BR3 Lewis Pairs (R= F

Oct 5, 2010 - Reactivity of 2,6-Lutidine/BR3 and Pyridine/BR3 Lewis Pairs (R = F, Me, C6F5): .... Association of frustrated phosphine–borane pairs i...
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J. Phys. Chem. A 2010, 114, 11738–11745

Reactivity of 2,6-Lutidine/BR3 and Pyridine/BR3 Lewis Pairs (R ) F, Me, C6F5): A Density Functional Study Dongling Wu, Dianzeng Jia,* Lang Liu, Li Zhang, and Jixi Guo Institute of Applied Chemistry, Xinjiang UniVersity, Urumqi 830046, P. R. China ReceiVed: June 1, 2010; ReVised Manuscript ReceiVed: September 14, 2010

The reactivity of 2,6-lutidine/BR3 and pyridine/BR3 Lewis pairs (R ) F, Me, C6F5) is investigated in detail by quantum chemical calculations. The observed reactivity difference of these pairs is interpreted in terms of the existence of a “frustrated complex” on the potential energy curve for coordination of Lewis acid and base, the profiles of local reactivity descriptors with respect to the bond distance between acid and base centers, and the thermodynamic/kinetic properties of the heterolytic dihydrogen cleavage reaction. The calculated results are shown to account well for the observed reactivity of these Lewis pairs. 1. Introduction In 2006,1 Stephan and co-workers reported for the first time that the nonmetal system of Mes2P(C6F4)B(C6F5)2 (Mes ) 2,4,6trimethylphenyl) could reversibly activate dihydrogen (H2). They further showed that simple combinations of bulky Lewis acids and bases such as (tBu)3P/B(C6F5)3 are capable of heterolytic cleavage of H2.2,3 In Stephan’s group and others’ efforts, Lewis acid/base combinations, Stephan termed “frustrated Lewis pairs” (FLPs),4 have been extended to include alkyl-linked phosphinoboranes5 as well as mixtures of electron-deficient boranes with sterically crowded imines,6,7 amines,8 and N-heterocyclic carbenes (NHC).9,10 Furthermore, the hydrogen-activating ability of these species has also been exploited in metal-free catalytic hydrogenation of imines,6,11 nitriles,6 aziridines,7,8 enamines,12 and silylenol-ethers13 under mild reaction conditions. In other words, the advent of this notion in reactivity provides new approaches in main group reactivity and catalysis. The ability of FLPs to activate small molecules (including H2,1-3 olefins,14 N2O,15 and so on) is thought to attribute to the steric encumbrance about Lewis acid and base sites that prevent or limit dative bond formation. As a result, the Lewis acid and base are available to provide active centers for bond activation. The mechanistic details of the FLP reactivity are the focus of interest. Stephan et al. proposed a mechanism of activation wherein Lewis acid activation of the substrate molecule is followed by attack of the Lewis base and vice versa. Another plausible mechanism involves the preorganization of acid and base into a weakly bound noncovalent complex (called “frustrated complex”),16 which provides active sites that are properly oriented for cooperative interaction with a small molecule. These preorganized sites can easily lead to activation of the substrate molecule and ultimate cleavage of chemical bonds. The latter model has been shown to account well for the reactivity of B(C6F5)3 with P(tBu)3,16,17 N-heterocyclic carbenes,10 imines,18,19 and ketones/aldehydes20 as well as the Mes2P(C6F4)B(C6F5)2 system.21 Erker et al.22 currently gave new mechanistic insights that the FLPs activate by polarization owing to the electric field created by their donor/acceptor atoms. On the other hand, the rapidly growing body of experimental studies shows the importance of the balance between steric and electronic features * To whom correspondence should be addressed. Phone: +86-9918580032. Fax: +86-991-8588883. E-mail: [email protected].

to afford FLP reactivity.23 Besides steric and kinetic effects, Rokob and other authors23,24 found several reactivity-determining factors, like acidity, basicity, and stability of product are important aspects of the H2 cleavage reaction that contribute to the thermodynamic feasibility on the basis of the investigation of a series of Lewis pairs. Despite the interest of FLP reactivity, it is still a challenging subject of ongoing study, in particular the relationship of such reactivity to that of classical Lewis acid-base adducts. Some hint of this relationship is offered by the recent observation of Holschumacher10 and Rokob18 that two minima associated with the datively and weakly bound structures can be identified on the potential energy curve for the interaction between Lewis acid and base. Rokob suggested that the weakness of the dative bond reduces the energy barrier and makes the H2 cleavage reaction more exothermic. Geier and Stephan25 recently proposed the notion that classical Lewis and FLP behavior are not exclusive regimes of reactivity by investigating the system of 2,6-lutidine (Lu)/B(C6F5)3 where equilibrium governs formation of classical adduct and free Lewis pair. Therefore, classical adduct formation does not mean the loss of FLP reactivity, like the Lu/B(C6F5)3 pair. Similarly, the inability of Lewis acid-base adduct formation itself is not sufficient to allow consecutive reaction of Lewis centers with H2, like the Lu/BMe3 pair.27 On the other hand, an insight into a chemical reaction requires a proper understanding of the chemical bonding, kinetics and reactivity that associated with the reaction.26 Thus, this article is focused on the reactivity behavior with the help of DFTbased chemical descriptors along the potential energy curves for complexation of Lewis base and acid, and its influence on the H2 splitting reaction is also discussed. To assess the reactive and kinetic differences between classical Lewis adduct and FLP reactivity, the Lu/BR3 (R ) -F, -Me, -C6F5)25,27 pairs are chosen to investigate computationally. For comparison, reactions of pyridine (Py) with these Lewis acids25,27-29 are also investigated. These pairs are chosen because they include (a) the Lewis pair that acts as both classical adduct and FLP capable of H2 activation (Lu/B(C6F5)3), (b) the pair that shows no evidence of adduct formation and fails to react with H2 (Lu/ BMe3), and (c) the pairs that only form classical adducts.

10.1021/jp105000x  2010 American Chemical Society Published on Web 10/05/2010

2,6-Lutidine/BR3 and Pyridine/BR3 Lewis Pairs

J. Phys. Chem. A, Vol. 114, No. 43, 2010 11739 TABLE 1: Relative Energies of the Classical Adductsa

2. Computational Details The calculations for the present study were carried out with the Gaussian 03 packages.30 It has been shown that B3LYP underestimates the energy of the central N-B dative bonds in NR3-BX3 compounds,31 whereas the M05-2X functional developed by Zhao32 was considered to better describe noncovalent interactions. Thus, geometries of all stationary points were fully optimized at the M05-2X/6-311G(d,p) level of density functional theory (DFT). Harmonic vibrational frequencies were further calculated to confirm whether the optimized geometries correspond to minima or transition states and to obtain thermodynamic quantities, including the enthalpy and Gibbs free energy. Transition states were checked to connect the respective minima by following IRC calculations.33 The relaxed potential energy scans with respect to the N-B distance were also done at the same level. In the last two decades, a series of DFT-based global and local descriptors have been proposed to investigate the chemical reactivity and site selectivity.34 The Fukui function is one of the widely used local reactivity descriptors.34c,d It reflects the propensity of the electronic density to deform at a given position to accept or donate electrons. The condensed-to-atom Fukui functions provide information about the reactive sites in a molecule. fk+ is used to analyze the reactive site of atom k for nucleophilic attack, and fk- is used to analyze the reactive site of atom k for electrophilic attack. The maximum value on fk+ or fk- is associated with the most reactive site. They approximately can be obtained by

f+ k ) qk(N + 1) - qk(N)

(1)

fk ) qk(N) - qk(N - 1)

(2)

where qk(N), qk(N + 1), and qk(N - 1) are the electronic population of atom k evaluated on the N, (N + 1), and (N - 1) electron systems with the ground-state geometry of the Nelectron species. fB+ and fN- have been calculated as local descriptors to investigate the reactivity behavior for the Lewis acid site of the B atom and the base site of the N atom along the increasing N-B distance. Separate calculations are done for the N, (N + 1), and (N - 1) electron systems with the geometry of the N-electron species, and Mulliken population analysis is used.35 Solvation free energies were determined by single-point IEFPCM/M05-2X/6-311G(d,p)36 calculations with the UA0 radii and toluene as solvent for the gas-phase-optimized geometries. The free energy for each species in solution is taken as the sum of the gas-phase free energy and the free energy of solvation. Bader’s atom-in-molecule (AIM) theory calculations with the use of the optimized geometry were performed with the AIM2000 software.37 3. Results and Discussion 3.1. Structural and Thermodynamic Properties for Coordination. In our calculations, the differences between the electronic energies, ∆Eelec and ∆E0, the enthalpies, ∆H, and free energies, ∆G, are highly consistent (Table 1) and the trend of free energies in the gas-phase and in toluene solution is similar. Thus, we focus the following discussion on the ∆Eelec data. We examined the Lu · · · BR3 and Py · · · BR3 interactions by deriving potential energy curves (PEC) with respect to N-B distances. Furthermore, to monitor the thermodynamic feasibility of the

adducts

R

Lu-BR3 F Me C 6F 5 Py-BR3 F Me C 6F 5

dN-B

∆Eelec

∆E0

∆H

∆G

∆Gsol

1.691 1.817 1.671/1.661exp 25 1.663 1.690 1.632/1.628exp 29

-25.0 -2.4 -21.8 -28.9 -18.1 -34.9

-22.8 1.7 -18.7 -27.0 -15.1 -32.6

-23.4 0.4 -19.0 -27.3 -15.9 -32.4

-10.7 17.2 -3.6 -16.2 -0.9 -19.1

-14.9 13.3 -6.1 -20.4 -3.0 -19.7

a ∆Eelec ) electronic energies, ∆E0 ) zero-point corrected electronic energies, ∆H ) enthalpies at 298 K, ∆G ) Gibbs free energies at 298 K, and ∆Gsol ) Gibbs free energies in toluene solution (in kcal/mol). dN-B is the N-B bond length of the adduct.

Figure 1. Potential energy curves for Lu/BF3 (a) and Py/BF3 (b) interactions. RN-B is the N-B bond length; ∆E is the zero-point uncorrected electronic energy. Also shown are the profiles of local reactivity descriptors fN- and fB+.

association/dissociation reaction for Lewis acid and base, we present the thermodynamical data calculated at T ) 25 °C (Table 1). For Lu/BF3 and Py/BF3 pairs, we are able to identify covalently bound adduct as a minimum on the PEC, with N-B bond lengths of 1.69 and 1.66 Å, respectively (Figure 1). The minimum is lower in energy (∆Eelec(Lu-BF3) ) -25.0 kcal/ mol, ∆Eelec(Py-BF3) ) -28.9 kcal/mol) with respect to the two isolated molecules. The calculations predict formation of stable adducts Py-BF3 and Lu-BF3, as the formation of them is calculated to be more exothermic. The potential energy curves for Lu/BF3 and Py/BF3 pairs obtained in our calculations confirm the experimental observations that 2,6-lutidine and pyridine can form classical adducts with BF3. In analogy with Lu/BF3 and Py/BF3 pairs, for the Py/BMe3 pair only a minimum with a N-B bond distance of 1.69 Å can

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Figure 2. Potential energy curves for Lu/BMe3 (a) and Py/BMe3 (b) interactions. Also shown are the profiles of local reactivity descriptors fN- and fB+.

Figure 3. Potential energy curve for Lu/B(C6F5)3 (a) and Py/B(C6F5)3 (b) with respect to the N-B distance. Also shown are the profiles of local reactivity descriptors fN- and fB+.

be identified on the PEC (Figure 2b), which is in full agreement with experimental reports. Although the Gibbs free energy change of the formation of Py-BMe3 (∆G ) -0.9 kcal/mol) indicates only a marginally exergonic reaction, the classical adduct is likely to form because only an adduct as an equilibrium geometry has been identified on its PEC. As for Lu/BMe3 pair, although the calculation predicts formation of a stable adduct (Figure 2a, min1, RN-B ) 1.82 Å, ∆Eelec ) -2.4 kcal/mol), the relaxed potential energy scan also predicts the existence of a weakly bound complex (min2) with an association energy of ∆Eelec) -5.1 kcal/mol and N-B bond length of 3.20 Å. It is worth noting that the PEC for coordination of Lu to BMe3 is essentially flat and the second minimum is slightly more stable by 2.7 kcal/mol than that of the classical adduct, which implies that interconversion between min1 and min2 is expected to occur easily. Interestingly, the classical adduct of Lu-BMe3 is predicted to form in a thermodynamically unfavored process, as the Gibbs free energy change (∆G ) 17.2 kcal/mol) is positive at room temperature. These results firmly suggest that the mixture of 2,6-lutidine and BMe3 is unlikely to form an adduct with BMe3 but inclined to exist as a weakly bound complex Lu · · · BMe3 (min2 of Figure 2a, ∆G ) -9.6 kcal/mol), which is consistent with experimental report. A relaxed potential energy scan for the Lu/B(C6F5)3 pair with respect to the N-B distance allowed us to identify two minima at R1 ) 1.67 Å and R2 ) 3.68 Å.38 The optimized structure of min1 has a N-B bond distance in line with the experimental value (Rexp ) 1.66 Å). This is in full aggrement with previous experimental studies25 of the Lu/B(C6F5)3 pair that pointed toward the existence of an equilibrium involving the classical

adduct and free Lewis pair. Formation of the dative bond between 2,6-lutidine and B(C6F5)3 leads to a stable classical adduct, which is the obtained product of the reaction at low temperature. Although the calculations predict formation of a classical adduct Lu-B(C6F5)3 (min1 in Figure 3a), partial dissociation of this adduct in solution is very likely to occur at room temperature, as the Gibbs free energy change of ∆G ) -3.6 kcal/mol indicates only a marginally exergonic reaction. In such a case, upon heating, the Gibbs free energy change will be negative for the reverse reaction, leading to dissociation of Lu-B(C6F5)3. Then the frustrated complex Lu · · · B(C6F5)3 (min2 in Figure 3a) is available to activate H2. This confirms the experimental observation of the coexistence of classical adduct and free Lewis pair in a 1:1 mixture of 2,6-lutidine and B(C6F5)3 at 25 °C, while cooling to -10 °C, reflecting the presence of primarily classical adduct. It implies, as Rokob et al. suggested,18 that the temperature-dependent equilibrium between the classical adduct and the frustrated complex might have the possibility of exchanging their reactivity behavior. An N-B distance of 3.68 Å is detected in Lu · · · B(C6F5)3, and the N and B atoms are oriented toward in close but noncoordinative contact with each other. A hydrogen molecule can easily fit into this void and may interact with both reactive centers of the Lu/B(C6F5)3 pair. In addition, the structure of Lu · · · B(C6F5)3 reveals that N · · · B contact (E(2)LPN-LP*B ) 0.23 kcal/mol), π-π stacking, and C-H · · · F interactions are responsible for this association and give rise to an appreciable association energy of -10.0 kcal/ mol. Calculation of the molecular graph of Lu · · · B(C6F5)3 according to the AIM method39 confirms the presence of the C-H · · · F, C-F · · · N, and other weak interactions (D-X · · · A)

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TABLE 2: Electronic Energies (au) of (N + 1) and (N - 1) Electronic States for Lewis Pairs at Noninteracting Distancea pairs

R

N + BR3-

N- + BR3

N + BR3+

N+ + BR3

Lu/BR3

F Me C 6 F5 F Me C 6 F5

-651.464310 -471.501333 -2535.749839 -572.816927 -392.853950 -2457.102456

-651.547288 -471.524788 -2535.619404 -572.897458 -392.874959 -2456.969574

-650.999072 -471.1737733 -2535.301591 -572.351689 -392.526350 -2456.654209

-651.261771 -471.239271 -2535.333887 -572.586365 -392.563866 -2456.658481

Py/BR3

a

N denotes the Lewis base Lu or Py, N- and BR3- denote the (N + 1) states, and N+ and BR3+ denote the (N - 1) states.

through the presence of the (3, -1) bond critical points between the corresponding X and A atoms with electron densities Fb(r) ) 0.007 and 0.006 au, respectively, rather low but proper for weak hydrogen bonds.40 As expected, we indeed computationally identified the classical adduct Py-B(C6F5)3 with an association energy of ∆Eelec) -34.9 kcal/mol and a N-B bond length of 1.63 Å, which is in fine aggrement with the experimental value.29 Formation of Py-B(C6F5)3 is calculated to be highly exergonic (∆G ) -19.1 kcal/mol), and thus, this adduct formation irreversibly can clearly be classified as nonfrustrated, resulting in the loss of FLP reactivity. In addition, a potential energy curve with respect to the N-B distance from 2.5 to 5.0 Å was also obtained (Figure 3b). It can be seen that the interaction energy ∆E rose with increasing N-B bond length and levels off to its highest value at RN-B ) 4.25 Å. Then the energy falls and a weakly bound complex (min2) with RN-B ) 4.59 Å was obtained. The coplanarity of B(C6F5)3 and pyridine changed slightly, reaching min2 (see Figure S1, Supporting Information), which suggests that the enhanced π-π stacking is mainly responsible for this energy falling and complex formation. Moreover, the N-B bond length of the complex is much longer than that of the frustrated complex of the Lu/B(C6F5)3 pair. These results suggest the absence of a frustrated complex for FLP reactivity at RN-B ) 2.5-5.0 Å. It seems that there are two types of FLP reactivity for the simple combination of a Lewis acid and base. One is the Lewis pair possessing sufficient steric bulk, such as the (tBu)3P/ B(C6F5)3 pair. The inability of the Lewis acid-base adduct formation as a result of the steric congestion leaves the acidity and basicity unquenched and allows H2 activation. The other one is the pairs consisting of sterically less demanding substituents. The existence of an equilibrium involving the classical adduct and the frustrated complex gives the possibility of exchanging their reactivity behavior. The equilibrium can ensure that dissociation of the dative bond occurs, and the thermal dissociation provides reactive centers for bond cleavage.18 The above-mentioned N-B bond length data of adducts reveal that the length in Lu-BR3 adducts is slightly longer than that seen in the corresponding Py-BR3 adducts despite the increased basicity of 2,6-lutidine over pyridine. The reason is that the steric impact of methyl substitution of 2,6-lutidine weakens the N-B bond. It implies that Py binds tightly to the borane center and is likely to preclude further H2 activation. As Rokob et al. proposed,18 Lu/BF3, Py/BF3, and Py/BMe3 can be regarded as classical Lewis pairs that exhibit only an unhindered dative adduct, which implies the active sites are quenched for further reactivity. The other pairs show thermally induced frustration. The binding energy of -34.9 kcal/mol for the Py/B(C6F5)3 pair and relatively larger N-B bond distance of the frustrated complex (min2) would limit its reactivity for H2 activation. The Lu/B(C6F5)3 pair exhibits a datively bound minimum (min1) lying well below its frustrated complex, a relatively small binding energy of -21.8 kcal/mol compared

to Py/B(C6F5)3, and an energy cost of about 11.8 kcal/mol moving from the classsical state to the frustrated state, indicating that the H2 activation reaction takes place with the reactive frustrated pair and as a consequence lowers the H2 activation barrier and increases the exothermicity. On the contrary, for Lu/BMe3, the existence of the frustrated complex slightly increases the energy barrier by reactant-state stabilization, which may be one of the reasons for the loss of FLP reactivity. 3.2. Chemical Reactivity along the Path of Acid-Base Coordination. As the reactivity of a chemical system, like the acid-base pair in this article, toward a reactant, like H2, depends primarily on the reactivity of the most reactive center, a reasonable approximation would be to compare the nucleo-/ electrophilicity values of only the most reactive center of the system. In the studied systems, the B atom is the most reactive center (electrophilicity) that undergoes nucleophilic attack and vice versa for the N atom; thus, the condensed to B and N atoms Fukui functions along the coordination are calculated and discussed. For free A, the condensed Fukui functions of atom k of A, R (R ) +, -), can be calculated by f k,A + f k,A ) qk,A(A-) - qk,A(A)

(3)

f k,A ) qk,A(A) - qk,A(A+)

(4)

As for the AB complex at noninteracting distance, two different equations are given, depending on the dissociation of the (N + 1) and (N - 1) electronic states of AB + f k,AB ) qk,A(A- + B) - qk,A(A + B) ) qk,A(A-) qk,A(A) (5) + f k,AB ) qk,A(A + B-) - qk,A(A + B) ) qk,A(A) qk,A(A) ) 0

(6)

f k,AB ) qk,A(A + B) - qk,A(A+ + B) ) qk,A(A) -

qk,A(A+)

(7)

f k,AB ) qk,A(A + B) - qk,A(A + B+) ) qk,A(A) qk,A(A) ) 0

(8)

R R where f k,A and f k,AB denote f R of atom k of A and AB at noninteracting distance, respectively, A and B denote the isolated molecules (N state), A- and B- denote the anion ((N + 1) state), and A+ and B+ denote the cation ((N - 1) state). Table 2 represents the electronic energies of (N + 1) and (N - 1) states for Lewis complexes at noninteracting distance. For

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Figure 4. Profiles of charge for the N and B atoms with respect to the N-B distance: Lu/BR3 pairs (top) and Py/BR3 (bottom).

Lu/BR3 and Py/BR3 (R ) F, Me) pairs, the anion dissociates as Lu- (Py-) and neutral BR3 and the cation dissociates as Lu+ (Py+) and BR3, since they are the energetically favorable processes. Thus, the value of fB+ for these pairs goes to zero, and fN- reaches the isolated value. As shown in Figures 1 and 2, the last value of fN- (about 0.04) is more or less equal to that of the isolated bases Lu (fN-(Lu) ) 0.043) and Py (fN-(Py) ) 0.042); the corresponding fB+ is smaller than that of free acids BF3 (fB+(BF3) ) 0.636) and BMe3 (fB+(BMe3) ) 0.517), which are as expected. In contrast to that of the Lu/BR3 and Py/BR3 pairs (R ) F, Me), fB+ at RN-B ) 5.0 Å is more or less equal to that of free acid B(C6F5)3 for Lu/B(C6F5)3 and Py/B(C6F5)3 pairs (Figure 3), since their anions dissociates as Lu (Py) and B(C6F5)3-. For the (N - 1) state of the Lu/B(C6F5)3 pair, the dissociation products are Lu+ and B(C6F5)3; thus, fN- increases as the N-B bond increases (Figure 3a). In the case of the Py/ B(C6F5)3 pair, although the (N - 1) state dissociates as Py+ and B(C6F5)3, fN- decreases along the increasing N-B distance, due to the slightly energetic difference of the dissociated products between (Py + B(C6F5)3+) and (Py+ + B(C6F5)3). On the other hand, it has been argued that the Fukui function is not the proper descriptor for the charge-controlled hardhard interactions, which are better described by charges than Fukui functions.41,42 Thus, the variations of net charges for the N and B atoms, relative to the N-B distance, have been calculated and presented in Figure 4. Additionally, the charge variations of the Lewis pairs containing soft acid BH3 are presented in Figure 4. The N atoms of all Lewis pairs behave

in similar fashions, and the values of qN are under -0.3. Starting from its highest value, the charge qN falls to the lowest value around min1 and then increases in the process of N-B bond breaking. The same trends are observed in the soft-soft interactions of Lu/BH3 and Py/BH3 pairs. The net charge of atom B in Lu/BH3 and Py/BH3 pairs shows a monotonic increase as the N-B bond distance increases. The same trends are observed in Lu/BMe3, Py/BMe3, and Lu/B(C6F5)3 pairs, which imply they are soft-soft interactions. Thus, the Fukui function is a proper descriptor for these Lewis pairs. In the case of the hard-hard interaction of Lu/BF3 and Py/ BF3 pairs, the net charge of B atom, qB, shows decreasing values is the process of N-B bond breaking. The variation of qB for the Py/B(C6F5)3 pair, relative to the N-B distance, also shows a similar trend. Thus, the reactivity of these pairs is better explained in terms of charges, since they are charge-controlled interactions. From the variations of qB for Lu/BF3, Py/BF3, and Py/B(C6F5)3 pairs, it can be seen that the electrophilicity of atom B decreases as the process of N-B bond breaking occurs because of the decreasing of qB, which clearly suggests loss of the acid site for H2 activation in these pairs. The profiles of fN- along the N-B distance for Lu/BMe3 and Py/BMe3 pairs show a similar trend. fN- falls to much lower values at the interacting distance, revealing the loss of nuclephilicity of N atoms as N atoms are bonded with B atoms. Then, fN- increases slightly in the process of N-B bond breaking. Finally, fN- levels off to their higher value (about 0.04), where they remain roughly constant. The reactivity of atom B for these

2,6-Lutidine/BR3 and Pyridine/BR3 Lewis Pairs

J. Phys. Chem. A, Vol. 114, No. 43, 2010 11743

Figure 5. Energies and structural parameters (Angstroms) of the hydrogen activation reaction by the Lu/BMe3 (black color) and Lu/B(C6F5)3 (red color) pairs. ∆E ) zero-point uncorrected electronic energy, ∆H ) enthalpies, ∆G ) Gibbs free energies, TS ) transition state, and RX-Y) the X-Y bond distance. Lu-B denotes a classical adduct, and Lu · · · B denotes a frustrated complex. Lu · · · H2 · · · B denotes an energy minimum we obtained in the H2 activation procedure, which corresponds to the reactant side. For details, see the Supporting Information.

two pairs is low at the interacting distance because the Lewis pair reaches a near-equilibrium geometry. fB+ of the Lu/BMe3 pair is the maximum at a N-B distance of 2.75 and 4.0 Å, respectively, which then decreases around min2. Although the N atom is highly reactive around min2, the B atom has a negative fB+ value along the N-B distance. It implies that the Lewis acid site has much less reactivity when dissociating the dative N-B bond, resulting in precluding H2 activation. The negative value of fB+ (Figure 2b) along the N-B distance for the Py/BMe3 pair also suggests loss of H2 activation. Figure 3a shows the profiles of fN- and fB+ for the Lu/B(C6F5)3 pair. Atoms N and B are the least reactive centers at min1 on formation of a dative bond, and the values of fN- and fB+ increase as the N-B bond distance increases. It should be noted that fNincreases rapidly from 3.0 Å to min2 (0.036-0.17), implying that atom N is the most favorable active center around min2. Similarly, atom B reveals a significant increase in the fB+ value after min1 and then increases slowly after min2. It is further shown that fN- and fB+ values around min2 of the Lu/B(C6F5)3 pair are much larger than that of the Lu/BMe3 pair. Thus, the N and B atoms of the equilibrium geometry min2 for the Lu/ B(C6F5)3 pair are suggested as the favorable acidic and basic centers for dihydrogen activation. 3.3. Reaction of Dihydrogen Cleavage. The results have shown that the potential energy curves of the Lu/BMe3 and Lu/ B(C6F5)3 pairs displayed two minima associated with the datively and weakly bound structures. Destabilization of the “frustrated complex” for the Lu/B(C6F5)3 pair reduces the energy barrier and increases the exothermicity of the H2 cleavage reaction.18 However, the Lu/BMe3 pair exhibits a datively bound minimum lying slightly above its frustrated complex form (Figure 2a) and much less reactive Lewis sites, which might be the reasons for its unreactivity. In order to gain deeper insight into the reactive difference between the Lu/ BMe3 and the Lu/B(C6F5)3 pairs, we obtained their H2 cleavage reaction path. In analogy to the reaction pathway theoretically derived for the heterolytic cleavage of H2 with (tBu)3P/B(C6F5)316 and NHC/B(C6F5)3,10 we are also able to locate a transition state (TS) of the Lu/B(C6F5)3 pair associated with the H-H bond cleavage (Figure S5, Supporting Information), which lies only 3.5 kcal/mol in energy above the frustrated complex Lu · · · B(C6F5)3 and H2. Cleavage of the H-H bond is

an exothermic process and yields the ion pair [2,6Me2C5H3NH]+[HB(C6F5)3]- ([LuH]+[HB(C6F5)3]-). Because of the absence of packing forces, the optimized structure of [LuH]+[HB(C6F5)3]- is not fully consistent with the X-ray data in that the NH and BH bonds are not oriented toward each other. However, it is worth noting that the π-π stacking between Lu and the pentafluorophenyl part is maintained in the optimized structures of the TS and the two corresponding minima as well as the frustrated complex Lu · · · B(C6F5)3, implying that the TS we located still describes an essentially direct route from Lu · · · B(C6F5)3 + H2 to the [LuH]+[HB(C6F5)3]- product. The H2 molecule can easily dissociate from the minimum Lu · · · H2 · · · B(C6F5)3 as the estimated energy barrier is only 6.5 kcal/mol, Figure 5. By comparison, the Lu/BMe3 pair reacting with H2 represents a larger barrier, lying 18.1 kcal/mol above the minimum of Lu · · · H2 · · · BMe3, and the process for H2 activation is thermodynamically unfeasible as ∆G ) 25.8 kcal/ mol. It is in line with experimental observation that there is no evidence for H2 activation of the Lu/BMe3 pair, although the pair exists as a free Lewis pair. Full cleavage of the H-H bond and formation of [LuH]+[HB(C6F5)3]- is predicted to be exothermic (∆E ) -29.8 kcal/mol) relative to the free Lu, B(C6F5)3, and H2. In comparison with the energy calculated for formation of [NHCH]+ [HB(C6F5)3]- from NHC, B(C6F5)3, and H2 (∆E ) -60.7 kcal/mol and ∆G ) -31.1 kcal/mol, respectively), it is obvious that the marginal exergonic nature of the former reaction (∆G ) -3.3 kcal/mol) probably is the reason for its reversible dihydrogen activation. It suggested that the inability of dihydrogen cleavage by Lu/ BMe3 is characterized by the high energy barrier and the thermodynamic unfeasibility of the reaction. To address the factors that contribute to the thermodynamic feasibility of the H2 cleavage reaction, we provide the reaction in the cycle of several steps. The partitioned reactions together with their values of ∆H and ∆G are compiled in Table 3. The calculated data suggest that the Lu/BMe3 pair has a more favorable adduct dissociation free energy (-17.22 kcal/mol) than Lu/B(C6F5)3 pair (3.64 kcal/ mol) to obtain an exergonic hydrogenation process. However, the major contribution to the overall reaction free energy is the much higher hydride affinity of B(C6F5)3 than that of BMe3. It

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TABLE 3: Enthalpy Change, ∆H, and Gibbs Free Energy Change, ∆G, for the Separated Reactions and the Overall Hydrogenation Reaction Lu/BMe3 ∆H

∆G

Lu/B(C6F5)3 ∆H

∆G

H2 f H + + H +412.70 +406.46 Lu-B f Lu + B -0.40 -17.22 +18.96 +3.64 Lu + H+ f LuH+ -230.57 -223.54 H + B f HB -66.10 -56.43 -128.88 -122.51 LuH+ + -HB f [LuH] + [HB]- -98.55 -87.68 -75.17 -63.71 Lu-B + H2 f [LuH]+[HB]17.07 21.59 -2.97 0.34

SCHEME 1: Reactivity of 2,6-Lutidine/BR3 and Pyridine/BR3 Lewis Pairs

implies that the acidity of the acceptor center plays an essential role in determining the thermodynamic feasibility of H2 activition. 4. Conclusions We carried out a series of DFT calculations to investigate the reactivity of the 2,6-lutidine/BR3 and pyridine/BR3 Lewis pairs, Scheme 1. The results show that the existence of the frustrated complex on the potential energy profile, much larger reactivity of the Lewis acid and base centers in the frustrated pair, and proper thermodynamic and kinetic properties are necessary to ensure H-H bond cleavage. The importance of the Lewis acidity to achieve the thermodynamic feasibility of H2 activition is also pointed out. Contrary to the Lu/B(C6F5)3 pair, the inability of H2 cleavage by the Lu/BMe3 pair is characterized by the stability of the frustrated complex, the lower reactivity of reactive sites, and the instability of the product (ion pair) as well as the high energy barrier of the dihydrogen cleavage reaction. Acknowledgment. We thank the National Natural Science Foundation of China (Grants 20866009 and 21062020) and the Natural Science Foundation of Xinjiang Uygur Autonomous region (Grant 2010211B06) for financial support. Yong Guo is acknowledged for fruitful discussions. Supporting Information Available: Geometry changes of Py/B(C6F5)3 pair with the N-B bond length R ranging from 4.00 to 4.75 Å, atom-condensed Fukui functions calculated by natural population analysis, and optimized structures of the transition state and two corresponding minima for dihydrogen activation by 2,6-lutidine/B(C6F5)3 and 2,6-lutidine/BMe3 pairs. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Welch, G. C.; Juan, R. R. S.; Masuda, J. D.; Stephan, D. W. Science 2006, 314, 1124. (2) Welch, G. C.; Stephan, D. W. J. Am. Chem. Soc. 2007, 129, 1880. (3) Ullich, M.; Lough, A. J.; Stephan, D. W. J. Am. Chem. Soc. 2009, 131, 52. (4) Stephan, D. W. Org. Biomol. Chem. 2008, 6, 1535. (5) Spies, P.; Erker, G.; Kehr, G.; Bergander, K.; Fro¨hlich, R.; Grimme, S.; Stephan, D. W. Chem.Commun. 2007, 5072.

(6) Chase, P. A.; Jurca, T.; Stephan, D. W. Chem. Commun. 2008, 1701. (7) Chase, P. A.; Welch, G. C.; Jurca, T.; Stephan, D. W. Angew. Chem., Int. Ed. 2007, 46, 8050. (8) Sumerin, V.; Schulz, F.; Nieger, M.; Leskela¨, M.; Repo, T.; Rieger, B. Angew. Chem., Int. Ed. 2008, 47, 6001. (9) Chase, P. A.; Stephan, D. W. Angew. Chem., Int. Ed. 2008, 47, 7433. (10) Holschumacher, D.; Bannenberg, T.; Hrib, C. G.; Jones, P. G.; Tamm, M. Angew. Chem., Int. Ed. 2008, 47, 7428. (11) Chen, D.; Klankermayer, J. Chem. Commun. 2008, 2130. (12) Spies, P.; Schwendemann, S.; Lange, S.; Kehr, G.; Fro¨hlich, R.; Erker, G. Angew. Chem., Int. Ed. 2008, 47, 7543. (13) Wang, H.; Fro¨hlich, R.; Kehr, G.; Erker, G. Chem. Commun. 2008, 5966. (14) McCahill, J. S. J.; Welch, G. C.; Stephan, D. W. Angew. Chem., Int. Ed. 2007, 46, 4968. (15) Otten, E.; Neu, R. C.; Stephan, D. W. J. Am. Chem. Soc. 2009, 131, 9918. (16) Rokob, T. A.; Hamza, A.; Stirling, A.; Soo´s, T.; Pa´pai, I. Angew. Chem., Int. Ed. 2008, 47, 2435. (17) Stirling, A.; Hamza, A.; Rokob, T. A.; Pa´pai, I. Chem. Commun. 2008, 3148. (18) Rokob, T. A.; Hamza, A.; Stirling, A.; Pa´pai, I. J. Am. Chem. Soc. 2009, 131, 2029. (19) Privalov, T. Eur. J. Inorg. Chem. 2009, 2229. (20) Nyhle´n, J.; Privalov, T. Dalton Trans. 2009, 5780. (21) Guo, Y.; Li, S. H. Inorg. Chem. 2008, 47, 6212. (22) Grimme, S.; Kruse, H.; Goerigk, L.; Erker, G. Angew. Chem., Int. Ed. 2010, 49, 1402. (23) Rokob, T. A.; Hamza, A.; Pa´pai, I. J. Am. Chem. Soc. 2009, 131, 10701, and references therein. (24) Gao, S.; Wu, W.; Mo, Y. J. Phys. Chem. A 2009, 113, 8108. (25) Geier, S. J.; Stephan, D. W. J. Am. Chem. Soc. 2009, 131, 3476. (26) Chattaraj, P. K.; Roy, D. R. J. Phys. Chem. A 2006, 110, 11401. (27) Brown, H. C.; Schlesinger, H. I.; Cardon, S. Z. J. Am. Chem. Soc. 1942, 64, 325. (28) Piers, W. E. AdV. Organomet. Chem. 2004, 52, 1. (29) Focante, F.; Mercandelli, P.; Sironi, A.; Resconi, L. Coord. Chem. ReV. 2006, 250, 170. (30) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision E.01; Gaussian, Inc.: Wallingford, CT, 2004. (31) Gilbert, T. M. J. Phys. Chem. A 2004, 108, 2550. (32) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157. For the M05-2X functional, see: (a) Zhao, Y.; Schultz, N. E.; Truhlar, D. G. J. Chem. Theory Comput. 2006, 2, 364. (b) Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008, 41, 157. (33) In order to locate the TS, we first carried out IRC calculations from the TS in both the forward and the reverse directions and then performed subsequent geometry optimizations to locate the two minima. (34) Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. ReV. 2006, 106, 2065. Geerlings, P.; de Proft, F.; Langenaeker, W. Chem. ReV. 2003, 103, 1793. For the descriptors of chemical reactivity, see: (a) Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512. (b) Parr, R. G.; von Szentpaly, L.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922. (c) Parr, R. G.; Yang, W. J. Am. Chem. Soc. 1984, 106, 4049. (d) Yang, W.; Mortier, W. J. J. Am. Chem. Soc. 1986, 108, 5708. (e) Ghosh, S. K.; Berkowitz, M. J. Chem. Phys. 1985, 83, 2976. (f) Chattaraj, P. K.; Maiti, B.; Sarkar, U. J. Phys. Chem. A 2003, 107, 4973. (g) Roy, R. K.; Krishnamurti, S.; Geerlings, P.; Pal, S. J. Phys. Chem. A 1998, 102, 3746. (h) Parthasarathi, R.; Padmanabhan, J.; Elango, M.; Subramanian, V.; Chattaraj, P. K. Chem. Phys. Lett. 2004, 394, 225. (i) Morell, C.; Grand, A.; Toro-Labbe´, A. J. Phys. Chem. A 2005, 109, 205. (j) Padmanabhan, J.; Parthasarathi, R.; Elango, M.; Subramanian, V.; Krishnamoorthy, B. S.; GutierrezOliva, S.; Toro-Labbe´, A.; Roy, D. R.; Chattaraj, P. K. J. Phys. Chem. A 2007, 111, 9130. (35) Natural population analysis is also used to calculate fk+ and fk-, see Supporting Information.

2,6-Lutidine/BR3 and Pyridine/BR3 Lewis Pairs (36) Tomasi, J.; Mennucci, B.; Cance`s, E. THEOCHEM 1999, 464, 211. (37) Biegler-Ko¨nig, F. AIM2000; University of Applied Sciences: Bielefeld, Germany, 2001. (38) Recently, Stephan and co-workers theoretically studied the Lu/ B(C6F5)3 pair. An optimization of the structure of the adduct obtained from experiment at the HF/3-21G level gave a structure with R ) 3.5 Å, and using the ONIOM(MPW1K) approach and a starting structure with R ) 1.6 Å gave a more reasonable structure with a N-B distance of 1.653 Å. The “weakly interacting” complex optimized to the structure with N-B distances of 3.4 (HF/3-21G) and >5.6 Å (ONIOM), respectively. For details,

J. Phys. Chem. A, Vol. 114, No. 43, 2010 11745 see: Geier, S. J.; Gille, A. L.; Gilbert, T. M.; Stephan, D. W. Inorg. Chem. 2009, 48, 10466. (39) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: New York, 1990. (40) Koch, U.; Popelier, P. L. A. J. Phys. Chem. 1995, 99, 9747. (41) Chattaraj, P. K. J. Phys. Chem. 2001, 105, 511. (42) Melin, J.; Aparicio, F.; Subramanian, V.; Galva´n, M.; Chattaraj, P. K. J. Phys. Chem. 2004, 108, 2487.

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