Strong Hyperconjugative Interactions in Isolated and Water

Article pubs.acs.org/JPCA

Strong Hyperconjugative Interactions in Isolated and Water Complexes of Desflurane: A Theoretical Investigation Dipankar Sutradhar,† Therese Zeegers-Huyskens,‡ and Asit K. Chandra*,† †

Department of Chemistry, North-Eastern Hill University, Shillong 793022, India Department of Chemistry, University of Leuven, 200F Celestijnenlaan, 3001 Heverlee, Belgium

‡

S Supporting Information *

ABSTRACT: Ab initio MP2/aug-cc-pvDZ and density functional B3LYP calculations with the 6-311++G(d,p) basis set are performed to investigate the conformation of desflurane (CHF2OCHFCF3), its acidity/basicity and its interaction with one water molecule. The calculations include the optimized geometries, the harmonic frequencies of relevant vibrational modes, the binding energies with water, and a detailed natural bond orbital (NBO) analysis Iincluding the NBO charges, the hybridization of the C atoms and the intra- and intermolecular hyperconjugations. The relative energies of the two most stable conformers are discussed as a function of the total hyperconjugative energies resulting from the interaction of lone pairs of the O and F atoms to the different antibonding orbitals of desflurane. The proton affinity is the same for both conformers but the acidity of the CH bond is larger for the less stable conformer. The binding energies of the complexes of two desflurane conformers with one water molecule range from −2.75 to −3.23 kcal mol−1. Depending on the structure of the complexes, the CH bonds involved in the interaction are contracted or elongated. The σ*(CH) occupation predominates over the hybridization effect in determining the CH bond length. There is an unexpected charge transfer to the external OH bond of the water molecule. This effect is in good agreement with theoretical data on the complexes between fluorinated dimethyl ethers and water and seems to depend on the number of F atoms implanted on the ether molecule.

1. INTRODUCTION Halogenated methane or ethane derivatives such as CHCl3 (chloroform) or halothane (CHClBrCF3) have been known for many years to possess anesthetic properties. This is also the case of halogenated methyl ethyl ether derivatives such as isoflurane (CF3CHClOCHF3), desflurane (CF3CHFOCHF2), or enflurane (CHFClCF2OCHF2). It has been recognized that general anesthetics act by perturbing intermolecular associations such as van der Waals interactions or hydrogen bonds without breaking or forming new covalent bonds. More specifically, the role of hydrogen bonding in anesthetics has been discussed in several works.1−8 Both simple alkane derivatives and halogenated ethers are characterized by CH bonds whose acidity is reinforced by the presence of halogen atoms and which are capable of acting as proton donors. The interaction between simple halogenated methane or ethane derivatives with guest molecules has been investigated in several works. This is the case for the interaction between CHCl39−18 or halothane.19−23 with proton acceptors. By comparison, fewer works have been devoted to the interaction between halogenated methyl ethyl ethers and guest molecules. It must be noticed that interaction between enflurane and acetone24 and water25 has been investigated in recent works. In this work, the interaction between desflurane and water is analyzed by theoretical methods. Desflurane has two CH bonds that can act as proton donors and one O atom that can act as a © XXXX American Chemical Society

proton acceptor, and therefore, several structures are possible. It should be mentioned that the fluorine atoms of desflurane can also act as proton acceptors, but such interactions are not considered in the present study. It is also important to notice that the atmospheric chemistry of several hydrofluoroethers has been studied in the reaction with OH radicals and chlorine atoms, with respect to the global warming potentials of these compounds.26−30 It is therefore important to investigate the interaction of desflurane with water which is one of the most important constituent of the atmosphere. In this regard, let us mention that the reaction between CF3CHFOCF3 and the OH radical has been investigated theoretically.27 It has been shown that in the reaction product CF3CFOCF3·H2O, the water molecule is hydrogen-bonded to one of the F atoms. The present work is arranged as follows. In the first part, the conformation of desflurane is discussed. Attention will be focused on hyperconjugative interactions, which are known to stabilize the structure of many organic compounds. The second part deals with the acidity and basicity of the different sites of Special Issue: Structure and Dynamics: ESDMC, IACS-2013 Received: February 26, 2013 Revised: April 2, 2013

A

dx.doi.org/10.1021/jp402023u | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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Figure 1. B3LYP optimized structures for two conformers (A and B) of desflurane.

dichroism (VCD).36,37 Theoretical studies performed using B3LYP/6-31G(d)32 or B3LYP/6-311++G(d,p)37 methods have shown that the two most stable conformers have the T conformation with the dihedral angle C1O2C3C4 equal to ∼145°. Structures of the two lowest energy conformers are shown in Figure 1. These two structures differ by the H5C1O2C3 dihedral angles, which are equal to ∼177° (T,t) (A) conformation and to ∼55° (T,g) (B) conformation. Depending on the level of calculations, the (T,t) conformation is more stable than the (T,g) one by 0.97 kcal mol−1 36 or 0.57 kcal mol−1.37 Our calculations reveal a difference of 0.91 kcal mol−1, in good agreement with these data. In a previous work, only the distances in the C1O2C3C4 skeleton have been reported36 and some vibrational modes mainly in the 1400− 1000 cm−1 region have been observed in VCD spectrum.36,37 Table 1 reports relevant distances and CH vibrational

desflurane. In the third part, the interaction between one water molecule and the two most stable conformers of desflurane is analyzed. The other possible conformers of desflurane are more than 2 kcal/mol higher in energy than the most stable conformer and unlikely to exist in normal temperature. The binding energies with water are calculated. The results of a NBO analysis, (occupation of antibonding orbitals, charge on individual atoms, charge transfer, hybridization) are discussed for the complexes. As outlined recently by Scheiner, NBO is one of the widely applied methods to examine chemical properties in general and molecular interactions in particular.31 Special attention will be paid to the anomeric effects, which are intimately related to the electronic delocalization in the isolated molecules as well as in their complexes.

2. COMPUTATIONAL METHODOLOGY The geometries of isolated desflurane conformers as well as their hydrogen-bonded complexes with one water molecule were fully optimized using the ab initio MP2/aug-cc-pvDZ and DFT based B3LYP/6-311++G(d,p)32 methods. Harmonic frequency calculations were carried out at the same level to characterize the stationary points. Charges on individual atoms, hybridization, orbital occupancies and second-order perturbation energies referred here as intra- and intermolecular hyperconjugation energies were obtained by the natural bond orbital (NBO) population scheme33 and using the B3LYP/6311++G(d,p) method. The hydrogen-bonding energies (-ΔEHB) of the complexes were calculated from the energy difference between the complexes and the monomers. The calculated values include the zero-point energy (ZPE) corrections and the basis set superposition errors (BSSE) computed by the counterpoise method.34 The proton affinity (PA) was calculated as the negative enthalpy change of reaction 1, whereas the deprotonation enthalpy (DPE) was computed from the enthalpy change of reaction 2 assuming the standard conditions in the gas phase. AH + H+ → AH 2+ AH → A− + H+

PA = −ΔH298K DPE = ΔH298K

Table 1. Relevant Parameters in the A and B Conformers of Desflurane (Distances in Å, Dipole Moment in D, Vibrational Frequencies in cm−1) As Obtained from B3LYP/ 6-311++G(d,p) Calculationsa r(C1H5) r(C1O2) r(C1F6) r(C1F7) r(O2C3) r(C3H8) r(C3F9) μ ν(C1H5) ν(C3H8) δ(C1H5) δ(C3H8)

A

B

1.0873 (1.0942) 1.3735 (1.3793) 1.3583 (1.3670) 1.3636 (1.3721) 1.3949 (1.4022) 1.0915 (1.0988) 1.3692 (1.3786) 1.74 3166 (16) (3235) 3108 (7) (3165) 1357−1405 1373−1452

1.0909 (1.0977) 1.3858 (1.3909) 1.3653 (1.3738) 1.3385 (1.3485) 1.3831 (1.3917) 1.0926 (1.0996) 1.3809 (1.3895) 1.92 3120 (20) (3188) 3096 (12) (3157) 1387−1397 1292−1358

a

Values in parentheses indicate the corresponding MP2/aug-cc-pvDZ results.

(1) (2)

frequencies. Let us notice that the more stable A conformer is characterized by a smaller dipole moment than the B conformer. The MP2 calculated bond lengths for the two conformers are also listed in Table 1. These values are somewhat larger than the corresponding B3LYP results, but the difference in bond lengths between the A and B conformers is predicted to be almost the same by both methods. Because the

35

The Gaussian 03 package was used for all of the calculations analyzed in the present work.

3. RESULTS AND DISCUSSION 3a. Conformation of Desflurane. The conformation of desflurane has been investigated by vibrational circular B



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Table 3. Hyperconjugation Energies (kcal mol−1) from O2, F6, F7, and F9 Lone Pairs to Various σ* Orbitals in the A and B Conformers of Desflurane

change in bonding parameters is the primary concern of this work, only the B3LYP results will be discussed hereafter. In a recent work,38 the conformation of isoflurane (CHF2OCHClCF3) has been investigated by microwave spectroscopy. The structural preferences of this molecule have been supported by ab initio calculations and NBO analysis, which suggest that the energy difference between the conformers can be accounted for, at least partly, by anomeric effects or in other words by a hyperconjugative interaction (HYPE) from the lone pairs to σ* antibonding orbitals. These interactions are particularly large when several F atoms are present in the molecules. Up to now, the anomeric effects in desflurane have not been investigated. We will analyze these effects in desflurane including the hyperconjugation to the σ*(CH) orbitals that were not considered for isoflurane.38 As a matter of fact, the changes in σ*(CH) occupation may be also important in a conformational analysis and there is no fundamental reason to delete them from the overall effect. Important NBO parameters for the C1H5 and C3H8 bonds (NBO charges, occupation of antibonding orbitals, hybridization of C at H5 and H8, second-order interaction energies) are listed in Table 2. Other interaction energies from the lone pairs of O2, F6, F7, and F9 to different antibonding orbitals are reported in Table 3.

A

B

0.863 0.149 0.444 0.186 42.5 32.7 30.1 28.6

0.867 0.135 0.445 0.182 48.7 35.8 30.5 28.4

0.65 2.81 3.87 7.05 6.83 7.0 0.56 17.34 11.43

A

B

13.64 14.53 4.07 16.01 11.68 14.07 11.29 13.51 12.76 7.47 0.63 119.7 87.5

14.0 5.45 2.64 17.07 11.28 13.47 11.55 15.71 11.84 7.14 0.53 110.6 63.2

This can be readily accounted for by larger LPO2 → σ*(CH) delocalizations in B than in A. Let us notice that the classical lone pair effect usually refers to the CH bond in the trans position but is not negligible for the CH bonds in the cis position, as demonstrated for fluorinated dimethyl ethers39,40 and enflurane.41 In agreement with these data, the sum of the hyperconjugation energies to the σ*(C1H5) and σ*(C3H8) bonds is by about 4 kcal mol−1 larger for the B conformer than for the A one. In contrast, the sum of the delocalization energies from the LPs of the O2, F6, F7, and F9 atoms to different σ* orbitals is sensibly larger (by about 9 kcal mol−1) for the A conformer than for the B one. The most striking difference is the LPO2 → σ*(C1F7) delocalization energy, which is 14.5 kcal mol−1 in A and 5.4 kcal mol−1 in B. This is in agreement with the larger C1F7 distance in A (1.363 Å) than in B (1.338 Å). These differences agree with the much larger σ*(C1F7) occupation in A (87.5 me) than in B (63.2 me). In the same order of ideas, the conformational preference of fluoromethanol42 and enflurane41 has also been explained by a larger delocalization of the O LPs to the σ*(CF) orbital as compared to the σ*(CH) one. These data are in agreement with the larger σ*(CF) acceptor ability as compared with the σ*(CH) one, as demonstrated for several organic compounds.43 The data of Tables 2 and 3 allow one to conclude that the sum of the second-order interaction energies involving all the bonds is larger in A than in B by about 4−5 kcal mol−1. This value is not the energy difference between the two conformers but rather represents the major impact on their conformational preference. The local interaction (attraction or repulsion) between the nonbonded atoms can also influence the conformational preference.44−47 In the present systems, the A conformer can be stabilized by an electrostatic interaction between the positively charged H8 atom and the negatively charged F7 atom (H8···F7 = 2.469 Å). Structure B can be stabilized by a electrostatic interaction between the H5 and F9 atoms (H5···F9 = 2.677 Å). Both conformers can be destabilized by electrostatic repulsion between two H or two F atoms (Figure 1). Our calculations do not predict a through space stereoelectronic interaction between the O2 LPs and the neighboring σ*(C4F12) orbital. As previously mentioned, the C1H5 and C3H8 distances are larger in the B conformer than in the A one. However, for the same conformer, the C1H5 distance is shorter than the C3H8 one, despite the larger σ*(C1H5) occupation. In the A

Table 2. Relevant NBO Parameters in the A and B Conformers of Desflurane (NBO Charges in e, Occupation of Orbitals (me), Hyperconjugation Energies (HYPE) to σ*(C1H5) and σ*(C3H8) in kcal mol−1) As Calculated at the B3LYP/6-311++G(d,p) Level q(C1) q(H5) q(C3) q(H8) σ*(C1H5) σ*(C3H8) %sC1(H5) %s C3(H8) HYPE σ(O2C3) → σ*(C1H5) LPO2 → σ*(C1H5)a LPO2 → σ*(C3H8)a LPF6 → σ*(C1H5)b LPF7 → σ*(C1H5) LPF9 → σ*(C3H8)b LPF11 → σ*(C3H8)b ΣHYPE → σ*(C1H5) ΣHYPE → σ*(C3H8)

HYPE LPO2 → σ*(C1F6) LPO2 → σ*(C1F7) LPO2 → σ*(C3C4) LPO2 → σ*(C3F9) LPF6 → σ*(C1O2) LPF6 → σ*(C1F7) LPF7 → σ*(C1O2) LPF7 → σ*(C1F6) LPF9 → σ*(O2C3) LPF9 → σ*(C3C4) LPF9 → σ*(C4F12) ΣHYPE σ*(C1F7)

6.57 6.17 6.07 6.10 0.57 20.1 12.84

a

Sum of the delocalization from the two O lone pairs, having sp1.5 and p-hybridization. bSum of the delocalization from the F lone pairs having p-hybridization.

The delocalization within the CF3 group remains almost constant in the two conformers. Indeed, the three CF distances are nearly the same in A and B. Further, the delocalization, as for example from the LPs of the F11 atom to the σ*(C4F12) antibond, is nearly the same for both conformers, being 15.46 kcal mol−1 in A and 15.51 kcal mol−1 in B. This delocalization will not be discussed hereafter. The data of Table 1 indicate that the C1H5 and C3H8 bonds are both more elongated in the B conformer than in the A one. C



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3c. Interaction between Desflurane and One Water Molecule. To the best of our knowledge, no experimental data have been reported for the interaction between desflurane and water. The structure of the complexes between the A and B conformers of desflurane with water is illustrated in Figure 2. For the A complexes, the interaction with water does not result in a marked change of the conformation; for the B complexes, the dihedral angles decrease by ca. 15°. The hydrogen bonding energies are indicated in Table 5. These energies calculated from the MP2 method are in good agreement with the corresponding B3LYP values. In all the structures, the A and B conformers are primarily bonded to water by CH···O hydrogen bonds except in the A-h5(1) complex where an OH···O interaction is also present, the intermolecular distances being composed between 2.121 and 2.550 Å. We could not find any complex with OH···O interaction for the B-conformer. Attempts for optimizing such structures always reduced to the ones reported here. The A conformer forms with water two complexes characterized by about the same energies, the first one being cyclic and characterized by a weak O14H13···O2 interaction and the second structure being characterized by a almost linear C1H5···O14 bond. In A-h8 and B-h5, there is also a O14H13···F interaction (H···F between 2.501 and 2.564 Å). Interestingly, in B-h5 and B-h8, the two CH bonds of desflurane are involved in the interaction, the water molecule acting as a biacceptor. The intermolecular distances suggest that the C1H5···O interaction is stronger than the C3H8···O one in B-h5 and the reverse holds for the B-h8 structure. No open OH···O structure could be predicted by our calculations. This is in line with the larger basicity of water (PA = 177 kcal mol−1) and its smaller acidity (DPE = 401 kcal mol−1). Let us remember that in the complexes between halogenated ethers and water, the O atom of the ethers acts as a proton acceptor when the PA of the ether is at least 173 kcal mol−1.40,50 As indicated by the binding energies, the complexes are rather weak. The energies are somewhat larger for the B conformer (−3.22 kcal mol−1) than for the A conformer (−2.53 to −2.93 kcal mol−1). This difference is in line with the larger acidity of the CH bond in the B conformer. This must be taken with caution owing the small differences between the parameters. The binding energies calculated from the MP2 results are in very good agreement with the corresponding B3LYP values, justifying further the reliability of our DFT calculations. Owing to the weakness of the interaction, the variation of the geometrical parameters resulting from the interaction with water are expected to be moderate. The CH distances along with the ν(CH) and δ(CH) vibrational frequencies are listed in Table 6. The data indicate various trends. When the C1H5 bond is involved in the interaction (A-h5, B-h5, B-h8), the C1H5 bond contracts by 1.3−1.4 mÅ and the ν(C1H5) frequencies are blue-shifted by 19−28 cm−1.51−59 In the B-h5 and B-h8 complexes, the C3H8 bond contracts by 1 and 0.7 mÅ and the corresponding vibrations blue-shifted by 12 and 9 cm−1. In contrast, in the A-h8 complex, both the C1H5 and C3H8 bonds are slightly elongated and the corresponding vibrations red-shifted by small amounts of 4 and 6 cm−1. Finally, in the linear A-h5(2) structure, the r(C1H5) distance remains practically unchanged (shift of 9 cm−1). As expected, the variations of the CH distances and the frequency shifts of the ν(CH) vibrations are linearly correlated.60 This correlation is shown as Supporting Information in Figure SI.

conformer, the C1H5 distance is by 4.2 mÅ shorter than the C3H8 distance despite the σ*(C1H5) occupation, which is larger by ca. 10 me than the σ*(C3H8) one. The σ(CH) population is the same for the two bonds (1.9866 e). The different distances can be accounted for by the hybridization of the C atoms, the C1(H5) atom having ca. 1.5% more scharacter than the C3(H8) one. In the B conformer, the C1H5 distance is by 1.7 mÅ shorter than the C3H8 one, despite the larger σ*(C1H5) occupation by 12.9 me. This effect is balanced by the larger σ(C1H5) population (1.9933 e) than the σ(C3H8) population (1.9862 e), and by the larger s-character, by ca. 2% of the C1(H5) atom as compared with the C3(H8) one. Let us also notice that for both conformers, the NBO charge on the H8 atom is by 0.03−0.04 e larger than that on the H5 atom. This is in agreement with Bent’s rule,48 which predicts an increase of the s-character of the C(H) hybrid orbital when the H atom becomes more positive. A vibrational spectrum can also characterize the conformers by different stretching vibrations (ν) related to the elongation of the CH bond and by different deformation vibrations (δ) related to the variation of the HCF angle. In an experimental VCD spectrum, each conformer has two ν(CH) stretching vibrations in the range 3055−3166 cm−1. Our calculations predict two ν(CH) vibrations at 3166 and 3108 cm−1 for the A conformer and two ν(CH) vibrations at somewhat lower frequencies, 3120 and 3096 cm−1 for the B conformer, in good agreement with the experimental data. This is as expected owing to the larger CH bond length in the B conformer as compared with the A one. In a VCD spectrum, the HC bending vibrations (δCH) are observed at 1357 and 1445 cm−1. Our calculations reveal some differences between the A and B conformers. For the A conformer; the δ(C1H5) modes are predicted at 1405 and 1357 cm−1 and at 1396 and 1387 cm−1 for the B conformer. No spectacular differences are predicted between 1300 and 1160 cm−1 for the two conformers (less than 10 cm−1). The largest differences are predicted for the vibrational modes between 1160 and 1080 cm−1, which contains a predominant ν(C1O2C3) character. In the A conformer these vibrations are predicted at 1116 and 1080 cm−1 and in the B conformer at 1156 and 1096 cm−1. 3b. Acidity and Basicity of Desflurane. The proton affinity of the O atom and the DPE of the C1H5 and C3H8 bonds of the two conformers of desffurane are indicated in Table 4. The PA of the two conformers is the same. The acidity Table 4. Proton Affinity (PA) of the O Atom and Deprotonation Enthalpy (DPE) of the CH Bonds in the A and B Conformers of Desflurane (kcal mol−1) Calculated at B3LYP/6-311++g(d,p) Level PA DPE (C1H5) DPE (C3H8)

A

B

150.5 364.4 362.3

150.6 360.5 355.9

of the C1H5 and C3H8 bonds is somewhat lower for the most stable A conformer. These values can be compared with the values calculated at the same level for CHF2OCHF2 where the CF3 group is replaced by a F atom (PA = 154.2 kcal mol−1, DPE = 366.7 kcal mol−1).40 The lower basicity and the larger acidity of the CH bonds of desflurane is related to the larger electron-attracting properties of the CF3 group.49 D



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Figure 2. B3LYP optimized structures for 1:1 complexes between water and two conformers (A and B) of desflurane. The values in parentheses indicate the MP2 results.

from 12 to 43 cm−1. In the B complexes, the blue shifts of the δ(CH) vibrations are between 1 and 33 cm−1 depending on the site of interaction. We will try to explain these results by considering the NBO data. Table 7 lists some relevant NBO data including the NBO charges on the different C and H atoms, the σ*(CH) occupation, the s-character of the C at the H along with the differences with respect to the isolated molecules. This table also reports the intermolecular hyperconjugation energies related to the charge transfer taking place from the O14 LPs of water to the σ*(C1H5) or σ*(C3H8) antibonds. We note at first an important classical effect. The positive charge decreases on the C atoms and increases on the H atoms in the CH bonds involved in the interaction. From this, a small increase of the s-character of the C(H) can be anticipated. Let us also notice that the increase of polarity of the C1H5 bond in the B-h5 complex is larger than in the B-h8 one, in agreement

Table 5. Hydrogen Bonding Energies (Including BSSE) for the Interaction of the A and B Conformers of Desflurane with One Water Molecule Calculated at the B3LYP/6-311+ +G(d,p) Level (kcal mol−1) system

EHBa

EHB (ZPE)

A-h5(1) A-h5(2) A-h8 B-h5 B-h8

−3.78 −3.82 −3.66 −4.67 −4.60

−2.75 (−2.87)b −2.93c −2.53 (−2.67) −3.23 (−3.48) −3.22 (−3.44)

a

Without ZPE correction. bThe values in parentheses are the MP2/ aug-cc-PVDZ results. cStructure could not be optimized at MP2 level.

The δ(CH) vibrational modes, although coupled with other modes, also appear to be sensitive to the interaction with water. In the A complexes, they are blue-shifted by amounts ranging

Table 6. r(CH) Distances (Å) and ν(CH) and δ(CH) Vibrational Frequencies (cm−1) in the Complexes between Desflurane and One Water Molecule As Obtained from B3LYP/6-311++G(d,p) Calculations (Variation of the Distances (mÅ) in Parentheses) r(C1H5) r(C3H8) r(C1F7) ν(C1H5) ν(C3H8) δ(C1H5) δ(C3H8) a

A-h5(1)

A-h5(2)

A-h8

B-h5

B-h8

1.0859 (−1.4) 1.0915 (0) 1.364(+1) 3194 (+28) 3110 (+2) 1380−1417 1369−1433

1.0872 (−0.1) 1.0915 (0) 1.367 (+4) 3175 (+9) 3108 (0) 1389−1445 1371−1432

1.0874 (+0.1) 1.0921(+0.6) 1.371 (+8) 3162(−4) 3102(−6) 1356−1400 1416−1460

1.0896(−1.3) 1.0916(−1.0) 1.343 (+5) 3140 (+20) 3108 (+12) 1391−1410 1290−1368

1.0896 (−1.3) 1.0919(−0.7) 1.343 (+5) 3139 (+19) 3105 (+9) 1368−1414 1296−1391−1464a

Three vibrational modes with predominant δ(CH) character. E



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Table 7. NBO Data for the CH Bonds in Water Complexes (NBO Charges in e, σ* Occupation in me, Second-Order Hyperconjugation Energy (HYPE) in kcal mol−1) (Variations in the Complexes in Parentheses)a

a

A-h5 (1)

A-h 5 (2)

A-h8

B-h5

B-h8

q(C1) q(H5) q(C3) q(H8) σ*(C1H5) σ*(C3H8) %sC1(H5) %sC3(H8) ΣHYPE → σ*(C1H5) ΣHYPE → σ*(C3H8) HYPEinter

0.851 (−0.012) 0.183 (+0.034) 0.443 (−0.001) 0.186 (0) 40.6 (−1.9) 33.0 (+0.3) 31.4 (+1.3) 28.6 (0) 14.82 (−2.52) 11.11 (−0.32) 2.10a

0.843 (−0.020) 0.189 (+0.040) 0.444 (0) 0.187 (+0.001) 42.4 (−0.1) 33.1 (+0.4) 31.7 (+1.6) 28.6 (0) 14.07 (−3.27) 10.87 (−0.56) 4.60a

0.865 (+0.002) 0.146 (−0.003) 0.421 (−0.023) 0.228 (+0.042) 42.6 (+0.1) 35.9(+3.2) 29.9 (−0.1) 30..3 (+1.7) 17.17 (−0.17) 9.95 (−1.48) 5.58b

σ*(C1F7) %s C1(F7)

83.8 (−3.7) 22 (−0.2)

84.9 (−2.6) 21.7 (−0.5)

93.5 (+6.0) 21.9 (−0.3)

0.859 (−0.14) 0.160 (+0.025) 0.441 (−0.004) 0.195 (+0.013) 46.8 (−1.9) 33.2 (−2.6) 31.4 (+0.9) 28.7 (+0.3) 16.8 (−3.3) 10.55 (−1.88) 0.55b 2.55c 64.3 (+1.1) 22.5 (−0.4)

0.860 (−0.007) 0.147 (+0.012 0.433 (−0.012) 0.206 (+0.024) 46.3 (−2.4) 35.2 (−0.6) 30.8 (+0.3) 29.2 (+0.8) 17.66 (−2.44) 10.75 (−2.09) 0.78b 2.78c 65.6 (+2.4) 22.6 (−0.3)

In italics, data for the CH bonds not involved in the interaction. bLP(O14) → σ*(C1H5). cLPO14 → σ*(C3H8).

Table 8. NBO Parameters for Water in the Different A and B Complexes (q in e, Σq in me, σ* in me, HYPE in kcal mol−1, Frequencies in cm−1) r(O14H13) r(O14H15) Σq(H2O) q(H13)a q(H15) q(O14) σ*(O14H13) σ*(O14H15) ΣHYPE → σ*(O14H13) ΣHYPE → (σ*(O14H15) νas(OH) νs(OH) Ias/Is

A-h5(1)

A-h5((2)

A-h8

B-h5

B-h8

0.9635 0.9618 3 0.472 0.467 −0.937 0.36 1.06 0.05 0.37 3918(86)b 3813(14) 6.1

0.9626 0.9624 9 0.471 0.470 −0.933 0.37 0.54 0.13 0.17 3920(83) 3816(17) 4.9

0.9630 0.9622 10 0.473 0.470 −0.934 0.37 1.09 0.05 0.37 3920(83) 3816(16) 5.2

0.9637 0.9623 6 0.476 0.472 −0.943 0.51 1.32 0.08 0.48 3915(87) 3811(19) 4.6

0.9634 0.9626 6 0.475 0.473 −0.941 0.28 1.14 0.06 0.38 3913(86) 3811(22) 3.9

In isolated H2O, r(OH) = 0.9618 Å, q(H) = 0.456 e, q(O) = −0.913 e, νas(OH) = 3926 cm−1 (57), νs(OH) =: 3821 cm−1 (9) (B3LYP/6-311+ +G(d,p) calculations). bThe IR intensities (km mol−1) are indicated in parentheses a

with the previous discussion. The variation of the σ*(CH) occupation depends on the nature of the complex. In the A-h5, B-h5, and B-h8 structures, the σ*(C1H5) occupation decreases. Similarly, the σ*(C3H8) occupation decreases in the B-h5 and B-h8 structures. In contrast, in the A-h8 complex, our calculations predict an increase of the σ*(C3H8) occupation. Let us notice that this increase parallels an elongation of the C3H8 bond. In the linear A-h5 (2) complex, the σ*(C1H5) occupation remains almost unchanged. As previously outlined and indicated in Table 7, the interaction with water results in a moderate increase of the s-character of the C at the C(H) in all the structures. As discussed in ref 57, the change of the CH bond length depends mainly on two factors: the change of hybridization of the C at the H and the intermolecular hyperconjugation to the σ*(CH) antibonding orbital. The σ(CH) occupancies remain almost the same in all the structures. The present results allow one to deduce the following correlation between the variation of the CH bond length (mÅ) and the corresponding NBO parameters (σ* in me):

where r represents the correlation coefficient. Let us notice that the coefficients of this equation depend on the nature of the interacting species. Anyway, for weak to medium complexes such as those involving methyl halogenides61 or methylene halogenides62 with hydrogen peroxide or haloforms with HNO,59 the σ*(CH) occupation seems to predominate over the hybridization effect in determining the CH bond length. As shown in Table 7, the largest intermolecular hyperconjugation energy of 5.58 kcal mol−1 is predicted for the A-h8 complex. In this complex, the C3H8 bond is elongated and the σ*(C3H8) occupation increases. It is the only complex where the intermolecular hyperconjugation exceeds the intramolecular one by a large amount. For the A-h8, B-h5, and B-h8 structures, the σ*(C1H5) or σ*(C3H8) occupations increase despite the intermolecular charge transfer to the corresponding σ*(CH) orbitals. This can be accounted for by a competitive effect between the intermolecular and intramolecular charge transfer to the corresponding σ*(CH) antibonds. As previously outlined, the HYPE values are particularly large for these fluorinated molecules and the interaction with water results in a decrease of the intramolecular effects by amounts ranging from 1.5 to 3.3 kcal mol−1. This effect has been outlined for the

Δr(CH) = 0.352[Δσ *(CH) − 0.05Δ%sC(H)] (r = 0.942)

(3) F



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Table 9. NBO Parameters in Complexes between Fluorinated Ethers and One Water Molecule (σ* in me, ΣHYPE in kcal mol−1) σ*(OH) σ*(OH)ext ΣHYPE → σ*(OH)b ΣHYPE → σ*(OH)ext b

CH3OCH2F. H2O

CH3OCHF2. H2O

CH2FOCHF2.H2O

CHF2OCHF2. H2O

14.0 0.2 5.8 σ*(OH)b, as in the case of desflurane complexes. The data of Tables 8 and 9 allow one to deduce the following correlation between the σ*(OH) occupation (in me) and the corresponding sum of second-order hyperconjugation energy (ΣHYPE in kcal mol−1). This correlation includes the σ*(OH) occupation of the bonded and external OH bonds of fluorinated dimethyl ethers and desflurane. σ*(OH) = 2.43ΣHYPE + 0.26

(r = 0.995)

(4)

The correlation is found to be quite good (with a correlation coefficient value of 0.995), as illustrated in Figure 3.

Figure 3. Plot of antibonding OH orbital population of water against total hyperconjugation energy (HYPE).

The parameters are relatively small, but they are coherent and reliable. Let us notice that very small hyperconjugations (0.32 kcal mol−1) and changes in NBO populations (1−4 me) have been recently considered for weak complexes, to discuss the bonding trends.31 Our results indicate that larger σ*(OH) occupation of the external OH bond of water is predicted for substituted ethers bearing several F atoms, as in CHF2OCHF2 or desflurane. G



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A last remark concerns the r(O14H13) and r(O14H15) distances and the corresponding ν(OH) vibrational frequencies. Usually, the OH distances (or their variations) in water complexes are related to the corresponding σ*(OH) occupation.50,40,70 In the present systems, the elongation of the two OH bonds is small and varies from 0 to 2 mÅ. The variations are not related to the corresponding σ*(OH) occupation nor to the charge transfer to these bonds. This may be related to the special properties of the polyfluorinated ethers discussed in the present work. The same remark also holds for the ν(OH) frequencies. The frequency shifts of the νas(OH) and νs(OH) vibrations are small, ranging from −5 to −13 cm−1. We must mention that the frequency shifts are predicted from the harmonic approximation, neglecting the effect of anharmonicity. However, one can expect the cancellation of this effect, at least partially, while calculating the frequency shifts in the complexes. The IR intensities seem to be more sensitive to complex formation. Indeed, the ratio of the IR intensities Ias/Is is equal to 6.3 in isolated water. This ratio is smaller (3.9 and 4.6) in the B complexes than in the A ones (4.9−6.1). The smaller intensity ratio may be indicative of a stronger bonding in the B complexes, as discussed in an earlier work.40 However, this must be taken with caution because B3LYP calculated IR intensities are not always reliable.

■

the complexes between fluorinated dimethyl ethers and water and seems to depend on the number of F atoms implanted on the ether molecule. This finding is strengthened by the fact that a good correlation is found between the σ*(OH) occupation of the two bonds of water in desflurane and fluorinated ether complexes and the corresponding hyperconjugation energies.

ASSOCIATED CONTENT

S Supporting Information *

List of second-order hyperconjugation interaction energies of σ*(OH) orbitals of water complexed with desflurane and figure of the correlation between the CH stretching frequency shift and the change in CH bond length of desflurane. This material is available free of charge via the Internet at http://pubs.acs.org.

■ ■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS A.K.C. acknowledges CSIR, India, for financial assistance through project no. 01(2494)/11/EMR-II. D.S. is thankful to NEHU for a research fellowship and Th.Z.H. thanks the University of Leuven for computer facilities.

■

4. CONCLUSIONS Ab initio MP2/aug-cc-pvDZ and density functional B3LYP calculations with the 6-311++G(d,p) basis set are carried out to investigate the conformation of desflurane (CHF2OCHFCF3), its acidity/basicity along with its interaction with one water molecule. Special attention is paid to a detailed NBO analysis and more specifically to the hyperconjugation energies, which are particularly large for this polyfluorinated ether. The most important conclusions emerging from our investigation are the following ones: 1. The relative stabilities of the two most stable conformers of desflurane depend, at least partly, on the total hyperconjugation energies from the O or F lone pairs to the antibonding orbitals of desflurane. Attraction or repulsion between the nonbonded atoms influence the conformation as well. 2. The proton affinity of the O atom is the same for the two conformers (150 kcal mol−1). The deprotonation enthalpy of the CH bonds is somewhat larger for the more stable A conformer (362−364 kcal mol−1) than for the less stable B conformer (356−360 kcal mol−1). 3. The binding energies of desflurane complexed with one water molecule are slightly larger for the B conformer (−3.2 kcal mol−1) than for the most stable complex of the A one (−2.9 kcal mol−1). In all the structures, one of the CH bonds of desflurane acts as a proton donor and closed structures with the OH bond as proton donor are formed in most of the cases. Depending on the structure of the complexes, the CH bond involved in the interaction is contracted, elongated, or remains unchanged. The intramolecular rearrangement predominates over the intermolecular one. 4. There is in the closed structures an unexpected charge transfer to the external OH bond of the water molecule. This charge transfer occurs mainly from the σ(CH) bonding orbital and from the LPs of the O or F atoms. This effect is in good agreement with theoretical data on

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Strong Hyperconjugative Interactions in Isolated and Water

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