The Strength of Hydrogen Bonds between Fluoro-Organics and

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A: Molecular Structure, Quantum Chemistry, and General Theory

The Strength of Hydrogen Bonds Between FluoroOrganics and Alcohols, a Theoretical Study Robert Evan Rosenberg J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b01148 • Publication Date (Web): 19 Apr 2018 Downloaded from http://pubs.acs.org on April 19, 2018

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The Journal of Physical Chemistry

The Strength of Hydrogen Bonds between Fluoro-Organics and Alcohols, a Theoretical Study

Robert E. Rosenberg* Transylvania University Department of Chemistry 300 North Broadway Lexington, KY 40508 (859) 233-8279 (phone) (859) 233-8171 (fax) [email protected]

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT

The Strength of Hydrogen Bonds between Fluoro-Organics and Alcohols, a Theoretical Study

Fluorinated organic compounds are ubiquitous in the pharmaceutical and agricultural industries. To better discern the mode of action of these compounds it is critical to understand the strengths of hydrogen bonds involving fluorine. There are only a few published examples of the strengths of these bonds. This study provides a high level ab initio study of inter- and intramolecular hydrogen bonds between RF and R’OH, where R and R’ are aryl, vinyl, alkyl, and cycloalkyl. Intermolecular binding energies average near 5 kcal/mol, while intramolecular binding energies average about 3 kcal/mol. Inclusion of zero-point energies and applying a counterpoise correction lessen the difference. In both series, modest increases in binding energies are seen with increased acidity of R’OH and increased electron donation of R in RF. In the intramolecular compounds, binding energy increases with the rigidity of the F-(C)n-OH ring. Inclusion of free energy corrections at 298 K result in exoergic binding energies for the intramolecular compounds and endoergic binding energies for the intermolecular compounds. Parameters such as bond lengths, vibrational frequencies, and atomic populations are consistent with formation of a hydrogen bond, and with slightly stronger binding in the intermolecular cases over the intramolecular cases. However, these parameters correlated poorly with binding energies.

(204 words)


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The Strength of Hydrogen Bonds between Fluoro-Organics and Alcohols, a Theoretical Study Introduction: In recent years, fluoro-organics have been increasingly used in pharmaceuticals and agricultural products.1 Incorporation of fluorine alters many molecular properties in a predictable way. Some notable properties include increased hydrophobicity, increased metabolic stability, increased acidity and decreased basicity of a neighboring group.2 Of particular interest for this work is the ability of fluorine bound to carbon to act as a hydrogen bond acceptor. These hydrogen bonds (HBs) have been invoked to explain binding of fluorinated compounds in DNA analogs3,4,5 and in proteins.6,7,8 However, beginning with early crystallographic work9,10 and continuing up through a 2012 review,11 doubt was cast on the very existence of HBs with fluoroorganics. These concerns are less relevant today due to new evidence, including: direct observation of a HB between CH3F and water in matrix-ir,12 synthesis of numerous fluoroorganics that contain intramolecular hydrogen bonds (IMHBs) 13,14,15,16 and several high level ab initio calculations.17,18,19 According to a recent review “it is now difficult to doubt the existence of hydrogen bonds involving organic fluorine.” 20 Despite the controversial existence of HBs with organic fluorine, fluoro-organics have been implicated as HB acceptors with a variety of donors, the most common being CH, NH, 21 and OH.20 Within this list, the HB with CH is somewhat contentious. 22,23 Cage compounds broaden the scope of HB-like interactions for fluoro-organics by providing a scaffold where they can interact with a wide range of electrophiles. 24 The typical HB acceptor is CF, as CHF2 and CF3 have been shown to form much weaker interactions. 25 This work will focus on the most common type of HB with organic fluorine, those between CF and OH. With the existential argument mostly resolved, it is still an open question if HBs with



organic fluorine are strong enough to affect other physical and chemical properties. 26 This issue has not been settled as there have been very few direct measurements of the strengths of these HBs. As part of a series of studies examining hundreds of HB pairs, only three compounds that contained fluorine were studied: 1-fluoropentane, 1-flurorooctane, and fluorocyclohexane.27 A recent paper used NMR spectroscopy to directly measure the strength of organo-fluorine HBs in a handful of compounds.25 Another recent report used computational chemistry to examine the binding of CH3F to small water clusters.28 For the strength of IMHBs, the literature is mostly silent, with the notable exception of 2-fluorophenol, which has been extensively studied.29 However, outside of these isolated examples, there has been no systemic study of HB strength to fluorine. To address this situation, this work uses high level ab initio calculations to examine the strengths of both inter- and intramolecular hydrogen bonds between fluoro-organics, RF, and alcohols, R’OH. These compounds are illustrated in Figure 1, below. Here, groups A and B refer to intermolecular complexes and groups C to G, to compounds capable of forming an intramolecular HB. Group A shows the 17 pairs of R’OH with CH3F. The 12 pairs of HOH binding to RF are illustrated in group B. The intramolecular series consists of 19 compounds where there is variation in (1) the hybridization of the carbons bound to O or F, (2) the size of the intramolecular rings (from 5-7), and (3) the conformational flexibility of the atoms that form the IMHB. The three main goals of this study are (1) to determine how structural features such as acidity, hybridization, and molecular geometry relate to binding energy (BE), (2) to help establish a reliable method in determining IMHB strength and (3) to compare the features of intermolecular HBs to their IMHB counterparts.


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H A

CH 3F

R'=Me, Et, iPr, tBu, Ph, c-CnH 2n–1 for n=3-6

B

RF

O

HOR' C

F D

(CH 2)n n=0-3

O

H

(CH 2)n

E

(CH 2)n

F

G

(CH 2)n (CH 2)m

O H

F

F

H

F

n=0-2 O

HOH

R=Me, Et, iPr, tBu, Ph, vinyl, isopropenyl, c-CnH 2n–1 for n=3-6

O

H

n=0,1 m=0,1,2

F (CH 2)n n=0,1,2

Figure 1. Compounds used in this study. Intermolecular HBs. A CH3F bound to R’OH. B RF bound to HOH. IMHBs. C 2-fluorocycloalkanols D 3-fluorocycloalkanols E fluorobicycloalkanols F 8-fluoronaphthalen-1-ol G 2-(fluoroalkyl)phenols Theoretical Methods Geometry optimization for all molecules has been carried out using MP2 theory within the frozen core approximation and the aug-cc-pXVZ (X=D and T) basis sets30 using Gaussian 09.31 Frequency calculations were performed at the MP2/aug-cc-pVDZ level as the aug-ccpVTZ basis set was not feasible for most of the larger complexes. In our earlier work, comparisons of the aug-cc-pVDZ calculated frequencies of small clusters showed excellent agreement with those calculated using aug-cc-pVTZ basis set.28 Frequency calculations were used to verify that the geometries were a minimum (no imaginary frequencies), to calculate a vibrational zero-point energy correction (VZPE), and for the analysis of the effect of HB on vibrational frequencies. Electron correlation at the CCSD(T)/aug-cc-pVTZ level was approximated as shown in Scheme 1, below. In previous work, we showed that this approximation scheme gave binding energies within a few hundredths of a kcal/mol of the explicit CCSD(T)/aug-cc-pVTZ calculations.28 Atomic populations were calculated by Natural Population Analysis (NPA)32 in Gaussian 09 at MP2/aug-cc-pVDZ level of theory. Values of



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bond critical points, BCPs, are calculated according to the theory of atoms in molecules, QTAIM,33 as implemented in AIMALL.34 E(CCSD(T)/aug-cc-pVTZ) ≈ E(MP2/aug-cc-pVTZ) + E(CCSD(T)/aug-cc-pVDZ) – E(MP2/aug-cc-pVDZ) Scheme 1. Approximation used for CCSD(T)/aug-cc-pVTZ For the intermolecular complexes, basis set superposition error (BSSE) was calculated using the counterpoise method (CP) of Boys and Bernardi.35 As there is still some question as to the validity of the CP method for BSSE,36 the method described by Sherrill was used,37 where half the CP correction is applied. Specifically, half of the BSSE for the MP2/aug-cc-pVTZ energy is added to the approximated CCSD(T)/aug-cc-pVTZ calculation described above. In our previous work, it was shown for that explicit BSSE correction for the two additional terms in the CCSD(T)/aug-cc-pVTZ approximation does not lead to appreciably different values.28 Since the data sets for the corrected and uncorrected energies follow the same trends, the conclusions in this work are not changed by the quality of the CP correction.

Results and Discussion 1.

Intermolecular complexes Binding energies (BE) for complexes RF with R’OH (RF•R’OH) are calculated in a

straightforward fashion as shown in equation 1. BE (RF with R’OH) = E (RF•R’OH) – E (RF) – E (R’OH)

(1)

Values for energies of binding of HOH with RF are listed in Table 1 below. When R is an acylic alkyl group (entries 1-4), the BE increases with increasing substitution on the R groups (from Me to Et to iPr to t-Bu). Each substitution of hydrogen for methyl is worth an average of about 0.4


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kcal/mol toward the BE. Here, the methyl group acts a stronger donor than hydrogen, increasing the basicity of RF, which, in turn leads to a larger BE. When R is cyclobutyl, cyclopentyl or cyclohexyl (entries 6-9), the BEs are close to that for R= iPr, in line with the previous reasoning. When R is cyclopropyl, the BE is lower, consistent with the electron withdrawing ability of the cyclopropyl ring relative to larger ring sizes. Changing the hybridization of the R group from sp3 to sp2 as in R = vinyl, R = isoproprenyl, and R = phenyl (entries 10-12), leads to lower BEs, consistent with the greater electron withdrawing ability of these groups relative to alkyl groups. Table 1

Binding energies of RF with HOH, (kcal/mol)

RF BEa ∆BSSEb ∆VZPEc ∆∆Gd CH3F —4.30 0.26 1.57 7.18 CH3CH2F —4.92 0.30 1.58 8.74 (CH3)2CHF —5.37 0.34 1.54 8.53 (CH3)3CF —5.63 0.35 2.85 11.18 c-C3H5F —4.18 0.27 1.42 7.77 c-C4H7F —5.44 0.35 1.62 9.15 c-C5H9F —5.73 0.40 1.62 9.58 c-C6H11F-eqe —5.33 0.34 1.52 8.69 e c-C6H11F-ax —5.08 0.35 1.51 8.73 CH2CHF —3.66 0.23 1.41 8.35 CH2C(CH3)F —3.91 0.27 1.41 8.45 C6H5F —4.04 0.31 1.38 8.16 Average —4.80 0.31 1.64 8.73 a b Binding energy as calculated in equation 1 and as defined by scheme 1 BSSE correction as described in theoretical methods. cVibrational zero-point energy correction. dFree energy and thermal corrections (298 K). eIn the ‘eq’ isomer, the fluorine atom is equatorial. In the ‘ax’ isomer, the fluorine atom is axial. Entry 1 2 3 4 5 6 7 8 9 10 11 12

Results for binding of R’OH to CH3F are listed in Table 2, below. Using the reasoning above, BEs should increase with more acidic R’OHs. This idea is supported by the strong correlation (r2 = 0.996) between BE and the available experimentally determined values of acidity for R’OH (entries 1-6). This result should be used with caution as this data set is small and the BEs span a limited range. The cycloalkanols (entries 7-10) have similar binding energies



to their acyclic counterparts, with cyclopropanol having a slightly smaller BE and cyclopentanol having a slightly larger BE. PhOH (entry 6), has a BE that is about 1 kcal/mol stronger than the alcohols, consistent with its higher acidity. Table 2

Binding energies of CH3F with R’OH, (kcal/mol)

R’OH BEa ∆BSSEb ∆VZPEc ∆∆Gd Aciditye HOH —4.30 0.26 1.57 7.18 390.3 CH3OH —4.51 0.31 1.03 7.47 382.2 EtOH —4.67 0.33 1.00 7.81 379.2 iPrOH —4.95 0.40 1.11 8.95 375.1 t-BuOH —4.95 0.44 1.06 8.83 374.7 PhOH —6.13 0.55 1.09 9.04 349.0 c-C3H5OH —4.62 0.35 0.94 7.66 f c-C4H7OH —4.91 0.43 1.06 8.81 c-C5H9OHf —5.87 0.49 1.08 9.36 f c-C6H11OH —5.12 0.46 1.04 8.73 Averageg —5.17 0.40 1.10 8.38 h Overall Average –5.02 0.36 1.32 8.52 a b Binding energy as defined by scheme 1 BSSE correction as described in theoretical methods. c Vibrational zero-point energy correction. dFree energy and thermal corrections (298 K). eGas phase energy of ROH à RO– + H+ (ref.38) Larger values indicate weaker acidity. f Boltzmann weighted average of conformers. Values for each conformer is shown in SI. g Includes all conformers. hAverage from Tables 1 and 2. Entry 1 2 3 4 5 6 7 8 9 10

Combining the data from Tables 1 and 2 gives an average BE for R’OH with RF of –5.02 kcal/mol, with slightly larger BEs in Table 2 vs. Table 1. These values are made less exoergic by relatively constant corrections for VZPE, BSSE, and free energy. The first two corrections add up to 1.7 kcal/mol and their inclusion still leads to negative BEs. However, the free energy correction at 8.5 kcal/mol is significantly larger than the largest BE, resulting in positive BEs for all complexes. Thus, while there is a HB between OH and F in these complexes, the unfavorable entropy contribution makes it unlikely that intermolecular complexes between R’OH and RF will be of much practical importance at all but the lowest temperatures.


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The data in Tables 1 and 2 can be compared to the limited existing data. For CH3F bound to H2O, the value calculated in this work is very close to the values in references 17-19, mainly because the methodology used is very similar. Two of the complexes from Table 1, fluoroethane (entry 2) and fluorocyclohexane (entries 8 and 9), have analogous experimental data. Thus, the enthalpy of binding for 1-fluoropentane to 4-fluorophenol in CCl4 at ambient temperature was found to be –2.50 kcal/mol and for fluorocyclohexane the corresponding value was found to be – 3.02 kcal/mol.27 Like the computational data, the experimental binding enthalpies were close to each other within this very limited data set. The experimentally determined enthalpies are also reasonably close to the calculated values. In the definition of the HB by IUPAC it is argued that the presence of HBs are accompanied by predictable changes in geometric features, vibrational frequencies, and atomic populations, and by the presence of bond critical points (BCPs) as stated below: 39 The X–H….Y angle is usually linear (180º) and the closer the angle is to 180º, the stronger is the hydrogen bond and the shorter is the H….Y distance. The length of the X–H bond usually increases on hydrogen bond formation leading to a red shift in the infrared X–H stretching frequency Estimates of charge transfer in hydrogen bonds show that the interaction energy correlates well with the extent of charge transfer between the donor and the acceptor and Analysis of the electron density topology of hydrogen-bonded systems usually shows a bond path connecting H and Y and a (3,–1) bond critical point between H and Y A summary of these features for the RF, R’OH complexes from Tables 1 and 2 are listed in Table 3, below. Values for all these complexes are listed in the Supporting Information. In one sense, the IUPAC expectations are well met as all properties are altered in the expected



direction. Geometrically, the average F…H bond length is 2.010 Å, well within the normal range for a hydrogen bond, the OH bond is slightly elongated, and the FHO bond angle averages about 150°. Vibrational frequencies shift about 50 cm–1 to the red and about 0.010 e are transferred from the base (RF, CH3F) to the acid (HOH, R’OH). BCPs between the fluorine atom and the hydroxyl hydrogen are present for all complexes. While the averages of these values are slightly less pronounced than those for the canonical HB of the water dimer, individual values for RF•R’OH (in the Supporting Information) are often as large or larger than the corresponding values for the water dimer. In another important sense, the IUPAC expectations are not met. Specifically, none of variables in Table 3 correlate well with BE. This is true for the aggregate set, shown in Table 3, and for selected subsets, available in the Supporting Information. Taken together, the data in Table 3 suggest that a HB is present but these data are not useful in the prediction of BEs for specific complexes. Table 3.

Geometric features, red shifts, population analysis, and BCPs for ROH, RF

complexes BEa (kcal/mol)

BCP ∆ν RFH ROH ∠OHF qF (Å)b (Å)b (°)b (cm–1)c (me—)d (me–)e Average —5.01 2.010 0.966 149.7 48.1 10.59 19.0 High —6.13 2.146 0.968 163.0 94.9 18.84 21.8 Low —3.66 1.936 0.964 132.6 —7.9 0.63 14.5 Water dimer —4.71 1.945 0.969 171.7 146.2 13.64 22.0 f Correlation 0.56 —0.66 —0.54 —0.28 —0.29 –0.62 a Binding energy (kcal/mol) as defined by equation (1), and as described in scheme 1. bRFH is the distance from the fluorine atom of RF to the hydrogen bound H atom in R’OH. ROH is length of the OH bond that is hydrogen bound. In water, this bond has a calculated length of 0.9614 Å. ∠OHF is the bond angle of the hydrogen bond. cThe change in the vibrational frequencies of the OH stretches upon complexation relative to either water (RF, HOH complexes) or to R’OH (CH3F, R’OH complexes). dThe charge on HOH for the RF/HOH complexes and the charge on CH3F for the CH3F/R’OH complexes in millielectrons. eBond critical point densities for the H…F bond in millielectrons. fCorrelation of the given column with the BE.


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2.

Compounds that can form intramolecular HBs While intermolecular HB energies can be rigorously calculated using equation 1, there is

no analogous method for determining IMHB energies as there is no unambiguous method to completely separate the two components of the HB. This has resulted in a number of strategies for calculating IMHB energies.40 The three most common approaches will be analyzed here: the cis-trans method, isodesmic reactions, and quantum theory of atoms in molecules, QTAIM. Cis-trans method. The cis-trans method, defined in equation 2 below, is the most commonly used approach to determine IMHB strengths. Here, the IMHB strength is simply the difference in energy between the cis conformer, which has an IMHB, and the trans conformer, which does not. The method is successful to the extent that the two conformers have the same steric, electronic, and dipole-dipole interactions. For this last interaction, the effects do not totally cancel as is illustrated in Figure 2 below for the case of 8-fluoronaphthalen-1-ol. The ideal dipole-dipole interaction occurs when the bond dipoles that result from the COH and CF groups are oriented 180° from each other. While neither the cis nor the trans form achieves this orientation, the former is closer to this ideal than the latter. The result is that the IMHB strength is overestimated by ∆Ecis-trans. There is no rigorous way to correct for this effect as “bond dipoles” are not true physical observables. IMHB strength = ∆Ecis-trans = E(cis) — E(trans)


(2)


O

H

F

cis

O

H

H O

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F

trans

F

H O

F

highest energy

lowest energy

Figure 2. (top) Only the cis form of 8-fluoronaphthalen-1-ol contains an IMHB. (bottom) The bond dipoles of the cis form are closer to the ideal arrangement than the trans form is. Isodesmic reactions. Isodesmic reactions have been used to improve on the cis-trans method for determining IMHB strengths,41 though they may not be applicable to larger networks of hydrogens bonds.42 In this work, the appropriate isodesmic reaction is that of ROHF and RH going to ROH and RF. This reaction is written twice, once for the cis form (equation 3) and once for the trans from (equation 4). Subtraction of equation 4 from equation 3, leads to equation 5. The left side of equation 5 is simply ∆Ecis-trans. The right side of equation 5 is the energy difference on changing the conformation of the OH group from cis to trans, designated as ∆Econformation in equation 6. As will be seen later in Table 4, since the cis form of ROH is typically higher in energy than the trans form, the isodesmic correction, ∆∆Eisodesmic often leads to larger IMHB strengths than the cis-trans method. The isodesmic method thus improves on the cistrans method by correcting for conformational factors of the hydroxyl group in each of the two conformers. Of course, the fluoro group has no conformational issues. This procedure is illustrated in Figure 3 below for the case of 8-fluoronaphthalen-1-ol. While isodesmic reactions improve on the cis-trans method, they do not solve other issues such as differences in electron repulsion between the cis and trans conformers.


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ROHF-cis + RH à ROH-cis + RF ROHF-trans + RH à ROH-trans + RF

(trans)

∆Erxn = ∆Eisodesmic-cis

(3)

∆Erxn = ∆Eisodesmic-trans

(4)

ROHF-cis – ROHF-trans à ROH-cis – ROH-trans

(5)

∆Econformation = E(ROH-cis) — E(ROH-trans)

(6)

∆∆Eisodesmic = ∆Ecis-trans – ∆Econformation

O

H

F

(7)

F

O

H

eq. 3 ROH-cis

ROHF-cis H O

F

F

H O

eq. 4 ROHF-trans

O

H

F

ROH-trans

H O

∆Ecis-trans

F

O

H

(eq. 2)

H O

∆Éconformation

(eq. 6)

Figure 3. Isodesmic reaction of ROHF-cis (top line) minus isodesmic reaction of ROHF-trans (middle line) leads to the idea that ∆∆Eisodesmic = ∆E(cis-trans) — ∆Econformation QTAIM correlation. In QTAIM theory, analysis of the electron density distribution can be used to locate BCPs between bonded atoms. The claim has been made that values of the BCP between hydrogen bonded atoms will positively correlate with the IMHB strength.43 There are two problems with this approach.44 First, as was seen above, population shifts between donor



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and acceptor do not correlate well with BEs for intermolecular HBed complexes. There is no reason to think that the value of the BCP would have a stronger correlation, as BCPs are another type of population analysis. Secondly, this method suggests that lack of a BCP means lack of an IMHB. Such an argument has been used in the case of 2-fluorophenol, where the existence of an IMHB is still an open question.29 However, the case is less clear with 2-methoxyphenol. We were unable to find a BCP for the IMHB. Yet both hydrogen abstraction experiments45 and 1H NMR titration with weak bases46 both indicate the presence of an IMHB in this molecule. The lack of a BCP is not limited to 2-methoxy- or 2-fluorophenol but to all the compounds studied here where the hydroxyl and fluoro groups are on adjacent carbons. As it is not clear that IMHBs must have a BCP for the HB, the values of BCPs cannot be used to predict the energy of an IMHB. While BCP densities will not be used to predict IMHBEs, these values will appear in tables in both the main text and the Supporting Information.

Binding energies Using the cis-trans and isodesmic methods, binding energies are calculated for compounds that form intramolecular HBs, denoted as IMHBE (intramolecular hydrogen bond energy). These compounds are illustrated in Figure 4 below and the energies are listed in Table 4 below. The isodesmic correction is not included if there is no ground state ROH conformer that corresponds to the geometry of the corresponding ROHF. The compounds are organized using three criteria: hybridization of the carbons, ring size of the IMHB, and topology of carbon skeleton. Table 4 Entry 1

Intramolecular hydrogen bond energies, (kcal/mol) compound 2-fluoroethanol

∆Ecis-transa —2.03


∆VZPEb 0.24

∆∆Gc 0.38

∆∆Eisodesmicd –0.12

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2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2-fluorocyclopropanol —1.57 —0.16 —0.27 –2.09 2-fluorocyclobutanol —2.82 0.04 0.04 –2.42 2-fluorocyclopentanol —3.05 0.32 0.63 –0.95 2-fluorochexanol-axF —3.07 0.31 0.52 –0.49 2-fluorochexanol-eqF —2.41 0.23 0.32 –0.49 3-fluoro-1-propanol —0.04 0.18 0.41 –0.11 cis 3-fluorocyclobutanol 1.59 —0.01 0.20 cis 3-fluorocyclopentanol —1.62 0.30 0.36 cis 3-fluorocyclohexanol —3.16 0.34 0.55 –0.58 4-fluoro-bicyclo[1.1.1]pentan-2-ol —4.84 0.54 0.88 –0.84 6-fluorobicyclo[2.1.1]hexan-5-ol —3.74 0.42 0.64 –0.99 6-fluorobicyclo[2.2.0]hexan-2-ol —4.65 0.49 0.82 0.08 6-fluorobicyclo[2.2.1]heptan-2-ol —4.44 0.39 0.71 –0.69 6-fluorobicyclo[2.2.2]octan-2-ol —4.07 0.41 0.66 –0.86 2-fluorophenol —2.80 0.17 0.24 0.00 2-(fluoromethyl)phenol —1.42 0.27 0.56 –0.20 2-(2-fluoroethyl)phenol —1.25 0.22 0.62 –0.42 8-fluoronaphthalen-1-ol —3.72 0.20 0.32 –1.15 Average —2.58 0.26 0.45 –0.42 a Binding energy as defined by equation 2. bVibrational zero-point energy correction. cFree energy and thermal corrections (298 K). dIsodesmic correction as defined in equation 7.

H O

O

F

H

O

(CH 2)n

n=0-3 entries 2-6

F (CH 2)n

(CH 2)n (CH 2)m

n=0-2 entries 8-10 O H

F

F (CH 2)n

(CH 2)n

H

n=0,1 m=0,1,2

entries 11-15 O

H

F

n=0,1,2 entries 16-18

entry 19

Figure 4. Intramolecular hydrogen bonds. Structures correspond to Table 4. The first fifteen entries in Table 4 have sp3 hybridization for all the carbons in the skeleton. Within this set, the first six entries have an IMHB with a F-C-C-O-H substructure that results in a five-membered ring. The simplest compound in this series is 2-fluoroethanol. The others are all 2-fluorocyloalkanols. For 2-fluorocyclohexanol, there are two isomers, one where



the F is axial and the OH equatorial (entry 5), the other where these groups are interchanged (entry 6). In this grouping, the IMHBEs are very tightly clustered with an average of just under 2.5 kcal/mol. Two values stand out as being particularly small, that for 2-fluorocyclopropanol and 2-fluoroethanol. The former can be rationalized by analogy with the intermolecular complex of cyclopropylfluoride and water, which had a weak HB due to the electron withdrawing ability of the cyclopropyl group. For 2-fluoroethanol, it will be argued that the conformational flexibility of the FCCO chain is what leads to the low IMHBE. This flexibility is greatly reduced in the fluorocycloalkanols and the resulting IMHBEs are higher. Inclusion of the isodesmic correction leads to slightly higher IMHBEs but does not qualitatively change the conclusions drawn from the cis-trans method. The isodesmic corrections for the small rings, entries 3 and 4, are anomalously large due to the unusually high strain energy of the ROH-cis conformation. While the calculated values for entries 1-6 are very much in line with previous work, the interpretation of these values remains controversial. This debate is illustrated with 2fluoroethanol, where this work’s calculated cis-trans energy gap of about 2 kcal/mol is very much in line with experiment47 and previous calculations by Cormanich et al.48 Authors of these works note that this energy gap is probably due to a combination of the gauche effect49 and an IMHB. Cormanich et al. argue that since no BCP is found between F and the hydroxyl H, there is no IMHB. This same research group uses this BCP criterion to argue for or against an IMHB in a series of planar compounds derived from 3-fluorobuta-1,3-dien-2-ol, concluding that IMHBs are strongly disfavored for geometric reasons. 50 The present work challenges this reasoning based on the counterexample of 2-methoxyphenol discussed earlier, which appears to have an IMHB but does not have the requisite BCP. Even if a BCP is not required for an IMHB, a second argument still needs to be made in favor of an IMHB. This argument starts with the


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assumption that the 2 kcal/mol cis-trans gap of 2-fluoroethanol is entirely due to the gauche effect and that the gauche effect will have the same value in entries 2-6. However, entries 3-6 all have cis-trans gaps that are larger than that of 2-fluoroethanol by as much as 1 kcal/mol. This excess energy is most economically explained as an IMHB. Agreeing with this point of view is Graton et al., who saw decreased acidities in 4-tert-butyl-2-fluorocyclohexanols relative to 4-tertbutylcyclohexanol, an effect they attributed to a weak IMHB.15 Entries 7-15 in Table 4 have an IMHB with a F-C-C-C-O-H substructure that results in a six-membered ring. Within this set, there is an obvious break in values between entries 7-10 and 11-15. In the first data subset, there is a great disparity in IMHBEs with no clear pattern emerging. The low IMHBE for 3-fluoro-1-propanol is consistent with the low IMHBE seen for 2-fluoroethanol, which was attributed above to conformational flexibility. For cis 3fluorocyclobutanol, the value for the IMHBE is endoergic. This is presumably due to the strain of the conformation of the OH group. In cyclobutanol itself, there is no stable conformer with a similar conformation of the OH group. The values for the larger rings (entries 9 and 10) are near the average value seen with the 2-fluorocycloalkanols. The value for the IMHBE of cis 3fluorocyclopentanol is slightly less, presumably due to conformational factors like those seen with the smaller cis 3-fluorocylcobutanol. Importantly, the six-membered IMHBEs are not significantly different from the five-membered ring size. The isodesmic correction could only be applied to two members of this subset and does not effect the conclusions above. The second data subset, entries 11-15, also contain the F-C-C-C-O-H motif, but the carbon skeleton consists of a bicyclic ring. The presence of a second ring significantly reduces the conformational flexibility of the OH and CF groups and increases the IMHBEs by over 1 kcal/mol relative to both the five- and six-membered monocyclic rings. Taken with the earlier



entries, it is clear that IMHBEs increase as their conformational mobility decreases: acyclic (entries 1, 7) < monocyclic (entries 2-6, 8-10) < bicyclic (entries 11-15). Only a few of the compounds from entries 7-15 have been examined in the literature. Somewhat by chance, there is enough literature data to bolster the hypothesis that IMHBs increase in strength with molecular rigidity. Unlike for entries 1-6, the existence of an IMHB in compounds capable of forming a six-membered ring is not controversial, as all compounds examined show a BCP consistent with an IMHB and none are subject to the gauche effect. The most flexible compound from entries 7-15 is 3-fluoro-1-propanol and it has a very weak IMHB. Based on the ∆G data in Table 4, the conformer of 3-fluoro-1-propanol with an IMHB is calculated to be present at 35% at 25 °C, which is only a marginally higher percentage than that calculated by Cormanich et al.,48 who found this conformer to have a gas phase percent population of 14% and that of Linclau et al., 16 who found the IMHBed conformer to be present at 8% at 25° C in CHCl3. Inclusion of a single ring, as in cis 3-fluorocyclohexanol, leads to a more rigid molecule and a stronger IMHB. Experimentally, the binding of N-methyl-2pyrrolidone in CCl4 to 4-tert-butyl-3-fluorocyclohexanol was found to be 1 kcal/mol less than to cis 4-tert-butylcyclohexanol.51 The authors attributed this difference to an IMHB between the F and OH groups on the fluorohydrin. Inclusion of a second ring, leads to a more rigid compound and a stronger IMHB. While there is no direct analogy in the literature to any of the bicyclic compounds 11-15 computed here, Holl et al. synthesized a series of polycyclic cage compounds where the IMHB is especially strong as judged by NMR data.24 Entries (16-19) all contain a phenol group. The series 2-fluorophenol, 2(fluoromethyl)phenol, 2-(2-fluoroethyl)phenol differ in the size of the ring formed by the IMHB. As can be seen, as the ring gets larger and more flexible, the IMHBE gets smaller. This is


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consistent with what was seen above. The final compound, 8-fluoronaphthalen-1-ol, has one of the largest IMHBEs and is also the one with the least conformational mobility. In comparing entries 16-19 to entries 1-15, there does not seem to be any appreciable effect of the aromatic ring on the IMHBE. Inclusion of isodesmic corrections leads to small increases in the IMHBEs but does not change any of the conclusions above. The IMHBEs of three compounds in this section have been studied previously. First, 2fluorophenol has received extensive investigation which has recently been summarized.29 The results are very much reminiscent of the discussion above for 2-fluoroethanol. The calculated cis-trans energy gap calculated here is similar to previous calculations. The lack of a BCP between F and the hydroxyl H has been used to argue against the existence of an IMHB.29 Unfortunately, extensive experimental work does not resolve the issue, with recent articles arguing both against29 and for51 the existence of an IMHB. Receiving considerably less attention is 2-(fluoromethyl)phenol. The results in this work are slightly smaller than an early DFT study using the cis-trans method (∆H = –2.1 kcal/mol)52 and slightly larger than a more recent study of free energy in CCl4 (∆G = –0.1 kcal/mol).53 Part of the discrepancy with the latter work and this work can be attributed to inclusion of solvent, which tends to lower HB strengths. The third compound studied before is 8-fluoro-4-methyl-1-naphthol, 54 which is a close model to 8-fluoronaphthalen-1-ol, studied here. While no values for binding energies were calculated, the authors did see large shifts in the 1H NMR spectrum. Looking at all the data in Table 4, it appears that the most important factor in determining IMHBEs is rigidity. Thus, increasing rigidity of the ring that contains the IMHB leads to increasing IMHBEs as seen in the series 3-fluoro-1-propanol < 2-fluoroethanol < cis 3fluorocyclohexanol ~ trans 2-fluorocyclohexanol < 4-fluoro-bicyclo[1.1.1]pentan-2-ol.



Somewhat unexpectedly, neither F-(C)n-OH ring size nor hybridization of the carbons that contain the fluoro and/or hydroxyl groups gave appreciably differences in the IMBEs. The energies given in Table 4 do not change significantly upon consideration of either VZPE or ∆G corrections, with the sum of the two effects averaging less than 1 kcal/mol. This is in marked contrast to the intermolecular case where ∆∆G is quite large and leads to positive BEs. To better characterize IMHBs, a summary of the geometry, vibrational frequencies, population changes, and BCPs for the compounds with intramolecular HBs is given in Table 5, below. A listing of all the individual values for these complexes are contained in the Supporting Information. Like the intermolecular complexes, the features in Table 5 are mostly consistent with the formation of an IMHB. Thus, IMHBs have relatively short F to H(O) distances, a slight elongation of the OH bond, larger OHF angles, red shifts in the vibrational frequencies, and transfer of charge from F to OH. While compounds with the F-C-C-O-H substructure lack a BCP between F and H, this does not always indicate the absence of an IMHB, as in the case of 2methoxyphenol mentioned earlier. However, none of these features correlate well with the IMHBEs, a result seen for the intermolecular complexes. Table 5.

Geometric features, red shifts, population analysis, and BCPs for ROHF

compounds qOH qCF BCP – d R ∠OHF ∆ν (cm FH (me–) trans 1 c (Å)b ROH(Å)b (°)b ) (me–)d (me–)e Average -2.58 2.13 2.16 126.23 28.84 0.84 -20.18 20.9 High -4.84 2.46 4.00 154.60 67.39 10.99 49.71 28.6 Low 1.59 1.84 0.00 103.20 10.51 -9.97 -47.19 12.0 Correlation 0.34 0.52 -0.01 0.57 0.08 0.04 –0.61 a b Binding energy (kcal/mol) as defined by equation (2). RFH is the distance from the fluorine atom of RF to the hydrogen bound H atom. ROH is length of the OH bond that is hydrogen bound. In water, this bond has a length of 0.9614 Å. ∠OHF is the bond angle of the hydrogen bond. cThe change in the vibrational frequencies of the OH stretches upon complexation relative ∆Ecisa


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to water. dThe charge on the OH atoms (qOH) and CF atoms (qCF).eThe density of the BCP between the hydroxyl hydrogen and the fluorine in millielectrons. Comparison of inter- and intramolecular hydrogen bonds. By combining the data from the first five tables for the intermolecular complexes and the compounds with intramolecular HBs, Table 6, below, allows comparison of the two types of HBs. The BE for the intermolecular case appears to be nearly 2.5 kcal/mol stronger than that of the IMHBs. This difference is reduced to just over 1 kcal/mol in favor of the intermolecular complexes when VZPE and BSSE corrections are taken into account. While geometric and vibrational properties don’t correlate well with BEs, these properties are also consistent with a stronger HB in the intermolecular complexes. Thus, the intermolecular complexes have shorter F…H(O) distances, larger OHF angles, and larger red shifts than the IMHB containing compounds. Chemical intuition suggests that intermolecular HBs should be stronger than their intramolecular counterparts. The former have the flexibility to achieve the ideal binding configuration while the latter are constrained by the geometry of the molecule. Table 6. Comparison of averages of selected properties for inter- and intramolecular HBs. (kcal/mol) f g BEa VZPEb BSSEc RFH (Å)d ∠OHF ∆ν (cm– ∆∆G BCP d 1 e ) (°) —4.93 1.30 0.38 2.01 149.7 48.1 8.67 19.0 Inter —2.58 0.26 0.00 2.13 126.2 28.8 0.45 20.9 Intra a Binding energy as defined by equations 1 (inter-) and 2 (intra-). bVibrational zero-point energy correction. cBE corrected for BSSE as described in theoretical methods. dRFH is the distance from the fluorine atom of RF to the hydrogen bound H atom. ∠OHF is the bond angle of the hydrogen bond. cThe change in the vibrational frequencies of the OH stretches upon complexation relative to water. fFree energy and thermal corrections (298 K). gBond critical point densities for the H…F bond in millielectrons. One factor that differs greatly for the two types of complexes is the ∆G correction. For the compounds with intramolecular HBs, the value is quite modest, with the result that the



average IMHBE is exoergic by about 2 kcal/mol. For the intermolecular complexes, the ∆G correction is substantial, causing all of the BEs to be endoergic. In practice this means that intermolecular complexes with fluoro-organics are unlikely to play a significant role in the solution phase under ambient conditions. However, IMHBs are energetically important and might exert effects in a chemical or biochemical system.

Conclusions Fluoro-organics form HBs to alcohols and phenols with typical BEs of about –5 kcal/mol. However, when free energy considerations are taken into account, the BEs become endoergic. Thus, a fluoro-organic would not be expected to form a HB with the OH group of a protic solvent. The case for IMHBs is quite different. On average, the hydrogen bond energies are slightly weaker than their intermolecular counterparts. These values are relatively insensitive to both the hybridization of the functionalized carbons and to the size of the new ring formed by the IMHB. However, the IMHB strength varies considerably with molecular flexibility, with the more rigid molecules leading to stronger IMHBEs. Unlike their intermolecular counterparts, the free energy correction is quite small in the intramolecular compounds, leading to exoergic binding energies. Thus, IMHBs with fluoroalcohols could play a significant role in chemical systems. A recent article reported that ortho-fluorination increased acidities of phenols.55 These HBs may also be important in biochemical settings, where an enzyme immobilizes a fluoroorganic drug near a suitable HB donor. Supporting Information. The Supporting information is available free of charge on the ACS Publications website at DOI: xxxxxxx.


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•

Complete Gaussian 09 reference, structures and energies, geometric features, vibrational red shifts, and population analyses for all complexes. (PDF)

The author declares no competing financial interest. ACKNOWLEDGMENT I am grateful to the donors of the Petroleum Research Fund of the American Chemical Society (55137UR4) for financial support of this work. REFERENCES 1

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The Strength of Hydrogen Bonds between Fluoro-Organics and

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