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On the Mechanism of Heterolytic Hydrogen Splitting by Frustrated Lewis Pairs: Comparison of Static and Dynamic Models Janos Daru, Imre Bako, András Stirling, and Imre Pápai ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.9b01137 • Publication Date (Web): 28 May 2019 Downloaded from http://pubs.acs.org on May 28, 2019
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ACS Catalysis
On the Mechanism of Heterolytic Hydrogen Splitting by Frustrated Lewis Pairs: Comparison of Static and Dynamic Models János Daru,†,‡ Imre Bakó,† András Stirling,*,† and Imre Pápai,*,† †
Research Center for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2, H-1117, Budapest, Hungary, and ‡ Present address: Lehrstuhl für Theoretische Chemie, Ruhr−Universität Bochum, 44780 Bochum, Germany ABSTRACT: Free energy surfaces generated via ab initio molecular dynamics simulations for H2 activation reactions with intramolecular frustrated Lewis pairs (FLPs) point to a concerted (single-step) mechanism of H-H bond cleavage. Statistical analysis carried out for a large number of reaction trajectories reveals notable asynchronicity in the development of donor-H and acceptor-H bonds with the latter being in a more advanced phase. These findings are fully consistent with the results of static quantum chemical calculations demonstrating that the previously established mechanistic picture of FLP-mediated heterolytic H2 cleavage remains plausible in a finite temperature dynamic model as well. As a consequence of asynchronicity, the excess kinetic energy released upon H2 cleavage is stored in the form of donor-H bond vibrations, which may influence the mechanism of catalytic hydrogenation. KEYWORDS: frustrated Lewis pairs, catalysis, hydrogenation, mechanism, molecular dynamics, dihydrogen activation
INTRODUCTION Development of bifunctional catalysts that involve two distinct functional groups, very often both acidic and basic functionalities, is currently considered to be a successful approach in synthetic chemistry.1 Rate acceleration in these systems is generally achieved via the cooperative action of active centers. The acid and the base can either interact with a single molecule and induce favorable bond activation, or they can simultaneously activate two different molecules allowing their fast intermolecular reaction in a subsequent step. The versatile reactivity of sterically hindered Lewis acid/base pairs discovered by Stephan2 represents an outstanding example of acid-base cooperativity. The chemistry of the so-called frustrated Lewis pairs (FLPs) has become an emerging research field over the past decade and a variety of intra- and intermolecular pairs have been developed and utilized for small molecule activation.3 The heterolytic cleavage of dihydrogen has been of particular interest in these studies since a number of FLPs were demonstrated to be efficient metal-free catalysts in hydrogenation reactions.4 A wide range of unsaturated organic substrates, including now carbonyl compounds as well,5 were successfully reduced by FLP-type catalysis.6 Quite remarkably, the asymmetric hydrogenation of selected compounds could also be achieved.7 The high reactivity of FLPs towards H2 is generally rationalized in terms of a two-step reaction mechanism as illustrated in Figure 1. The first step corresponds to the initial formation of a reactive intermediate represented by a "preorganized" form of the unquenched Lewis donor/acceptor (D/A) pair (often referred to as "frustrated complex" or "encounter complex"), which then interacts with H2 in a cooperative manner resulting in the heterolytic H-H bond splitting. This mechanistic view has been largely established from the results of computational studies,8 which revealed that intermolecular D/A pairs can associate via non-covalent
interactions and yield weakly bound complexes having their acid/base sites positioned and oriented properly for simultaneous interactions with an H2 molecule.9 The reactive forms of intramolecular FLPs could also be identified computationally and they correspond to particular open isomeric structures of these molecules.10 The second step of the reaction is the actual H2 cleavage process. The transition states (TS) computed for the H2 splitting step are often characterized as early transition states with a specific end-on D∙∙∙H2 and side-on H2∙∙∙A arrangement of the reacting partners.9c,11 a)
*
D
G
H H
TSHH
A
+ H2
D∙∙∙A (encounter complex)
D/A
H2 cleavage (step 2)
preorganization (step 1)
DH+/AH−
b) D/A
k1 k-1
D∙∙∙A
k2 + H2
DH+/AH−
v = (k1k2/k-1)[D][A][H2] Figure 1. Reaction mechanism of FLP mediated dihydrogen activation: (a) qualitative free energy profile; (b) associated rate law for the
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intermolecular case. D and A refer to Lewis donor and acceptor components.
The free energy balance of the D/A + H2 DH+/AH reaction is primarily related to the acid-base properties of the Lewis centers, but other factors (such as stabilizing electrostatic interactions in the product state and/or intramolecular cooperativity) may also appreciably influence the overall thermodynamics.12 Assuming that the encounter complex formation is a rapid equilibrium prior to the ratedetermining H2 activation step, the rate law of the overall reaction for intermolecular FLPs is formally identical to that obtained for a termolecular process (Figure 1b).13 The reactivity of FLPs in H2 activation can be attributed to simultaneous electron transfer (ET) processes, namely by D *(H2) and (H2) A electron donations.9a;14 These interactions take place cooperatively similarly to transition metal induced H2 activation, and lead to weakening and ultimate cleavage of the H-H bond, which is coupled with D-H and A-H bond formations. An alternative reactivity model has also been proposed,9c which emphasizes the role of electric field (EF) created by the active centers of the encounter complex; however, the relevance of this model as a conceptual basis in FLP-type H2 activation could be questioned.15 Nevertheless, a recent computational study16 reiterates the central role of the EF, and the authors claim to provide a unified reactivity concept for H2 activation via FLPs.17 Classical molecular dynamics (MD) simulations using extended models with explicit solvent treatment provided further insight into the nature of the encounter complex state.18 The results pointed to low probability of donor-acceptor association in solution phase, which could be related to entropic and solvent effects both favoring the dissociated states. Nevertheless, the association of phosphine/borane pairs has been successfully probed by NMR measurements.19 The association process was found to be slightly endergonic in agreement with the results of MD simulations. Evidence for encounter complex formation in solution was also obtained from neutron scattering studies.20 The MD simulations also confirmed the fast equilibrium between the D/A and D∙∙∙A states as no appreciable free energy barrier between these two states could be found.18a Advanced ab initio molecular dynamics (AIMD) techniques have also been applied to model FLP-type H2 activation21 and hydrogenation processes.22 This computational approach enables to generate finite-temperature reaction trajectories using atomic forces computed "on-the-fly" via electronic structure methods, and therefore it is appropriate to describe the sequence of molecular events and finite temperature effects in the reaction.23 Interestingly, the results of AIMD simulations led the authors to conclude that the mechanism of H2 activation could be more complex than that deduced from previous static DFT calculations, which focus on stationary points of potential energy surfaces (PESs). For instance, Pu and Privalov described "quasi-bound" D∙∙∙H2∙∙∙A states on the reaction pathway explored for the tBu3P/B(C6F5)3 + H2 system.21b,c In previous static DFT studies, this type of termolecular encounter state could be identified computationally as a transient intermediate only in a unique combination of Lewis donor/acceptor sites.11f Furthermore, in a recent study,21f Ensing et al. examined the same reaction by DFT-based metadynamics simulations, and based on the computed free energy surface (FES), the H2 activation was
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characterized as a multiple-step process involving H2 polarization, hydride transfer and proton transfer as separate elementary steps. These findings suggest that the reactivity model of FLP mediated dihydrogen activation illustrated in Figure 1, in particular, the mechanism of the H2 cleavage process, could be challenged in a dynamic picture. In light of these new developments, we decided to reinvestigate some of the previously studied FLP + H2 reactions using the AIMD methodology. In our present work, we consider three hydrogen activation reactions that involve intramolecular frustrated Lewis pairs (see Scheme 1), which have been well described both experimentally and computationally. This set of covalently linked FLPs includes the ethylene-linked phosphine-borane 1 developed by Erker et al.,9c the "molecular tweezer" amino-borane 2 introduced by Repo et al.,10b and the geminal P/B pair 3 reported by Slootweg, Lammertsma et al.10c With the choice of intramolecular FLPs, we wish to focus on the H2 activation step, without explicitly considering the first, preorganization step. Our main goal is to describe the heterolytic H2 splitting event in a dynamic perspective and assess whether the conclusions of recent AIMD simulations can be generalized. As shown below, the results of our present study support the previously established mechanistic view that the cleavage of molecular H2 occurs via a single transition state that corresponds to the concerted action of Lewis donor/acceptor FLP sites. C6F5
Mes P Mes
B
H2
C6F5
1H2
1
C6F5
N
B
H2
N
H B
C6F5 C6F5
2H2 Ph
Bu P t Bu
H
C6F5
2
t
H C6F5 B C6F5
H Mes P Mes
B
H2
Ph
3
H Bu P t Bu
t
H B
Ph Ph
3H2
Scheme 1. Investigated H2 activation reactions.
COMPUTATIONAL METHODS In this work, Born-Oppenheimer molecular dynamics simulations were performed using the CP2K program package.24 The BLYP-D3 exchange-correlation functional25,26 was used to describe the electronic structure of the molecular models. Short range, molecularly optimized double- basis sets augmented with a set of polarization functions27 were employed to expand the valence orbitals. An auxiliary basis set of plane waves with a kinetic energy cutoff of 300 Ry was employed to expand the electronic charge densities. The effect of the ionic cores was described by the GTH pseudopotentials optimized to the selected functional.28 The reactions were simulated in periodically repeated simulation box with a size of 20.0 × 20.0 × 20.0 Å3. The simulation box contained an
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intramolecular FLP and an H2 molecule. The canonical (NVT) MD calculations were performed at T = 300 K using timesteps of 0.5 fs. The temperature was controlled with the NoséHoover thermostat chain.29 The FESs of the reactions were explored as a function of collective variables (CVs) that are able to distinguish between reactant, transition and product states and to reliably describe the reaction mechanism. We have selected coordination numbers (CNs) as CVs. A CN describes the bond formation and breaking between two atoms (for formulas, see Supporting Information (SI)). At atomic distances much larger than the typical bond length of the two atoms the function takes a value close to zero. At lengths shorter than a cut-off bond distance, the coordinate takes a value close to one. The CNs can be combined to include situations when multiple bond formations can occur. In the present study we used two collective variables (see Scheme 2): CV1 is the sum of two CNs capturing the bond formations between the H atoms of dihydrogen and the Lewis centers of the FLPs (it can vary from 0 to 2); CV2 is a CN indicating the presence or the absence of the H-H bond (it varies from 1 for molecular state to 0 for dissociation). CN HH CN DH
D
H
H
collective var iables: CN AH
CV 1 = CN DH + CN AH
A
CV 2 = CN HH
Scheme 2. Definition of collective variables (CVs) in terms of coordination numbers (CNs).
Two different sampling techniques were used to explore the FESs of the present reactions. We first employed metadynamics simulations30,31 to characterize the reaction pathway and identify the transition state region between the reactant and product states. The simulations were initiated from the reactant states and conducted until several transition state recrossing events could be observed. In order to prevent the CVs to visit unimportant regions of the FES (e.g. H2 being appart from the reactive centers), a harmonic potential energy wall was introduced for CV1. Due to the bias potential, the FES is artificially deepened in the region of reactant states resulting in an overestimation of the forward free energy barriers. Although metadynamics can in principle be used to compute free energy barriers,32 this was out of scope of the present work. Further technical details of metadynamics simulations are given in the SI. To refine the obtained FESs,
we used another sampling technique, namely, the umbrella sampling method.33 The choice of the CVs was verified by committor analysis.34 In these calculations, we carried out microcanonical (NVE) AIMD simulations launching 1500 trajectories from configurations in the saddle-point regions with random initial velocities assigned from the Maxwell-Boltzmann distribution corresponding to T = 300 K. These trajectories were propagated until they arrived at either the reactant or product states. The committor value was computed from the ratio of trajectories reaching these states. Furthermore, the zero temperature string method35 was used to locate the minimum free energy path (MFEP) on the FESs, which is analogous to intrinsic reaction coordinate (IRC)36 used in static quantum chemical calculations to connect the transition states located on the PESs with energy minima. This optimized pathway was used to construct a single reaction coordinate, the reaction path coordinate (RPC).37 This coordinate efficiently monitors the progression of the reaction: it runs from 0 to 1 as the system evolves from the reactant to the product state, so this single CV captures the entire reaction mechanism. The committor trajectories were further analyzed in terms of the RPC. The details of the statistical analysis are given in the SI. To make direct comparison between the reaction pathways obtained from dynamic simulations and static calculations, the transition states of the three investigated H2 cleavage processes were identified with the latter approach, and the corresponding IRC pathways were computed as well. In these calculations, which were carried out using the Gaussian 09 package,38 we used the same functional as in our dynamic simulations (BLYP-D3)25,26 along with the 6-311G(d,p) basis set. RESULTS Free energy surfaces. As a first step in our mechanistic investigation, we explored the FESs for the H2 splitting processes mediated by the three FLPs 1-3 (Scheme 1). The FESs explored along the two collective variables CV1 and CV2 via metadynamics are depicted in Figure 2. All surfaces exhibit well defined minima in the CV1 0, CV2 1 and CV1 2, CV2 0 regions, which correspond to reactant and product states of these reactions, respectively. These states are separated by transition areas, which appear to be rather flat, and notably, no additional minima, not even shallow minima, could be identified on the computed FESs.
TS2
TS1
CV2
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TS3 1 + H2
2 + H2
3 + H2 2H2
1H2 CV1
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3H2
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Figure 2. Free energy surfaces obtained from metadynamics for reactions with FLPs 1 (A), 2 (B) and 3 (C). The minimum free energy and IRC pathways are indicated by white circles and blue lines, respectively. Contour lines are spaced at 5 kcal/mol intervals.
C)
CV1
CV2
B)
CV2
A)
CV2
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CV1
CV1
Figure 3. TS regions of free energy surfaces obtained from umbrella samplings for reactions with FLPs 1 (A), 2 (B) and 3 (C). Positions from where trajectories were initiated are indicated by dots. Blue and red colors refer to trajectories that reached reactant and product states in the simulations. Following the minimum free energy pathways MFEPs from the reactant states (white circles in Figure 2), the transition states of reactions with FLPs 1 and 2 are reached via small changes in variable CV2 (only slight elongations of H2), pointing to early transition states in these cases. On the other hand, the TS region of the reaction with 3 is found to be in a fairly advanced phase along the MFEP (CV2 is about 0.5 in the TS). After leaving the TS regions, the systems reach rapidly the product states with a simultaneous increase in both CVs indicating that the progress of the heterolytic H2 splitting correlates strongly with the formation of the donor-H and acceptor-H bonds. All these findings are consistent with the results of previous static DFT calculations. The IRC pathways superimposed to the FESs (blue lines in Figure 2) follow closely the MFEPs providing further support for the agreement. The TS regions of the free energy surfaces obtained from umbrella samplings are depicted in Figure 3. They also reveal typical saddle-shape surfaces with no local minima in the vicinity of TSs, which is again consistent with single-step H2 cleavage processes. The results of committor analysis are illustrated in Figure 3 as well. The positions from where the committor trajectories were initiated are represented by dots, and the color marks whether the trajectories reached the reactant or the product states (blue and red color, respectively). The computed probabilities (the average committor values) are 0.63, 0.59 and 0.45 for reactions with FLPs 1, 2 and 3, which are reasonably close to the ideal 0.5 value confirming the relevance of collective variables CV1 and CV2 to describe the mechanism of the present reactions.39 Statistical analysis of trajectories. Additional insight into the dynamic aspects of the H2 splitting step can be obtained by analyzing the distribution of relevant structural parameters collected along the committor trajectories and contrasting them with the evaluation of these parameters on the corresponding IRC pathways. Considering the 1 + H2 reaction as an example, we selected three bond distances, namely the H-H distance in the dissociating H2 molecule, the P-H and the B-H distances and plotted their distributions as a function of the reaction coordinate RPC (see Figures 4a-c). The
distribution of the P-H/B-H distance pairs compiled along the committor trajectories are displayed in Figure 4d. The IRC pathways projected onto the actual coordinates are also depicted in these plots for comparison.40
Figure 4. Relative distributions of structural parameters for reaction 1 + H2 obtained from the trajectories of the committor analysis. A, B and C: distances H-H, B-H and P-H, respectively along the reaction path CV (RPC); D: distribution of the observed P-H/B-H distance pairs. Labels R, P and TS indicate reactant, product and transition states. Continuous line: IRC pathway projected onto the actual coordinates.
As pointed out previously by Pu and Privalov in their AIMD studies of the tBu3P/B(C6F5)3 + H2 reaction, the computed finite temperature reaction trajectories may deviate from the minimum energy pathways, which correspond to the T = 0 K
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limit. The kinetic energy effects of finite temperature simulations are well reflected in the distribution plots as well: the bond distances vary in a certain range along the entire reaction path. More specifically, Figures 4a and 4b show relatively narrow distributions for the H-H and B-H distances with respect to the IRC curve, while the P-H distribution is somewhat broader in the entrance stage of the reaction (Figure 4c). The larger mobility of the H atom that transfers to the phosphorus upon H2 cleavage is associated with the asynchronicity in the formation of the P-H and B-H bonds with the latter being in a more advanced stage. The asynchronous nature of the heterolytic H-H bond splitting is apparent in Figure 4d as well, where the distribution of P-H/BH bond distances and the change in the slope of the IRC curve indicates that the development of the P-H bond lags well behind the B-H bond formation. Note also that the mean B-H and P-H bond distances in the TS region are around 1.6 and 2.1 Å,41 respectively, which points to a significant difference in the development of these bonds.42 The asynchronous formation of the B-H and P-H bonds was also observed and highlighted by Ensing et al. in their metadynamics simulation studies on the tBu3P/B(C6F5)3 + H2 system, however, based on a very shallow free energy minimum found nearby the TS region, the authors concluded that the cleavage of the H-H bond takes place in two separate elementary steps: the hydride is first captured by the boron atom and then the free proton is transfered to the phosphorus center. The distribution plots in Figure 4 display intense bright areas in the TS region indicating that these molecular configurations are more abundant among the entire set of structures sampled by the trajectories. This feature is related to conditions used in the generation of committor trajectories (initial structures taken from the TS region with random initial velocities) and also to the flat nature of the potential energy surface in the TS region. These conditions imply that a large number of trajectories reside in the TS region for a relatively long time period before entering the reaction entrance/exit channels, increasing the proportion of these configurations on the distribution plots. Similar observations were reported by Pu and Privalov for the tBu3P/B(C6F5)3 + H2 reaction, and the trajectories “trapped” in the TS region were associated with "quasi-bound" states that were suggested to contribute to the reaction mechanism. As noted above, we find no evidence for any transient reaction intermediate for the present reactions (no local minima exist on the computed free energy surfaces), therefore, the stepwise mechanistic scenario of the heterolytic H2 cleavage with the intramolecular FLPs investigated herein can be safely ruled out. The remarkable agreement between the distributions of the finite temperature structural data and the corresponding IRC projections in Figure 4 corroborates that the single-step concerted mechanism of H2 splitting proposed from the results of static DFT studies for these reactions is an adequate mechanistic view in a dynamic picture as well. Analysis of velocity distributions. An important difference between the static and dynamic computational mechanistic studies is that the latter approach incorporates the kinetic energy of molecules, which is worth examining because it carries valuable information about the finite temperature effects. Herein, we carried out a statistical analysis of atomic velocities for the committor trajectories to probe how the equilibrium Boltzmann energy distribution set up for the TS ensembles evolves along the trajectories that lead either to
reactant or to product states.43 The results are presented in Figure 5. The first notable feature in this figure is that in all cases the kinetic energy gained after leaving the TS is basically distributed among the four atoms participating directly in the H2 splitting, whereas the rest of the atoms keep their original average kinetic energies.44 The evolution of atomic temperatures is in good accordance with the nature of the transition states of the three reactions. For instance, for reactions with early TSs (i.e. 1 + H2 and 2 + H2), the average atomic temperatures are significantly higher at the product states as compared to those at the reactants states, but this striking asymmetry in the temperature evolution is not seen for the reaction with FLP 3. Another interesting trend in the temperature evaluation curves is that at the product sides, the H atom bonded to the donor centers has a significantly higher temperature than the other atoms in all reactions. In contrast, the temperature of the H atom attached to the boron atom is increased only slightly along the path from the TS to the product state. The marked difference between the temperatures of the two hydrogens signifies the asyncronicity in the formation of the D-H and AH bonds.45 These results imply that a significant portion of excess energy gained upon the H2 splitting process is stored in the vibrations associated with the D-H group. Although thermalization of this excess energy (via intramolecular vibrational coupling or molecular collisions) can occur at the product state, vibrationally excited D-H groups may play an important role in FLP-catalyzed hydrogenation reactions.
Figure 5. Average temperature of selected atoms along the RPC as obtained from the committor trajectories for reactions with FLPs 1 (A), 2 (B) and 3 (C). Selected atoms: Lewis donor center (D in blue), acceptor center (A in red), H atom transfered to D (in turquoise), H atom transferred to A (in orange). Grey area represents temperature interval for the rest of the atoms defined by the instantaneous minimum and maximum average atomic temperature values.
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The H atoms have an excess kinetic energy at the entrance side of the reactions as well. In reactions with early TSs, the H atoms are moderately heated (400-600 K), while the other atoms do not need to be activated as indicated by their temperature fluctuations around 300 K. For the reaction with FLP 3, where much higher activation energy is required,10c,15 both the Lewis centers and the H atoms need to be activated at a much higher average temperature. In addition, a part of the activation energy is provided by the higher kinetic energy of the rest of the atoms. The higher kinetic energy of the H2 molecule can be interpreted as a necessary investment to overcome the initial repulsion at the entrance to reach the active centers of the FLPs. Further insight into the activation process can be obtained by decomposing the average kinetic energy of H2 atoms at the entrance channels into translational, rotational and vibrational components (see Figure 6).46 The common feature of these temperature vs. RPC plots is that the activation energy is stored predominantly in the translational degrees of freedom. Indeed, in all cases the vibrational and rotational temperatures are very close to the equilibrium 300 K, and the available excess energy is accumulated in the translational motion of H2. These results point to a very simple dynamic picture for H2 activation by these intramolecular FLPs: sufficiently mobile H2 molecules without the requirement of rotational or vibrational excitations can reach the unquenched Lewis centers and they can easily undergo H-H bond cleavage.
In this work, we have examined the reaction mechanism of FLP-mediated heterolytic H2 cleavage via ab initio molecular dynamics (AIMD) simulations. Our primary motivation was to assess the validity of the reactivity model that was established from the results of standard static DFT calculations. The computed free energy surfaces derived for the reactions with three different intramolecular FLPs suggest that the heterolytic H2 splitting process takes place in a single concerted step as described previously. We find no computational evidence for the step-wise mechanism, not even for transient reaction intermediates, as implied by recent AIMD simulations reported for the tBu3P/B(C6F5)3 + H2 reaction. The statistical analysis carried out for a large number of reaction trajectories launched from the transition state regions reveals solid agreement between the distributions of the finite temperature structural data and the corresponding IRC pathways derived from static calculations, providing further support for the single-step concerted H2 cleavage mechanism. The IRC pathways are found to follow closely the minimum free energy paths as well. The statistical analysis points to notable asynchronicity in the formations of the donor-H and acceptor-H bonds with the latter being ahead in development. This feature of FLPassisted H2 activation has been noted in several static DFT studies, and it has been highlighted in a recent AIMD study as well. An important consequence of the asynchronicity is that most of the excess kinetic energy (i.e. reaction heat) released upon H2 cleavage is accumulated in the form of donor-H bond vibrations, resulting in enhanced reactivity of this site in a subsequent event, for instance, in a possible catalytic proton transfer step. In conclusion, this work demonstrates that the previously proposed simple mechanistic picture of FLP-mediated H2 cleavage remains plausible in a finite temperature dynamic model as well, at least when intramolecular FLPs are considered. Although we have no specific reason to assume that intermolecular FLPs operate via a different mechanism, additional AIMD studies might be required to ascertain this view. It appears that the asynchronicity in the formation of donor-H and acceptor-H bonds upon the H2 cleavage process is a general feature of FLP-type H2-activation, which may influence the mechanism of the entire catalytic cycle as well. This aspect may have important implications for catalyst design. ASSOCIATED CONTENT Supporting Information Computational details and Cartesian structures from static DFT calculations.
Figure 6. Temperature evolution of the reactant H atoms and their decomposition into translational, rotational and vibrational degrees of freedom along the RPC reaction coordinate at the reactant side for reactions reactions with FLPs 1 (A), 2 (B) and 3 (C). Color code used in the figure: gold - total; blue - rotational; green - vibrational; red translational degrees of freedom. For each plot, the scale of the horizontal (RPC) axis is adjusted to span the reactants - TS region, hence no scale is given for this coordinate.
CONCLUSIONS
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AUTHOR INFORMATION Corresponding authors *E-mail:
[email protected] *E-mail:
[email protected] ORCID András Stirling: 0000-0002-1696-7932 Imre Pápai: 0000-0002-4978-0365 ACKNOWLEDGMENTS
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coordinates
of
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This project was supported by NKFIH (grants K-116034 and K-115660). Computational resources provided by the NIIF Supercomputer Center are acknowledged. REFERENCES 1. For reviews on bifunctional catalysis, see: a) Dixon, D. J. Bifunctional catalysis. Beilstein J. Org. Chem. 2016, 12, 10791080; b) Georgiou, I.; Ilyashenko, G.; Whiting, A. Synthesis of Aminoboronic Acids and Their Applications in Bifunctional Catalysis. Acc. Chem. Res. 2009, 42, 756768; c) Paul, D. H.; Abraham, C. J.; Scerba, M. T.; Aldem-Danforth, E.; Lectka T. Bifunctional Asymmetric Catalysis: Cooperative Lewis Acid/Base Systems. Acc. Chem. Res. 2008, 41, 655663; d) Grützmacher, H. Cooperating Ligands in Catalysis. Angew. Chem., Int. Ed. 2008, 47, 18141818; e) Setoyama, T. Acid–Base Bifunctional Catalysis: An Industrial Viewpoint. Cat. Today 2006, 116, 250262. 2. Welch, G. C.; San Juan, R. R.; Masuda, J. D.; Stephan, D. W. Reversible, Metal-Free Hydrogen Activation. Science 2006, 314, 11241126. 3. For recent reviews on FLP chemistry, see: a) Topics in Current Chemistry; Erker. G., Stephan, D. W., Eds.; SpringerVerlag, Berlin, 2013, Vols. 332 and 334; b) Stephan, D. W.; Erger, G. Frustrated Lewis Pair Chemistry: Development and Perspectives. Angew. Chem., Int. Ed. 2015, 54, 64006441; c) Stephan, D. W. Frustrated Lewis Pairs. J. Am. Chem. Soc. 2015, 137, 1001810032; d) Stephan, D. W. Frustrated Lewis Pairs: From Concept to Catalysis. Acc. Chem. Res. 2015, 48, 306316; e) Stephan, D. W. The Broadening Reach of Frustrated Lewis Pair Chemistry. Science 2016, 354, aaf7229. 4. For related reviews, see: a) Stephan, D. W.; Erker, G. Frustrated Lewis Pairs: Metal‐free Hydrogen Activation and More. Angew. Chem. Int. Ed. 2010, 49, 4676; b) Stephan, D. W.; Greenberg, S.; Graham, T. W.; Chase, P.; Hastie, J. J.; Geier, S. J.; Farrell, J. M.; Brown, C. C.; Heiden, Z. M.; Welch, G. C.; Ullrich, M. Metal-Free Catalytic Hydrogenation of Polar Substrates by Frustrated Lewis Pairs. Inorg. Chem. 2011, 50, 1233812348; c) Stephan, D. W.; Erker, G. Frustrated Lewis Pair Mediated Hydrogenations. Top. Curr. Chem. 2013, 332, 85110; d) Sumerin, V.; Chernichenko, K.; Schulz, F.; Leskelä, M.; Rieger, B.; Repo, T. Amine-Borane Mediated Metal-Free Hydrogen Activation and Catalytic Hydrogenation. Top. Curr. Chem. 2013, 332, 111155; e) Paradies, J. Metal‐Free Hydrogenation of Unsaturated Hydrocarbons Employing Molecular Hydrogen. Angew. Chem. Int. Ed. 2014, 53, 35523557; f) Hounjet, L. J.; Stephan, D. W. Hydrogenation by Frustrated Lewis Pairs: Main Group Alternatives to Transition Metal Catalysts? Org. Process Res. Dev. 2014, 18, 385391; g) Scott, D. J.; Fuchter, M. J.; Ashley, A. E. Designing Effective ‘Frustrated Lewis Pair’ Hydrogenation Catalysts. Chem. Soc. Rev. 2017, 46, 56895700; h) Paradies, J. From Structure to Novel Reactivity in Frustrated Lewis Pairs. Coord. Chem. Rev. 2019, 380, 170183; i) Lam, J.; Szkop, K. M.; Mosaferi, E.; Stephan, D. W. FLP Catalysis: Main Group Hydrogenations of Organic Unsaturated Substrates. Chem. Soc. Rev. 2019, doi: 10.1039/C8CS00277K; j) Paradies, J. Mechanisms in Frustrated Lewis Pair‐Catalyzed Reactions. Eur. J. Org. Chem. 2019, 283294.
5. a) Scott, D. J.; Fuchter, M. J.; Ashley, A. E. Nonmetal Catalyzed Hydrogenation of Carbonyl Compounds. J. Am. Chem. Soc. 2014, 136, 1581315816; b) Mahdi, T.; Stephan, D. W. Enabling Catalytic Ketone Hydrogenation by Frustrated Lewis Pairs. J. Am. Chem. Soc. 2014, 136, 1580915812; c) Gyömöre, A.; Bakos, M.; Földes, T.; Pápai, I.; Domján, A.; Soós, T. Moisture-Tolerant Frustrated Lewis Pair Catalyst for Hydrogenation of Aldehydes and Ketones. ACS Catal. 2015, 5, 53665372. 6. For follow-up works focusing on development and application of water-tolerant FLP catalysts, see: a) Scott, D. J.; Simmons, T. R.; Lawrence, E. J.; Wildgoose, G. G.; Fuchter, M. J.; Ashley, A. E. Facile Protocol for Water-Tolerant “Frustrated Lewis Pair”-Catalyzed Hydrogenation. ACS Catal. 2015, 5, 55405544; b) Fasano, V.; Radcliffe, J. E.; Ingleson, M. J. B(C6F5)3-Catalyzed Reductive Amination Using Hydrosilanes. ACS Catal. 2016, 6, 17931798; c) Scott, D. J.; Phillips, N. A.; Sapsford, J. S.; Deacy, A. C.; Fuchter, M. J.; Ashley, A. E. Versatile Catalytic Hydrogenation Using A Simple Tin(IV) Lewis Acid. Angew. Chem. Int. Ed. 2016, 55, 1473814742; d) Fasano, V.; Ingleson, M. J. Expanding Water/Base Tolerant Frustrated Lewis Pair Chemistry to Alkylamines Enables Broad Scope Reductive Aminations. Chem. Eur. J. 2017, 23, 22172224; e) Bakos, M.; Gyömöre, Á.; Domján, A.; Soós, T. Auto‐Tandem Catalysis with Frustrated Lewis Pairs for Reductive Etherification of Aldehydes and Ketones. Angew. Chem. Int. Ed. 2017, 56, 52175221; f) Dorkó, É.; Szabó, M.; Kótai, B.; Pápai, I.; Domján, A.; Soós, T. Expanding the Boundaries of Water‐Tolerant Frustrated Lewis Pair Hydrogenation: Enhanced Back Strain in the Lewis Acid Enables the Reductive Amination of Carbonyls. Angew. Chem. Int. Ed. 2017, 56, 95129516; g) Sapsford, J. S.; Scott, D. J.; Allcock, N. J.; Fuchter, M. J.; Tighe, C. J.; Ashley, A. E. Direct Reductive Amination of Carbonyl Compounds Catalyzed by a Moisture Tolerant Tin(IV) Lewis Acid. Adv. Synth. Catal. 2018, 360, 10661071; h) Hoshimoto, Y.; Kinoshita, T.; Hazra, S.; Ohashi, M.; Ogoshi, S. Main-Group-Catalyzed Reductive Alkylation of Multiply Substituted Amines with Aldehydes Using H2. J. Am. Chem. Soc., 2018, 140, 72927300; i) Fasano, V.; LaFortune, J. H. W.; Bayne, J. M.; Ingleson, M. J.; Stephan, D. W. Air- and Water-stable Lewis Acids: Synthesis and Reactivity of P-trifluoromethyl Electrophilic Phosphonium Cations. Chem. Commun. 2018, 54, 662665; j) Fasano, V.; Ingleson, M. J. Recent Advances in Water-Tolerance in Frustrated Lewis Pair Chemistry. Synthesis 2018, 50, 17831795. 7. For reviews and recent reports on asymmetric hydrogenations, see: a) Chen, D.; Klankermayer, J. Frustrated Lewis Pairs: From Dihydrogen Activation to Asymmetric Catalysis. Top. Curr. Chem. 2013, 334, 126; b) Feng, X.; Du, H. Metal-Free Asymmetric Hydrogenation and Hydrosilylation Catalyzed by Frustrated Lewis Pairs. Tetrahedron Lett. 2014, 55, 69596964; c) Shi, L.; Zhou, Y.G. Enantioselective Metal‐Free Hydrogenation Catalyzed by Chiral Frustrated Lewis Pairs. ChemCatChem. 2015, 7, 5456; d) Paradies, J. Chiral Borane-Based Lewis Acids for Metal Free Hydrogenations. Top. Organomet. Chem. 2018, 62, 193216; e) Meng, W.; Feng, X.; Du, H. Frustrated Lewis Pairs Catalyzed Asymmetric Metal-Free Hydrogenations and Hydrosilylations. Acc. Chem. Res., 2018, 51, 191201; f)
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Zhang, Z.; Du, H. A Highly cis‐Selective and Enantioselective Metal‐Free Hydrogenation of 2,3‐Disubstituted Quinoxalines. Angew. Chem. Int. Ed. 2015, 54, 623626; g) Lindqvist, M.; Borre, K.; Axenov, K.; Kótai, B.; Nieger, M.; Leskelä, M.; Pápai. I.; Repo, T. Chiral Molecular Tweezers: Synthesis and Reactivity in Asymmetric Hydrogenation. J. Am. Chem. Soc., 2015, 137, 40384041; h) Zhang, Z.; Du, H. Enantioselective Metal-Free Hydrogenations of Disubstituted Quinolines. Org. Lett. 2015, 17, 62666269; i) Zhou, Q.; Zhang, L.; Meng, W.; Feng, X.; Yang, J.; Du, H. Borane-Catalyzed Transfer Hydrogenations of Pyridines with Ammonia Borane. Org. Lett. 2016, 18, 51895191; j) Han, C.; Zhang, E.; Feng, X.; Wang, S.; Du, H. B(C6F5)3-Catalyzed Metal-Free Hydrogenations of 2-quinolinecarboxylates. Tetrahedron Lett. 2018, 59, 14001403; k) Liu, X. Q.; Liu, T.; Meng, W.; Du, H. Asymmetric Hydrogenation of Imines with Chiral Alkenederived Boron Lewis Acids. Org. Biomol. Chem., 2018, 16, 86868689; l) Tu, X.-S.; Zeng, N.-N.; Li, R.-Y.; Zhao, Y.-Q.; Xie, D.-Z.; Peng, Q.; Wang, X.-C. C2‐Symmetric Bicyclic Bisborane Catalysts: Kinetic or Thermodynamic Products of a Reversible Hydroboration of Dienes. Angew. Chem. Int. Ed. 2018, 57, 1509615100. 8. For a review on computational studies of FLP-type hydrogen activation, see: Rokob, T. A.; Pápai, I. Hydrogen Activation by Frustrated Lewis Pairs: Insights from Computational Studies. Top. Curr. Chem. 2013, 332, 157211. 9. For studies pointing to the importance of noncovalent (dispersion) interactions in the preassociation step, see: a) Rokob, T. A.; Hamza, A.; Stirling, A.; Soós, T.; Pápai, I. Turning Frustration into Bond Activation: A Theoretical Mechanistic Study on Heterolytic Hydrogen Splitting by Frustrated Lewis Pairs. Angew. Chem., Int. Ed. 2008, 47, 24352438; b) Kim, H. W.; Rhee, Y. Dispersion‐Oriented Soft Interaction in a Frustrated Lewis Pair and the Entropic Encouragement Effect in its Formation. Chem. Eur. J. 2009, 15, 1334813355; c) Grimme, S.; Kruse, H.; Goerigk, L.; Erker, G. The Mechanism of Dihydrogen Activation by Frustrated Lewis Pairs Revisited. Angew. Chem., Int. Ed. 2010, 49, 14021405; d) Zeonjuk, L. L.; Vankova, N.; Mavrandonakis, A.; Heine, T.; Röschenthaler, G.-V.; Eicher, J. On the Mechanism of Hydrogen Activation by Frustrated Lewis Pairs. Chem. Eur. J. 2013, 19, 1741317424; e) Zeonjuk, L. L.; Petkov, P.; Heine, T.; Röschenthaler, G.-V.; Eicher, J.; Vankova, N. Are Intramolecular Frustrated Lewis Pairs Also Intramolecular Catalysts? A Theoretical Study on H2 Activation. Phys. Chem. Chem. Phys. 2015, 17, 1068710698; f) Das, S.; Mondal, S.; Pati, S. K. Mechanistic Insights into Hydrogen Activation by Frustrated N/Sn Lewis Pairs. Chem. Eur. J. 2018, 24, 25752579. 10. For related studies, see: a) Spies, P.; Erker, G.; Kehr, G.; Bergander, K.; Frölich, R.; Grimme, S.; Stephan, D. W. Rapid Intramolecular Heterolytic Dihydrogen Activation by a FourMembered Heterocyclic Phosphane–Borane Adduct. Chem. Comm. 2007, 50725074; b) Sumerin, V.; Schulz, F.; Atsumi, M.; Wang, C.; Nieger, M.; Leskelä, M.; Repo, T.; Pyykkö, P.; Rieger, B. Molecular Tweezers for Hydrogen: Synthesis, Characterization, and Reactivity. J. Am. Chem. Soc. 2008, 130, 1411714119; c) Bertini, F.; Lyaskovskyy, V.; Timmer, B. J. J.; de Kanter, F. J. J.; Lutz, M.; Ehlers, A. W.; Slootweg, J. C.; Lammertsma, K. Preorganized Frustrated Lewis Pairs. J. Am.
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Chem. Soc. 2012, 134, 201204; d) Lu, G.; Li, H.; Zhao, L.; Huang, F.; Wang, Z.-X. Computationally Designed MetalFree Hydrogen Activation Site: Reaching the Reactivity of Metal−Ligand Bifunctional Hydrogenation Catalysts. Inorg. Chem. 2010, 49, 295301. 11. The bent arrangement of the DHHA fragment of the transition states has been highlighted in several works: a) Holschumacher, D.; Bannenberg, T.; Hrib, C. G.; Jones, P. G.; Tamm, M. Heterolytic Dihydrogen Activation by a Frustrated Carbene–Borane Lewis Pair. Angew. Chem., Int. Ed. 2008, 47, 74287432; b) Nyhlén, J.; Privalov, T. “Frustration” of Orbital Interactions in Lewis Base/Lewis Acid Adducts: A Computational Study of H2 Uptake by Phosphanylboranes R2P=BR′2. Eur. J. Inorg. Chem. 2009, 27592764; c) Privalov, T. On the Possibility of Conversion of Alcohols to Ketones and Aldehydes by Phosphinoboranes R2PBR′R′′: A Computational Study. Chem. Eur. J. 2009, 15, 18251829; d) Lu, Z.; Cheng, Z.; Chen, Z.; Weng, L.; Li, Z. H.; Wang, H. Heterolytic Cleavage of Dihydrogen by “Frustrated Lewis Pairs” Comprising Bis(2,4,6‐tris(trifluoromethyl)phenyl)borane and Amines: Stepwise versus Concerted Mechanism. Angew. Chem., Int. Ed. 2011, 50, 1222712231; e) Camaioni, D. M.; GinovskaPangovska, B.; Schenter, G. K.; Kathmann, S. M.; Autrey, T. Analysis of the Activation and Heterolytic Dissociation of H2 by Frustrated Lewis Pairs: NH3/BX3 (X = H, F, and Cl). J. Phys. Chem. A 2012, 116, 72287237; f) Könczöl, L.; Makkos, E.; Bourissou, D.; Szieberth, D. Computational Evidence for a New Type of η 2‐H2 Complex: When Main‐Group Elements Act in Concert To Emulate Transition Metals. Angew. Chem., Int. Ed. 2012, 51, 95219524. 12. Rokob, T. A.; Hamza, A.; Pápai, I. Rationalizing the Reactivity of Frustrated Lewis Pairs: Thermodynamics of H2 Activation and the Role of Acid−Base Properties. J. Am. Chem. Soc. 2009, 131, 1070110710. 13. Calorimetric studies on H2 by the Mes3P/B(C6F5)3 pair (Mes = 2,4,6-C6Me3H2) found the rate to be modelled as a single termolecular step. See: Houghton, A. Y.; Autrey, T. Calorimetric Study of the Activation of Hydrogen by Tris(pentafluorophenyl)borane and Trimesitylphosphine. J. Phys. Chem. A 2017, 121, 87858790. 14. Hamza, A.; Stirling, A.; Rokob, T. A.; Pápai, I. Mechanism of Hydrogen Activation by Frustrated Lewis Pairs: A Molecular Orbital Approach. Int. J. Quantum Chem. 2009, 109, 24162425. 15. Rokob, T. A.; Bakó, I.; Stirling, A.; Hamza, A.; Pápai, I. Reactivity Models of Hydrogen Activation by Frustrated Lewis Pairs: Synergistic Electron Transfers or Polarization by Electric Field? J. Am. Chem. Soc. 2013, 135, 44254437. 16. Skara, G.; De Vleeschouwer, F.; Geerlings, P.; De Proft, F.; Pinter, B. Heterolytic Splitting of Molecular Hydrogen by Frustrated and Classical Lewis Pairs: A Unified Reactivity Concept. Sci. Rep. 2017, 7, 16024−. 17. Surprisingly, the authors of Ref. 16 refer to the Hammond's postulate as a widespread anecdotal view and argue that structurally different transition states (e.g. analogous early and late TSs) imply two fundamentally different H2 activation mechanisms. 18. a) Bakó, I.; Stirling, A.; Bálint, S.; Pápai, I. Association of Frustrated Phosphine–Borane Pairs in Toluene: Molecular
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Dynamics Simulations. Dalton Trans. 2012, 41, 9023−9025; b) Dang, L. X.; Schenter, G. K.; Chang, T. M.; Kathmann, S. M.; Autrey, T. Role of Solvents on the Thermodynamics and Kinetics of Forming Frustrated Lewis Pairs. J. Phys. Chem. Lett. 2012, 3, 3312−3319; c) Kathmann, S. M.; Chang, T. M.; Schenter, G. K.; Parab, K.; Autrey, T. Experimental and Theoretical Study of Molecular Response of Amine Bases in Organic Solvents. J. Phys. Chem. B 2014, 118, 4883−4888. 19. Rocchigiani, L.; Ciancaleoni, G.; Zuccaccia, C.; Macchioni, A. Probing the Association of Frustrated Phosphine–Borane Lewis Pairs in Solution by NMR Spectroscopy. J. Am. Chem. Soc. 2014, 136, 112−115. 20. Brown, L. C.; Hogg, J. M.; Gilmore, M.; Moura, L.; Imberti, S.; Gärtner, S.; Gunaratne, H. Q. N.; O’Donnell, R. J.; Artioli, N.; Holbrey, J. D.; Swadźba-Kwaśny, M. Frustrated Lewis Pairs in Ionic Liquids and Molecular Solvents – A Neutron Scattering and NMR Study of Encounter Complexes. Chem. Commun., 2018, 54, 8689−8692. 21. a) Pu, M.; Privalov, T. Ab Initio Dynamics Trajectory Study of the Heterolytic Cleavage of H2 by a Lewis Acid [B(C6F5)3] and a Lewis Base [P(tBu)3]. J. Chem. Phys. 2013, 138, 154305; b) Pu, M.; Privalov, T. How Frustrated Lewis Acid/Base Systems Pass through Transition‐State Regions: H2 Cleavage by [tBu3P/B(C6F5)3]. ChemPhysChem 2014, 15, 2936−2944; c) Pu, M.; Privalov, T. Ab Initio Molecular Dynamics Study of Hydrogen Cleavage by a Lewis Base [tBu3P] and a Lewis Acid [B(C6F5)3] at the Mesoscopic Level—Dynamics in the Solute–Solvent Molecular Clusters. ChemPhysChem 2014, 15, 3714−3719; d) Pu, M.; Privalov, T. Chemistry of Intermolecular Frustrated Lewis Pairs in Motion: Emerging Perspectives and Prospects. Isr. J. Chem 2015, 55, 179−; e) Pu, M.; Heshmat, M.; Privalov, T. Liberation of H2 from (o-C6H4Me)3P—H(+) + (−)H—B(p-C6F4H)3 Ion-Pair: A Transition-State in the Minimum Energy Path versus the Transient Species in Born-Oppenheimer Molecular Dynamics. J. Chem. Phys. 2017, 147, 014303; f) Liu, L.; Lukose, B.; Ensing, B. Hydrogen Activation by Frustrated Lewis Pairs Revisited by Metadynamics Simulations. J. Phys. Chem. C 2017, 121, 2046−2051. 22. a) Heshmat, M.; Privalov, T. Computational Elucidation of a Role That Brønsted Acidification of the Lewis Acid‐Bound Water Might Play in the Hydrogenation of Carbonyl Compounds with H2 in Lewis Basic Solvents. Chem. Eur. J. 2017, 23, 11489−11493; b) Heshmat, M.; Privalov, T. Testing the Nature of Reaction Coordinate Describing Interaction of H2 with Carbonyl Carbon, Activated by Lewis Acid Complexation, and the Lewis Basic Solvent: A BornOppenheimer Molecular Dynamics Study with Explicit Solvent. J. Chem. Phys. 2017, 147, 094302; c) Heshmat, M.; Privalov, T. Surprisingly Flexible Oxonium/Borohydride Ion Pair Configurations. J. Phys. Chem. A 2018, 122, 3713−3727; d) Heshmat, M.; Privalov, T. Structurally Flexible Oxocarbenium/Borohydride Ion Pair: Dynamics of Hydride Transfer on the Background of Conformational Roaming. J. Phys. Chem. A 2018, 122, 5098−5106. 23. Marx, D.; Hutter, J, Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods, Cambridge University Press, Cambridge, 2009. 24. The CP2K Developers Group. Available at: www.cp2k.org; VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and Accurate Density Functional Calculations Using a Mixed
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34. Li, W.; Ma, A. Recent Developments in Methods for Identifying Reaction Coordinates. Mol. Sim. 2014, 40, 784793. 35. Maragliano, L.; Vanden-Eijnden, E. On-the-fly String Method for Minimum Free Energy Paths Calculation. Chem. Phys. Lett. 2007, 446, 182−190. 36. Fukui, K. The Path of Chemical Reactions - the IRC Approach. Acc. Chem. Res. 1981, 14, 363−368. 37. Branduardi, D.; Gervasio, F. L.; Parrinello, M. From A to B in Free Energy Space. J. Chem. Phys. 2007, 126, 054103. 38. Gaussian 09, Revision D.01, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; 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.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.;
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Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian, Inc., Wallingford CT, 2009. 39. The deviation from the ideal 0.5 value is due to the asymmetric shape of the FESs in the TS regions from where the trajectories were initiated. 40. Relative distributions of structural parameters for reactions 2 + H2 and 3 + H2 are provided in the SI. 41. The equilibrium B-H and P-H bond distances in the zwitterionic product of the 1 + H2 1H2 are 1.22 and 1.40 Å (optimized structures are provided in the SI). 42. The asynchronous character of FLP induced H2 splitting was observed in several static DFT studies as well. See for instance refs. 9c, 10c, 11d,e. 43. For details of the velocity analysis, see Supporting Information. 44. To illustrate changes from the equilibrium T = 300 K generated for TS ensembles, the average atomic kinetic energies (Ki = mivi2/2) were converted to temperatures (Ti) via Ti = 2Ki/3kB, where kB is the Boltzmann constant. 45. At the transition state, the D-H bond is very far from the equilibrium distance measured in the product molecule (2.1 Å versus 1.4 Å, see Figure 4d), therefore the hydrogen of the DH bond will gain a substantial amount of kinetic energy when moving towards the product state. 46. The equations employed for the velocity decomposition are provided in the SI.
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TS
D∙∙∙A + H2
concerted mechanism
DH+/AH−
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