Ab Initio Study of Benzene−BX3 (X = H, F, Cl) Interactions

184

J. Phys. Chem. B 1999, 103, 184-191

Ab Initio Study of Benzene-BX3 (X ) H, F, Cl) Interactions P. Tarakeshwar, Sang Joo Lee, Jin Yong Lee, and Kwang S. Kim* Center for Superfunctional Materials and Center for Biofunctional Molecules, Department of Chemistry, Pohang UniVersity of Science and Technology, San 31, Hyojadong, Pohang 790-784, Korea ReceiVed: August 14, 1998; In Final Form: October 30, 1998

Quantum mechanical ab initio calculations at the MP2/6-311++G** level of theory have been used to predict the binding energies and geometries of benzene-BX3 and ethene-BX3 (X ) H, F, Cl) complexes. Single point calculations at a much higher level of correlation (MP4) and larger basis sets (6-311++G(2df,p) + diffuse(d,p)) have also been carried out. The calculations reveal interesting trends in their binding energies and geometries. The binding energies indicate that all of them are weakly bound van der Waals complexes with the exception of the C2H4-BH3 complex. While complexes involving BF3 are the weakest (binding energies) in cases of both ethene and benzene, there is a reversal in the relative order of the binding energies as one moves from ethene to benzene. Thus C6H6-BCl3 is more tightly bound than C6H6-BH3. The geometry exhibited by the lowest energy conformer in cases of complexes involving benzene is different from those involving ethene. In contrast to most weak van der Waals interactions involving benzene, H-π, and aromaticaromatic, the boron atom lies directly over one of the benzene carbons. This observation has been explained by comparing the geometries obtained in complexes involving both benzene and ethene. More importantly, there is strong evidence of an unusual increase in the nucleophilicity of one of the benzene carbons in the lowest energy conformer of systems involving benzene, which implies that Lewis acid-aromatic ring interactions have an important role in electrophilic aromatic substitution reactions.

Introduction The importance of noncovalent interactions in determining the structures and reactivity of organic,1 organometallic,2 and biological3 molecules has led to extensive investigations of interactions involving aromatic-π systems.4-12 The role of these interactions in determining the stability of proteins6a and their functional utiltity have attracted a lot of attention.4 The structural features of some of these systems have been detected in exquisite experiments in the gas phase and extensively validated by wideranging theoretical studies. These interactions can be broadly classified as cation-π,5-7 π-H,8,9 and aromatic-aromatic ring10,11 interactions. Apart from metal ions or organic cations, hydrogen is the electropositive group in nearly all these interactions involving the π electron cloud of the aromatic rings.5-9 While interactions involving the former are generally characterized by high binding energies dominated by electrostatic contributions, those involving the latter are mostly weak van der Waals interactions with energies generally below 10 kcal/mol. We therefore thought it would be interesting to investigate whether atoms or systems other than hydrogen or cations can interact with the π electron cloud of the aromatic ring. Given the electron deficient nature of boron-containing compounds and their extensive use as catalysts (halides like BF3) in a large number of reactions involving aromatic rings,13 we felt it would be interesting to theoretically investigate the nature of interactions prevailing in these systems. There have been a number of experimental and theoretical studies of donor-acceptor complexes involving BH3, BF3, and BCl3.14-25 Most of these studies involve interactions with aliphatic compounds. The few studies which involve aromatic rings have studied the interactions of fluorobenzene or benzaldehyde with boron containing compounds.21 Almost all of them

have been characterized as Lewis acid-base complexes (complexes which on dissociation yield two closed-shell fragments) with large variations in binding energies. For example, the theoretically evaluated binding energies of the complexes of BH3, BF3, and BCl3 with CO are 25.1, 4.7, and 4.0 kcal/mol, respectively.18 A recent experimental and theoretical study of the van der Waals complexes of BF3 with the unsaturated hydrocarbons ethene and propene is particularly interesting.19 BF3 was found to be directly placed over the π bond of ethene and propene. The complexation enthalpies were determined to be -2.4 and -2.8 kcal/mol in liquid argon.19 Thus, given the absence of both experimental and theoretical studies on the interactions of aromatic rings with boroncontaining compounds, the present study reports the results of a high-level theoretical study on the nature of their interactions. In addition to the evaluation of the binding energies and the preferred modes of interaction, a detailed analysis of the vibrational frequencies has also been done for these complexes. In the course of the discussion, we also highlight the major differences in structures of the minimal energy conformers of aromatic complexes of boron compounds vis-a-vis the olefinic complexes of the same. Finally, we provide evidence of an unusual role of these boron-containing compounds in electrophilic aromatic substitution reactions, wherein they are employed as catalysts. Computational Methods A detailed conformational search followed by full geometry optimizations was carried out using ab initio26 calculations at the second-order Møller-Plesset (MP2) level using the 6-31+G* basis set on different initial geometries of C6H6 and BH3 (Figure 1). Vibrational frequencies were then evaluated at the MP2/631+G* level on each of the above conformers to identify the

10.1021/jp9833810 CCC: $18.00 © 1999 American Chemical Society Published on Web 12/16/1998

Ab Initio Study of Benzene-BX3 Interactions

Figure 1. Various orientations of the C6H6-BH3 complex that have been optimized at the MP2/6-31+G* level. The figures in parantheses are the relative energies (in kcal/mol) of the benzene-borane complexes.

real minimal energy structures. The two lowest energy conformers (out of which one was the global minima) were then subject to further optimizations at the MP2 level using the 6-311++G** basis set. Single point calculations were further carried out on the MP2/6-311++G** optimized geometries using a very large basis set, MP2/6-311++G(2df,p) + diffuse(d,p) (abbreviated as MP2/6-311++G(3df,2p). The exponents of the diffuse d basis functions for B, C, F, and Cl are 0.0501, 0.0783, 0.2188, and 0.0938 respectively, and that of the diffuse p function for H is 0.188. In the case of the interactions of BF3 and BCl3 with C6H6, we carried out a full geometry optimization on two conformers at the MP2/6-31+G* level. Vibrational frequencies were evaluated on the lowest energy conformer to confirm that they were true minima. As in the case of C6H6-BH3, further optimizations were carried out at the MP2/6-311++G** level, which were followed by single point calculations at the MP2/ 6-311++G(3df,2p) level. A similar strategy was employed for ethene-BX3 interactions. Consequent to one of the referee’s suggestions, single point calculations at the fourth-order MøllerPlesset (MP4) level of theory with single, double, triple, and quadruple substitutions were carried out on some selected conformers at their MP2/6-311++G** optimized geometries. It should particularly be pointed out that MP4 evaluations of binding energies of van der Waals complexes are meaningful only if the triples substitution is explicitly considered. The vibrational frequencies and hence the zero point energies (ZPE) were evaluated only at the MP2/6-31+G* level. Basis set superposition error (BSSE) corrections were carried out using the counterpoise method.27 It is important to point out that in case of weak van der Waals interactions involving benzene, a 100% BSSE correction highly underestimates the binding energy and furthermore is less consistent than the uncorrected energies. Therefore, instead of a full BSSE correction, we have often found it useful to employ a 50% BSSE correction for comparison with experimentally evaluated binding energies.28 Consequent to one of the referee’s comments on the 50% BSSE correction employed in this study, we would like to state that

J. Phys. Chem. B, Vol. 103, No. 1, 1999 185 there are two types of errors in calculations using a truncated basis set, i.e., the BSSE and the basis set incompletion error (BSIE). These two errors have opposite sign. Both errors can, in principle, be corrected by saturating the basis set. Correcting for the BSSE would leave the BSIE uncorrected. We therefore think that, for a comparison with experimental values, a compromise has to be drawn on the kind of correction employed. It should be pointed out that estimated data as obtained from correction procedures like the counterpoise method,27 is not undisputed.29 This fact has been reiterated in earlier theoretical studies on Lewis acid-base complexes.18 Furthermore, in the course of the discussion on our calculations, we clearly show that the best agreement with the experimentally determined enthalpies and binding energies is only obtained when one employs the 50% BSSE correction. In either case, both the 50% and 100% BSSE corrected binding energies are listed in the Tables. All calculations were carried out using a Gaussian-94 suite.26 Natural bond orbital (NBO)30 analysis was carried out for all the uncomplexed monomers and for all the conformers of C6H6-BX3 and C2H4-BX3 complexes to highlight the shifts in electron density upon complexation. NBO’s are the localized set of easily recognizable Lewis-like (σ and π bond, lone pair, and core) and non-Lewis (σ* and π* antibond and Rydberg) orbitals, which are optimal in the sense of orthonormality and maximum occupancy of the Lewis set. An important feature of the NBO method, is that unlike other charge partitioning schemes, the presence of diffuse functions in the basis sets does not affect the results.30 Results and Discussion Seven conformers 1-7 were obtained, after an evaluation of various possible orientations of BH3 toward C6H6 was followed by full geometry optimizations at the MP2/6-31+G* level. Five of the above conformers exhibit a π type of interaction, while the remaining two have a σ type of interaction. It is interesting to note that conformer 4 has the so-called H‚‚‚H interaction.31 However, both conformers 4 and 5 have higher energies and, since the focus of this study was on Lewis acid interactions with π systems, no further investigations were carried out on them. The values of the relative energies for the seven conformers depicted in Figure 1 clearly indicate that conformers 6 and 7 are the lowest energy conformers. Conformer 6 is a true minimal energy structure (all positive vibrational frequencies), while 7 has two imaginary vibrational frequencies. The other three conformers (1-3) exhibiting π type interactions also have two or three imaginary vibrational frequencies. Given the similarity of the structures of BH3, BF3, and BCl3, we expect that the lowest energy conformers for C6H6-BF3 and C6H6BCl3 would be similar to those observed in C6H6-BH3. Hence calculations at the various levels were carried out only on two conformers of C6H6-BF3, 8 and 9, and two conformers of C6H6-BCl3, 10 and 11 (Figure 2). The fact that conformers 8 and 10 are true minima is affirmed by the evaluation of the vibrational frequencies at the MP2/6-31+G* level (all positive vibrational frequencies). All subsequent discussions are limited to the properties exhibited by these six conformers. In order to highlight the salient differences between the binding of Lewis acids with olefins and aromatic systems, we also present the results of our calculations on ethene-BX3 systems (Figure 3). In case of ethene-BH3, though conformer 12 is not the lowest energy structure (a σ complex is the actual lowest energy structure), we include it in our discussion because it exhibits a π type of interaction. Conformer 12, however, is a local

186 J. Phys. Chem. B, Vol. 103, No. 1, 1999

Figure 2. Structures of the MP2/6-31+G* optimized C6H6-BF3 (8, 9) and C6H6-BCl3 (10, 11) complexes.

Figure 3. Structures of the MP2/6-31+G* optimized C2H4-BH3 (12), C2H4-BF3 (13), and C2H4-BCl3 (14) complexes.

minimum (all positive vibrational frequencies). It is of interest to note that an earlier theoretical study on the interaction of ethene and borane to explain the hydroboration reaction had shown that the binding energy of a π complex (similar to conformer 12) at the MP2/3-21G level to be around 12.8 kcal/ mol.32 A π type of interaction is also exhibited in the interaction of BF3 with ethene and propene.19 Geometries It can be seen from Figures 1 and 2 that in conformers 6, 8, and 10, the boron atom is directly placed over one of the benzene carbons while in conformers 7, 9, and 11 the boron atom lies on the C6 axis of benzene. There are subtle changes in the geometries of conformers depending on the position of the boron atom. When they are compared to the corresponding monomer geometries, there are insignificant changes in the geometries of the monomers in conformers 7, 9, and 11. On the other hand, there are slight changes-in the geometries of the monomers in confomers 6, 8, and 10. Thus the B-H bond length changes from 1.190 in BH3 to 1.192 and 1.193 Å in conformer 6, the B-F bond length changes from 1.318 in BF3 to 1.317 and 1.321 Å in conformer 8, and the B-Cl bond length changes from 1.738 in BCl3 to 1.735 and 1.743 Å in conformer 10. Interestingly, the B-X bond, which lies over the benzene π plane, is shorter than the other two B-X bonds. In case of the C-C bond lengths (1.399 Å) of benzene, while there is a perceptible increase in the C-C bond length (1.403 Å) of benzene closest to the boron atom in conformer 6, no significant changes are observed in conformers 8 and 10. In case of the ethene-BH3 interaction, the B-H bond lengths are 1.204 and 1.194 Å, respectively. The increases in the B-F and B-Cl bond lengths in ethene-BF3 and ethene-BCl3 are, however, smaller, which can be readily understood from donoracceptor considerations.22 The BsCdC distance in the ethene

Tarakeshwar et al. complexes shows large variations. Thus, while it is 1.763 Å in C2H4-BH3, it is 3.331 Å in C2H4-BCl3. The location of the BX3 moiety over the benzene π plane is particularly interesting. It can be seen from Table 1 that in conformers 6, 8, and 10, there is a gradual increase in the Bs benzene plane distance as one progresses from BH3 to BCl3. This increase can easily be explained, when one takes into account the increased repulsion between the X atom and the benzene plane as one moves from BH3 to BCl3. However, it is more difficult to account for the small decrease (rather than the expected increase) in the Bsbenzene plane distance in conformer 9, when compared to conformers 7 and 11. We believe that this decrease is due to an increased orbital overlap between the fluorine p(π) orbitals and the 2b1u orbital of benzene, as a result of nearly identical BsF bond lengths (1.318 Å) and the benzene centroid CsC distances (1.399 Å). Such an optimal orbital overlap is, however, not feasible in 7 (no p(π) orbital) and 11 (B-Cl bond length is 1.740 Å). A comparison of the Bsbenzene plane and BsCdC plane distances shows that in conformers 8 and 10, the B atom is closer to the benzene plane than B is to the ethene double bond in 13 and 14. The perturbation of the π system in benzene in conformer 6, 8, and 10 results in a very slight bending of the corresponding H atom out of benzene (2-3°). This is very small when compared to the bending of 9.9° observed in complexes of Si cation and benzene, which are very tightly bound by electrostatic interactions (binding energies of 44 kcal/mol).7a Similarly, the repulsion between the benzene π plane and the B-X σ orbitals lying above it results in a slight pyramidalization of the B-X bond in conformer 6. Owing to the larger intermolecular separation in conformers 8 and 10, there is no pyramidalization of the B-X bond. Binding Energies The binding energies shown in Table 1 indicate that BX3 is more tightly bound to the benzene ring in conformers 6, 8, and 10 than in conformers 7, 9, and 11. While there is a gradual increase in the binding energies in conformers 7, 9, and 11, there is a curious dip in the case of 8, when compared to that of 6 and 10. The binding energy in the case of conformers 6, 7, 10, and 11 is dominated by electron correlation energy (ΑEcor) with an extremely small contribution from the electrostatic energy (∆Ees). In the case of conformers 8 and 9, ∆Ees seems to be as important as ∆Ecor. Given the general behavior of donor-acceptor complexes, wherein the binding energy is expected to be dominated by electrostatic interactions (Lewis acidity of the acid determines the binding energy), the present results are interesting because the relative strengths of these Lewis acids are in the order BCl3 > BF3 > BH3.33 It has generally been accepted that the relative acidity depends on the nature of the Lewis base, which is chosen as a bonding partner in donor-acceptor complexes. Thus, BCl3 forms stronger bonded complexes than BF3 with the strong Lewis bases NH3 and NMe3, while the weak Lewis bases CO and MeCN form stronger bonds with BF3 than BCl3.18 The present study clearly shows that aromatic systems are an exception to this rule. Thus even though benzene is considered a weak Lewis base, it forms stronger complexes with BCl3 than with BF3. It is interesting to compare the binding energies obtained for the benzene-BX3 complexes with the energies evaluated for other complexes involving BX3 systems. Thus the MP2/631++G(3df,2p) binding (BSSE corrected) energies for the ethene-BF3 and ethene-BCl3 complexes are 3.59 and 3.69 kcal/mol, respectively (Table 2). The BSSE corrected MP2/6-

Ab Initio Study of Benzene-BX3 Interactions

J. Phys. Chem. B, Vol. 103, No. 1, 1999 187

TABLE 1: Binding Energies and Selected Distances of Benzene-BX3 Complexesa MP2/6-31+G*

-∆ENe -∆EBe -∆Ee -∆Eo -∆Ecor -∆Ees -∆H298 RB-Φ RB-X

6 (Cs)

7 (C3V)

8 (Cs)

9 (C3V)

4.50 2.40 3.45 2.42 6.43 0.23 1.70 2.616 1.192 1.194

2.64 1.22 1.93 0.91 3.15 0.92 1.67 3.354 1.192

5.59 1.76 3.68 2.44 5.74 5.90 2.06 2.944 1.327 1.331

4.53 1.70 3.11

MP2/6-311++G(3df,2p)b

MP2/6-311++G** 10 (Cs)

7.13 1.78 4.46 3.57 4.37 9.47 6.52 1.27 3.03 3.277 3.252 1.329 1.731 1.740

11 (C3V)

6 (Cs)

6.33 1.45 3.89

6.08 3.58 4.83 3.80 8.75 10.04 1.59 0.46 3.08 3.544 2.456 1.737 1.192 1.193

7 (C3V)

8 (Cs)

9 (C3V)

3.33 1.70 2.51 1.49 4.24 0.96 2.25 3.255 1.191

5.56 1.86 3.71 2.47 5.56 4.49 2.09 2.988 1.321 1.317

5.00 1.48 3.24

10 (Cs)

8.92 2.33 5.63 4.74 4.80 11.92 4.94 1.17 4.20 3.250 3.223 1.318 1.734 1.743

11 (C3V)

6 (Cs)

8.17 1.73 4.95

6.74 4.84 5.79 4.76 10.93 10.63 1.47 0.43 4.04 3.470 (2.456) 1.740 (1.192) (1.193)

7 (C3V)

8 (Cs)

3.62 2.39 3.00 1.98 4.51 0.97 2.74 (3.255) (1.191)

6.04 3.01 4.53 3.29 6.11 4.74 2.91 (2.988) (1.321) (1.317)

9 (C3V)

10 (Cs)

11 (C3V)

5.47 2.76 4.12

9.08 4.44 6.76 5.89 5.27 12.06 5.24 1.30 5.33 (3.250) (3.223) (1.318) (1.734) (1.743)

8.31 3.93 6.12 10.98 1.65 (3.470) (1.740)

All energies are in kcal/mol; distances are in Å. -∆ENe and -∆EBe represent the binding energies without and with BSSE correction, respectively. ∆Ee is chosen to represent the mid value of ∆ENe and ∆EBe as upper and lower bounds, respectively. ∆Eo is the ZPE-corrected ∆Ee. ∆H298 is the enthalpy at 298.15 K and 1.0 atm. The frequencies for ZPE and thermal corrections were evaluated at the MP2/6-31+G* level. The electron correlation energy ∆Ecor is the value of the Ee(MP2) subtracted by Ee(HF) at the MP2-optimized geometry. ∆Ees is the electrostatic (chargecharge) interaction energy evaluated using NBO charges. RB-Φ and RB-X are the distances from boron to the benzene plane and the X (X ) H, F, Cl), respectively. In cases of 6, 8, and 10, one X lies on the benzene plane while the other two equivalent X’s are outside. b MP2/6-311++G(3df,2p)// MP2/6-311++G**. a

TABLE 2: Binding Energies and Selected Distances of Ethene-BX3 Complexesa MP2/6-31+G* -∆ENe -∆EBe

-∆Ee -∆Eo -∆Ecor -∆Ees -∆H298 RBsCdC RBsXc

MP2/6-311++G(3df,2p)b

MP2/6-311++G**

12 (Cs)

13 (Cs)

14 (Cs)

12 (Cs)

13 (Cs)

14 (Cs)

12 (Cs)

13 (Cs)

14 (Cs)

11.89 6.64 9.27 5.03 18.21 0.41 6.36 1.763 1.197 1.206

4.14 1.78 2.96 2.12 3.20 4.96 1.70 2.922 1.330 1.330

3.43 0.99 2.21 1.57 3.93 0.80 0.97 3.382 1.736 1.737

14.27 9.79 12.03 7.67 20.43 1.81 9.12 1.782 1.194 1.204

3.86 1.73 2.80 1.96 2.83 3.27 1.54 3.001 1.319 1.320

4.32 1.15 2.73 2.09 4.90 0.72 1.49 3.331 1.739 1.740

19.98 17.24 18.61 14.25 21.55 1.40 15.70 (1.782) (1.194) (1.204)

4.39 2.80 3.59 2.75 3.28 3.44 2.33 (3.001) (1.319) (1.320)

4.79 2.59 3.69 3.05 5.42 0.80 2.45 (3.331) (1.739) (1.740)

a All energies are in kcal/mol; distances are in Å. -∆EN and -∆EB represent the binding energies without and with BSSE correction, e e respectively. ∆Ee is chosen to represent the mid value of ∆ENe and ∆EBe as upper and lower bounds, respectively. ∆Eo is the ZPE-corrected ∆Ee. ∆H298 is the enthalpy at 298.15 K and 1.0 atm. The frequencies for ZPE and thermal corrections were evaluated at the MP2/6-31+G* level. The electron correlation energy ∆Ecor is the value of the Ee(MP2) subtracted by Ee(HF) at the MP2-optimized geometry. ∆Ees is the electrostatic (chargecharge) interaction energy evaluated using NBO charges. RBsCdC and RBsX are the distances from boron to the midpoint of the CdC bond of ethene and the X (X ) H, F, Cl), respectively. b MP2/6-311++G(3df,2p)//MP2/6-311++G**. c First distance occurs twice; second occurs once.

TABLE 3: MP4 Binding Energies of Selected Conformers of the Ethene-BX3 and Benzene-BX3 Complexesa 12(C2H4-BH3) -∆ENe -∆EBe -∆Ee ∆Ecor

13(C2H4-BF3)

14(C2H4-BCl3)

6(C6H6-BH3)

MP2

MP3b

MP4c

MP2

MP3b

MP4c

MP2

MP3b

MP4c

MP2

MP3b

MP4c

14.27 9.79 12.03 20.43

11.25 6.55 8.90 17.41

12.13 7.33 9.73 18.29

3.86 1.73 2.80 2.83

3.78 1.63 2.70 2.75

4.01 1.75 2.88 2.98

4.32 1.15 2.73 4.90

3.68 0.52 2.10 4.26

4.08 0.81 2.44 4.66

6.08 3.58 4.83 10.04

4.46 1.95 3.20 8.42

5.49 2.83 4.16 9.45

All energies are in kcal/mol. -∆ENe and -∆EBe represent the binding energies without and with BSSE correction, respectively. ∆Ee is chosen to represent the mid value of ∆ENe and ∆EBe as upper and lower bounds, respectively. The electron correlation energy ∆Ecor is the value of the Ee(MPn) (n ) 2, 3, 4), subtracted by Ee(HF) at the MP2-optimized geometry. b MP3/6-311++G**//MP2/6-311++G**. c MP4(SDTQ)/6-311++G**// MP2/6-311++G**. a

31++G(3df,2p) binding energies for conformers 8 and 10 of the C6H6-BF3 and C6H6-BCl3 complexes on the other hand are higher (4.53 and 6.76 kcal/mol, respectively) than the binding energies of the ethene-BF3 and ethene-BCl3 complexes. However, the BSSE-corrected binding energy of conformer 12 (which is not the global minima) of the ethene-BH3 complex is 18.61 kcal/mol, which is higher than the binding energies evaluated for conformers 6 and 7 of the C6H6-BH3 complex. Thus, we have further evidence of an unusual trend in the binding energies of complexes of boron-containing Lewis acids with weak Lewis bases like benzene. Given the dominance of the electron correlation energy

(∆Ecor) to the binding energy observed in these complexes, it is useful to evaluate its contribution at higher levels of theory. The binding energies obtained at the MP4 level of theory for some selected conformers are shown in Table 3. It can be seen from Table 3 that the binding energies evaluated for both the C2H4-BF3 (∆ENe (MP2) ) 3.86 kcal/mol; ∆ENe (MP4) ) 4.01 kcal/mol) and C2H4-BCl3 (∆ENe (MP2) ) 4.32 kcal/mol; ∆ENe (MP4) ) 4.08 kcal/mol) complexes are nearly similar at the MP2 and MP4 levels. This similarity persists even after BSSE corrections. On the other hand, in case of both the C2H4BH3 and C6H6-BH3 complexes, the binding energies evaluated

188 J. Phys. Chem. B, Vol. 103, No. 1, 1999

Tarakeshwar et al. Vibrational Frequencies

TABLE 4: Calculated MP2/6-31+G* Vibrational Frequency Shifts of Conformers 6, 8, and 10 of C6H6-BH3, C6H6-BF3, and C6H6-BCl3 from the Calculated Frequencies of Benzenea modeb

C6H6-BH3 (6)

ν1 ν12 ν12 ν15 ν15 ν5

3.1 4.8 2.5 5.3 1.4 4.6

C6H6-BF3 (8)

C6H6-BCl3 (10)

Stretching Frequencies 1.5 3.1 0.6 3.5 0.6 2.0

-0.3 0.9 -1.3 1.1 -1.1 0.1

Out-of-Plane Ring Bending Frequencies 27.7 40.8 15.5 31.7 20.8 50.7 13.6 19.2 5.1 13.2 9.7 12.9

ν19 ν19 ν7 ν11 ν11 ν4

In an earlier paper on the interaction of benzene with the hydrogen halides, we had highlighted the importance of the relative trends and shifts in vibrational frequencies in understanding the structure and energetics of van der Waals complexes.28d Hence even though there have been no experimental reports of the vibrational structure of the benzene-BX3 complexes, the vibrational frequency shifts of C6H6 and BX3 in C6H6-BX3 (only for conformers 6, 8, and 10) and C2H4BX3 with respect to the frequencies in its monomeric state are shown in Tables 4 and 5. Of the six vibrational frequencies in BX3, three of them are stretching, while the remaining are bending modes. A cursory glance at Table 5 clearly shows that as one progresses from BH3 to BCl3, the red shifts become smaller and in the case of one of the antisymmetric stretching modes (ν1) there is a small blue shift in the case of C6H6BCl3. A similar trend is observed in the case of the C2H4-BX3 complexes; however, when compared to the C6H6-BX3 complexes, the red shifts are higher. Interestingly, though the outof-plane bending mode appears lower than the in-plane bending modes in BH3, it appears above in the case of both BF3 and BCl3. Though Table 4 displays only those modes of benzene that exhibit significant shifts when compared to the monomeric benzene, it reveals some interesting facets. Thus, in marked contrast to the frequencies involving BX3, the benzene stretching frequencies are blue shifted. However, as one moves from BH3 to BCl3 there is a gradual decrease in the blue shifts with some of the stretching frequencies in C6H6-BCl3 exhibiting red shifts. The out-of-plane bending modes indicate that C6H6-BF3 complexes exhibit more pronounced blue shifts than either C6H6-BH3 or C6H6-BCl3. This contrasts with the low binding energies of C6H6-BF3 as compared to C6H6-BH3 and C6H6BCl3. Though theoretically evaluated frequencies of the van der Waal modes cannot be employed in comparison with the experimentally determined frequencies, the relative trends are more reliable and informative. Therefore, the theoretically evaluated frequencies of the van der Waals modes of these complexes are shown in Table 6. One of interesting van der Waals modes, which reflects the ease at which the van der Waals

24.1 12.0 31.5 11.6 6.2 8.1

a All frequencies are in cm-1. b The fundamental modes are numbered according to Herzberg.34

at the MP4 level are lower than those obtained at the MP2 level. However, the decrease in binding energies at the MP4 level in the case of C2H4-BH3 (15%) is far higher than the decrease observed in C6H6-BH3 (10%). Given the above information, it can be presumed that the binding energies for both the C6H6BF3 and C6H6-BCl3 complexes at the MP4 level would be close to their MP2 values. In the absence of any experimental study on Lewis acidbenzene interactions, it is difficult to judge the accuracy of these theoretically predicted binding energies. However, in a recent study, the experimentally determined binding energy (which was obtained from the complexation enthalpies determined in liquid argon) for the ethene-BF3 complex was found to be 3.4 kcal/ mol.19 It can be seen from Table 2, that our theoretically predicted binding energy (MP2/6-311++G(3df,2p)) of 3.6 kcal/ mol for this complex is in good agreement with this experimental result. Further, the calculated enthalpy of complexation (2.33 kcal/mol) for this ethene-BF3 complex, at 298 K is also in excellent agreement with the experimentally determined enthalpy of 2.4 kcal/mol.19 In order to facilitate future experimental studies on these systems, the theoretically predicted enthalpies at 298.15 K and 1.0 atm are listed in Tables 1 and 2.

TABLE 5: Comparison of the Frequencies of the Stretching and Bending Modes of BH3, BF3, and BCl3 and Their Frequency Shifts in the Complexed States at the MP2/6-31+G* Levela mode

a

BH3

C6H6-BH3

C2H4-BH3

BF3

C6H6-BF3

C2H4-BF3

BCl3

C6H6-BCl3

C2H4-BCl3

-12 [408] -13 [372] -9 [4]

1003 1003 496

2 [310] -14 [310] -3 [1]

-3 [346] -4 [373] -2 [1]

-49 [248] -2 [12] -3 [10]

478 272 272

-19 [27] 0 [0.6] -0.2 [0.4]

-20 [22] 0 [0.6] 0 [0.6]

V1 ν2 ν3

2783 2783 2644

-15 [111] -32 [103] -18 [14]

-90 [151] -172 [48] -84 [28]

1443 1443 872

Stretching -2 [342] -20 [333] -6 [3]

V4 ν5 ν6

1187 1249 1249

-47 [229] -13 [13] -19 [9]

-66 [14] -40 [10] -53 [81]

696 472 472

Bending -43 [279] -1 [10] -3 [8]

All frequencies are in cm-1. IR intensities (km/mol) are enclosed in square brackets adjacent to the frequency shifts.

TABLE 6: Comparison of the van der Waals Modes Evaluated for C6H6-BX3 and C2H4-BX3 Complexes at the MP2/6-31+G* Levela

a

modeb

C6H6-BH3

C2H4-BH3

C6H6-BF3

C2H4-BF3

C6H6-BCl3

C2H4-BCl3

τz bip bop sz φip φop

19 83 115 124 455 463

693 509 43 363 735 895

60 59 26 94 87 91

88 111 24 100 97 175

68 54 27 86 54 67

146 96 21 73 54 58

All frequencies are in cm-1. b The van der Waals mode definitions are given in ref 28d.

0.49 0.19, 0.19 0.31

0.21

0.31 0.23, 0.21 0.02

0.21

0.01 0.20/0.18 qH

a First charge occurs once; second occurs twice. b Charge of carbon closest to the boron atom. The charges of the remaining carbon atoms are within the range given below it. c Charge of hydrogen closest to the boron atom. The charges of the remaining hydrogen atoms are around the range given beside it.

0.18, 0.18 0.21

0.49

0.34 -0.11 -0.21

0.34 -0.10, -0.10a -0.22b -0.20 to -0.21 0.21,c ∼0.21 0.34 -0.11 1.44 -0.48, -0.48a -0.37 1.44 -0.48 -0.21

1.44 -0.48, -0.48a -0.24b -0.20 to -0.21 0.21,c ∼0.21 1.43 -0.48 -0.25 -0.04, 0.03a -0.33 0.36 -0.12 -0.20 0.37 -0.13

BCl3 C2H4-BF3 13 9 C6H6-BF3 8 BF3 C2H4-BH3 12 7 C6H6-BH3 6 BH3

0.23 -0.10, -0.11a -0.25b -0.18 to -0.20 0.23,c ∼0.21 p{π} population at B

There have been innumerable theoretical reports on the electronic structure of donor-acceptor van der Waals complexes. The heart of the debate is whether donor-acceptor bonds are mainly caused by electrostatic interactions or whether nonelectrostatic (covalent) contributions, induced by charge transfer from the donor to the acceptor, are dominant. Though the hard-soft acid-base (HSAB) model considers electrostatic and covalent interactions as the principal components of interaction, the process of transforming the qualitative HSAB model into a quantitative model has been tenuous.36 There have

-0.20/-0.36

Electronic Structure

TABLE 7: MP2/6-311++G(3df,2p)-NBO Charges for All Complexes

Unfortunately, there is no single way in which to derive accurate electron populations at atoms. Although different methods lead to different populations, one might expect that the changes in population in the uncomplexed and complexed states would be similar among different methods. Thus we made use of Weinhold’s natural population analysis (NPA),29 which is based on the NBO procedure described in the Methods section. Table 7 lists the NPA charges for all the atoms in all the monomers and complexes studied. It can be seen from Table 7 that BH3 complexes differ from the other structures by a much higher change of the partial charge at boron toward a more negative value, while the hydrogen atoms become less negatively charged. Since the B atom in BH3 has a true empty p orbital as compared to that in BF3 and BCl3 owing to charge donation from the halogen lonepair electrons, the charge transfer to B is more in the case of C6H6-BH3. The p(π) population of B in BH3, BF3, and BCl3 illustrates this point. However, it can clearly be seen from Table 7 that the increased charge transfer is observed only in the case of conformer 6. We believe that the major reason for the stability of conformer 6 over 7 is that in the orbital mixing, the benzene π-HOMO in 7 directs two lobes toward BH3, each having an opposite sign while in 6, the orbital interaction is maximized by directing a single lobe. This argument is illustrated in Figure 4, wherein the HOMOs of conformers 6 and 7 are displayed. Furthermore, to highlight the major difference between the bonding of BH3 with aromatic-π and olefinic-π systems, the HOMO of conformer 12 of the ethene-BH3 system is also shown in Figure 4. The significant differences in the olefinic π-pz orbital interactions (wherein there is a symmetric transfer of charge from the π system of ethene to the empty pz orbital of boron) and the aromatic π-pz orbital interactions (wherein there is an asymmetric transfer of charge) can be observed in Figure 4. A similar type of aromatic π-pz interaction observed in a benzene-carbocation system eventually leads to the formation of a σ bond.35 Additionally, the olefinic π-pz interaction is stronger than the aromatic π-pz interaction. This can be rationalized by the very short boron-ethylene distances (1.78 Å as compared to 2.46 Å in case of boron-aromatic system distances). This short distance leads to a greater orbital overlap and hence a stronger interaction. Further, the close approach in case of the olefinic systems is facilitated by the absence of any hindrance to the hydrogens. In the case of the aromatic system, one of the hydrogens lies directly over the π cloud. The charges for the hydrogen atoms of BH3 in conformers 6 and 12 illustrate this point.

C6H6-BCl3 10 11

Charge Distributions

partial charges qB qX qC

C2H4-BCl3 14

complex dissociates, is the stretching mode sz. It can be seen that there is a gradual decrease in the frequencies of this mode as one progresses from BH3 to BCl3.

0.34 -0.12, -0.12a -0.36

J. Phys. Chem. B, Vol. 103, No. 1, 1999 189

C6H6/C2H4

Ab Initio Study of Benzene-BX3 Interactions

190 J. Phys. Chem. B, Vol. 103, No. 1, 1999

Figure 4. Second HOMO of 6 and the HOMOs of 7 and 12 at the MP2/6-311++G(3df,2p) level. In the case of 6 the eigenvalues of the first two HOMOs are nearly degenerate, wherein the second HOMO exhibits the transfer of charge. In the case of 7, both degenerate first and second HOMOs exhibit no transfer of charge.

been many attempts in the recent past that have tried to circumvent this problem. Thus a Morokuma analysis of the interactions in H3N-BH3 suggests that the stabilization is mainly electrostatic, while the extended geminal model of Røeggen emphasizes nonelectrostatic contributions.37,38 A recent study by Glendening and Streitwieser using the natural energy decomposition analysis (NEDA), which is based on the NBO procedure comes to the conclusion that H3N-BH3 is significantly stabilized by charge-transfer interactions.16 Therefore, an NBO analysis was carried out at the MP2/6-311++G(3df,2p) level for all these systems. Second-order perturbation theory analysis of the Fock matrix in the NBO basis suggests that the interaction of the aromatic-π system with the empty pz orbital of boron, alone stabilizes conformer 6 by -23 kcal/mol, while it is only -3 kcal/mol in conformer 7. Interestingly, it also reveals a significant interaction (stabilization of about -4 kcal/mol) between the σ C-H bond of benzene and the boron empty pz orbital in conformer 6. The σB-H bond lying over the benzene π plane also interacts with the aromatic π* orbital of benzene in conformer 6. Significantly, all the aforementioned interactions are absent in conformer 7. A comparative analysis of the C6H6-BF3 and C2H4-BF3 complexes indicates that the extent of stabilization of the π-pz interaction is nearly the same ∼5 kcal/mol in both these complexes. There seems to be no significant energetic contribution from the π-pz interaction in both C6H6-BCl3 and C2H4BCl3 systems. In the case of the C6H6-BF3 and C6H6-BCl3 systems, additional orbital interactions seem to stabilize the conformers 8 and 10 over 9 and 11. Notable among them are back-donations from the filled boron and fluorine p orbitals to the π* orbitals of benzene.

Tarakeshwar et al. that there is a significant increase in the negative charge of the carbon closest to boron in conformers 6, 8, and 10. It is interesting to point out that a similar increase in the negative charge of the benzene carbon closest to silicon is observed in C6H6-Si+.7a We would specifically like to highlight the case of conformer 9 (C6H6-BF3). It can clearly be seen that, though no changes are observed in cases of the charges of boron and fluorine in BF3, there is a significant increase in the negative charge of the carbon (and hence the nucleophilicity) closest to boron. It can therefore safely be said that Lewis acids (boron compounds in this study) in addition to the generation of the electrophile have a significant role in the activation of the aromatic ring in electrophilic aromatic substitution reactions. Conclusion The binding energies, geometries, and vibrational frequencies have been evaluated for benzene-BX3 and ethene-BX3 (X ) H, F, Cl) complexes at the MP2 and MP4 levels using fairly large basis sets. The evaluated binding energies indicate a gradual increase in the interaction energy of these complexes as one progresses from H to Cl. The zero-point energy (ZPE) corrected binding energies of benzene-BX3 (X ) H, F, Cl) complexes (3-6 kcal/mol) are significantly higher than that of the benzene-water (1.6-2.8 kcal/mol),8,9 benzene-benzene (∼2 kcal/mol),11 and water-water (∼3.0 kcal/mol)40 systems. However, they are lower than the binding energies of the interaction of cations with benzene or other donor-acceptor complexes.5-7 No significant changes are observed in the geometries of the monomers in their complexed states. However, in the lowest energy conformer of these complexes, the BX3 moiety lies over one of the benzene carbons. This is different from what is observed in complexes of BX3, with olefinic-π systems. This geometry can be associated with the ease at which the benzene π orbitals can overlap with the empty pz orbital of boron. Though the boron pz orbital is partially filled in BF3 and BCl3, the geometry of 8 and 10 is unaffected. However, the stabilization accruing as a result of this π-pz overlap diminishes considerably. There is a significant increase in the negative charge of the benzene carbon closest to boron in conformers 6, 8, and 10. The resulting increase in the nucleophilicity of this carbon would facilitate the attack of an electrophile. Thus, Lewis acids, in addition to the generation of the electrophile, have an unusual but vital role of activating the aromatic ring for an electrophilic attack.

Implications In a recent paper of ours on the interaction of AlCl3 with benzene, an unusual increase in the nucleophilicity (negative charge) of one of the benzene carbons as a result of its close proximity to benzene was observed.39 Since AlCl3 is employed as a catalyst in Friedel-Craft’s reaction (which is one of the leading examples of electrophilic aromatic substitution reactions), the increase in nucleophilicity could be associated with the ease in which the electrophile could attack the benzene carbon as a result of a significant lowering in the activation energy. Thus we had propounded a new role (activation of the aromatic ring) for AlCl3 in Friedel-Craft’s reaction, which we believe is vital in understanding the chemistry of electrophilic aromatic substitution reactions. Therefore, it is interesting to observe whether such an increase in the nucleophilicity of one of the carbon atoms is observed in the complexes of BH3, BF3, and BCl3 with benzene. It can clearly be seen from Table 7

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