Hydrogen and Halogen Bonding in Cyclic FH(4-n):FCln Complexes

Article Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

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Hydrogen and Halogen Bonding in Cyclic FH(4‑n):FCln Complexes, for n = 0−4 Janet E. Del Bene,*,‡ Ibon Alkorta,*,§ and José Elguero§ ‡

Department of Chemistry, Youngstown State University, Youngstown, Ohio 44555, United States Instituto de Química Médica (IQM-CSIC), Juan de la Cierva, 3, E-28006 Madrid, Spain

§

S Supporting Information *

ABSTRACT: Ab initio MP2/aug′-cc-pVTZ calculations have been carried out to investigate the six unique cyclic quaternary complexes FH:FH:FH:FH, FH:FH:FH:FCl, FH:FH:FCl:FCl, FH:FCl:FH:FCl, FH:FCl:FCl:FCl, and FCl:FCl:FCl:FCl stabilized by F−H···F hydrogen bonds and F−Cl···F halogen bonds. The binding energies of these complexes decrease as the number of FH molecules decreases, and therefore as the number of hydrogen bonds decreases, indicating that hydrogen bonds are primarily responsible for stabilities. Nonadditivities of binding energies are synergistic for complexes with 4, 3, and 2 FH molecules, but antagonistic for those with 1 and 0 FH molecules. In addition to depending on changes in F−F, F−H, and F−Cl distances, complex binding energies are also influenced by two sets of angular parameters. These include the external F−F−F angles which must sum to 360° in these cyclic structures, and the internal H−F−F angles for hydrogen bonds and F− Cl−F angles for halogen bonds, which measure the deviation from linearity of these bonds. Transition structures present the barriers to converting an equilibrium structure to an equivalent equilibrium structure on the potential surfaces. These barriers increase as the number of FH molecules decreases. EOM-CCSD spin−spin coupling constants 2hJ(F−F) across hydrogen bonds in complexes tend to increase with decreasing F−F distance. They increase dramatically in transition structures, but show no dependence on the F−F distance. The one-bond coupling constants 1hJ(F−H) are relatively small and negative in complexes, increase dramatically, and are positive in transition structures. 1J(F−H) values are greatest for the covalent F−H bond. Coupling constants 1xJ(F−Cl) across halogen bonds are relatively small and positive in complexes, and increase dramatically in transition structures. The largest values of 1J(F−Cl) are found for covalent bonds.

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bonding parameters, spin−spin coupling constants 2hJ(F−F), 1 J(F−H), and 1hJ(F−H) for F−H···F hydrogen bonds and 1 J(F−Cl) and 1xJ(F−Cl) for F−Cl···F halogen bonds in complexes and transition structures have been computed. It is the purpose of this paper to report and discuss these quaternary complexes and their properties.

INTRODUCTION Clusters of hydrogen fluoride molecules linked by hydrogen bonds have been studied extensively.1−10 These studies provided information about cyclic tetramers, including structures, binding energies, proton-transfer barriers, tunneling effects, and NMR chemical shifts and spin−spin coupling constants. In contrast, although studies of halogen bonds in binary complexes of FCl with FH,11 FCl,12,13 H2O,14 NH3,15,16 CNH,17 CH3,18 H2CO,19 F3CCl,20 and the anion Cl− 21 have been published, investigations of cyclic complexes (FCl)n or mixed cyclic complexes containing FCl and FH have not been reported. To partially fill this void, we have carried out a systematic study of cyclic quaternary complexes with the formula FH(4‑n):FCln for n = 0−4 that are stabilized by F−Cl···F halogen bonds and F−H···F hydrogen bonds. Equilibrium cyclic structures and transition structures on the potential surfaces have been identified, and the binding energies of complexes and the barriers presented by transition structures have been computed. The transition state barriers separate two equivalent minima. Cooperative effects on binding energies have been analyzed to determine whether they are synergistic or diminutive. In addition to charge-transfer energies and © XXXX American Chemical Society

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METHODS Searches of the potential surfaces FH(4‑n):FCln for n = 0−4, were carried out for cyclic quaternary complexes and transition structures containing F−H···F hydrogen bonds and F−Cl···F halogen bonds. These searches were carried out at secondorder Møller−Plesset perturbation theory (MP2)22−25 with the aug′-cc-pVTZ basis set.26 This basis set was derived from the Dunning aug-cc-pVTZ basis set27,28 by removing diffuse functions from H atoms. Frequencies were computed to establish that the complexes correspond to equilibrium structures on their potential surfaces with no imaginary Received: January 8, 2018 Revised: February 16, 2018

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DOI: 10.1021/acs.jpca.8b00236 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Table 1. Binding Energies (−ΔE, kJ mol−1), F−F and F−H Distances (R, Å), H−F−F Angles across Hydrogen Bonds (∠, deg), and F−Cl−F Angles (∠, deg) across Halogen Bonds in Binary Complexes

frequencies, and that transition structures have one imaginary frequency along a coordinate which connects two minima. Optimization and frequency calculations were performed using the Gaussian 09 program.29 The binding energies of the complexes were computed as the negative energy (−ΔE) for the formation of the complex from the corresponding FH and FCl monomers. For consistency, the binding energies of the transition structures were computed in the same way, so that a positive binding energy means that the structure is stable relative to the corresponding monomers, while a negative value indicates that the transition structure is not bound. Nonadditivities were also computed as the difference between the energy of formation of the quaternary complex (ΔE) and the sum of the ΔE values for the formation of the corresponding binary complexes. A negative value of the nonadditivity means that the complex is more stable than the corresponding binary complexes, that is, energetic effects are synergistic. A positive value means that the complex is less stable than the corresponding binary complexes, and energetic effects are antagonistic. The electron densities of complexes and transition structures have been analyzed using the atoms in molecules (AIM) methodology30−33 employing the AIMAll34 program. The topological analysis of the electron density produces the molecular graph of each. This graph identifies the location of electron density features of interest, including the electron density (ρ) maxima associated with the various nuclei, and saddle points which correspond to bond critical points (BCPs). The zero gradient line which connects a BCP with two nuclei is the bond path. The electron density at a selected bond critical point (ρBCP), the Laplacian (∇2ρBCP) at that point, and the total energy density (HBCP) have also been computed. The Natural Bond Orbital (NBO) method35 has been used to obtain charge-transfer energies for the complexes using the NBO-6 program.36 Since MP2 orbitals are nonexistent, the charge-transfer interactions have been computed using the B3LYP functional with the aug′-cc-pVTZ basis set at the MP2/ aug′-cc-pVTZ complex geometries. This allows for the inclusion of some electron correlation effects. Coupling constants 2hJ(F−F), 1hJ(F−H), and 1J(F−H) for F−H···F hydrogen bonds, and 1J(F−Cl) and 1xJ(F−Cl) for F− Cl···F halogen bonds were evaluated using the equation-ofmotion coupled cluster singles and doubles (EOM-CCSD) method in the CI (configuration interaction)-like approximation,37,38 with all electrons correlated. For these calculations, the Ahlrichs39 qzp basis set was placed on 19F atoms, and the qz2p basis set on 35Cl and 1H atoms. The coupling constants were evaluated as the sum of the paramagnetic spin orbit (PSO), diamagnetic spin orbit (DSO), Fermi contact (FC), and spin dipole (SD) terms. The EOM-CCSD calculations were performed using ACES II40 on the HPC cluster Oakley at the Ohio Supercomputer Center.

binary complex

−ΔE

R(F−F)

R(F−H)a

∠H−F−Fb

FH:FH FH:FCl binary complex

19.1 9.9 −ΔE

2.750 2.867 R(F−Cl)c

0.928 0.925 R(F−Cl)d

6 5 ∠F−Cl−Fe

FCl:FH FCl:FCl

11.1 12.6

2.707 2.743

1.646 1.642

178 178

The proton donor F−H molecule. b∠H−F−F = 0° for linear hydrogen bonds. cThe intermolecular halogen bond distance. dThe covalent bond distance. e∠F−Cl−F = 180° for linear halogen bonds. a

FH:FCl. The H−F−F angles in the hydrogen-bonded complexes indicate that the hydrogen bonds deviate only slightly from linearity. The nearly linear F−Cl−F arrangement, evident from the F−Cl−F angles of 178° in the halogenbonded complexes, facilitates electron donation by F through the σ-hole on Cl. Quaternary Complexes. Binding Energies and Nonadditivities. The structures, molecular graphs, and total energies of the cyclic quaternary complexes are given in Table S1 of the Supporting Information. Figure 1 illustrates the six unique FH:FH:FH:FH, FH:FH:FH:FCl, FH:FH:FCl:FCl, FH:FCl:FH:FCl, FH:FCl:FCl:FCl, and FCl:FCl:FCl:FCl complexes, and the numbering system which has been employed. Table 2 presents the binding energies of these complexes and the nonadditivities of binding energies. The binding energies range from 36 kJ mol−1 for (FCl)4 to 118 kJ mol−1 for (FH)4. These data and Figure 2 show that the binding energies of the quaternary complexes decrease dramatically as the number of FH molecules decreases, and therefore, as the number of hydrogen bonds decreases. The correlation coefficient of the second-order trendline is 0.992. Thus, the number of hydrogen bonds is the prime determiner of the relative stabilities of these quaternary complexes. Table 2 also presents the nonadditivities of binding energies of the quaternary complexes. These range from +14 kJ mol−1 for (FCl)4 to −41 kJ mol−1 for (FH)4. The nonadditivities are negative for complexes which have 4, 3, and 2 hydrogen bonds. Thus, in the complexes FH:FH:FH:FH, FH:FH:FH:FCl, FH:FH:FCl:FCl, and FH:FCl:FH:FCl, nonadditivities are synergistic, which means that the binding energies of the quaternary complexes are greater than the sum of the binding energies of the four corresponding binary complexes. The complexes FH:FCl:FCl:FCl and FCl:FCl:FCl:FCl have 1 and 0 hydrogen bonds, respectively, and positive nonadditivities which are antagonistic. The nonadditivities once again emphasize the dominance of F−H···F hydrogen bonds in stabilizing these cyclic complexes. Structures. The unique F−F and F−H distances associated with F−H···F hydrogen bonds are reported in Table 3. As expected, the F−F distance decreases from 2.75 Å in FH:FH to between 2.52 and 2.66 Å for F−H···F−H hydrogen bonds in the quaternary complexes, and from 2.87 Å in FH:FCl to between 2.75 and 2.83 Å for F−H···F−Cl hydrogen bonds in these same complexes. The F−H distances for F−H···F hydrogen bonds increase in the quaternary complexes from 0.928 Å in FH:FH to between 0.935 and 0.952 Å, and from 0.925 Å in the FH:FCl binary complex to between 0.930 and 0.934 Å in the quaternary complexes. These comparisons

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RESULTS AND DISCUSSION Binary Complexes. The binary complexes which give rise to the quaternary complexes are the hydrogen-bonded complexes FH:FH and FH:FCl, and the halogen-bonded complexes FCl:FH and FCl:FCl. Their binding energies, intermolecular distances, and selected covalent bond distances and bond angles are reported in Table 1. Among the binary complexes, FH:FH has the greatest binding energy, followed by the binding energies of the halogen-bonded complexes FCl:FCl and FCl:FH. The most weakly bound binary complex is B


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Figure 1. Six quaternary complexes, illustrating the numbering system.

In addition to distance changes, complex binding energies are influenced by angular structural parameters. These include one set of four angles that might be called the external angles, since they refer to the F−F−F angles that are not directly associated with a particular hydrogen or halogen bond. Rather, their sum must be 360° for cyclic complexes. The second set consists of two internal angles, H−F−F and F−Cl−F. A value of the H− F−F angle greater than 0° indicates the deviation from linearity of the hydrogen bond. A value of the F−Cl−F angle less than 180° measures the deviation from linearity of the halogen bond. It is advantageous to first examine the external F−F−F angles, which are given in Table 5. Since the FH:FH:FH:FH and FCl:FCl:FCl:FCl complexes have C4h symmetry, the four F atoms are located at the corners of a square and the F−F−F angles are 90°. The F−H···F hydrogen bonds and the F−Cl···F halogen bonds in these complexes must adjust to this symmetry constraint. Similarly, since the FH:FCl:FH:FCl complex has C2h symmetry, the four F atoms are located at the corners of a rectangle, with the longer sides defined by the F−F distances associated with F− Cl···F halogen bonds. This means that the internal angles must also adjust to this symmetry constraint. The remaining complexes have only Cs symmetry, which allows both internal and external angles to adjust to best accommodate the hydrogen and halogen bonds. The consequences of having cyclic geometries can be seen in Table 6, which provides the H−F−F hydrogen bond angles, which show the deviation from linearity of hydrogen bonds, and the F−Cl−F angles, which illustrate the deviation from linearity of halogen bonds. The 5−1−2 angle for the F5−H1···F2 hydrogen bond has its largest deviation from linearity of 9° in the two symmetryconstrained structures FH:FH:FH:FH and FH:FCl:FH:FCl. However, since this angle has values of 6 and 5° in the binary complexes FH:FH and FH:FCl, respectively, this is not a

Table 2. Binding Energies (−ΔE) and Nonadditivities of Binding Energies (δΔE, kJ mol−1) of Quaternary Complexes complex

−ΔE

δΔE

FH:FH:FH:FH FH:FH:FH:FCl FH:FH:FCl:FCl FH:FCl:FH:FCl FH:FCl:FCl:FCl FCl:FCl:FCl:FCl

117.8 76.1 55.9 51.0 42.6 36.3

−41.4 −7.7 −2.8 −9.0 +3.6 +14.1

indicate once again that the F−H···F hydrogen bonds are stronger in the quaternary complexes than in the corresponding binary complexes. The unique covalent and halogen bond F− Cl distances are reported in Table 4. The F4−Cl8 covalent bond distances are longer than the covalent F−Cl distances in the corresponding binary complexes. The intermolecular F1− Cl8 halogen bond distance in complexes with the bonding scheme F4−Cl8···F1−H5 is shorter than the distance of 2.707 Å in FCl:FH. These data suggest that the F4−Cl8···F1 halogen bond is stronger than the halogen bond in the corresponding binary complex. The slightly longer F1−Cl8 halogen bond distance of 2.757 Å in FCl:FCl:FCl:FCl compared to a distance of 2.743 Å in FCl:FCl suggests that the halogen bonds in this complex are weaker than the halogen bond in the binary complex, consistent with the diminutive nonadditivity effect in this quaternary complex. The intermolecular F4−Cl7 distance is significantly longer in FH:FH:FCl:FCl and FH:FCl:FCl:FCl, indicating that these bonds are weaker than the halogen bond in the binary complex FCl:FCl. The intermolecular Fx-Fy distances in Fx-H···Fy hydrogen bonds and the intermolecular Cl−Fy distances in Fx-Cl···Fy halogen bonds are typical of traditional hydrogen and halogen bonds, respectively. The Fx-H and Fx-Cl distances are typical covalent bond distances. C


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Figure 2. Binding energies and nonadditivities of binding energies of quaternary complexes versus the number of FH molecules.

Table 3. Unique F−F and F−H Covalent and Hydrogen Bond Distances (R, Å) for F−H···F Hydrogen Bonds in Quaternary Complexesa

a

complex

R(1−2)

FH:FH:FH:FH FH:FH:FH:FCl FH:FH:FCl:FCl FH:FCl:FH:FCl FH:FCl:FCl:FCl

2.519 2.645 2.654 2.828 2.792

R(2−3)

R(3−4)

2.658 2.754

2.772

R(1−5)

R(2−6)

R(3−7)

0.939 0.932

0.934

0.952 0.938 0.935 0.930 0.930

R(2−5) 1.588 1.722 1.726 1.916 1.871

R(3−6)

R(4−7)

1.719 1.824

1.881

F−F and F−H distances for FH:FCl hydrogen bonds are given in italics.

Table 4. Unique F−Cl Covalent Bond and Halogen Bond Distances (R, Å) in Quaternary Complexesa

a

complex

R(1−8)

R(4−8)

FH:FH:FH:FCl FH:FH:FCl:FCl FH:FCl:FH:FCl FH:FCl:FCl:FCl FCl:FCl:FCl:FCl

2.574 2.582 2.668 2.636 2.757

1.664 1.650 1.659 1.651 1.648

R(4−7)

R(3−7)

3.224

1.652

2.936

1.649

R(3−6)

R(2−6)

2.730

1.655

F−Cl distances in F−Cl···F−Cl halogen bonds are given in italics.

hydrogen bond with an H7−F3−F4 angle of 14°. In contrast, the 1−8−4 angle for halogen bonds has a value of 160°, indicating a deviation from linearity of 20° in the FH:FH:FH:FCl complex. However, it is the 4−7−3 angle that shows the greatest deviation from linearity with values of 128° in FH:FH:FCl:FCl and 150° in FH:FCl:FCl:FCl. It is noteworthy that the external angles are not constrained to be 90° in these two complexes, which implies that these large deviations from linearity better accommodate the hydrogen bonds. Since the binding energies of the quaternary complexes indicate that hydrogen bonds are stronger than halogen bonds, it is the halogen bonds that are more distorted from linearity. The nonlinearity of the halogen bonds provides for the best binding energy compromise between F−H···F hydrogen bonds and F···Cl−F halogen bonds, which appears to be weighted in favor of hydrogen bonds.

Table 5. Complex Symmetries and Unique F−F−F Angles (∠, deg) in Quaternary Complexes complex

symmetry

∠1−2−3

∠2−3−4

∠3−4−1

∠4−1−2


C4h Cs Cs C2h Cs C4h

90 111 119 90 102 90

101 85 90 77

75 65

72 91

81

100

significant change. The hydrogen bond 6−2−3 angles in FH:FH:FH:FCl and FH:FH:FCl:FCl are not symmetry constrained. The 6−2−3 angles of 1 and 3°, respectively, indicate that these hydrogen bonds are essentially linear. The largest deviation from linearity is found for the F3−H7···F4 D


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The Journal of Physical Chemistry A Table 6. Unique H−F−F Hydrogen-Bond and F−Cl−F Halogen-Bond Angles (∠, deg) in Quaternary Complexesa ∠H−F−F

a

complex

∠5−1−2


9 8 6 9 6

∠F−Cl−Fa

∠6−2−3

∠7−3−4

∠1−8−4

1 3

14

160 173 165 174 169

4−7−3

3−6−2

128 150

171

Halogen-bond F−Cl−F angles which occur in an F−Cl···F−Cl arrangement are given in italics.

Table 7. Unique Charge-Transfer Energies (kJ mol−1) for Hydrogen and Halogen Bonds in Quaternary Complexes hydrogen bondsa

a

complex

2 → 5−1


96.9 50.8 47.3 21.5 24.2

halogen bondsb

3 → 6−2

4 → 7−3

1 → 8−4

52.1 28.2

26.4

23.0 22.2 15.4 17.1 9.7

4 → 7−3

3 → 6−2

0.9 4.3

11.3

Charge-transfer Flp → σ*H−F. bCharge-transfer Flp → σ*Cl−F.

Table 8. Unique F−F and F−H Distances (R, Å) for F···H···F Hydrogen Bonds, Binding Energies (−ΔE), and Barriers (E‡, kJ mol−1) of Transition Structures, and Transition Structure Symmetries complex FH:FH:FH:FH FH:FH:FH:FCl FH:FH:FCl:FCl FH:FCl:FH:FCl FH:FCl:FCl:FCl FCl:FCl:FCl:FCl a

R(1−2) 2.271 2.310 2.317 2.322 2.305

R(2−3)

R(1−5)

R(2−5)

R(2−6)

a

2.306

1.141 1.218 1.187 1.161a 1.153a

1.100 1.130

1.153a

−ΔE

E‡

sym

68.4 −28.1 −117.9 −106.1 −144.2 −167.4

49.4 104.3 173.8 157.0 186.8 203.7

D4h C2h C2h D2h C2h D4h

Symmetric hydrogen bond.

Figure 3. Equilibrium FH:FH:FH:FH complex and the transition structure which leads to a second equivalent equilibrium structure.

Charge-Transfer Energies. The charge-transfer energies for the quaternary complexes are reported in Table 7. The Flp → σ*H−F charge-transfer energies are greater than the Flp → σ*Cl−F energies, again indicating that F−H···F hydrogen bonds are the dominant intermolecular interaction. The greatest charge-transfer energy by far is F2lp → σ*H5−F1 in FH:FH:FH:FH. In all complexes except FH:FH:FH:FCl, this is the largest charge-transfer energy. That energy in the FH:FH:FH:FCl is 50.8 kJ mol−1, compared to 52.1 kJ mol−1 for F3lp → σ*H6−F2. For F−Cl···F halogen bonds, the F1lp → σ*Cl8−F4 charge-transfer energy is significantly greater than any other. Quaternary Transition Structures. Structures and Binding Energies. The structures, total energies, and molecular graphs of the transition structures are reported in Table S2 of

the Supporting Information. These structures have higher symmetry than the corresponding complexes, as can be seen from Table S2 and Table 8. Figure 3 illustrates the FH:FH:FH:FH equilibrium structure in which the bonding scheme is F1−H5···F2−H6···F3−H7···F4−H8···F1, the transition structure with symmetric hydrogen bonds, and an equivalent equilibrium structure with a bonding scheme F1··· H5−F2···H6−F3···H7−F4···H8−F1. This figure illustrates how proton transfer may occur through a symmetric transition structure to produce an equivalent equilibrium structure. Of course, it is only the labels of the F and H atoms that distinguish between the two equilibrium structures. Only the FH:FH:FH:FH transition structure with a binding energy of 68.4 kJ mol−1 is bound relative to the corresponding isolated monomers. The remaining transition structures have E


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Figure 4. Transition state binding energies and barriers versus the number of FH molecules.

negative binding energies which indicate that they are unbound. The transition structures present the barrier to converting one equilibrium structure to an equivalent structure through proton and chlorine transfer. These barriers range from 49 kJ mol−1 for FH:FH:FH:FH to 204 kJ mol−1 for FCl:FCl:FCl:FCl. Figure 4 presents plots of the binding energies and the barriers associated with transition structures versus the number of FH molecules. The correlation coefficients of the second-order trendlines are 0.994 and 0.983, respectively. The unique F−F and F−H distances for F···H···F hydrogen bonds in transition structures are reported in Table 8. It is evident that the F−F bond distances in the transition structures decrease relative to the equilibrium complexes. The covalent F−H distances increase and the intermolecular F−H distances decrease in the transition structures. Thus, the hydrogen bonds are proton-shared hydrogen bonds in the transition structures, and some of these are symmetric proton-shared hydrogen bonds, as indicated in Table 8. Table 9 indicates that similar

Scheme 1

have proton- or chlorine-shared bonds, (r1 − r2) is zero if F··· X···F is a symmetric intermolecular bond, or is small and either positive or negative for asymmetric, proton-shared or chlorineshared bonds. The parameter (r1 + r2) in systems with linear F−X···F bonds is the distance between the two F atoms involved in the interaction. If these bonds deviate from linearity as they do in the quaternary complexes, the sum (r1 + r2) is an approximation to the F−F distance. eqs 1 and 2 involving r1 and r2 arise from the Steiner− Limbach relationships for weak interactions.41−43

Table 9. Unique F−Cl Distances (R, Å) for F−Cl···F Halogen Bonds in Transition Structures

a

complex

R(1−8)


1.885a 1.870 1.903a 1.876 1.901a

R(4−8)

(1)

(r1 + r2) = 2r0 + (r1 − r2) + 2b ln(1 + e−(r1− r2)/ b)

(2)

The exponentials in eq 1 represent the valence contributions of the covalent and intermolecular bonds around the atom X. The sum of these contributions is equal to 1, the valence of X. eq 2 can be derived from eq 1. Figure 5 provides plots of (r1 + r2) versus (r1 − r2) for hydrogen and halogen bonds, respectively, based on eq 2. Points for r1 equal to the covalent bond distance appear at negative values of (r1 − r2), and those for intermolecular bonds are at positive values. The protonshared and halogen-shared bonds appear at values of (r1 − r2) near zero. It is also apparent from these plots that the F−F distance is significantly shorter in transition structures compared to equilibrium structures. AIM Bonding Data for Complexes and Transition Structures. The AIM bonding data including electron densities (ρBCP), Laplacians (∇2ρBCP), and energy densities (HBCP) for all F−H bonds in complexes and transition structures are given in Table S3 of the Supporting Information. These data are easily visualized in Figure S1, in which these parameters are plotted against the F−H distance. Each parameter is indicative of the presence of covalent and intermolecular bonds in complexes, and proton-shared hydrogen bonds in transition structures. Similarly, Table S4 provides the values of ρBCP, ∇2ρBCP, and HBCP for halogen bonds in these

R(4−7)

1.953 1.934

e(r0− r1)/ b + e(r0− r2)/ b = 1

1.911a

Symmetric halogen bond.

changes occur in the halogen bonds. Specifically, the covalent F−Cl distances increase and the halogen bond F−Cl distances decrease in the transition structures relative to the equilibrium complexes. These bonds are chlorine-shared halogen bonds, and in some transition structures, the halogen bonds are symmetric, as indicated in Table 9. The hydrogen and halogen bonds may also be analyzed in terms of two distance parameters, r1 and r2, which are defined in Scheme 1. r1 is the F1−X distance, and r2 is the F2−X distance. The parameter (r1 − r2) is negative when r1 is the covalent bond, since the covalent F1−X distance is shorter than the intermolecular F2−X distance. (r1 − r2) is positive when r1 is the intermolecular bond. In the transition structures which F


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Figure 5. (r1 + r2) vs (r1 − r2) (Å) for (a) hydrogen and (b) halogen bonds. The fitted curves based on eq 2 have R2 values greater than 0.99.

Table 10. Unique Coupling Constants complex FH:FH:FH:FH FH:FH:FH:FCl FH:FH:FCl:FCl FCl:FCl:FH:FCl FH:FCl:FCl:FClb a

2h

J(1−2)

24.2 −9.3 −16.4 −33.6

2h

2h

J(F−F), 1J(F−H), and

J(2−3)

7.3 −16.6

2h

J(3−4)

−33.3

J(F−H) (Hz) for F−H···F Hydrogen Bonds in Complexesa

1h

1

J(1−5) 499.3 504.7 508.6 516.6

1

J(2−6) 530.5 536.3

1

1h

J(3−7)

1h

J(2−5)

−45.0 −36.9 −38.0 −18.7

532.0

J(3−6)

−35.6 −29.7

1h

J(4−7)

−17.8

Coupling constants for FH:FH and FH:FCl binary complexes are reported in Table S7. bSD term for FH:FCl:FCl:FCl could not be computed.

Table 11. Unique Coupling Constants 2hJ(F−F) and 1hJ(F− H) (Hz) for F···H···F Hydrogen Bonds in Transition Structures

same complexes, and Figure S2 provides plots of these parameters versus the F−Cl distance. The covalent and traditional halogen bonds in complexes and the chlorine-shared halogen bonds in transition structures are easily identified. Values of these parameters are typical of inter- and intramolecular bonds.44,45 Spin−Spin Coupling Constants for Complexes and Transition Structures. The components of spin−spin coupling constants 1J(F−H), 1hJ(F−H), and 2hJ(F−F) across F−H···F hydrogen bonds, and 1J(F−Cl) and 1xJ(F−Cl) across halogen bonds for the quaternary complexes are reported in Table S5 of the Supporting Information. Components of 1h J(F−H) and 2hJ(F−F) across F···H···F hydrogen bonds and 1x J(F−Cl) across F···Cl···F halogen bonds in transition structures are given in Table S6. These data illustrate once again the importance of terms other than the FC term for determining total coupling constants involving 19F. The FC term is not even the dominant term contributing to 2hJ(F−F) and 1J(F−H) in complexes and 1xJ(F−Cl) in transition structures. Table S5 reports only the PSO, DSO, and FC terms for the complex FH:FCl:FCl:FCl, since it was not possible to compute the SD term due to the large number of basis functions and the low symmetry of this complex. Only total J values are presented and discussed below for coupling constants in complexes and transition structures. Coupling Constants 1J(F−H), 1hJ(F−H), and 2hJ(F−F) for Hydrogen Bonds in Complexes and Transition Structures. The values of the coupling constants 1J(F−H), 1hJ(F−H), and 2h J(F−F) for complexes are given in Table 10, and 1hJ(F−H) and 2hJ(F−F) for transition structures are reported in Table 11. 2h J(F−F) varies from −34 Hz to +24 Hz in the complexes as the F−F distance varies by 0.31 Å. In the transition structures, 2h J(F−F) increases dramatically and varies between +253 and +439 Hz as the F−F distance decreases dramatically relative to the equilibrium structures. However, this distance varies only

complex FH:FH:FH:FH FH:FH:FH:FCl FH:FH:FCl:FCl FH:FCl:FH:FCl FH:FCl:FCl:FCl

2h

J(1−2) 296.8 252.6 361.0 263.1 334.9

2h

J(2−3)

438.8

1h

J(1−5) 120.5 39.6 80.8 96.6 101.5

1h

J(2−5) 219.0 194.5

1h

J(2−6)

145.6

by 0.031 Å in the transition structures. Figure 6 presents a plot of 2hJ(F−F) versus the F−F distance. The correlation coefficient for the second-order trendline for the complexes is only 0.84, while 2hJ(F−F) values for transition structures show no dependence on the F−F distance. The absence of a good correlation between 2hJ(F−F) and the F−F distance is a result of the cyclic structures of these complexes and transition structures, and the influence of other bonds that interact with a particular F−H···F hydrogen bond. 1 J(F−H) and 1hJ(F−H) values for complexes, and 1hJ(F−H) for transition structures are reported in Tables 10 and 11, respectively. Although the F−H distance always increases in the quaternary complexes relative to the corresponding binary complexes, 1J(F−H) may increase or decrease. The longest F− H bond is F1−H1 in FH:FH:FH:FH, and 1J(F1−H1) has its smallest value of 499 Hz. 1J(F2−H6) and 1J(F3−H7) for FH:FH:FH:FCl, and 1J(F2−H6) for FH:FH:FCl:FCl are the largest F−H coupling constants, but these are not found at the shortest F−H distances. 1hJ(F−H) values are negative in the complexes at the long F−H distances across hydrogen bonds, and vary from −45 to −18 Hz. In the transition structures which have proton-shared hydrogen bonds, 1hJ(F−H) values change sign46 and vary between 40 and 219 Hz. These values are significantly greater than 1hJ(F−H) and significantly less than 1J(F−H) for complexes, as expected. Figure 7 illustrates G


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Figure 6. 2hJ(F−F) across hydrogen bonds versus the F−F distance in complexes and transition structures.

Figure 7. 1J(F−H) and 1hJ(F−H) for complexes and 1hJ(F−H) for transition structures versus the F−H distance.

Table 12. Unique Coupling Constants 1J(F−Cl) and 1xJ(F−Cl) (Hz) for F−Cl···F Halogen Bonds in Complexesa and Transition Structures complexes complex FH:FH:FH:FCl FH:FH:FCl:FCl FH:FCl:FH:FCl FCl:FCl:FCl:FClb FCl:FCl:FCl:FCl

1

J(8−4) 806.5 762.8 802.3 770.3

1

J(7−3) 808.9

transition structures

1x

J(8−1) 104.2 115.2 90.0

1x

J(7−4) 6.9

88.9

1x

J(8−1) 639.0 703.4 671.9 683.9 621.2

1x

J(8−4) 539.4 671.7 569.1

1x

J(7−4)

633.0

a

Coupling constants for binary FCl:FH and FCl:FCl complexes are given in Table S7. bSD term for the FH:FCl:FCl:FCl complex could not be computed.

for 1xJ(F7−Cl4) for FH:FH:FCl:FCl. Its very small value of 7 Hz correlates with the long F7−Cl4 distance in this complex. 1x J(F−Cl) values for transition structures are between 539 and 703 Hz. Thus, they are intermediate between 1J(F−Cl) and 1x J(F−Cl) for complexes. However, both R(F−Cl) and 1xJ(F− Cl) have values in transition structures that are much closer to the values of these parameters for covalent F−Cl bonds rather than intermolecular halogen bonds in complexes. This is evident from Figure 8, which illustrates the variation of F−Cl coupling constants with the F−Cl distance in complexes and

the distance dependence of these coupling constants using a third-order trendline with a correlation coefficient of 0.995. Coupling Constants 1J(F−Cl) and 1xJ(F−Cl) for Halogen Bonds in Complexes and Transition Structures. Coupling constants 1J(F−Cl) and 1xJ(F−Cl) for complexes and 1x J(F−Cl) for transition structures are reported in Table 12. 1 J(F−Cl) values in complexes may increase or decrease relative to the corresponding binary complexes, and range from 763 to 809 Hz. 1xJ(F−Cl) values in complexes increase relative to the binary complexes, with values between 89 and 115 Hz, except H


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Figure 8. 1J(F−Cl) and 1xJ(F−Cl) versus the F−Cl distance in complexes and transition structures.

transition structures. The third-order trendline has a correlation coefficient of 0.989.

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4

CONCLUSIONS Ab initio MP2/aug′-cc-pVTZ calculations have been carried out to investigate the six unique cyclic quaternary complexes F H : F H : F H : F H , F H : F H : F H: F C l , FH : F H : F C l :F C l , FH:FCl:FH:FCl, FH:FCl:FCl:FCl, and FCl:FCl:FCl:FCl stabilized by F−H···F hydrogen bonds and F−Cl···F halogen bonds. The results of these calculations support the following statements. 1 The binding energies of these complexes range from 36 to 188 kJ mol−1, and decrease as the number of FH molecules and therefore, as the number of hydrogen bonds decreases. Thus, hydrogen bonds are primarily responsible for the stabilities of these complexes. Nonadditivities of binding energies are synergistic for complexes with 4, 3, and 2 FH molecules, but antagonistic for those with 1 and 0 FH molecules, and range from −41 to +14 kJ mol−1. Both binding energies and nonadditivities exhibit a second-order dependence on the number of FH molecules in the complex. 2 F−F distances decrease and F−H distances increase in the complexes relative to the corresponding binary complexes. The covalent F−Cl distances tend to increase and the intermolecular F−Cl distances tend to decrease in the quaternary complexes relative to the corresponding binary complexes, although there are a few exceptions. 3 In addition to distance changes, complex binding energies are influenced by two sets of angular structural parameters. The first of these are the external F−F−F angles, which are fixed at 90° in the tetramers (FH)4 and (FCl)4, and in the FCH:FCl:FH:FCl complex, and must sum to 360° for the remaining complexes. The second set consists of the H−F−F angles for hydrogen bonds and the F−Cl−F angles for halogen bonds, which measure the deviation from linearity of these bonds.

5

6

7

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Since the halogen bonds are weaker, they tend to show larger deviations from linearity. Flp→σ*H−F charge-transfer energies across hydrogen bonds are greater than Flp→σ*Cl−F charge-transfer energies across halogen bonds, indicating once again that hydrogen bonding is the dominant intermolecular interaction. Transition structures, which present the barriers for converting an equilibrium structure to an equivalent equilibrium structure, have been found on all intermolecular surfaces. The barrier heights for this process range from 49 kJ mol−1 for (FH)4 to 204 kJ mol−1 for (FCl)4, and increase as the number of FH molecules decreases. Spin−spin coupling constants 2hJ(F−F) across hydrogen bonds in complexes tend to increase with decreasing F− F distance. They increase dramatically in transition structures, but show no dependence on the F−F distance. The one-bond coupling constants 1hJ(F−H) are relatively small and negative in complexes, but increase dramatically and are positive in transition structures. 1J(F−H) values are greatest for the covalent F−H bonds in complexes. The F−H coupling constants exhibit a third-order dependence on the F−H distance. Spin−spin coupling constants 1xJ(F−Cl) across halogen bonds are relatively small and positive in complexes, and increase dramatically in transition structures. The largest values of F−Cl coupling constants are found for 1J(F− Cl) for covalent bonds.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.8b00236. Geometries, total energies, and molecular graphs of complexes and transition structures; AIM bonding parameters for hydrogen and halogen bonds in complexes and transition structures; plots of AIM I


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parameters for hydrogen bonds and halogen bonds; components of spin−spin coupling constants 1J(F−H), 1h J(F−H), and 2hJ(F−F) for hydrogen bonds and 1J(F− Cl) and 1xJ(F−Cl) for halogen bonds in complexes and transition structures; and coupling constants across hydrogen bonds and halogen bonds in binary complexes (PDF)

AUTHOR INFORMATION

Corresponding Authors

*(J.E.D.B.) E-mail: [email protected]. Telephone: +1 330609-5593. *(I.A.) E-mail: [email protected]. Telephone: +34 915622900. ORCID

Janet E. Del Bene: 0000-0002-9037-2822 Ibon Alkorta: 0000-0001-6876-6211 José Elguero: 0000-0002-9213-6858 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out with financial support from the Ministerio de Economia,́ Industria y Competitividad (Project No. CTQ2015-63997-C2-2-P) and Comunidad Autónoma de Madrid (S2013/MIT2841, Fotocarbon). Thanks are also given to the Ohio Supercomputer Center and CTI (CSIC) for their continued computational support.

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Hydrogen and Halogen Bonding in Cyclic FH(4-n):FCln Complexes

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