the corresponding acid, the better the molecule is at accepting protons as a base. Since hydrogen bonding can be considered partial accept of a proton, it is not surprising, that the hydrogen bond acceptor strength is correlated with basicity.94

Table 5. pKa values of the corresponding acid and calculated APT charges (au) on the accepting nitrogen atom in the monomers. Compound

pKaa

APT charge Nb

TMA

9.80

-0.66

Pyr

5.23

-0.39

AN

-4.20

-0.33

tensor (APT) charges show that the overall observed trend (TMA > Pyr > AN) correlates with the calculated partial charge on the nitrogen atom in the three monomers, as shown in Table 5. Given the electrostatic contribution to the hydrogen bond, a larger charge difference between the monomer units agrees well with increased hydrogen bond strength. Secondly, the localization of the nitrogen lone pair correlates with the hydrogen bond (and total interaction) strength. This is visualized in Figure 5, by plotting the electrostatic potential energy (isovalue of -35 kcal/mol) surface for the three different acceptor molecules. This corresponds to the surface at which a proton, if placed there, would feel an attraction of 35 kcal/mol. The figure clearly shows that the lone pair in TMA is more localized to the area in which the hydrogen bond is formed, while the lone pair in AN covers a significantly larger area. That means that TMA will allow for a larger orbital overlap of the lone pair with the σ*(OH) bond of the hydrogen bond donor and thereby a stronger hydrogen bond. This is reflected in the electron density of the AIM bond critical point of the hydrogen bond: For each donor, the density increases from AN to Pyr to TMA, see Table S24. A rationalization for the degree of localization of the lone pair can be found in the hybridization of the nitrogen atom. The nitrogen atom in TMA is sp3 hybridized and the large p-character leads to it being more localized. In contrast, the large s-character of the sp hybridized nitrogen atom leads to a rather diffuse and delocalized lone pair for AN. The degree of scharacter in the lone pair has previously been correlated with proton affinities.95

a From

references 91-93. b Calculated at the ωB97X-D/aug-cc-pVTZ level of theory. The hydrogen bond acceptor strength can be explained in terms of the combination of two effects. Firstly, calculated atomic polar

Figure 5. Electrostatic potential energy (isovalue -35 kcal/mol) surface calculated at the ωB97X-D/6-31+G(d) level of theory.

7



For CH hydrogen bond donors, the opposite trend has been observed so that C(sp)-H forms the strongest hydrogen bond followed by C(sp2)-H, while C(sp3)-H forms the weakest hydrogen bonds to the same acceptor, which correlates with the acidities.96-98

CONCLUSION Using gas phase Fourier transform infrared (FTIR) spectroscopy, we have detected the hydrogen bonded complexes of methanol (MeOH), ethanol (EtOH) and 2,2,2-trifluoroethanol (TFE) with acetonitrile (AN) as the acceptor. Comparison of measured and calculated wavenumbers suggest that the conformers observed in the spectra are linear with a clear hydrogen bond to the nitrogen atom. The observed redshifts of the fundamental OH-stretching vibration in the three complexes are 52, 50 and 100 cm-1 for MeOH-, EtOH-, and TFE-AN, respectively. Based on the measured spectra and calculated oscillator strengths, the room temperature equilibrium constants for the MeOH-AN, EtOH-AN and TFE-AN complexes are determined to be ~0.017, 0.035 and 0.26, respectively, corresponding to Gibbs free energies of formation of ~10, 8.3 and 3.4 kJ/mol. The uncertainty in the determined equilibrium constants is a factor of three for EtOH-AN, a factor of two for TFE-AN, while the value for MeOH-AN is more approximate. We compare the redshifts and equilibrium constants of the nine complexes with the three alcohols and the acceptors trimethylamine (TMA), pyridine (Pyr) and AN. For these complexes, we clearly demonstrate the expected trend, that the hydrogen bond acceptor strength of nitrogen depends on its hybridization; TMA (sp3 hybridized) is a better acceptor than Pyr (sp2 hybridized), which is in turn a significantly better acceptor than AN (sp hybridized) with these donors. This is demonstrated in the gas phase, which means that the effect is independent of solvent effects and other potential influences in the liquid phase. The trend is explained by a decreasing negative charge on N as well as increasing s-character and thus decreased localization in the lone pair in the series from TMA to Pyr to AN and is reflected in the basicity of the acceptors.

Page 8 of 13

AUTHOR INFORMATION Corresponding Author *Henrik G. Kjaergaard, [email protected]. Phone: +45-35320334 Fax: +45-35320322

ORCID Kristian H. Møller: 0000-0001-8070-8516 Alexander Kjaersgaard: 0000-0002-0985-0613 Anne S. Hansen: 0000-0002-6285-586X Lin Du: 0000-0001-8208-0558 Henrik G. Kjaergaard: 0000-0002-7275-8297 Present Addresses † Environment Research Institute, Shandong University, Shanda South Road 27, 250100 Shandong, China

ACKNOWLEDGMENT We are grateful to Kasper Mackeprang for helpful discussions regarding the LMPT model, and Xue Yang and Siyang Li for preliminary calculations. We acknowledge the Center for Exploitation of Solar Energy, University of Copenhagen, Danish Center for Scientific Computing, National Natural Science Foundation of China (91644214) and Shandong Natural Science Fund for Distinguished Young Scholars (JQ201705) for funding.

ABBREVIATIONS FTIR, Fourier transform infrared; MeOH, methanol; EtOH, ethanol; TFE, 2,2,2-trifluoroethanol; AN, acetonitrile; Pyr, pyridine; TMA, trimethylamine; TEA, triethylamine; F12, CCSD(T)F12a/cc-pVDZ-F12; LM, local mode; LMPT, local mode perturbation theory; NCI, non-covalent interactions; APT, atomic polar tensor; AIM, Atoms In Molecules; g, gauche; t, trans.

ASSOCIATED CONTENT Supporting Information. Figure showing condensation of AN, spectra showing the effect of water subtraction, detailed description of equilibrium constant determination, description of the pressure correction employed for the Pyr complexes, description of the vibrational coupling in TFE-TMA, NCI figures all complexes, relative conformational energies, structures of the conformers of the Pyr and TMA complexes, calculated Gibbs free energies and equilibrium constants, pressures and temperatures of spectra shown in main manuscript, Lorentzian fit to MeOH-AN, 1D and 2D LM and LMPT calculated wavenumbers and oscillator strengths, fundamental OH-stretching in EtOH-AN and TFE-Pyr showing larger spectral region, experimental details for all experiments, oscillator strengths and temperatures used to determine equilibrium constants, uncertainties from linear fits and electron densities in AIM bond critical points. This material is available free of charge via the Internet at http://pubs.acs.org. Optimized structures of complexes and monomers at the ωB97X-D/aug-cc-pVTZ and F12 levels of theory are available at: http://www.erda.dk/public/archives/YXJjaGl2ZS1QclRkcFU=/pu blished-archive.html

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Hybridization of Nitrogen Determines Hydrogen-Bond Acceptor

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