Analysis of the Activation and Heterolytic Dissociation of H2 by

Jun 4, 2012 - Frustrated Lewis Pairs: NH3/BX3 (X = H, F, and Cl) ... and Tom Autrey ... heterolytic dissociation promoted by prototype Lewis acid/base...
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Analysis of the Activation and Heterolytic Dissociation of H2 by Frustrated Lewis Pairs: NH3/BX3 (X = H, F, and Cl) Donald M. Camaioni,* Bojana Ginovska-Pangovska, Gregory K. Schenter, Shawn M. Kathmann, and Tom Autrey Chemical and Materials Science Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, Washington 99352, United States S Supporting Information *

ABSTRACT: We performed a computational study of H2 activation and heterolytic dissociation promoted by prototype Lewis acid/base pairs NH3/BX3 (X = H, F, and Cl) to understand the mechanism in frustrated Lewis pairs (FLPs). Although the NH3/BX3 pairs form strong dative bonds, electronic structure theories make it possible to explore the potential energy surface away from the dative complex, in regions relevant to H2 activation in FLPs. A weakly bound precursor complex, H3N·H2·BX3, was found in which the H2 molecule interacts side-on with B and end-on with N. The BX3 group is pyramidal in the case of X = H, similar to the geometry of BH5, but planar in the complexes with X = F and Cl. The latter complexes convert to ion pairs, [NH4+][BHX3−] with enthalpy changes of 7.3 and −9.4 kcal/mol, respectively. The minimum energy paths between the FLP and the product ion pair of the chloro and fluoro complexes were calculated and analyzed in great detail. At the transition state (TS), the H2 bond is weakened and the BX3 moiety has undergone significant pyramidal distortion. As such, the FLP is prepared to accept the incipient proton and hydride ion on the product-side. The interaction energy of the H2 with the acid/base pair and the different contributions for the precursor and TS complex from an energy decomposition analysis expose the dominant factors affecting the reactivity. We find that structural reorganization of the precursor complex plays a significant role in the activation and that charge-transfer interactions are the dominant stabilizing force in the activated complex. The electric field clearly has a role in polarizing H2, but its contribution to the overall interaction energy is small compared to that from the overlap of the pN, σH−H, σ*H−H, and pB orbitals at the TS. Our detailed analysis of the interaction of H2 with the FLP provides insight into the important components that should be taken into account when designing related systems to activate H2.

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INTRODUCTION The activation of hydrogen and small molecules in catalytic transformations for energy storage and utilization is a topic of great interest.1 Metals are typically used as catalysts in H2 activation,2 though the discovery of the activation of H2 by nonmetal containing frustrated Lewis acid−base pairs (FLPs) by Stephan and co-workers, sparked the field of metal-free catalysis using main group organic-based molecules.3−6 The availability of nontransition metal catalysts opens new opportunities for the development of catalytic processes that could provide both economical and environmental advantages. The FLPs of B(C6F5)3 with bulky tertiary phosphines, first studied by Stephan et al.,7 have received much attention,8−12 as have the FLPs of amines (B/N)13−18 and carbenes (B/C).19,20 While many FLPs have been found to efficiently cleave the H2 bond, the mechanistic details of H2 activation have not been fully elucidated.21 Several groups have advanced the theoretical characterization of the mechanism with much of the effort focused on B/P systems,8−10,12,22,23 not withstanding the work of Summerin et al.,13,14 Guo et al.,16 and, most recently, Erős et al.24 on B/N systems. Rokob et al.25 have rationalized the © XXXX American Chemical Society

reactivity in thermodynamic terms taking into account the acid−base strengths of the Lewis pairs. The reactions are thought to proceed by insertion of H2 into a reactive pocket, held together by dispersive forces between the Lewis acid and Lewis base.9 Once in the pocket, the H2 dissociates with little or no barrier to form the protonated baseborohydride ion pair. Papai and co-workers9,24 have emphasized the role of cooperative orbital interactions in rationalizing such a mechanism. In their analysis, the barrier for activation involves polarizing the H 2 molecule via simultaneous interaction of the hydrogen orbitals with the filled and unfilled orbitals of the FLP. The barrier to activation is then associated with overcoming steric/repulsive forces to maximize these interactions, which are favorable to the formation of the products. However, Grimme et al.8,26 emphasized that there is no need to consider the involvement of FLP/H2 orbitals in the activation. They proposed a simple model in which the electric Received: April 25, 2012 Revised: June 3, 2012

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Figure 1. Minimum energy path for reaction 1, X = Cl, calculated at B3LYP-D/DZVP2; electronic energies in kcal/mol with single-point G3(MP2)B3LYP//B3LYP-D/DZVP2 electronic energies in parentheses.

field generated in the pocket of the FLP lowers the barrier for dissociation of the H2 molecule. Here, we report a detailed study of the activation and dissociation of H2 in the prototype system comprised of ammonia and BX3 (X = H, F, and Cl) compounds.

energies, enthalpies, and free energies of the optimized structures were determined from frequency calculations using the harmonic oscillator-rigid-rotor approximation with entropies corrected for rotational symmetry number.34 Minimum energy geometries were confirmed to be bound states by the absence of imaginary frequencies, and TSs were validated by the presence of one imaginary frequency. The energies of B3LYP-D/DZVP2 structures were calculated at the G3(MP2)B3LYP35 level of theory in Gaussian98. We refer to these energies as G3(MP2)B3LYP//B3LYP/DZVP2. The protocol was as follows: a frequency calculation was performed at the B3LYP/6-31G* level to generate a checkpoint file from which the G3(MP2)B3LYP calculation was started using the G3MP2B3(startMP2) keyword. Calculations were also carried out at the CCSD(T) level of theory and compared to the G3(MP2)B3LYP results. The MEP for activation of H2 by NH3 and BCl3 was calculated using the DirDyVTST; Direct Dynamics for Variational Transition State Theory interface to NWChem.36 This reaction path, shown in Figure 1, was calculated using the corrected local quadratic approximation (CLQA) Page-McIver integrator37 with a step size of 0.005 a.u., and the Hessian was recalculated every fourth step. The natural bond orbital (NBO) analysis was performed using the NBO 5.0 package38 using the default input provided by NWChem. We calculated the influence of the electric field that the acid/base pair imposes on H2 along the MEP, by embedding the H2 system in the Hartree potential (VH)39 of the Lewis acid/base pair, using a development version of NWChem.40 To build the Hartree potential for NH3/BCl3, the full system was divided into two fragments (NH3/BCl3 and H2) using the Bader’s approach.41 This method uses the electronic charge density of the atoms to identify the so-called zero-flux surfaces, where the charge density perpendicular to the surface is a minimum. The H2 fragment was removed from the total density grid of the full system, and the Hartree potential was calculated from the charge density of the NH3/BCl3 fragment. The field produced by the NH3/BCl3 pair, as well as the dissociation barriers for H2 in fields of different strengths, were calculated with Gaussian98. Energy decomposition analysis was done using the LMOEDA42 approach implemented in GAMESS and the B3LYP-D/DZVP2 level of theory. Images of molecular structures and orbitals were generated with MacMolPlt.43

H3N·BX3 + H 2 → H3N· H 2 · BX3 → [NH4 +][BHX3−] (1)

Although the dative-bonded complex on the left-hand side of reaction 1 lacks the frustration usually required for facile activation of H2, it is possible to explore the potential energy surface (PES) away from the dative complex using electronic structure theory. Thus, we explored how the interaction between H2 and the Lewis pairs evolve on the minimum energy path (MEP) between the latter complexes in eq 1. We used a combination of methods (vibrational, NBO, and Mayer bond analyses) to characterize bond making and bond breaking along the path. Furthermore, we examined the electric field created by the acid/base pair as a function of the reaction coordinate and performed energy decomposition analyses of interactions in the NH3·H2·BCl3 precursor and transition state (TS) complex to show the relative contributions of electrostatic, dispersion, and charge transfer components. We find that activation of H2 is accompanied by significant structural reorganization about the B atom and that polarization or charge-transfer interactions are the dominant stabilizing force in the activated complex. The electric field clearly plays a role in polarizing H2, but its contribution to the overall interaction energy is small compared to the orbital interactions that ultimately lead to product formation. Similar analyses applied to real FLPs will clearly elucidate the role of orbital interaction and electric field in the activation of H 2, and allow determination of whether orbital interactions should be considered in designing new FLPs.

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COMPUTATIONAL METHODS

We used the NWChem,27 GAMESS,28 and Gaussian29 computational chemistry programs for electronic structure calculations. Minimum energy structures were optimized using dispersion-corrected30 density functional theory31 (DFT-D), the B3LYP functional,32 and the DZVP2 basis set.33 Zero-point B

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RESULTS AND DISCUSSION We studied the mechanism of H2 activation in prototype Lewis pairs: NH3·BX3 (X = H, F, and Cl). The results for X = H show that the [NH4+][BH4−] ion pair is not stable in the gas phase. All attempts to minimize the preformed ion pairs resulted in proton transfer to form the complex, H3N·H2·BH3. In a similar study of this system, Pyykkö and Wang showed that a cluster of 4 ion pairs is needed to stabilize the ions.44 However, our calculations show that the ion pairs for X = F and Cl may exist in the gas phase, stabilized by Coulombic attraction, along with formation of H3N−H···X−BHX2 hydrogen bonds. There is a barrier to reaction that separates the ion pair from the bonded and frustrated Lewis pairs. In addition to the minima, we located the TS structures, and for X = Cl, we calculated the MEP from the precursor complex to the ion pair successor complex. The reaction for X = F is endothermic, and while less relevant to the process of H2 activation, it is interesting to compare with X = H, which has a similar hydride affinity but does not activate H2, and with X = Cl, which has a greater hydride affinity.45 In the subsections below, we provide structural and thermochemical data for species involved in reaction 1, as well as a detailed analysis of the MEP for the X = Cl system (Figure 1). NH3 Adducts of BX3. The binding enthalpies for NH3 to BX3, calculated at various levels of theory are provided in Table 1. The levels include our baseline method, B3LYP-D/DZVP2,

DZVP2 values in Table 1 differ by 0.1 and 0.6 kcal/mol from these values. Thus, we trust this variant of the G3 method to produce chemically accurate energies for these system. Interaction of H2 with BX3 and NH3 with H2·BX3. The structures of these complexes optimized at the B3LYP-D/ DZVP2 level of theory are shown Figure 2. In the structure of

Table 1. Dative Bond Enthalpies in kcal/mol at 298 K

NH3BX3

G3(MP2) B3LYP// B3LYP-D/ DZVP2

B3LYPD/ DZVP2

B3LYP-D/augcc-pVTZ// B3LYP-D/ DZVP2

MP2/aug-ccpVTZ// B3LYP-D/ DZVP2

NH3BH3 NH3BF3 NH3BCl3

27.6 19.5 24.2

27.4 24.3 23.0

27.0 19.2 21.2

29.6 23.0 29.2

Figure 2. Structures of H2·BX3 and NH3·H2·BX3 complexes: (a) X = H, (b) F, and (c) Cl; distances in Å.

H2·BX3, H2 interacts with BCl3 and BF3 in a fashion similar to the interaction of H2 with BH3,49 although with less distortion of the BX3 fragment. Ammonia interacts with the H2·BX3 complexes by forming a hydrogen bond to one end of the H2 molecule. An analogous precursor complex has been calculated for the 2,6-lutidine/B(C6F5)3 FLP.16,18 In the structure with X = Cl (Figure 2c), the N···H(H) distance is 2.49 Å, the N−H− H angle is nearly linear at 171°. The H−H−B angle is 82°. The H−H distance at 0.747 Å is similar to the 0.745 Å found in an isolated H2. The BCl3 moiety is planar, and the B···H distance is 2.93 Å. The structure for the H3N·H2·BCl3 precursor complex at the B3LYP-D/DZVP2 level is also shown in the top left of Figure 1. The structure of the NH3·H2·BF3 precursor complex is similar to NH3·H2·BCl3, with the N···H distance of 2.46 Å, H− H distance of 0.75 Å, and B···H distance of 2.57 Å. The N···H− H angle is nearly linear at 165°, and the H−H···B angle is 78°. The BF3 moiety is nearly planar, with a dihedral angle F−B− F−F of 175°. The NH3·H2·BH3 pair has an elongated H−H bond of 0.82 Å and N−H and B−H bonds of 2.0 Å and 1.48 Å, respectively. Although the bond lengths are significantly different from the structures where X = F or Cl, the angles are similar (N···H−H is 163° and B···H−H is 79°). Unlike the BCl3 and BF3 moieties that are nearly planar, the BH3 moiety is more distorted with a dihedral angle H−B−H−H of 143°. Very similar structures were found using the MP2 theory; however, the aug-cc-pVTZ basis set was needed to obtain a minimum energy structure for the NH3·H2·BCl3 complex. We used the G3(MP2)B3LYP//B3LYP-D/DZVP2 method to calculate the enthalpies tabulated in Table 2.

which we used to optimize the geometries, and single-point calculations on these geometries at B3LYP-D/aug-cc-pVTZ, MP2/aug-cc-pVTZ, and G3(MP2)B3LYP. The results for NH3BH3 may be compared to the previously reported result of 27.7 kcal/mol at the CCSD(T)/CBS.46 The agreement between different levels of theory is excellent in this case. The MP2 value overestimates the binding enthalpy by ∼2 kcal/mol, suggesting the need for higher level treatment of correlation and basis set effects such as provided by the G3(MP2) and G3(MP2)B3LYP methodologies. Literature values are 27.7 and 27.6 kcal/mol,47 respectively. We also obtain the value of 27.6 kcal/mol when using the G3(MP2)B3LYP method, starting from the B3LYP-D/DZVP2 geometry (see Table 1). Additional comparison of these methods for calculating binding enthalpies of BH3 with Lewis bases of N, O, P, S, and As are available in ref 47, and binding enthalpies of BH3 with Lewis bases of alkylated borane amines are reported in ref 46. For the NH3BF3 and NH3BCl3, there is more variability between the levels of theory. As with NH3BH3, the MP2 theory overestimates the binding enthalpy relative to the G3(MP2)B3LYP//B3LYP-D// DZVP2. Single-point B3LYP-D/aug-cc-pVTZ calculations gave smaller binding enthalpies by ∼2 kcal/mol. Accurate calculations have been performed by Plumley and Evanseck at the QCISD(T)/aug-cc-pVQZ//MP2/6-311++G(3df,2p) level of theory.48 They reported values of 19.6 (X = F) and 23.8 (X = Cl) kcal/mol. The G3(MP2)B3LYP//B3LYP-D// C

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shortened to 1.64 and 1.74 Å, respectively. Although we find the barrier calculated by the G3(MP2)B3LYP//B3LYP-D/ DZVP2 and CCSD(T)/6-311+G(2d,2p)//B3LYP-D/DZVP2 theories to be higher and the reaction less exothermic compared to the B3LYP-D/DZVP2 theory (Table 3), the position of the TS is shifted only slightly toward products along the intrinsic reaction coordinate (IRC) shown in Figure 1, to s = 0.28 Å, where the structure has rH−H = 0.86 Å, rB−H = 1.49 Å, and rN−H = 1.59 Å (see Tables S5 and S6, Supporting Information). The B−H and N−H bonds, incipient in the TS, continue to form on the product side of the barrier to give rise to ion pairs stabilized by hydrogen bonds. The first-formed ion pair (see Figure 1) has two hydrogen bonds of the type N− H···Cl−B and resides in a shallow minimum. The global minimum for the ion pair has three hydrogen bonds such that the proton and hydride are farthest apart and noninteracting. For X = Cl, it is 7.3 kcal/mol below the precursor complex and 17.1 kcal/mol above the NH3BCl3·H2 pair (bottom left in Figure 1). We also calculated the barrier for H2 heterolysis in NH3·H2·BCl3 by forcing C3 symmetry at the stationary points to constrain the N, H2, and B atoms to be linear. This constraint maximizes the distance between the chlorine atoms and N-hydrogens and minimizes the Coulombic attraction between them. Thus, the importance of these interactions may be inferred by comparison with the nonlinear system. The TS for heterolytic scission (maximum energy) of the C3 structure was found with an H−H distance (0.84 Å) that is longer and B···H and N···H distances (1.49 and 1.57 Å, respectively) that are shorter than the TS with nonlinear N, H2, and B atoms, suggesting that the linear TS is more product-like than the nonlinear TS. The C3 precursor and TS complexes are destabilized by 0.5 and 5.7 kcal/mol, respectively, at the G3(MP2)B3//B3LYP-D/DZVP2 level, which shows that the interactions between Cl and N−H are more important in the TS than in the reactant complex indicative of the TS being relatively more polarized. In the TS complex with X = F, the H−H distance is 0.96 Å, and the B···H∂− and N···H∂+ distances are 1.40 Å and 1.36 Å, respectively. The only stable form of the ion pair [NH4+][HBF3−] has three H···F hydrogen bonds such that the B−H bond points away from the NH4+ ion. Two of these bonds have a distance of 1.71 Å, and one is 2.40 Å long. The barrier is ∼19 kcal/mol at the G3(MP2)B3LYP//B3LYP-D/DZVP2 level (Table 3). The structure corresponds to a late TS, i.e., more similar to the product geometry. For this reaction, B3LYP-D/ DZVP2 significantly underestimated both the barrier and the reaction energy in part due to basis set incompleteness.50 As mentioned earlier and reported by Pyykkö and Wang,44 the reaction of H3N·H2·BH3 does not give a stable ion pair, [NH4+][BH4−]. Given that the hydride affinities of BF3 and BH3 are essentially the same,45 the interaction of NH4+ with HBF3− must be more stabilizing than the interaction with BH4−. The NBO natural charge analysis of HBF3−, shows a charge of −0.63 on each of the F atoms, and a charge of +1.10 on B. The charges on NH4+ are +0.48 on all H atoms and −0.90 on N. In BH4−, the charge is strongly localized on B, with a charge of −0.70, and small charges of −0.10 on the hydrogen atoms. Therefore, we conclude that the electrostatic stabilization of the [NH4+][BHX3−] ion pair is greater for X = F compared to X = H due to the greater negative charge on the F atoms.

Table 2. Enthalpies to Form H2·BX3 and NH3·H2·BX3 Complexes from the Moleculesa X

H2 + BX3 → H2·BX3, ΔH°298 (kcal/mol)

NH3 + H2 + BX3 → H2·BX3, ΔH°298 (kcal/mol)

H F Cl

−1.4 (−3.0) +0.8 (+0.5) +0.5 (+0.3)

−4.2 (−7.9) −0.2 (−3.3) −0.1 (−1.1)

a

G3(MP2)B3LYP//B3LYP-D/DZVP2; B3LYP-D/DZVP2 values in parentheses.

The H3N·H2·BCl3 complex (Figure 2c) resides in a shallow minimum (−0.1 kcal/mol at the G3(MP2)B3LYP//B3LYP-D/ DZVP2 level) on the MEP (Figure 1). As such, the structure is a precursor to heterolytic splitting of H2, and therefore, we refer to it as the precursor complex in the subsequent text. Similar to BCl3, the enthalpy to form NH3·H2·BF3 is −0.2 kcal/mol and for NH3·H2·BH3 is −4.2 kcal/mol. The H2·BX3 complexes with X = F and Cl have positive enthalpies for their formation at T = 298 K, showing that the complexes are less stable than the separated molecules. However, the interaction of H2·BX3 with NH3 is stabilizing, such that the formation of the precursor complexes (NH3·H2·BX3) is exothermic for X = H and thermoneutral for X = F and Cl. Heterolytic Scission of H2 in the H3N·H2·BX3 Complex. Barriers and enthalpies for heterolytic scission of H2 in the H3N·H2·BX3 complexes with X = F and Cl are listed in Table 3. Table 3. Enthalpies for Activation and Heterolytic Dissociation of H2 in NH3·H2·BX3 Complexesa X

NH3·H2·BX3 → [NH3·H2·BX3]‡, ΔH‡298 (kcal/mol)

NH3·H2·BX3 → [NH4+][HBX3−], ΔH°298 (kcal/mol)

F Cl

18.9 (9.2) 13.5 (8.3)

9.4 (1.3) −7.3 (−10.7)

a

G3(MP2)B3LYP//B3LYP-D/DZVP2; B3LYP-D/DZVP2 values in parentheses.

They were calculated using the G3(MP2)B3LYP//B3LYP-D/ DZVP2 and B3LYP-D/DZVP2 levels of theory. Single-point calculations at B3LYP-D/aug-cc-pVTZ//B3LYP-D/DZVP2 and MP2/aug-cc-pVTZ//B3LYP-D/DZVP2 theories maybe found in Table S1, Supporting Information. Generally, they obtain intermediate values. In the case of X = F, barriers and reaction energies calculated with the aug-cc-pVTZ basis set are closer to the G3(MP2)B3LYP//B3LYP-D/DZVP2 values. In the case of X = Cl, the barrier, but not the reaction energy, is closer. The most stable structures for the product ion pairs, [NH4+][HBX3−], have 3 hydrogen bonds such that the N−H and B−H bonds are pointing away from each other. At the G3(MP2)B3LYP//B3LYP-D/DZVP2 level, scission to this structure is 9.4 kcal/mol endothermic for H3N·H2·BF3 and 7.3 kcal/mol exothermic for H3N·H2·BCl3. The difference is similar to the difference in hydride affinities of BF3 (72.7 kcal/mol) and BCl3 (93 kcal/mol).45 At the B3LYP-D/DZVP2 level of theory, the barriers are lower and reaction energies are more favorable. Below, we describe the transition states and product ion pairs for X = Cl. The results for X = F are subsequently presented and discussed with respect to the system with X = Cl. The structure of the TS for X = Cl is shown in Figure 1 (top center). The H−H distance is stretched to 0.81 Å. The BCl3 group is pyramidal, and the B···Hδ− and N···Hδ+ distances have D

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Analysis of the MEP in the TS Region for NH3·H2·BCl3. In this section, we present and discuss analyses of the geometries along the reaction path for activation and heterolytic scission of H2. The analyses described include vibrational, natural bond orbital (NBO), Mayer bond order, and electric field analyses. Our purpose is to characterize the changes in these properties that accompany/facilitate the change from molecular complex to ion pair. This change occurs roughly in the range −1 ≤ s ≤ 1, where s is the intrinsic reaction coordinate (see Figure 1). While our focus is mainly on the system with X = Cl, at times we will make comparisons to the system with X = F to show the effect of the substituent on the course of the reaction. The results are presented below. Vibrational Analysis. We calculated the vibrational frequencies along the MEP and estimated the adiabatic barrier for the reaction by adding the zero-point correction to the potential energy. The imaginary (unbound) mode of the DFTD TS is small at 361 cm−1 and unexpected, considering such a strong bond is being broken. Comparatively, the vibrational analysis of the TS structure for H3N·H2·BF3 shows a greater imaginary mode of 666 cm−1 and a much weaker H−H stretch at ∼2000 cm−1 consistent with the TS being later on the MEP. However, inspection of the imaginary mode in H3N·H2·BCl3 shows that it predominantly reflects the interaction of the H2 molecule with BCl3, accompanied by pyramidal distortion of BCl3 and slight elongation of the H−H bond. The adiabatic TS is shifted toward the products, where the H−H bond is ∼0.83 Å (s = 0.127 Å) (increased from 0.81 Å at the classical TS). Calculation of the free energy ΔG298 along the MEP further moves the barrier toward the product region, where the s = 0.132 Å, the H−H bond is 0.84 Å and the H−H stretch is ∼2592 cm−1. The stretching frequency of the H2 molecule in the TS is reduced to 3373 cm−1 from 4362 cm−1 in the precursor complex. The bond is weakened at the TS but not broken. At the point corresponding to the adiabatic barrier (s = 0.127 Å), the mode corresponding to the H−H stretch is further reduced to 3130 cm−1. Following the MEP in the range −1 Å ≤ s ≤ 1 Å, we find that the imaginary mode contains a significant contribution from the symmetric deformation internal coordinate in BCl3 (defined as θ = 90 + ∑31βi − ∑31αi, where α and β are the Cl−B−Cl and H−B−Cl angles, as recommended by Pulay at al.51), reflected in the linear correlation (r2 = 0.997) between the internal coordinate θ and the intrinsic reaction coordinate, s. This is consistent with the reaction coordinate being strongly correlated with the distortion of BCl3 from planar to tetrahedral geometry coupled with the B−H bond formation. In contrast, the H−H stretch shows no significant changes in the entrance channel, i.e., no significant contributions to the IRC mode, and only rapidly changes when the reaction is in the exit channel. Values of rH−H vs θ BCl3 deformation and s are plotted for points along the MEP in Figure 3. It shows that the BCl3 fragment undergoes significant deformation along the path, whereas the H−H distance changes most on the product side of the TS. Single-point energy calculations at the G3(MP2)B3LYP//B3LYP-D/DZVP2 level along the MEP show the barrier moving toward the product region s = 0.28 Å (0.31 Å for the zero-point corrected barrier); not enough to place it in the exit channel. In the case of BF3, the change of the H−H distance vs the BF3 internal coordinate is similar; however, the TS shows a more distorted BF3 (θ = 58°) and longer H−H bond. Thus, we conclude that the energy to break the H−H bond is derived from the energy gained in forming the B−H

Figure 3. Plot of the H−H distance vs the BCl3 internal coordinate, θ,51 and the intrinsic reaction coordinate, s, for heterolytic dissociation of NH3·H2·BCl3. The pyramidal distortion of the BCl3 fragment precedes the H−H bond scission; (red ×) TS with rH−H = 0.81 Å and θ = 38°, where θ = 90 + ∑31βi − ∑31αi and αi and βi are the Cl−B−Cl and H−B−Cl angles, respectively. Note that s and θ are linearly correlated.

and N−H bonds and the resulting electrostatics, as well as the H-bond interactions in the ion pair. Pyykkö and Wang arrived at a similar conclusion in their analysis of H2 activation by trans2,6-dimethyl-2,6-diphenylpiperidine/B(C6F5)3.44 Our finding that the activation barrier is associated with pyramidalization of BCl3 and BF3 suggests that the barrier may be manipulated by inducing pyramidal distortion about the boron center, as well as by changing the electronic character of the ligands. From this point of view, preorganizing the geometry of the boron center to be pyramidal could be a viable strategy for tuning the reactivity of the boron center.52,53 Mayer Bond Order Analysis. We performed a Mayer bond order analysis along the MEP, to gain insight into the relative order for H−H bond breaking and B−H and N−H bond formation. In the precursor complex, the H−H bond order is 0.97 and B−H and N−H bond orders are negligibly small at 0.02 and 0.00, respectively. At the TS, where the H−H distance equals 0.81 Å, the H−H bond order is 0.7, consistent with the vibrational analysis (discussed above) that the H−H bond is weakened at the TS. The B−H and N−H bond orders are 0.28 and 0.12, respectively. This suggests that formation of the B−H bond precedes formation of the N−H bond, i.e., the bond formation is sequential. Figure 4 shows how the bond orders change along the MEP in the range, −1.1 ≤ s ≤ 1.1 Å, where s = 0.0 Å corresponds to the TS. It shows that the B−H and N− H bond orders increase more rapidly after the TS. On the product side, where s ≈ 0.5 Å, the bond orders of both H−H and B−H are 0.5, suggesting that cleavage of the H2 bond is concerted with formation of the B−H bond. At this same point on the reaction path, the bond order for the N−H bond is about 0.3. In the ion pair successor complex, the bond orders for B−H and N−H are 0.99 and 0.91, respectively. Similar behavior was observed in the boron−phosphorus FLP systems studied by Grimme et. al.8 and Bertini et al.,23 although Papai12 found symmetric bond formation for the B−H and P−H bonds in the (tBu)3P·B(C6F5)3·H2 system. For the BF3 system, we also see asymmetric bond formation. The B−H and H−H bond indices are nearly the same at the TS, 0.52 and 0.48, respectively, indicative of significant H−H bond breaking and E

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The pN, with 1.73 electrons, is still present. A similar picture is maintained until rH−H = 1.05 Å (s = 0.68 Å), where the σN−H bonding orbital (occupancy 1.99) and σ*N−H antibonding orbital (occupancy 0.30) arise, replacing the pN and sHδ+, giving MO configuration very similar of the ion pair successor complex (see Figure 1). Continuing along the MEP, the occupancy of σ*N−H quickly diminishes and virtually disappears at the successor complex. The second-order perturbative theory within the NBO framework gives estimates of the stabilization energies ΔE(2), associated with the donor−acceptor interactions. The energies are calculated using eq 2 ΔE(2) = qi

Figure 4. Mayer bond order analysis of structures on the MEP for NH3·H2·BH3. Points for the precursor and successor complexes are not shown. Their respective bond orders are H−H, 0.97, 0.00; B−H, 0.02, 0.99; and N−H, 0.00, 0.91. The vertical dashed red line marks the point where the bond orders of B−H and H−H are both 0.5.

F(i , j)2 εi − εj

(2)

where qi is the occupancy of the donor orbital, εi and εj are the orbital energies for the electron donating and the electron accepting orbital, respectively, and F(i,j) are the off-diagonal NBO Fock matrix elements. Large energy stabilization is indicative of a good orbital overlap between the electron donating and the electron accepting NBO orbitals. In this reaction, the large stabilization energies are associated with the donation of σH−H to the unfilled pB (∼87.4 kcal/mol at the TS), and the donation of pN to σ*H−H (∼35.1 kcal/mol at the TS). The stabilization energies of structures on the MEP are plotted in Figure 6. In the exit channel, these stabilization energies

B−H bond forming having occurred. The N−H bond order is 0.37 showing that it is less developed. NBO Analysis. We also carried out NBO analysis along the MEP in the range −1.1 ≤ s ≤ 1.1 Å. The NBO analysis provides information on changes in the bonding and provides a framework for quantifying the electron donor−acceptor interactions via perturbation theory.38 The electron occupancies of the orbitals involved in the donor−acceptor interactions are plotted in Figure 5. Bond reorganization can be seen to start

Figure 5. Orbital occupancies from NBO analyses of structures on the MEP for reaction of the NH3·H2·BCl3 complex: (red) σH−H, (green) pN, (pink) p*B, (light blue) σB−H, (blue) sHδ+, (black) σN−H. The structures bracket the TS at s = 0 Å and the product side of the path where heterolytic dissociation of H2 occurs.

Figure 6. NBO stabilization energies ΔE(2) associated with the main donor−acceptor interactions along the MEP for NH3·H2·BH3. Images of the TS orbitals are shown.

at s = −0.5 with the emergence of the pB orbital with a partial occupancy of ∼0.5 electrons. At the TS (s = 0), there is 1.75 electron occupancy of the bonding σH−H orbital and small (∼0.11) occupancy of the antibonding σ*H−H orbital. The lone pair pN has occupancy of 1.88, and the unfilled p orbital on B is 0.51. The natural charges are Hδ+ = 0.2 and Hδ− = −0.1. Moving away from the TS, and toward products, the occupancy of σH−H decreases to 1.6 at rH−H = 0.92 Å (at s = 0.48 Å), and the occupancy of the σ*H−H orbital, increases to 0.21. Similarly, the pB orbital increases to 0.59 electrons, and pN orbital decreases to 1.75 electrons. As the H−H bond stretches to 0.94 Å (at s = 0.5 Å), the NBO analysis no longer detects bonding between the two H atoms. At this point, we may consider the H−H bond to be broken. A B−H bond with occupancy of 1.61 and an Hδ+ atom with 0.68 electrons replace the H−H bond.

increased to 185.3 and 76.8 kcal/mol, respectively, as the H−H stretches to 0.92 Å (s = 0.5 Å), and at rH−H = 0.94 Å (not shown in Figure 4), are replaced by pN donation to sHδ+ (161.2 kcal/mol), σB−H donation to sHδ− (250.1 kcal/mol). At rH−H = 1.05 Å, the strongest stabilizations are achieved by the interaction of the σB−H with the σ*N−H (106.8 kcal/mol). This stabilization quickly decreases as the reaction proceeds to the products; at rH−H = 1.31 Å, it is 34.2 kcal/mol. We conclude from the above analyses of the MEP for the H3N·H2·BCl3 system that the reaction occurs in three stages: (1) the weakening of H−H and distortion of BCl3 moiety from planar to pyramidal in preparation to make a B−H bond; (2) the breaking of the H−H bond and formation of the B−H bond and Hδ+; and (3) the formation of the N−H bond. The F

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first stage includes the TS and extends into the exit channel to the point where the H−H bond is substantially weakened or broken, thus mirroring the behavior of FLPs in which the Lewis acid is BCF.8,44 The distinction between the second and the third stage is a result of the asynchronous interaction of H2 with the acid/base pair. However, in the endothermic reaction of H3N·H2·BF3, the TS is more product-like due to the smaller HA and greater distortion energy of the BF3 molecule.45 This reaction is better characterized as concerted with stages 1 and 2 occurring simultaneously. Analysis of the Electric Field in the H3N·H2·BCl3 System. Grimme et al.8 have suggested that a common property in the activation of H2 by different FLPs is the strength of the field in the region of the H2 (0.04−0.06 a.u.). We have analyzed how the electric field between B and N changes along the MEP and find that the field increases in the region of the incipient hydride ion from precursor to successor complex.39 Although strong field lines run through the space that is occupied by the H2 molecule in the TS structure (see Figure 7), the field lines

Figure 8. Magnitude of the electric field (|∇VH|) created by the NH3/ BCl3 Lewis pair at the positions of the hydrogens in the H2 molecule and projected along the H−H bond as a function of the reaction coordinate s. The horizontal blue dashed line marks a threshold field for barrierless dissociation of H2.

polarization of the molecular complex, due to B−H and N−H bond formation, creates an electric field consistent with the H− H bond being broken at this point. Energy Decomposition Analysis of Intermolecular Interactions in the Precursor and TS Complex for NH3·H2·BCl3. We employed the localized molecular orbital energy decomposition analysis (LMOEDA) approach of Su and Li,42 to decompose the pairwise interactions of H2, BCl3, and NH3 in the precursor and TS complexes into electrostatic (ES), exchange (EX), repulsion (REP), polarization (POL), and dispersion (DISP) components. The ES, EX, and REP components arise from interactions of the filled localized orbitals. The POL component is due to orbital relaxation. Large values of POL correspond to the interacting monomer orbitals undergoing significant change in shape (rehybridization) in the supermolecular complex (precursor or TS complex). The DISP component represents the weak intermolecular forces (London forces)54 arising from instantaneous polarization in the interacting monomers due to the correlated motions of electrons. It is estimated as the difference between the B3LYP functional correlation energy of the super molecule and the sum of the correlation energies of the monomers, plus the difference in Grimme’s empirical dispersion corrections30 between the super molecule and the monomers. The total interaction energy, which is the sum of the above-defined components, may be understood as the negative of the energy for dissociation (−DE) of the complex into monomers according to eqs 3−5 with the constraint that the monomer geometries are kept the same as in the super molecule. (Note that, in eq 3, the slash character (/) designates the vacant space that is occupied by H2 in the precursor and TS complexes.)

Figure 7. Map of the Hartree potential and electric field in the H3N/ BCl3 pair at the geometry of the TS: red and green isosurfaces correspond to potentials of 1.9 V and −1.9 V, respectively, and the blue electric field lines correspond to a magnitude of 10.3 V/Å. The H2 molecule is shown in the picture merely to illustrate its position in TS; it was not included in the calculation of the field.

intersect the H−H bond at an angle of ∼45°, such that the strength of field in the direction of the H−H bond is attenuated. Thus, the field is less effective at polarizing and weakening the H−H bond. We calculated the magnitude of the field projected along the H2 bond, for each point of the MEP, by removing the H2 and probing the field at the points in space occupied by the H atoms. The change of the field along the MEP is shown in Figure 8. At the geometry of the precursor complex (s ≪ −1), the magnitude of the field in the direction of the H−H bond is 1−2 V/Å (0.01−0.02 a.u.). Along the path, the field is not homogeneous and is consistently stronger at the position of the Hδ+, until s = 0.42 Å. At the TS, the strength of the field is 1.5 V/Å (0.03 a.u.) at the position of the Hδ− and 3.6 V/Å (0.07 a.u.) at the position of the Hδ+, similar to the field strength reported by Grimme et al.8 for phosphine/borane FLPs, e.g., t Bu3P/B(C6F5)3. Furthermore, we find that the field increases to ∼4.6 V/Å (0.09 a.u.) at s = 0.58 Å, where the NBO analysis shows that the H2 is cleaved on the MEP. Grimme has calculated that the H2 molecule, aligned with the electric field, dissociates heterolytically without a barrier when the field strength is greater than ∼5.1 V/Å (0.1 a.u.).8 Therefore, the

Thus, the monomers in eqs 3−5 differ fundamentally depending on whether they derive from the precursor or the G

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Table 4. LMOEDA Data for Interaction Energies in the Precursor and TS Complexesa

a

entry

interaction

ES

EX

REP

POL

DISP

total

1 2 3 4 5 6

NH3−H2−BCl3 NH3H2−BCl3 NH3−H2BCl3 [NH3−H2−BCl3]‡ [NH3H2−BCl3]‡ [NH3−H2BCl3]‡

−0.4 −0.9 −1.7 −29.7 −26.4 −21.7

−2.4 −1.1 −2.6 −41.6 −27.3 −17.6

10.1 8.4 10.5 137.9 92.6 55.4

−6.7 −6.1 −6.5 −59.1 −42.3 −23.6

−2.6 −3.0 −2.9 −9.9 −8.3 −5.6

−1.9 −2.7 −3.2 −2.3 −11.7 −13.0

In kcal/mol; ES = electrostatic, EX = exchange, REP = repulsion, and DISP = dispersion.

formation occurring earlier than N−H bond formation (see Figure 4). The LMOEDA results show that polarization is the dominant stabilizing component in the TS, being about twice the value of the ES component in H2 interaction. Su and Li42 attribute the polarization component to (1) the distortion of the orbitals and (2) consequent bond formation. In our case, this polarization arises from (1) distortion of the H2 orbitals induced by the field of the NH3/BCl3 monomer and of the monomer orbitals induced by the field of the polarized H2, plus (2) stabilization due to charge transfer via donor−acceptor interactions, e.g., σH−H → pB and pN → σ*H−H. To separate these two contributions to the polarization component, we extracted the charge transfer-term by accounting for the interaction associated with the distortion of the orbitals of each fragment in the presence of the field of the other fragment. This interaction contains two components: (1) the distortion of the H2 in the field created by the NH3/ BCl3 monomer and (2) the distortions of NH3/BCl3 monomer in the presence of the field created by the distorted H2. The first component is estimated by embedding the H2 monomer in the Hartree potential39 of the NH3/BCl3 monomer, thus polarizing the orbitals of the embedded fragment, but not allowing them to interact with the orbitals of the B/N pair. We then remove the potential and relax the orbitals, recovering the energy of polarization due to the field. The second contribution, i.e., the polarization of the NH3/BCl3 pair due to the induced field of the H2 monomer, was estimated in a similar way. The H2 monomer was represented by point charges placed at the geometry of the H atoms. The point charges create a field that distorts the orbitals of the NH3/BCl3. Removing the point charges and relaxing the orbitals, recovered the energy of polarization due to the field created by H2. The energy to distort the H2 in the field of NH3/BCl3 is −6.5 kcal/ mol and the energy to distort the NH3/BCl3 from the induced field in the H2 is −1.6 kcal/mol. From this analysis, it appears that the charge transfer accounts for −51 kcal/mol of the interaction energy and that it is the dominant stabilizing term at the TS. In summary, the energy decomposition analysis shows that the total interaction energy of H2 with NH3/BCl3 does not change significantly from the precursor complex to the TS complex, but the different contributions to the interaction energy are very different, meaning that the reaction requires a fine balance of destabilizing and stabilizing contributions to the overall interactions. This analysis shows that the charge transfer is the largest stabilizing component to interactions in the TS complex, demonstrating the importance of favorable orbital overlap between the monomers. The electrostatic component, which can be interpreted as the interaction through the electric fields that the monomers create, plays a lesser but important role. Consequently, understanding and controlling both types

TS dimer. For example, the BCl3 monomer is planar in the precursor complex but pyramidal in the TS complex, Furthermore, the H2 monomer is stretched by 0.06 Å, and the rB−H and rN−H distances are shorter in the TS complex. The LMOEDA results are shown in Table 4. When comparing the total interaction energies, we note that energies are small (2−3 kcal/mol) in the precursor complex. Among the components that make up the interaction of H2 in the precursor complex (see Table 4, entry 1), the REP (10.1 kcal/ mol) component is dominant, but it is largely compensated for by the EX, POL, and DISP components (−2.4, −6.7, and −2.4 kcal/mol, respectively). Although not obvious from the small total interaction energy, there is a small, yet significant, bonding interaction in the precursor complex. The components of the interactions of BCl3 and NH3 in the precursor complex (entries 2 and 3 in Table 4) are comparable to the components of the H2 interaction (entry 1, Table 4) and consistent with the weak forces expected in such a molecular complex. In the TS complex, the NH3 and BCl3 interactions are larger (−11.7 and −13.0 kcal/mol) than in the precursor complex, whereas the interaction of H2 (−2.3 kcal/mol) is relatively unchanged. However, all of the components are significantly larger than in the precursor complex (see Table 4). The REP component is very large and only compensated for by the sum of the other components. Furthermore, the ES component in the H2, BCl3, and NH3 interactions (entries 4−6 in Table 4) are significant in the TS, indicative of increased electric fields in the TS, as shown above. The POL terms are much larger too, implying the importance of orbital interactions leading to bond formation. This is consistent with the NBO analysis and the large donor/acceptor energies calculated at the TS. Similar observations about the importance of the orbital interactions have been made in the molecular orbital analysis of the H2 cleavage by the tBu3P/B(C6F5)3 FLP reported by Papai et al.12 where most of the activation energy is attributed to the distortion of the three fragments to maximize the orbital overlap leading to bond formation on the product side. In our system, we find that the distortion is mostly associated with the rehybridization of the BCl3 moiety. The components for NH3 and BCl3 interactions are smaller than those for H2. Furthermore, while the sums of the EX, REP, POL, and DISP components of the NH3 and BCl3 interactions are ∼10% larger than the corresponding components in the H 2 interaction, the DISP and ES components sum to values that are 40% and 60% larger, respectively, than in H2. It suggests that the DISP and ES components in the BCl3 and NH3 interactions are also present in the NH3/BCl3 fragment, for example, as in hydrogen bonds, N−H···Cl−B, and long-range ES and DISP interactions involving the N and B atoms. Finally, we note that the BCl3 components are larger that NH3 components, a trend that is consistent with B−H bond H

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supported by the Laboratory Directed Research and Development program at the Pacific Northwest National Laboratory (PNNL) and was performed in part using the Molecular Science Computing Facility in the William R. Wiley Environmental Molecular Sciences Laboratory, a U.S. Department of Energy (DOE) national scientific user facility located at PNNL. G.K.S. and S.M.K. acknowledge support by the U.S. Department of Energy’s (DOE) Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences. Battelle operates PNNL for DOE.

of interaction will be essential in the efforts to design efficient FLP systems for H2 activation.

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CONCLUSIONS We described a study of the activation and heterolytic scission of H2 by prototypical Lewis acid/base pairs: ammonia and BX3 (X = H, F, and Cl), analyzing in detail the reaction path for H2 cleavage in NH3/BCl3. Although not sterically frustrated, the hydride affinity (95.8)45 of BCl3 and proton affinity (204.0 kcal/mol)55 of NH3 are large enough to cause heterolytic scission of H2 with a relatively low barrier even in the gas phase. The mechanism of H2 activation by NH3/BCl3 involves a precursor complex primarily held together by dispersive and weak bonding and electrostatic interactions giving rise to a structure with an H−H−B angle of 82° and N−H−H angle of 172°. Noteworthy about the MEP is that the barrier is largely associated with the pyramidal distortion of the BCl3 fragment to accept Hδ−. The H2 bond (rH−H = 0.81 Å) is weakened at the TS but not broken. In this way, the system mirrors the behavior of FLPs with the B(C6F5)3 Lewis acid.8,44 Our analysis of the orbital and electric field effects show that the electric field alone is not sufficient to break the H−H bond. Orbital interactions contribute significantly to the activation/polarization of the H− H bond. The NBO analysis shows very strong donor/acceptor interactions at the TS between the lone pair of nitrogen and the antibonding orbital in H2, as well as the bonding orbital on H2 and the unoccupied p orbital on boron. The importance of orbital interactions is also supported by the LMOEDA. It shows that the polarization component to the interaction energy of H2 in the TS dominates over the electrostatic component and, furthermore, that the contribution to the interaction energy from electric field induced polarization is small compared to the stabilization from orbital interactions. For NH3/BF3, the reaction is endothermic such that the TS occurs later on the reaction path. The BF3 group is more distorted (θ = 58°), and the H−H distance (rH−H = 0.96 Å) is greater. These features point to the activation of the Lewis pair and heterolytic cleavage of H2 being concerted in the NH3/BF3 system. Finally, our detailed analysis of the interactions of H2 in the precursor and TS complexes of the NH3/BCl3 system provides insight into important factors that should be considered when designing systems for efficient hydrogen activation. For example, inducing a degree of pyramidal distortion of B should enhance orbital overlap with H2, increasing both POL and ES components and lowering the barrier to activate H2.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates for the optimized structures, as well as energetics for these structures and selected points along the MEP. Complete reference 29 is also provided. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Niri Govind for useful discussions and his development version of NWChem. This research was I

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