Does Fluoromethane Form a Hydrogen Bond with Water? - The

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Does Fluoromethane Form a Hydrogen Bond with Water? Robert E. Rosenberg* Department of Chemistry, Transylvania University, 300 North Broadway, Lexington, Kentucky 40508, United States S Supporting Information *

ABSTRACT: Fluorinated organic compounds have become increasingly important in the pharmaceutical and agricultural industries. However, even the simplest aspects of these compounds are still not well understood. For instance, it is an open question as to whether fluoroorganics can form a hydrogen bond. To answer this question, this work compares the complex CH3F···HOH with 10 other complexes including the water dimer, the water−ammonia dimer, the methane−water dimer, and the methane dimer, among others. The features that are compared include binding energy and its electrostatic and dispersive components, geometry, vibrational frequencies, charge transfer, and topological analysis of the electron density. All of these are consistent with a hydrogen bond forming in CH3F···HOH. Moreover, all features of this dimer appear to be quite similar in kind, although slightly lesser in degree, than the corresponding features of the water dimer.

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INTRODUCTION

In recent years, fluorine containing organic molecules have become increasingly important, comprising as much as 20% of new drugs and 30% of agrochemicals.1 Despite their widespread use, some very basic aspects of these compounds are not well understood. Of these, the focus here is whether fluoroorganic compounds can form hydrogen bonds, termed CFHBs. This is important as hydrogen bonding (HB) plays such an important role in the structures of biomolecules. For DNA analogues2−4 and in proteins,5,6 the questions concerning CFHBs have not been answered unambiguously. A search of crystal structure databases argued strongly against CFHBs,7,8 although this view has been challenged.9 While a few reports of intramolecular CFHBs have surfaced,10−15 diaxial 3-fluorocyclohexanols do not form CFHBs in the solid state, despite the favorable arrangement of the relevant atoms.16 Matrix isolation infrared spectroscopy of CH3F···H2O supports the existence of a CFHB in the solid state.17 High-level ab initio studies argue for a CFHB in CH3F···H2O (1), finding a binding energy (BE) of just under 4 kcal/ mol.18−20 This work will build on those earlier studies by comparing 1 to the following dimers: water−water (2), methanol−water (3), dimethyl ether−water (4), ammonia− water (5), methylamine-water (6), trimethylamine−water (7), water−methane (8), fluoromethane−fluoromethane (9), fluoromethane−methane (10), and methane−methane (11) (Figure 1). These dimers were chosen to illustrate a range of HB strength, from the classical HB dimers (2−7), to the borderline HB dimers (8−10), to the non-HB dimer (11). The goal here is to see into which category 1 best fits. Recently, IUPAC has published a consensus view of the definition of HB.21,22 This paper will draw heavily from that work in order to look at the major aspects of HB in 1−11 including BE, the electrostatic and dispersive components of the BE, geometry, vibrational frequency, charge transfer from donor to acceptor, and topological analysis of the electron density. © 2012 American Chemical Society

THEORETICAL METHODS

Geometry optimization has been carried out using MP2 theory and the aug-cc-pXVZ, (X = D, T, and Q) basis sets23 using Gaussian 09.24 Frequency calculations were used both to verify that the geometries were a minimum (no imaginary frequencies) and for the analysis of the effect of HB on vibrational frequencies. Frequency calculations were performed at the MP2/aug-cc-pVTZ level as the aug-cc-pVQZ basis set was too large for use with the bigger dimers. Electron correlation at the CCSD(T)/ aug-cc-pVQZ level was approximated using the following scheme: E(CCSD(T)/aug‐cc‐pVQZ) ≈ E(MP2/aug‐cc‐pVQZ) + (E/(CCSD(T)/aug‐cc‐pVTZ − E(MP2/aug‐cc‐pVTZ))

For the smaller systems, (1, 2, 5, 8, and 11), the approximation scheme gave BEs within a few hundredths of a kcal/mol of the explicit CCSD(T)/aug-cc-pVQZ calculations. Basis set superposition error (BSSE) was calculated using the counterpoise method (CP) of Boys and Bernardi.25 For the approximation scheme above, the BSSE value uses the CP correction for all three terms. As there is still some question as to the validity of the CP method for BSSE,26 both the corrected and uncorrected values for binding energies are presented. Since the uncorrected energies at the CCSD(T)/aug-cc-pVQZ level deviate from the CP corrected energies by only a few tenths of a kcal/mol, the conclusions drawn from either set of data will be essentially the same. Received: August 28, 2012 Revised: October 10, 2012 Published: October 11, 2012 10842

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Figure 1. Dimers used in this work.

path is a path that connects two atoms such that every point on the path is a maximum of electron density in the directions orthogonal to the path. The Laplacian of ρ, ∇2ρ, measures concentration of charge and describes the nature of a critical point. For a bond between two atoms, the Laplacian of the bond critical point will be positive.

Two schemes were used to decompose the electron density into its components: symmetry-adapted perturbation theory (SAPT)27 and localized molecular orbital energy decomposition analysis (LMO-EDA).28 For both methods, the aug-ccpVTZ basis set was used as the aug-cc-pVQZ was too large for use on our computers. The SAPT (and related SAPT2) methodology decomposes the energy into electrostatic, exchange, induction, and dispersion contributions. The LMOEDA method decomposes energy into electrostatic, exchange, repulsion, polarization, and dispersion terms. While this breakdown is slightly different than that of SAPT, the electrostatic and dispersion terms are defined similarly. An important difference between the two methods is that LMOEDA describes dispersion effects better than SAPT, as the former is able to use the CCSD(T) level of theory. Within the SAPT software, the SAPT2 method was used as it corresponds roughly to an MP2 calculation, while SAPT corresponds to MP4. Recently, SAPT was used to argue for the importance of dispersion in DFT and DFT-D methods in hydrogen bonding.29 In an earlier study, SAPT was used to analyze the hydrogen bonding in 5.30,31 LMO-EDA was used from within the GAMESS32 software package. While LMO-EDA does not have as long a history as SAPT, it has been used recently to analyze the hydrogen bonds in the water−hexamer.33,34 Atomic populations were calculated by two methods: natural population analysis (NPA)35 in Gaussian 09 and atoms in molecules (AIM)36,37 using AIMALL.38 Population analysis for both methods was done using the MP2/aug-cc-pVTZ level of theory and the “density=current” keyword in Gaussian 09. NPA required the further keyword, “pop=npa”, while AIM analysis required “out=wfn”, followed by analysis using AIMALL. Topological analysis of the charge density was also conducted using AIMALL. In AIM, a bond critical point is a minimum of electron density, ρ, along a bond path. A bond

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RESULTS AND DISCUSSION Binding Energy. The BE of a dimer is probably the most widely used and important criterion in diagnosing the presence of HB. Both uncorrected and CP corrected CCSD(T)/aug-ccpVQZ BEs of complexes 1−11 are shown in Table 1, below. Qualitatively, these values are relatively insensitive to the choice of basis set, the method of electron correlation, or correction for BSSE as judged by their similarity to both calculations from other works and to lower-level calculations from this work. Quantitatively, the most important factor is the size of the basis set, where the smaller the basis set, the larger the calculated BE. Between the lowest (uncorrected MP2/aug-cc-pVDZ) and highest levels of theory (CP corrected CCSD(T)/aug-ccpVQZ) used in this work, there was an average difference of only 0.64 kcal/mol and a maximum difference of just 1.64 kcal/ mol. Results from lower level calculations and from other works can be found in the Supporting Information. Looking at the BEs in Table 1, it is clear that the largest BEs come from compounds 2−7. These compounds contain a classical HB between the OH donor and the N or O atom of the acceptor. Within this strong group, the nitrogen containing compounds 5−7 have significantly larger BEs than those with oxygen, 2-4. A noteworthy, but smaller effect is that methyl substitution on the acceptor atom increases the BE (3 vs 2 and 6 vs 5) by about 1 kcal/mol, although the presence of additional methyl groups (4 vs 3 and 7 vs 6) has little to no effect. This effect was seen earlier in a study of the HB of

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Table 1. Binding Energies, Zero-Point Vibrational Energies, and Proton Affinities of 1−11 (kcal/mol) complex

BEa

BE (BSSE)b

ZPVEc

1 2 3 4 5 6 7 8 9a 9b 10 11

−4.20 −5.13 −6.13 −6.12 −6.53 −7.74 −7.95 −1.11 −1.71 −2.62 −1.00 −0.46

−3.94 −4.89 −5.85 −5.76 −6.31 −7.46 −7.48 −0.98 −1.55 −2.38 −0.87 −0.42

1.51 2.10 1.87 1.84 2.21 2.13 1.93 0.78 0.47 0.65 0.56 0.39

proton affinityd

proton affinityf

140.1 161.9 177.3 186.2e 201.0 212.1 223.9e 128.0

143.1 165.6 180.3 189. 204.0 206.6 226.8 129.9

Figure 2. A plot of the experimental proton affinity (298 K) of the hydrogen bond acceptor versus the calculated binding energy of the complex for 1−7. All values are in kcal/mol.

a

Equals the energy of the complex minus the energies of the monomers. CCSD(T)/aug-cc-pVQZ. bBinding energy corrected for basis set superposition error. cEquals the ZPVE of the complex minus the ZPVEs of the two monomers. dProton affinity of the hydrogen bond acceptor. Proton affinity = ΔH(BH+) − ΔH(B) − ΔH(H+), 298 K. CCSD(T)/aug-cc-pVQZ. eCCSD(T)/aug-cc-pVTZ. fExperimental. See ref 40.

predict a BE for 1 of −3.63 kcal/mol. This value is reasonably close to the best calculated value. Judging by BE alone, 1 appears to be a classically HB complex. This result is somewhat at odds with the scarcity of evidence for solution phase and solid state CFHBs. Perhaps, the BE of 1 is not solely due to a CFHB but is due to some additional attractive interaction. Below, three possible attractive interactions in 1 will be examined: (1) F···H(O) HB, (2) CH···O(H) HB, and (3) a dipole−dipole interaction between the H2O and CH3F molecules. The CH···O interaction can be approximated using a direct and an indirect method. Complex 8−CH4-donor is a complex between HOH and CH4, where the O is constrained to interact with a CH bond. This is not a stable complex of 8 as judged by frequency analysis. In 8−CH4-donor, the BE of the CH···O interaction is under 0.7 kcal/mol. This estimate is lower than would be expected for the corresponding interaction in 1 since CH4 is much less acidic than CH3F. A better estimate is obtained by looking at 1−CHO-linear, a complex where the CH···O bond is constrained to be colinear. The BE of this complex is 1.6 kcal/mol, stronger than that of 8−CH4-donor, but much weaker than in 1, the unconstrained complex of CH3F and H2O (Table 2). The CH···O interaction can be

dimethyl ether and dimethyl sulfide to hydrogen cyanide.39 To some extent, both of these trends can be explained by the proton affinity of the acceptor, the calculated and experimental40 values of which are also shown in Table 1. Sophisticated approaches that show the relationship between HB strength and proton affinity have been around for some time.41 This work uses a more qualitative statement employed in the IUPAC definition of the hydrogen bond: “The pKa of X− H and pKb of Y−Z in a given solvent correlate strongly with the energy of the hydrogen bond formed between them.”22 As one would expect, this statement is largely consistent with the data for compounds 2−7. At the other end of the binding regime are the very weakly bound dimers. In 11, there is no question of HB: the small attractive forces are due to dispersion. Complexes 8 and 10 have slightly stronger BEs than 11. These complexes are also different from 11 in that they both contain basic atoms that can, in theory, be used as HB acceptors. In line with this view, in complex 10, the F atom of CH3F is the atom nearest to the CH4 molecule. For complex 8, the water is “donating” a hydrogen to the methane. Complex 8−CH4-donor, which has the methane “donating” its hydrogen to the basic oxygen atom, has a less negative BE than 8 and is discussed below. While there has been some discussion about the presence and importance of HB such as C−F···H−C in 10 42 and considerable discussion about these issues for O···H−C interactions in species such as 8−CH4-donor,43 it is clear that the BEs in both cases are quite weak, with values of less than 1 kcal/mol. It is not difficult to place complex 1. With 81% of the BE of 2, and over 400% of the BE of 8 or 11, it is clear that 1 is better placed into the strong group, 2−7. Indeed, the BE of 1 compared to 2−7 is consistent with the proton affinity of CH3F. As shown in Figure 2, a plot of BE versus proton affinity of the HB acceptor for 1−7 shows a linear relationship with an r2 of 0.93. Removal of 1 degrades the fit, r2 = 0.86. Alternatively, a plot of BE versus proton affinity using 2−7 gives a straight line which can be used with the proton affinity of CH3F to

Table 2. Binding Energy for Partially Optimized Structures (CCSD(T)/aug-cc-pVQZ, kcal/mol) complex

BE

BE (BSSE)

1−CHO-linear 1−CFHB-linear 8−CH4-donor

−1.71 −3.54 −0.72

−1.59 −3.30 −0.65

estimated indirectly by looking at 1−CFHB-linear, where the CF···H(O) angle is fixed at 180°, and the CH···O interaction disappears. The BE of 1−CFHB-linear compared to 1 suggests that the CH···O interaction in 1 is worth at most 0.60 kcal/mol. While each of these methods gives a slightly different value, it is clear that the CH···O interaction is not the major stabilizing interaction in 1. The magnitude of the dipole−dipole interaction in 1 can be estimated using 9, the CH3F dimer. This is a reasonable model as the dipole moment of CH3F (1.859 D, exp.;44 2.057 D, calc.) is very similar to that for HOH (1.884 D, exp.;45 1.991 D, calc.). In 9a, where the two CH3F molecules are aligned similar to the molecules in 1, the interaction energy is about 1.5 kcal/ mol. This number is an upper limit as it does not account for 10844

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stabilization due to a favorable CF···HC interaction. In 9b, where the CH3F molecules are roughly antiparallel, the interaction energy is just under 2.4 kcal/mol. This is still less than that seen in 1, despite the significantly more favorable dipole−dipole interaction in 9b. It is now possible to put a lower limit on the energy of the CFHB in 1. If the CH···O interaction from 1−CHO-linear of 1.6 kcal/mol is added to the dipole−dipole interaction of 1.5 kcal/mol of 9a, this still leaves 0.8 kcal/mol for a lower limit for the CFHB bond in 1. While this number is not large, it does firmly establish that intrinsically CFHB is a stabilizing interaction. Furthermore, the true value of the CFHB is likely to be significantly higher than the lower limit. First, the CH...O bond in 1 may be as much as 1 kcal/mol weaker than in 1− CHO-linear as seen in 1−CFHB-linear. Second, in the approximation above, the dipole−dipole interaction of 1− CHO-linear is not counted toward its BE. In effect, the simple addition scheme using 1−CHO-linear and 9a double counts the dipole−dipole interaction. Finally, in dimers such as 2−7, the dipole−dipole interaction is typically folded in with the HB strength. The discussion above has not included vibrational corrections due to zero-point vibrational energy, (ZPVE). This factor reduces the BE for all complexes, with bigger effects seen for larger and more strongly bound complexes. However, as can be seen in Table 1, inclusion of ZPVE does not change the qualitative conclusions above. Thus, 2−7 still have the strongest BEs, 8, 10, and 11 now have very low BEs, and the BE of 1 is now 85% of the value for 2. Decomposition of the energy into its components. Using theoretical methods, it is now possible to calculate the relative importance of each of the energetic components to the BE in a given complex. In the traditional view of HB, the dominant attractive interaction is electrostatic. The recently published IUPAC definition of HB is broader:22 Attractive interactions arise from electrostatic forces between permanent multipoles, inductive forces between permanent and induced multipoles, and London dispersion forces. If an interaction is primarily due to dispersion forces, then it would not be characterized as a hydrogen bond. Below, these criteria will be applied to complexes 1−11 using two theoretical methods: SAPT and LMO-EDA. The data are shown in Table 3. The electrostatic energies for complexes 1−11 correlate well (r2 = 0.98) with BEs, as shown in Figure 3. Within the N and O series, the presence of a methyl group leads to a significant increase in the electrostatic energy, an interaction that does not diminish much after the addition of the first methyl group. This last aspect more closely parallels the proton affinity of the acceptor than it does the overall BE. A second, similar trend is that the higher the BE of a complex, the higher the ratio of the electrostatic energy to the BE. Thus, the N complexes showed the highest ratio’s, followed by the O complexes, complex 1, and last, by the weak complexes 8−11. Once again, the ratio for 1 falls well above that seen for the weak complexes and at the lower end of the range for the strong complexes. While the ratios for 8−11 are the lowest, they are still substantial. All of these conclusions are equally valid for both the SAPT2 and LMO-EDA schemes as both methods calculate the electrostatic energy within 0.2 kcal/mol of each other. As with the comparison of proton affinity to BE, it can be shown that the electrostatic energy of 1 is the value that is expected for a classic HB complex. Thus, a plot of the BE of 2−

Table 3. Energy Decomposition Values for Complexes 1−11 (kcal/mol) complex

EEa SAPT

EEa LMO

DISPb SAPT

DISPb LMO

1 2 3 4 5 6 7 8 9a 9b 10 11

−5.59 −8.30 −9.74 −10.43 −11.85 −13.76 −15.62c −0.91 −1.45 −2.99 −0.78 −0.26

−5.77 −8.39 −9.67 −10.22 −11.91 −13.58 −15.00c −0.76 −1.49 −3.09 −0.70 −0.22

−2.26 −2.10 −2.91 −3.39 −2.90 −3.95 −4.49c −1.17 −1.50 −1.80 −1.41 −0.78

−1.48 −1.17 −1.81 −2.42 −1.82 −2.69 −2.65c −1.17 −1.23 −1.36 −1.33 −0.77

a

Calculated electrostatic contribution to the energy, aug-cc-pVTZ. SAPT refers to SAPT2 which is similar to MP2. LMO refers to LMOEDA and uses CCSD(T). bCalculated dispersion energy. caug-ccpVDZ.

Figure 3. A plot of electrostatic energy versus binding energy for complexes 1−11. Values of electrostatic energy are the average of the SAPT2 and LMO-EDA methods. All values are in kcal/mol.

7 versus the average of the electrostatic energies from SAPT2 and LMO-EDA leads to a decent linear relationship (r2 = 0.94). Using this line, the BE of complex 1 predicts an average electrostatic energy of −5.72 kcal/mol, which is only 0.04 kcal/ mol more negative than the directly calculated value. A corresponding plot of proton affinity versus electrostatic energy for 2−7, leads to a line with a slightly better fit (r2 = 0.96) and a prediction of 5.39 kcal/mol for the electrostatic energy of 1. Thus, the electrostatic attraction energy of complex 1 is just what is to be expected for a classic HB system. Unlike the electrostatic energy, the calculation of dispersion shows significant differences within the two methodologies. In general, SAPT2 gives more negative values than LMO-EDA, with complex 7 showing the largest deviation of 1.84 kcal/mol. Since LMO-EDA is able to use the CCSD(T) level of theory, these values should be more reliable. However, the discussion below is consistent with both models. To some extent, the dispersive component to the BE follows trends similar to those of the electrostatic component: dispersion energy increases with BE. Here, as might be expected, the addition of a methyl group leads to a significant increase in the dispersion energy. The ratio of the dispersive energy to the BE, however, is opposite to the trend seen for the corresponding ratio of the electrostatic energy to BE. Complexes 1−7 all have ratios from 0.4 to 0.6 (SAPT) or 0.2 to 0.4 (LMO-EDA), while complexes 8, 10, and 11 have ratios above 1.0. Complexes 9a and 9b show intermediate values. 10845

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Again, it can be shown that the OH lengthening of 1 is near what is expected for a classic HB complex. Thus, a plot of the proton affinity of 2−7 versus the OH bond lengthening gives a line that can be used to predict an ROH for 1 of 0.9601 Å, which is 0.0027 Å shorter than the calculated value. This prediction should be used with caution as the bond changes for all species are quite small. With this caveat, it is interesting to note that 1 shows an ROH lengthening even larger than that expected for a classic HB species. For complexes 2−7, the O−H···Y bond angle varies very little, from a low of 162.9° (6) to a high of 171.8° (2). In 1, the corresponding angle of 145.8° is slightly smaller. While this could be interpreted that 1 has a weak or nonexistent HB, that conclusion is unwarranted for two reasons. First, this angle is well above the minimum value of 110° set by IUPAC. Second, increasing bond angle does not correlate with BE. The complex with the bond angle closest to linear (2), has the weakest BE of this set of compounds. If anything, there seems to be an inverse correlation between this bond angle and BE. As was seen in looking at BE, the geometric features of 1 are similar to those of the classic HB complexes 2−7. Vibrational Analysis. Intimately tied to the geometric changes in the previous section are changes in vibrational frequencies. Specifically, the lengthening of the O−H bond of the HB donor should lead to a concomitant red shift in that bond.22 However, this rule must be used carefully, as “there are, however, certain hydrogen bonds in which the X−H bond length decreases and a blue shift in the X−H stretching frequency is observed.”22,46,47 The interpretation of shifts in vibrational analysis is also complicated by the mixing of frequencies of similar energies. Vibrational shifts for dimers 1−8 are shown in Table 5. For dimers 1−5 and 7, experimentally observed vibrational shifts

Since an attractive interaction is not deemed HB if it is “primarily due to dispersion”, it is worth looking at the ratio of the electrostatic energy to the dispersive energy in these complexes. The classic HB complexes 2−7 show ratios mostly in the 3−4 range (SAPT2) or 5−7 range (LMO-EDA), while the weak complexes have ratios that range from 0.3 to about 1.0 (SAPT2) or 0.3 to 1.2 (LMO-EDA). In both methods, complex 1 is at the lower end of the classic HB scheme but much higher than the weaker complexes. The other exception is 9b, which has a ratio of 1.7 (SAPT2) and 2.3 (LMO-EDA). Even though this complex has a maximal dipole−dipole interaction, it still has a lower ratio than 1, an effect that can be ascribed to the importance of CFHB in the latter. In short, the BE of complex 1 is dominated by a large electrostatic term, in much the same way that the classically HB complexes 2−7 are. Geometry. Another important indicator for the presence of HB is geometry. Here, both the traditional view and that given in the IUPAC report agree on two important geometric features: The X−H···Y hydrogen bond angle tends toward 180° and should preferably be above 110°. The length of the X−H bond usually increases on hydrogen bond formation.22 The IUPAC report diverges in one important way from the traditional view: the X,Y distance is no longer thought to be a reliable indicator of HB. Complexes 1−8 will be analyzed with these criteria in mind. As shown in Table 4, for complexes 2−7 the Y···H distance (RY···H) varies from 1.865 Å (7) to 1.958 Å (4). In 1, RY···H is a Table 4. Geometric Features of Complexes 1−8 (MP2/augcc-pVQZ) dimer

RY···H (Å)a

ROH (Å)b

angle ∠OH···Y (°)

1 2 3 4 5 6 7 8

1.9926 1.9429 1.8906 1.8668 1.9583 1.9044 1.8653 2.5289

0.9628 0.9663 0.9684 0.9700 0.9727 0.9762 0.9802 0.9597

145.83 171.76 165.51 163.62 169.69 162.92 165.95 166.36

Table 5. Change in Vibrational Frequency of the Water Molecule OH Stretches upon Complexation (cm−1)

a

Distance between the basic donor atom and the hydrogen bound H of HOH. bLength of the hydrogen bound OH bond in water. For HOH, the calculated ROH is 0.9589 Å.

bit longer at 1.993 Å. In contrast, the weakly bound complex 8 has a C···H(OH) distance over 2.5 Å. Unlike the energetic components analyzed above, RY···H does not correlate well with the BE of the complex, as the O complexes form shorter but not stronger HBs than the N complexes. However, if the basic atom stays the same, then substitution of an H for CH3 in the HB acceptor results in significant shortening of RY···H in both the 2−4 and 5−7 series. For complexes 2−7, the bound O−H distance (ROH) in water lengthens in a range from 0.0074 Å (2) to 0.0213 Å (7). In 1, ROH has a lengthening of 0.0039 Å, which is just under 53% of that seen in 2. In contrast, for 8, the bond lengthening is only 0.0008 Å, which is just under 11% of that seen in 2. As stated in the IUPAC report, this lengthening should correlate with HB strength. Indeed, a plot of bond lengthening versus BE for 1−7 shows a decent fit (r2 = 0.94). A marginally better fit is seen in a plot of bond lengthening versus proton affinity of the HB acceptor (r2 = 0.95).

dimer

ν1a (calc.)b

ν1 (exp.)c

ν3d (calc.)b

ν3 (exp.)c

1 2 3 4 5 6 7 8

−37.2 −103.2 −149.2 −185.1 −233.8 −313.9 −405.4 −4.7

−11 −66.6 −99.3 −113.6 −274.7

−20.7 −32.6 −37.0 −40.5 −40.0 −44.0 −49.5 −7.3

−12 −22.2 −30.6 −29.5 −32.9

−277

−36

a

The asymmetric OH stretch in HOH. bMP2/aug-cc-pVTZ. References for the experimental values are given in the main text. d The symmetric OH stretch in HOH. c

from matrix-isolated IR spectra are included.17,48−52 In almost every case, the calculated frequency shifts are more negative than those found experimentally. However, similar trends are seen in both data sets. Thus, it can be seen that for the classic HB molecules 2−7, the calculated red shifts in ν1 (the asymmetric OH stretch in the water molecule) correlate reasonably well with BE (r2 = 0.91) and even better with proton affinity (r2 = 0.95). Smaller but measurable changes are also seen in ν3 (the symmetric OH stretch in the water molecule), though the values are relatively insensitive to the structure of the dimer. Complex 1 shows a small, but significant, calculated red shift in ν1 of just under 40 cm−1. When these values are included 10846

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with the data set 2−7, the correlation between BE and Δν1 improves slightly (r2 = 0.93) while that between proton affinity and Δν1 stays the same (r2 = 0.96). Using a different approach, the values for 2−7 for BE versus Δν1 can be used to predict a blue shift of 13 cm−1 for 1. While this prediction is close to neither the experimental nor the calculated value, it does hint that given the BE of 1, one might not expect much of a red shift in ν1. Finally, as shown in Figure 4, a plot of the experimental

charges is slightly worse (r2 = 0.88). These data are consistent with the IUPAC statement given above. Inclusion of data for 1 improves the correlation between BE and charge transfer, to r2 = 0.95 for NPA and to r2 = 0.93 for AIM. The plot for the NPA calculated charge transfer versus BE for 1−7 is shown in Figure 5. Alternatively, the equations for

Figure 5. A plot of charge transfer between molecules versus binding energy of the complex for 1−7. Charges are calculated using NPA with the units expressed as electrons × 1000. Binding energies are in kcal/ mol.

Figure 4. A plot of the experimentally determined red shift of ν1 (asymmetric OH stretch, cm−1) versus calculated binding energy (kcal/mol) for 1−5 and 7.

2−7 can be used to predict the charge transfer for 1. Here, NPA data predicts a charge transfer of −0.0062 e for 1 while the direct calculation yields −0.0089 e. The AIM data predicts a charge transfer of −0.0057 e and calculates −0.0054 e. In both cases the calculated charge transfer for 1 is either in line with (AIM) or greater than (NPA) that predicted for a classically HB species. While not explicitly mentioned in the IUPAC report, it seems that proton affinity of the donor should also correlate with the extent of charge transfer. Indeed, plots of charge transfer vs proton affinity for 2−7 fit similarly (NPA (r2 = 0.96), AIM (r2 = 0.92)) to the corresponding plots for BE. Inclusion of compound 1 maintains (NPA, r2 = 0.96) or improves (AIM, r2 = 0.96) this correlation. The important point is that, once again, compound 1 behaves like a classically HB species. Topological Analysis. The analysis of topology of electron density using AIM can also be used to analyze HB. The IUPAC definition of HB states: “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”.22 Earlier, Koch and Popelier had a broader and more quantitative list of eight criteria based on topological analysis.53 Two key indicators from this list are that HB exists if ρ at the bond critical point has a value between 0.002 and 0.034 au and if ∇2ρ at the bond critical point had a value in the range 0.024 to 0.139 au. A more quantitative approach was taken by Parthasarathi et al.54 who looked for correlations between ρ and ∇2ρ with BE for 28 dimers that ranged in calculated BE from 0.11 to 49.7 kcal/mol (MP2/aug-cc-pVDZ). They found a very good linear relationship between HB strength and ρ and a good relationship between HB strength and ∇2ρ. They use these data to show that there is a “smooth transition from weak (van der Waals) hydrogen bond to moderate (classical) and strong hydrogen bond.” The data in this work will be analyzed in this context. As can be seen in Table 6, complexes 2−7 clearly satisfy Popelier’s criteria (and therefore the less stringent IUPAC

red shift versus calculated BE for 1−5 and 7 leads to a straight line with a modest correlation (r2= 0.82) that improves significantly (r2 = 0.94) if the value for 5 is removed. In contrast to complex 1, complex 8 shows very small calculated shifts in both ν1 and ν3. Thus, the vibrational spectrum of 1 is consistent with a CFHB. Charge Transfer. In addition to measurable physical quantities, HB has also been characterized by theoretical means. As stated in the IUPAC report, “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.”22 Here, NPA and the AIM theory will be used to analyze the extent of this charge transfer. Table 6 shows the amount of charge transfer from donor to acceptor in complexes 1−8. Using either theoretical method, charge transfer follows the familiar trends: acceptor atoms that are more basic and have more methyl groups lead to higher values of charge transfer. For the NPA charges of compounds 2−7, a plot of charge transfer versus BE yields gives a reasonable fit (r2 = 0.92). The same correlation using the AIM Table 6. Charge Transfer and Topological Analysis for Complexes 1−8 dimer

charge transfera (NPA)

charge transfera (AIM)

ρb

∇2ρb

1 2 3 4 5 6 7 8

8.9 15.4 19.9 23.7 27.3 34.0 40.8 0.2

5.4 18.8 21.3 23.3 37.4 41.5 47.5 5.6

0.0183 0.0247 0.0291 0.0322 0.0298 0.0348 0.0398 0.0074

0.0800 0.0818 0.0889 0.0911 0.0694 0.0726 0.0705 0.0309

a

Total number of electrons transferred form the hydrogen bond acceptor to water. Units are e × 1000. bIn atomic units. 10847

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guidelines), with values of ρ and ∇2ρ well within the listed ranges. Importantly, complex 1 is characterized as a CFHB by these measures as well. Attempts to quantify these data led to only a modest relationship between BE and ρ. For 2−7, the r2 equals 0.81, which improves to 0.90 with the addition of 1. When the values from 2−7 are used to predict the value for 1, the prediction (0.021 e) is for a modestly higher value than is seen (0.018 e). For ∇2ρ, the relationship with BE was almost random, (2−7 give r2 = 0.44; 1−7 give r2 = 0.26). Complex 8 shows much smaller values of ρ and ∇2ρ than complex 1. While small, these values are large enough to state that 8 has a HB according to Koch and Popelier. The scheme of Parthasarathi et al. places complex 8 into the category of weak HB and complex 1 at the border of weak and moderate HB. Although the quantitative aspects of both of these schemes are somewhat arbitrary, analysis of the topology of the electron density clearly shows a CFHB in complex 1.

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CONCLUSION In looking at the BE, the electrostatic and dispersive components of the BE, geometries, vibrational frequencies, charge transfer, and topological features of the electron density of a variety of complexes, it is clear that the F atom in CH3F acts as a hydrogen bond acceptor in its complex with water. Furthermore, this hydrogen bond is about 80% as strong as the hydrogen bond in the water dimer and is significantly stronger than the interactions seen in weakly bound dimers such as the methane dimer and the water−methane heterodimer. Other features of the fluoromethane−water dimer parallel the corresponding features seen in the water dimer, though they are less pronounced in the former. Preliminary data, not shown here, suggest that these trends continue as the effects of solvation are included.

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ASSOCIATED CONTENT

S Supporting Information *

Structures and energies of complexes; binding energies of complexes, SAPT and LMO-EDA energies of complexes; ratios of electrostatic, dispersive, and BEs to each other; plots of geometric, vibrational, charge transfer, and topological features versus either binding energy or proton affinity; and a list of other works that calculate binding energies for these structures (17 pages). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(859) 233-8279 (phone); (859) 233-8171 (fax); e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author would like to thank the Kenan and Jones Foundations at Transylvania University for grants that support this work. The author would also like to thank Kenneth Moorman and the Computer Science Program at Transylvania University for use of their computers.

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REFERENCES

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