Microsolvation of Fluoromethane - The Journal of Physical Chemistry

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Microsolvation of Fluoromethane Robert Evan Rosenberg J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b07063 • Publication Date (Web): 30 Aug 2016 Downloaded from http://pubs.acs.org on August 31, 2016

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The Journal of Physical Chemistry

Microsolvation of Fluoromethane

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

ACS Paragon Plus Environment


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ABSTRACT

Microsolvation of Fluoromethane

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 potential for and strength of hydrogen bonds involving fluorine. It is known that CH3F forms a hydrogen bond with H2O in the gas phase but does not dissolve in bulk water. This paper examines CH3F surrounded by one to six water molecules. For systems of similar topology, CH3F formed hydrogen bonds of nearly the same strength as water. While CH3F can bind to a second water cluster with only a modest loss in binding energy, it must bind to these clusters as a double hydrogen bond acceptor. This means that CH3F cannot form a low energy cyclic 2D hydrogen bonding network with water molecules, which limits its solubility in bulk water. However, CH3F should be able to bind to the periphery of small hydrogen bonding networks. These conclusions were not appreciably altered by SMD calculations. A more complete consideration of solvation, especially entropic effects, was not undertaken. Data for geometries, population changes, and vibrational frequency shifts were also analyzed and compared to binding energies.

(191 words)


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Microsolvation of Fluoromethane 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 of the more important 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, which will be termed a CFHB. Indeed, CFHBs have been invoked to explain binding of fluorinated compounds in DNA analogs3,4,5 and in proteins.6,7,8 From early crystallographic work9,10 up through a 2012 review of the literature11 doubt was cast on the existence or importance of CFHBs. Today, however, there is significant evidence for the existence of CFHBs including direct observation of a hydrogen bond between CH3F (F) and water (W) in matrix-ir,12 synthesis of numerous compounds that contain intramolecular CHFBs,13,14,15,16 and several high level ab initio calculations17,18,19 A recent paper used NMR spectroscopy to directly measure the strength of CFHBs.20 There is still much that is unknown about CFHBs. While ab initio calculations show that the CFHB between F and W is 85% as strong as the corresponding hydrogen bond, HB, in the water dimer,19 F has very limited solubility in water.21 This paper examines the intermediate cases, those where F is bound to a small number of water molecules. Besides explaining why F does not dissolve in water, these findings will also provide data that can be used to improve the understanding of how fluorocarbons interact with a small number of water molecules and how they partition between aqueous and organic layers. A more complete understanding is likely with the inclusion of entropic effects, which were not considered in this work. Ultimately, these



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factors would be combined to understand the binding of fluorinated molecule in small hydrophobic pockets of proteins. Specifically, this paper will look at four classes of complexes. The first category includes the lowest energy complex of F with each size of water cluster, from one to six (Wn, n = 1-6). These complexes, F•Wn, will be compared to complexes of water of the same size, Wn+1. The second category focuses on complexes where both the F•Wn and the Wn+1 complexes have the same topology in their HB network. The third category includes structures where F is bound to two or three water complexes, written as F•Wm•Wn. The final category examines complexes where F is bound to different types of W’s. The type of a given W is distinguished by how many donors and acceptors are bound to it. In all four groupings, the binding energy, geometry, vibrational frequencies, and population changes will be determined and compared to suitable model systems. To account for different solvent environments, SMD solvent corrections for ether, N,N-dimethylacetamide (DMA), and water will be performed.

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 sets22 using Gaussian 09.23 Frequency calculations were performed at the MP2/aug-cc-pVDZ level as the aug-ccpVTZ basis set was too large for most of the larger complexes. Comparisons of the aug-ccpVDZ calculated frequencies of small clusters with those calculated using aug-cc-pVTZ basis set showed excellent agreement. 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


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correlation at the CCSD(T)/ aug-cc-pVTZ level was approximated as shown in Scheme 1, below. In the Supporting Information, it is shown that for the smaller clusters the approximation scheme gave binding energies within a few hundredths of a kcal/mol of the explicit CCSD(T)/aug-ccpVTZ calculations. Atomic populations were calculated by Natural Population Analysis (NPA)24 in Gaussian 09 at MP2/aug-cc-pVDZ level of theory.

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 Basis set superposition error (BSSE) was calculated using the counterpoise method (CP) of Boys and Bernardi.25 As there is still some question as to the validity of the CP method for BSSE,26 the method described by Sherrill was used,27 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 the Supporting Information, it is shown that explicit BSSE correction for the two additional terms in the CCSD(T)/aug-cc-pVTZ approximation does not lead to appreciably different values. As 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. SMD calculations28 as implemented in Gaussian 09 were used to correct for solvent effects. Here, the optimized MP2/aug-cc-pVDZ gas phase structures were used for all calculations. The SMD calculations are performed using three solvents to give a wide range of dielectric constants, ether (4.33), DMA (37.8), and water (80.1). Conformational searches



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Water clusters Wn The geometries and energies of the water clusters, Wn are well characterized.29 Due to the relatively large number of structures for n ≥ 5, typically only those structures that were within about 2 kcal/mol of the global minimum were chosen for this work. Additional higher energy structures were included if they had the same topology in their HB network as a suitable F•Wn complex. For example, W4-c was included because it can be formed by substitution of F with W in F-W3-a. Initial water structures are taken from ref. 29 and re-optimized using the computational methods in this work. The geometries and energies of all the water clusters used are contained in the Supporting Information. CH3F•(H2O)n complexes F•Wn. Other than n = 1, the structures of F•Wn for n ≥ 2 have not been reported. For n = 2 and 3, a complete set of F•Wn were located by either appending F to the unique sites on a given Wn or appending W to the unique sites on a given F•Wn-1. The principles gleaned from these smaller structures were used to generate selected F•Wn’s for n = 4-6. For the larger complexes, the goal was to locate the lowest energy complex within each HB network topology for each value of n. Specific topologies include: (1) F forms a single HB to a Wn cluster, (2) F forms two bonds to a single Wn cluster, (3) F forms one HB to each of two or three Wn clusters, and (4) F replaces a W in a Wn that has a 2D HB network. Category 1 was the global minimum for n = 1-5 and involved binding F to the periphery of the lowest energy Wn, Wn-a. Category 2 involved only two structures, F•W4-c and F•W6-a. In both cases, the fluorine forms a HB to the hydrogen atom from adjacent W’s. For F•W4-c, this arrangement was very similar energetically to its category 1 counterpart, F•W4-d. F•W6-a was the global minimum for n = 6. Category 3 was well populated for the binding of F to two clusters. In these cases, only the lowest energy


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topology for each water cluster, Wn, was used. A typical example might be F•W•W3, which designates F bound to both W and to W3-a. Only one example was found for F bound to three water clusters, denoted as F•W•W•W. Larger molecules with three groups on F were energetically unstable relative to F bound to two water clusters. Thus, F•W•W•W2 is unstable relative to F•W•W3. Category 4 is notable for not being populated. All efforts to substitute F for W in a cyclic Wn complex failed. This is an important case and will be discussed further. The geometries and energies of all complexes are in the Supporting Information.

Results and Discussion. One of the major questions at hand is how the strength of the CFHB between F and an OH group changes as F bonds to different complexes Wn. The first step taken here was to find the lowest energy structures of F•Wn for n = 1–6. These are illustrated in Figure 1, below. For n = 1–5, these structures closely resembled the structure of F forming a single HB to the periphery of the lowest energy Wn structure, Wn-a. For n = 6, the lowest energy structure had F attached to two adjacent W’s in W6-c. Here, the W6-c isomer incorporated in the complex is within one kcal/mol of Wn-a. < Insert Figure 1 here >

Table 1.

n 1 2 3 4 5 6

Binding Energies of F•Wna and Wn+1b complexes. (kcal/mol)

BE (F•Wn) –4.31 –6.99 –5.64 –5.32 –6.26 –7.90

BE (F•Wn) (VZPE)c –2.74 –5.25 –4.29 –4.09 –5.82 –6.53

BE (F•Wn) (BSSE)d –4.05 –6.60 –5.22 –4.88 –5.77 –7.27

BE (Wn+1) –5.21 –11.04 –12.13 –8.85 –10.85 –11.86


BE (Wn+1) (VZPE)c –3.11 –7.79 –9.23 –6.66 –7.43 –9.11

BE (Wn+1) (BSSE)d –4.97 –10.61 –11.62 –8.49 –10.25 –11.32


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a

Binding energy of F to Wn as defined by equation (1). bBinding energy of W to Wn as defined by equation (3). cBE corrected for VZPE as described in theoretical methods. dBE corrected for BSSE as described in theoretical methods.

Binding energies of F to Wn, BEs, as defined by equation (1) below, are listed in Table 1, above. Table 1 lists three values of the BE, uncorrected, corrected for VZPE, and corrected for BSSE. This discussion will focus on the BSSE corrected BEs, but the qualitative conclusions are the same regardless of which set of values are chosen. The BE of F•W is near –4 kcal/mol, a value consistent with previous work.17–19 When F binds to W2, the CFHB is significantly stronger, worth nearly –7 kcal/mol. Corresponding additions of F to larger Wn’s led to a fairly narrow range of values for BE’s, –4.88 to –7.27 kcal/mol, with an average of –5.78 kcal/mol. For the complex F•W6, it could be argued that the BE is even larger than what is reported above, as the optimal W6-a is used in equation (1) but in F•W6-a, the actual CFHB is between F and W6-c. Seen in that light, the BE of F•W6-a would be more negative by 0.76 kcal/mol. The important point is that the CFHBs for all F•Wn’s (n ≥2) are higher than for F•W. BE (F•Wn) = E(F•Wn) – E(F) –E(Wn).

(1)

The conclusions above are also true for the solution phase as can be seen from the data in Table 2, below. Regardless of the solvent used, the BE of F to W remained the weakest of all the complexes. In ether, the BE’s were mostly reduced by about 40% relative to the gas phase, leaving the relative ordering of the BE’s unchanged. In comparing the BE’s of the more polar solvents to the gas phase, the smaller F•Wn complexes, n ≤ 3, showed a significantly larger reduction in BE than the larger complexes did, an effect that is more pronounced in water.

Table 2. n

Gas phase and SMD Binding Energies of F•Wn complexes.a (kcal/mol). gas

ether

DMA

water


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1 –4.49 –2.69 –2.06 –2.16 2 –7.27 –3.96 –2.91 –2.52 3 –6.04 –3.54 –2.70 –3.15 4 –5.74 –3.43 –2.82 –3.49 5 –5.82 –3.30 –2.81 –3.87 6 –6.75 –5.40 –4.19 –5.01 a Binding energy of F•Wn as defined by equation (1). Energies are for the MP2/aug-cc-pVDZ gas phase geometries. Values are not corrected for BSSE. In the definition of the HB by IUPAC,30 it is shown that the presence of HBs often correlate with geometric features, vibrational frequencies, and population transfers of the complexes. Applying this to compounds F•Wn, one would expect short F…H distances (RFH), nearly linear OH…F angles (∠OHF), lengthened (F)H…O bonds (ROH), red shifted νOH’s, and charge transfers from Wn to F (qF). This application is straightforward except for νOH where vibrational analysis is complicated by the mixing of frequencies of similar energies. Indeed, it is not readily possible nor worthwhile to tease out the change in a single νOH due simply to the F…HO bond. Instead, the reported values, ∆ν’s, show the deviation in the sum of the νOH’s in the presence and absence of F as shown in equation (2) below. In equation (2), it is important that the Wn of the complex F•Wn correspond to the same topology as the Wn in the Σ νOH (Wn) term. Thus, the ∆ν for F•W6-a uses Wn-c, as both have the same “book” form for the W6 fragment.

∆ν = Σ νOH (F•Wn) – Σ νOH (Wn)

(2)

It can be seen from Table 3 that as a whole the complexes F•Wn do indeed have the characteristics of an HB compound, with short RFH’s, a mildly elongated ROH, a not quite linear ∠OHF, charge transfer from F to Wn, and red shifts in ∆ν. None of these features correlate (r2) well with BE, with the best correlation, between ∆ν and BE, of only 0.5.



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The poor correlation of BE to geometric, vibrational, and population analyses is probably due to the diversity of the topologies of the HB networks exhibited by the Wn’s that are bound to the F•Wn’s. Thus, F•W and F•W2-a are bound to Wn’s in a linear, or 1D HB network, F•W3-a and F•W4-a are bound to Wn’s in a cyclic, or 2D HB network, and F•W5-a and F•W6-a are bound to Wn’s in a polycyclic, or 3D HB network.

Table 3.

Geometric features, population analysis, and red shifts for F•Wn complexes.

BE (BSSE)a RFH (Å)b ROH(Å)b ∠OHF (°)b qF (e–)c ∆ν (cm–1)d 1.997 0.965 146.5 0.00554 –49 -4.05 F•W –6.60 1.879 0.973 163.2 0.00736 –187 F•W2-a –5.22 2.008 0.966 150.8 0.00535 –145 F•W3-a –4.88 2.034 0.966 147.1 0.00453 –117 F•W4-a –5.77 2.035 0.966 149.3 0.00518 –67 F•W5-a –7.27 2.079 0.965 151.7 0.00573 –162 F•W6-a 0.00 0.40 0.26 0.53 r2 a Binding energy of F to Wn as defined by equation (1), corrected for BSSE. bRFH is the distance from the fluorine atom of F to the hydrogen bound H atom. ROH is length of the OH bond that is hydrogen bound. In W, this bond has a length of 0.9614 Å. ∠OHF is the bond angle of the hydrogen bond. cThe charge on F. dThe change in the vibrational frequencies of the OH stretches upon complexation as defined by equation (2). The bonding of F to Wn complex can be placed in better context by comparing it to the binding of W to Wn. BE’s of W to Wn as defined by equation (3) below, are listed in Table 1, above. Addition of W to W to form W2 leads to an HB worth a little less than 5 kcal/mol, a value which is 20% higher than the analogous CFHB in F•W. Adding a W to W2 to form W3-a leads to a stabilization of over 10 kcal/mol, a value considerably higher than both the binding of W to W but also than the –7 kcal/mol for the BE of F•W2-a. This difference might be accounted for by noting that addition of W to W2 leads to a cyclic array of HBs and the formation of two additional HBs. However, adding a W to W3-a or to W4-a leads to a similarly large stabilization but retains the cyclic HB array and adds only a single HB. On average, addition of W to Wn to


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form Wn+1 yields a BE just over –10 kcal/mol, a value markedly more negative than the corresponding –5 to –6 kcal/mol value for F to Wn. Thus, while both F and W bind better to Wn than to W, this effect is more pronounced for the “normal” HBs of W than for the CFHBs of F. BE (W to Wn) = E(Wn+1) – E(W) –E(Wn)

(3)

The gas phase trends above continue to hold in solution as shown in Table 4, below. In ether, BE’s for Wn complexes were reduced relative to the gas phase by an average of 25%, which is less than the 40% reduction seen for reduction of the BE’s of F•Wn. In DMA the BEs are reduced by an average of 33%, with the same complexes that showed large reductions in BE in ether showing large reductions in DMA. The results for water showed more variation. While the BE of W2-a is still weakest, three other complexes are within a kcal/mol. Overall reductions in BE averaged over 50%, with the largest reduction just under 70%. From these data, it can be concluded that inclusion of solvent effects increases the gap between the BEs of F to Wn vs. W to Wn.

Table 4.

Gas phase and SMD binding energies of Wn+1, W to Wn complexes.a (kcal/mol) gas

ether

DMA water –5.26 –4.33 –3.91 –3.09 W2-a –11.10 –7.20 –5.87 –3.44 W3-a –12.38 –10.06 –9.17 –6.82 W4-a –9.03 –7.13 –6.50 –4.45 W5-a –10.90 –6.86 –5.37 –3.75 W6-a –12.24 –10.11 –9.39 –7.50 W7-a a Binding energy of F•Wn as defined by equation (1). Energies are for the MP2/aug-cc-pVDZ gas phase geometries. Values are not corrected for BSSE.

The comparison between F and W above shows that W is better at forming complexes with Wn than F is. Thus, the computational data supports the well-known empirical result that fluoro-organics in general and F in particular are not soluble in water. What is not obvious is



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why. There are three possible reasons for this: 1) bonds between W and Wn are stronger than those between F and Wn, 2) W is able to form HBs to two or more isolated Wn clusters while F can only bond to one Wn, 3) W is able to form 2D and 3D HB networks that are unavailable to F. Each of these reasons will be examined in turn.

Comparing F•Wn to Wn+1 In order to properly compare the HB strength of F to W in their complexes with Wn, one must choose structures F•Wn such that substitution of W for F leads to a W•Wn with the same HB network topology as F•Wn. Of all the F•Wn’s examined in this study, only seven fulfill the criteria above. These seven comparisons are shown in Figure 2, below. In the other F•Wn structures, the corresponding W•Wn structure reorients into a new topology. As a simple example, F•W2-a forms a linear array of HBs. Replacing F with W initially results in a linear structure that is energetically unstable with respect to W3-a, which has a cyclic array of HBs. < Insert Figure 2 here > ∆BE (F•Wn vs. Wn+1) = BE (Wn+1) – BE (F•Wn)

(4)

For all comparisons, the ∆BE’s are defined as in equation (4) above, where the terms are found using equations (1) for BE (F•Wn) and equation (3) for BE (Wn+1). The values of ∆BE are listed in Table 5, below. When F is bound to W in F•W, the bond is nearly 1 kcal/mol weaker than for the corresponding W2, a reduction of about 20%. The ∆BE’s of W2, W3-a, or W4-a with F are similar to those for W. Indeed for F•W3-a vs. W4-c, F forms the stronger bond with W3. For the remaining comparisons, the difference favors Wn+1, but by a maximum of 1.7 kcal/mol. Thus, while the HB in F•W is 20% weaker than for W•W, binding to larger complexes decreases this difference to an average of 12.5%. Solution phase data widen the gap


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between F•Wn and Wn+1 slightly. This is due to a smaller reduction in BE for the solvation of Wn+1 versus that for F•Wn. As was seen earlier, solvation effects were smallest with ether, larger with DMA, and somewhat variable with water. Values for BEs in solution are listed in the Supporting Information.

Table 5.

Gas phase ∆BE’s for F•Wn vs. Wn+1. a (kcal/mol)

Comparisonb ∆BE(BSSE) Comparisonb ∆BE(BSSE) F•W vs W2 –0.93 F•W5-e vs W6-e –0.48 F•W2-b vs W3-d –0.32 F•W6-e vs W7-d –1.70 F•W3-a vs W4-c 0.21 F•W6-f vs W7-c –1.02 F•W4-a vs W5-d –0.09 a ∆BE is defined by eq. (4) in the text and are calculated for CCSD(T)/aug-cc-pVTZ as described in scheme 1 and are corrected for BSSE . bStructures are shown in Figure 2.

The average differences in the values of the geometric features, population changes, and vibrational shifts for F•Wn minus those for Wn+1 are listed in Table 6 below. Because Wn+1 has one more high frequency vOH than F•Wn due to the additional W, the values for ∆∆ν are adjusted according to equation (5). ∆∆ν = Σ νOH (F•Wn) – Σ νOH (Wn+1) + Σ νOH (W)

(5)

All of the differences in Table 6 point towards a more pronounced HB in Wn+1 than in F•Wn, a result mildly at odds with the BE data in Table 5 which shows HBs of similar strength. As in the previous section, these variables are poorly correlated with ∆BE. Values for all variables used in Table 6 are listed in the Supporting Information.

Table 6.

Geometric features, population analysis, and red shifts for F•Wn vs. Wn+1

Comparison Ave. difference r2e

∆BEa ∆RHB (Å)b ∆ROH(Å)b ∆∠HB (°)b ∆qHB(e-)c ∆∆ν (cm–1)d 0.62 0.089 -0.005 -28.4 -0.00479 111 0.03 0.02 0.02 0.34



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a

∆BE is defined by eq. (4) in the text. ∆BE are calculated for CCSD(T)/aug-cc-pVTZ as described in scheme 1 and are corrected for BSSE b∆RHB is the difference in the lengths of the HBs between F•W and Wn+1. ∆ROH is difference in the lengths of the OH bonds that are hydrogen bound between F•W and Wn+1. ∆∠HB is the difference in the angles of the HB between F•W and Wn+1. c∆qHB is the difference in the charge transfer to the HB acceptor between F•W and Wn+1. d∆∆ν is the difference in the red shifts of the OH stretches between F•W and Wn+1 as defined by equation (5). eThe correlation coefficient between that property and ∆BE. Taken as a whole, it could be argued that, all things being equal, F binds to Wn almost as strongly as to W. This conclusion is somewhat weakened by the solution phase data and the data from Table 6. More importantly, in many of these comparisons, the most stable F•Wn is being compared to a sub-optimal Wn+1. For the most stable Wn+1’s, there is no corresponding F•Wn. The explanation for this is found in the next two sections.

Binding of F to multiple Wn’s One key feature of Wn complexes is the formation of 2D and 3D HB networks starting with n = 3. The analogous F•Wn complexes rarely formed these higher dimensional HB networks. All attempts to find a stable cyclic structure for F•W2 analogous to W3-a led to F•W2-a, a linear structure. For F•W3 the cyclic structure analogous to W4-a was unstable with respect to F•W3-a, which resembles F bound to periphery of W3-a and is topologically equivalent to W4-c. The trend continues for higher n, with two minor exceptions. For F•W4, there is a bisected structure, F•W4-c where the F is bound to H’s from two adjacent W’s of W4b. However, this structure is inferior to the global minimum F•W4-a, where F forms a single HB to the periphery of W4-a. For F•W6, a bisected structure between F and W6-c is the global minimum. The structure is similar to F•W4-c, in that F is bound to two adjacent W’s in W6-c. Even in these cases, F is not integral to the main ring structure but instead bonded to the periphery of the ring.


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It is possible that F is not incorporated into cyclic HB arrays with Wn because there is a severe energy penalty for adding a second or third Wn cluster to the F•Wn complex. To this end, the eight complexes F•Wm•Wn (n + m ≤ 6) were built. In this notation, F•W2•W3 would indicate F bound to two separate water clusters, W2 and W3. An additional complex F•W•W•W that has three independent W’s bound to F was also constructed. Larger complexes with three distinct water clusters such as F•W2•W•W proved to be unstable with respect to decomposition to F•W3•W. All nine complexes are shown in Figure 3, below. The BE of these complexes is defined by equation (6) and the values are placed in Table 7, below.

Table 7.

BE’s of complexes F•Wn•Wma (kcal/mol). BE –4.05 –3.54 –3.41 –3.68 –3.76

BE

BE –5.22 F•W4 –4.85 F•W•W4 –4.67 F•W2•W4 –4.60

–6.60 F•W3 F•W F•W2 –5.96 F•W•W3 F•W•W F•W•W2 –5.61 F•W2•W3 F•W2•W F•W2•W2 –6.04 F•W3•W3 F•W3•W F•W3•W2 –6.60 F•W4•W F•W4•W2 F•W•W•W a Binding energy of F•Wm to Wn as defined by equation (6). BE are calculated for CCSD(T)/aug-cc-pVTZ as described in scheme 1 and are corrected for BSSE .

BE –4.88 –4.59 –4.52 –3.13

< insert Figure 3 here >

BE (F•WnWm) = E(F•WnWm) – E(F•Wn) – E(Wm)

(6)

Addition of a single W to F•Wn to form F•Wn•W for n = 1–4, led to a remarkably similar BE that ranged from –3.41 to –3.76 kcal/mol. The average BE is roughly 10% less than the BE of –4.05 seen for F to W. Addition of a third water molecule to from F•W•W•W also led to an



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additional drop-off in BE of about 10% relative to the BE of W to F•W. Addition of W2 to F•Wn for n = 1–4 led to similarly tight range of BEs, from –5.61 to –6.24 kcal/mol. The average BE is once again about 10% less than the value for W2 to F. Addition of W3-a to F•Wn, n = 1–3 led to BEs from –4.60 to –4.85 kcal/mol, which is about 10% less than the value for F•W3-a. Finally, addition of W4-a to F•Wn, n = 1–2 led to BEs of –4.59 and –4.52, less than a 7% dropoff from binding of W4-a to F. These values across the entire spectrum are quite consistent: binding of Wn to F decreases the affinity of F for the second ligand Wm by about 10% regardless of the values of n and m. The solution phase data do not appreciably alter these conclusions. The effects of the solvent are similar to those in previous sections, a nearly 40% reduction in BE for ether, a slightly larger reduction for DMA, and a significant and variable reduction for water. These data are listed in the Supporting Information. The averages and standard deviations for the geometric features for F•Wm•Wn and those for F•Wn.are listed in Table 8. In this notation, the values for F•Wn•W encompass the four compounds F•W•W, F•W2•W, F•W3•W, and F•W4•W and the geometric features refer to those that bond F to W. From the averages, it can be seen that for all the variables, the average value for F•Wm•Wn is quite similar to that for F•Wn, with RFH within 0.07 Å, ROH within 0.002 Å, and ∠OHF within 8°. From the standard deviations, it can be seen that within a series the geometric features have little variance. Both findings are consistent with the BE data. A complete listing of the geometric features is contained in the Supporting Information. Unlike earlier sections, Table 8 does not include values for charge transfer and vibrational frequencies as interpretation of these values is unduly complicated by the presence of the second cluster.

Table 8.

Average values for geometric features of F•WnWma


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RFH (Å) ROH(Å) ∠OHF (°) F•W 1.997 0.965 146.5 b F•Wn•W 2.027(0.013) 0.965(0.001) 145.3(1.2) F•W2 1.879 0.973 163.2 0.967(0.002) 159.2(9.7) F•Wn•W2b 1.947(0.063) F•W3 2.008 0.966 150.8 b 1.985(0.066) 0.966(0.002) 153.9(9.3) F•Wn•W3 F•W4 2.034 0.966 147.1 0.967(0.002) 155.0(12.4) F•Wn•W4b 1.962(0.076) a RFH is the distance from the fluorine atom of F to the hydrogen bound H atom. ROH is length of the OH bond that is hydrogen bound. In W, this bond has a length of 0.9614 Å. ∠OHF is the bond angle of the hydrogen bond. bValues are for the averages over these values for all species n. Numbers in parentheses are standard deviations.

Types of W’s Since it was established above that F can form sufficiently strong HBs to W and that F can bind to multiple groups Wn with only a minor loss in BE, it must be the inability of F to act as both an HB donor and an HB acceptor that causes F to be insoluble in bulk water. To better support this hypothesis, the bonding of W in bulk water is examined. Recently, Akase and Aida have identified nine possible local HB types of W’s in their study of bulk water clusters.31 In their notation, a W designated a is an HB acceptor and a W with a d is an HB acceptor. For this work an additional symbol, dF, is added to signify donation of a hydrogen to an F receptor. The various types are formed by combining these descriptors. Thus, a W of type ddFa is a donor to one W, a donor to one F, and an acceptor from a third W. Including only those W types bound to F leaves six unique types as shown in Scheme 2. Representative complexes for F bonding to each type are shown in Figure 4, below.



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Scheme 2.

The six different types of W’s bound to F. in bold.

< Insert Figure 4, here > The BE’s in this section are defined as in equation (1) and are listed in Table 9. Table 9 lists the unique (dF, ddF, dFa, dFaa) or average (ddFa, ddFaa) BEs of F to each type of W. Values for all the BEs for types ddFa and ddFaa are listed in the Supporting Information. The BEs in Table 9 are consistent with the chemical intuition that the bonds between F and W will be strengthened by electron donors and weakened by electron acceptors to W. Thus, the strongest binding by far is seen in the sole dFaa complex, F•W4-g, where F is bound to W4-d. The next strongest complex is formed with F•W2-a, the only example of a dFa complex. At the other


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extreme, the weakest binding is seen for F•W2-b, the only example of a ddF complex. As expected, the BE of dF falls between these extrema.

Table 9.

Average gas phase binding energies for each different types. a (kcal/mol)

types example BE types example BE b dFaa F•W4-g ddFa (11) F•W3-a –7.66 –5.11 d Fa F•W2-a dF F•W –6.60 –4.05 b F•W5-f ddFaa(6) ddF F•W2-b –5.16 –3.62 a Binding energy of F to Wn as defined by equation (1). BEs are calculated for CCSD(T)/aug-ccpVTZ as described in scheme 1 and are corrected for BSSE . bThis is just one example of this type of bonding. Values given are average values for the category.

The analysis of the intermediate cases, ddFa and ddFaa, is more nuanced. Looking at the average BE for ddFa, it is apparent that the binding is stronger here than for dF. This implies that the effect of a donor is stronger as an activating group than an acceptor is as a deactivating group. Further confirmation of this is seen in that the increase in BE seen for dFa relative to dF is greater than the decrease seen between ddF relative to dF. However, the data for ddFaa tells a different story. Here, the BE for ddFaa is very similar to ddFa suggesting that the second donor has little to no effect on the BE. Also, the BE of ddFaa is weaker than for dFa. Thus, while adding a donor and an acceptor to dF to form ddFa is stabilizing, adding a donor and an acceptor to dFa to form ddFaa is actually destabilizing. The conclusions above are further complicated by two additional factors. First, the data for ddFa and ddFaa are reported in Table 9 as averages. In the Supporting information it is shown that there is a wide range of values for both groups, from –4.10 to –5.78 kcal/mol for ddFa and from –4.42 to –6.06 kcal/mol for ddFaa. The second complication appears when solvent effects are considered. Complete data for solvation effects are in the Supporting Information. In ether, the BEs are ordered as in the gas phase. In the more polar DMA, the



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dFaa, dFa, ddFaa, and ddFa types have similar BEs to each other and have more exoergic BEs than dF and ddF.. In water, ddFaa and ddFa have the most exoergic BEs. These results may be due to a genuine solvent effect or may be an artifact of the calculations where solvent effects appear to have a bigger effect on the smaller complexes (dFaa, dFa) than on the larger ones, (ddFaa, ddFa).

Table 10.

Geometric features, population analysis, and red shifts for various types of F•Wn

BEa types (F•Wn) RFH (Å)b ROH(Å)b ∠OHF (°)b qF (e-)c ∆ν (cm–1)d dFaa -7.66 1.834 0.971 158.6 0.01031 -229 d Fa -6.60 1.879 0.973 163.2 0.00736 -187 e ddFaa (6) -5.16 1.992 0.966 144.8 0.00593 -72 e ddFa (13) -5.11 1.995 0.966 152.0 0.00587 -110 dF -4.05 1.997 0.965 146.5 0.00554 -49 ddF -3.62 2.079 0.963 141.5 0.00342 -34 2f r 0.93 0.75 0.91 0.96 a b Binding energy of F to Wn as defined by equation (1). corrected for BSSE. RFH is the distance from the fluorine atom of F to the hydrogen bound H atom. ROH is length of the OH bond that is hydrogen bound. In W, this bond has a length of 0.9614 Å . ∠OHF is the bond angle of the hydrogen bond. cThe charge on F. dThe change is the sum of the vibrational frequencies of the OH stretches upon complexation as defined by equation 2. eValues shown are the averages for these complexes. The number of examples used in the averages are shown in parentheses. fThe correlation coefficient between that property and BE. As in the previous sections, BEs are compared to geometric features, population changes, and vibrational frequency shifts. Data for the averages of each type are shown in Table 10, while the complete set of values for the ddFa and ddFaa complexes are in the Supporting Information. As can be seen form Table 10, shortening of the RFH bond length, increase in charge transfer qF, and increase in the red shift of the νOH’s (∆ν) were all excellent predictors of stronger HBs between F and Wn. The bond angle ∠OHF is a less reliable reporter for BE.. All in all, the compounds in this section show the strongest correlations between geometry, population, vibrational analysis and BEs.


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Unfortunately, these correlations break down when the details of the types ddFa and ddFaa are explored further. Within each group there is literally no correlation between BE and any of the parameters used. The lack of correlation is illustrated well by F•W4-d and F•W5-b which have similar ∆ν’s (–62 and –67 cm–1, respectively) but have a wide range of BEs (–4.10 and –5.77 kcal/mol, respectvely).

Why F does not dissolve in bulk water. The analysis of types above can now be used to explain why F is not incorporated into cyclic HB networks . Figure 5 illustrates two hypothetical cyclic structures, one is composed of just W, the other of F and W. In the former, represented by the actual molecules W3-a, W4-a, and W5-a, all the W molecules are of type da. Substitution of W for F, leads to a radical change in this structure since F must act as a double HB acceptor. The W’s bound to this F are now of type dFa instead of da, which, based on the section comparing F•Wn to Wn+1, should be only mildly destabilizing. More significantly, one of the W’s is forced into the energetically inferior dd type. No stable representatives of this topology were found.

< Insert Figure 5 here >

This analysis can be made more concrete by looking at the four isomers of W4: and comparing them to their F•W3 analogs. The two lowest energy isomers of W4, W4-a and W4-b, have the W’s in a ring, where each W is of type da. There is not and can not be an analogous F•W3 compound because F can not mimic the da type of W. The lowest energy structure for F•W3 is F•W3-a, where F takes the place of the type a W located on the periphery of W4-c as



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shown in Figure 6, below. Earlier it was shown that the HBs of F•W3-a were similar in energy to those of W4-c. However, W4-c is 7 kcal/mol higher in energy than W4-a, a value that provides a crude estimate of the penalty for incorporation of F into bulk water. In principle, a type aa W of W4-d could be replaced by F to form a cyclic F•W3 illustrated in Figure 6. In the event, this cyclic structure is unstable relative to F•W3-a. This result is not surprising since W4d is 5 kcal/mol inferior to W4-c. Thus, F is not incorporated into the HB network of bulk water not because its HBs are weak, but because it cannot assume the da bonding type.

< Insert Figure 6 here >

Conclusions. In most respects, the bonding of F to Wn resembles that of W to Wn. The HBs are nearly of the same strength when the geometries of Wn are similar. Both F and W can bond to multiple complexes Wn with only a slight loss of BE. Yet W but not F can act as both an HB donor and an HB acceptor. This allows W but not F to form cyclic HB networks that are significantly lower in energy than branched or linear topologies. If a cyclic structure were to include F, one of the W’s in the ring is forced into an inferior binding arrangement. Instead, initially formed cyclic structures of this type reorganize to place F on the periphery of the cyclic HB network. The result is that, compared to W, F cannot effectively bind to a growing water cluster and therefore fluoro-organics are not soluble in water. This result does not consider entropic effects which may play a large role in solvation. However, fluoro-organics can form a single HB to both W and to small clusters Wn. One can imagine Wn serving as a model for the interior of a protein that has incorporated a small


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number of water molecules. In this situation, a drug molecule that contained a fluorine atom could clearly form a HB to one of the HB donors present in the folded protein.

Supporting Information. Full Gaussian 09 reference, structures and energies of F•Wn and Wn complexes, validation of approximation scheme and of BSSE correction, SMD energies, key bond lengths and angles, changes in vibration frequencies upon complexation, population analyses. (32 pages) The Supporting information is available free of charge on the ACS Publications website at DOI: xxxxxxx. 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. I would like to thank Dr. Jamie Snyder for help with creating the figures. REFERENCES 1

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Zhou, P.; Jianwei Zou, J.; Tian, F.; Shang, Z. Fluorine Bonding — How Does It Work In Protein−Ligand Interactions? J. Chem. Inf. Model. 2009, 49, 2344–2355. 7 Dalvit, C.; Vulpetti, A. Fluorine–Protein Interactions and 19F NMR Isotropic Chemical Shifts: An Empirical Correlation with Implications for Drug Design Chem. Med. Chem 2011, 6, 104-114. 8 Lu, Y.; Wang, Y.; Xu, Z.; Yan, X.; Luo, X.; Jiang, H.; Zhu, W. C−X···H Contacts in Biomolecular Systems: How They Contribute to Protein−Ligand Binding Af

Microsolvation of Fluoromethane - The Journal of Physical Chemistry

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