The Mechanism of H2 Activation by (Amino)Carbenes

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Mar 23, 2011 - shown that bubbling hydrogen into a solution of both cyclic or acyclic alkyl amino carbenes produces only the corresponding alkane products ...

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The Mechanism of H2 Activation by (Amino)Carbenes Fernanda Duarte and Alejandro Toro-Labbe* Laboratorio de Química Teorica Computacional (QTC), Facultad de Química, Pontificia Universidad Catolica de Chile, Santiago, Chile ABSTRACT: We have computationally investigated the mechanism of the H2 activation reaction by (amino)carbenes compounds. Describing the electronic activity taking place during the reaction through the Reaction Electronic Flux, it has been possible to elucidate the mechanism of the hydrogen activation process and assign the energetic cost associated to every chemical event that drives the process along the reaction coordinate; this is crucial information to rationalize the reported experimental results. It has been observed that the substituent effect may induce early charge-transfer phenomena that increases the energy barrier and lowers the exothermicity of the reaction. Reversibility of the process is discussed in light of specific interactions defining the components of the reverse activation energy.

1. INTRODUCTION Hydrogen, H2, is not only considered to be the fuel of the future, but is also vital in several industrial processes, organic synthesis, and also in biological functions.1,2 The overwhelming majority of systems known to activate H2 under ambient conditions involve reaction at a transition metal center, where the bond activation is facilitated by interaction of the σ-bonding orbital of H2 with a vacant d orbital on the metal and through a backdonation from an occupied metal d orbital to the empty σ* orbital of H2.1 Despite the fact that bond activation by transition-metal complexes has enormous utility, there are nonetheless certain disadvantages, for example many precious metals, such as platinum, can be environmentally unfriendly and difficult or economically prohibitive to synthesize. Metal-free systems that either react with or liberate H2 are rare;3 H2 activation at nonmetals under ambient conditions has only been observed by Li and Xu in the fullerene system;4 Power and co-workers have reported addition of H2 to digermanes5 and, more recently, Stephan and co-workers have reported heterolytic splitting of H2 by phosphine-borane species.6,7 These systems, termed as “frustrated Lewis pairs”, combine sterically hindered Lewis acid and Lewis base moieties and can be considered the analog of heterolytic cleavage of H2 at metal centers. More recently, Bertrand and co-workers have also demonstrated that certain singlet cyclic (alkyl)(amino)carbenes can activate H2 without a separate Lewis acid partner under mild conditions.8 Singlet carbenes have an sp2-type lone pair and an empty p orbital, and therefore it might be expected that they are suitable for donation and back-donation that activate H2, thus mimicking the behavior of metals. These experiments have shown that bubbling hydrogen into a solution of both cyclic or acyclic alkyl amino carbenes produces only the corresponding alkane products, the bi(amino)carbenes were inert toward H2 (Scheme 1). It was found that (alkyl)(amino)carbenes can also cleave the CdO bond to afford amino ketenes9 and activate the N-H bond in NH3, a reaction that is rare for transition metals.8,10 r 2011 American Chemical Society

Concerted as well as stepwise mechanisms for activation reactions with singlet carbenes are conceivable, where the favored route strongly depends on both the polarity of the bond being activated and the philicity of the carbene. The stepwise reaction pathway is expected for nucleophilic or electrophilic carbenes, while for biphilic carbenes, the activation process can become concerted.11,12 Computational investigations, have suggested a concerted, asynchronous process for the activation of C-H, H-H, and N-H bonds; additionally, it has been shown that molecular hardness (η)13 may be used as a guide to predict the reactivity of carbenes toward the X-H bond.14-16 In this work, the H2 activation reaction, induced by a set of carbenes will be studied. In order to rationalize the experimental results, the chemical events that drive the H2 activation reaction and the influence of the substituent will be analyzed in detail through a combined use of conceptual DFT based reactivity descriptors13,17,18 within the framework defined by the Reaction Force analysis.19

2. THEORETICAL BACKGROUND 2.1. The Reaction Force. For any process with energy profile E(ξ), along the reaction coordinates ξ, the reaction force F(ξ), is defined as follows:19

FðξÞ ¼ -

dE dξ

ð1Þ

For any elementary step, the reaction force is characterized by a minimum and a maximum located at ξ1 and ξ2, which are the inflection points of E(ξ). For a one-step process, where the reactants (R) and the products (P) are separated by an energy barrier, these points provide a natural partitioning of the reaction coordinate into three regions, the so-called reactants, transition Received: July 29, 2010 Revised: February 3, 2011 Published: March 23, 2011 3050

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Scheme 1. Sketch of the H2 Activation Reaction by (Amino)Carbenes

state, and products regions. Our experience in a series of studies20-23 has been that within each region tends to dominate certain factors. The reactant region (ξR e ξ e ξ1) involves preparation of reactants to chemical transformation and is dominated by structural arrangements. The transition state region (ξ1 < ξ < ξ2) involves transition from activated reactants to activated products, it is here where most bond breaking/ forming processes occur and electronic reordering is predominant. Finally, the product region (ξ2 e ξ e ξP), again is dominated by structural arrangements, mainly structural relaxation that leads to the final equilibrium geometry of the products. The reaction force analysis provides a natural decomposition of the activation and reaction energies, ΔE‡ and ΔE°, into different components that emerge from the above definition of reaction regions:24 ΔE‡ ¼ ½EðξTS Þ - EðξR Þ ¼ W1 þ W2 ΔEo ¼ ½EðξP Þ - EðξR Þ ¼ W1 þ W2 þ W3 þ W4 where, W1 ¼ W3 ¼ -

R ξ1 ξR

R ξ2

ξTS

W2 ¼ -

FðξÞdξ > 0

FðξÞdξ < 0

W4 ¼ -

R ξTS ξ1

R ξP ξ2

ð2Þ ð3Þ

FðξÞdξ > 0

FðξÞdξ < 0

ð4Þ

are the reaction works associated to processes occurring at every stage of the reaction. 2.2. Reaction Electronic Flux: A Partition Scheme. DFT provides the theoretical framework for rationalizing chemical reactions in term of the response of the molecular system toward the variation of N (the total number of electrons) and υ(r) (the external potential). The response to changes in N, when the external potential remains constant, is measured at first order by the chemical potential μ.13,17 This quantity has been related conceptually to the electronegativity χ of a system:25  μ¼

DE DN

context of Koopman’s theorem: 1 μ = ðεL þ εH Þ 2

Equation 6 provides a way to determine numerical values of μ all along the reaction coordinate, thus leading to μ(ξ). Associated to eq 6, a new concept called reaction electronic flux (REF) has been introduced:26   dμ JðξÞ ¼ ð7Þ dξ The J(ξ) profile has proven to be useful in the characterization of electronic activity that is actually taking place along the reaction coordinate.27,28 In analogy with thermodynamics concepts, the changes of the chemical potential along the reaction coordinate can be interpreted as describing the spontaneity of electronic reordering processes that takes place during the reaction. For instance, positive values of REF will entail spontaneous changes in the electronic density which, in our experience, are related with bond strengthening or forming processes. In contrast to this, negatives values of REF indicate non spontaneous electronic reordering that should be associated with bond weakening or breaking processes. It is useful to rationalize the electronic activity characterized by the REF through the phenomenological decomposition of J(ξ) in terms of electronic polarization and transfer contributions:27-29 JðξÞ ¼ Jp ðξÞ þ Jt ðξÞ

¼ -χ

ð5Þ

Operational schemes for the calculation of this quantity are based on the three-point finite-difference approximation to ((∂E)/ (∂N)).13 This quantity may be further approximated with the frontier HOMO and LUMO molecular orbital energies in the

ð8Þ

The polarization flux is calculated when the reactive complex is partitioned into n molecular fragments27-29 which are treated separately along the reaction coordinate through the counterpoise method.30,31Thus, the polarization flux is defined as the sum of the fragments fluxes: n

Jp ðξÞ ¼

 υðrÞ

ð6Þ

∑ JpðiÞðξÞ i¼1

with JpðiÞ ðξÞ ¼ -

  Ni dμi N dξ

ð9Þ

ð10Þ

where Ni is the number of electrons of fragment i and N is the total number of electrons of the whole system. For example, the 3051

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polarization flux of a bimolecular reaction A þ B should be given by the following: Jp ðξÞ ¼ JpðAÞ ðξÞ þ JpðBÞ ðξÞ     NA dμA NB dμB ¼ N dξ N dξ

electrons, two Fukui functions have been introduced through the finite difference approximation: fþ(r), that measures the electrophilic power at point r in the molecule and f-(r) measuring the nucleophilic power at r.33 In 2005, Morell et al.18 proposed a new descriptor for chemical reactivity, termed the dual descriptor:

ð11Þ

Δf ðrÞ = ½f þ ðrÞ - f - ðrÞ = ½FLUMO ðrÞ - FHOMO ðrÞ ð17Þ

where μA(ξ) and μB(ξ) are the chemical potentials of A and B, respectively. In this context, the polarization flux of fragment i accounts for the deformation of its electronic density formed by Ni electrons, in response to the external field created by the other fragment(s). In the present work, the arbitrary fragmentation of the supermolecule [carbene:H2] in carbene and H2 moieties was actually taken all along the reaction coordinate. The flux associated to electronic transfer is then given by the following:

Δf(r) allows the electrophilic and nucleophilic regions within a molecule be detected simultaneously; it will be positive in electrophilic regions and negative in nucleophilic regions.

Jt ðξÞ ¼ JðξÞ - Jp ðξÞ ¼ -

  dμ þ dξ

n

∑ Ni i¼1 N

  dμi dξ

ð12Þ

Making use of the equalization principle for the chemical potential, expressed as follows:   Ni μðξÞ μi ðξÞ ¼ i¼1 N nf



ð13Þ

leads to the following expression for eq 7: dμ ¼ JðξÞ ¼ dξ

  Ni dμ ¼ i ¼ 1 N dξ nf



n

∑ J ðiÞðξÞ i¼1

ð14Þ

Now, using eqs 9, 10, and 14, the electronic transfer flux between the fragments can be expressed as follows: nf   nf   Ni dμi Ni dμ Jt ðξÞ ¼ i ¼ 1 N dξ i ¼ 1 N dξ nf   n Ni d ðiÞ ½μi ðξÞ - μðξÞ ¼ ¼ Jt ðξÞ ð15Þ i¼1 i ¼ 1 N dξ

∑ ∑





thus featuring a difference of chemical potentials, a clear signature of electronic transfer. It can be observed that within this scheme, eq 8 provides a physical partition of the reaction electronic flux through the polarization and transfer terms. On the one hand, eqs 9, 10, 14, and 15 provide a chemical partition of the REF, now in terms of contributions associated with the reacting fragments. Polarization, transfer, and total fluxes associated to each fragment can be directly obtained through the use of the above equations. 2.3. Fukui Functions and the Dual Descriptor. The Fukui function, f(r) introduced by Parr and Yang32 is a local property that describes the local changes in the electron density of the system due to an infinitesimal perturbation in the total number of electrons N, at constant external potential υ(r):   DFðrÞ ð16Þ f ðrÞ ¼ DN υðrÞ f(r) reflects the ability of a molecule to accept (donate) electrons from (to) another system. Due to the discontinuity of the derivative of the electron density with respect to the number of

3. COMPUTATIONAL METHODS All the structures have been fully optimized using the Becke3 for exchange34 and Lee-Yang-Parr for correlation35-37 (B3LYP) functionals with standard 6-311G** basis set. The minimum energy path in going from reactants to products were calculated through the intrinsic reaction coordinate procedure (IRC = ξ).38,39 Frequency calculations on reactants, transition states, and products were performed to confirm the nature of the corresponding critical point along the reaction path. Using the geometries obtained from the IRC procedure, molecular properties were determined through single point calculations at the same level of theory. The counterpoise method using the H2 þ carbene fragmentation, keeping the geometry they have at each point along the reaction coordinate, was used to determine the individual chemical potentials and then the polarization fluxes. Natural Bond analyses (NBO)40 were carried out to obtain Wiberg bond index and the natural charges along the reaction coordinate. All calculations were carried out using the Gaussian 03 program.41 4. RESULTS AND DISCUSSION 4.1. Energy and Reaction Force Profiles. Scheme 1 shows the reactions under study: reactions R1 and R2 are model systems for the H2 activation by tert-butyl diisopropylamino carbene (R10 ) and 5,5-bi(methyl) N-(2,6-diisopropylphenyl)-3cyclohexane cyclopentene, respectively; reactions R3 and R4 are model systems for the H2 activation by Bis(diisopropylamino)carbene (R30 ) and 2,5-bis(tert-butylamino)cyclopentene, respectively. The energy and reaction force profiles are displayed in Figures 1 and 2; Table 1 contains the energetic information of the reactions. In what follows, we will analyze model reactions R1-R4 and in Section 4.6, reactions R10 and R30 will be discussed in the light of the precedent results. All reactions are thermodynamically controlled, being strongly exothermic. Reactions R1 and R2 exhibit ΔE° values that are about twice those of R3 and R4. However, Table 1 shows that the energy barrier are considerably higher in R3 and R4 with respect to the values of R1 and R2. These results indicate that the presence of a second amino group is unfavorable both kinetically and thermodynamically, since it decreases the exothermicity of the reaction by a factor of 1.8 and increases the energy barrier by a factor of 1.7. Although they do not give insights about the nature of the energy barrier or the aspects that might be inhibiting the reactions, these results are consistent with the fact that bi(amino)carbene systems are experimentally inert toward the H2 activation.8 To get a more detailed vision on the energetic barrier, the reaction force analysis is of great utility.19 The amount of work involved at each step along ξ was obtained by integration 3052

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Figure 1. Energy profile (in kcal/mol) for the H2 activation reactions R1-R4.

Figure 2. Reaction force profile (in kcal/[mol ξ]) for the H2 activation reactions R1-R4.

of the reaction force as indicated by 4. According to previous studies,20-22 the first step of the activation process of an elementary step is dominated by structural rearrangements needed to activate the system, whereas the second one is

dominated by reordering in the electronic cloud. It can be observed in Table 1 that in all reactions, the energy barrier is determined by W1, it represents more than 70% of the energy barrier. This amount of work principally, but not exclusively, involves the 3053

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approach of the H2 molecule to the carbene center, leading to changes in angles C-(H-H) and X-C-X(X = N,C). The work that follows in the TS region, from ξ1 to the transition state, is given by W2. The contributions of W2 to ΔE‡ is smaller than W1 and almost the same for all reactions (less than 30%). However, it is important to note that if one compares R1 and R3, W1 increases by 63%, while W2 increases by about 83%. This observation suggests that the presence of a second amino group inhibits the reaction by acting mainly on the electronic part of the activation energy. It has already been mentioned that the presence of a second amino group increases the activation energy and its components by a factor of about 1.7; the situation is opposite for the reverse reaction where the activation energy decreases by a factor of 1.2 and the components W3 and W4 present a different pattern of change: while W3 remains quite constant, W4 experiments considerable changes due to the presence of the second amino group, it decreases by a factor about 1.5. In this context, the Table 1. Reaction Energy (ΔE°); Forward (ΔE6¼ f ) and Reverse (ΔE6¼ r ) Energy Barriers Together with the Works Associated to the Different Stages of in the H2 Activation Processa reaction

a

ΔE°

ΔE6¼ f

ΔE6¼ r

W1

W2

W3

W4

R1

-58.3

21.3

79.6

15.9

5.4

-46.3

-33.3

R2

-54.2

23.7

77.9

17.3

6.4

-45.5

-32.4

R3

-33.2

34.3

66.7

24.4

9.9

-45.2

-21.5

R4 R10

-30.2 -59.7

35.0 18.9

65.2 78.6

25.6 14.5

9.4 4.4

-43.8 -47.9

-21.4 -30.7

R30

-43.5

27.4

70.9

22.3

5.2

-41.6

-29.3

All values are in kcal/mol.

irreversibility of the reactions seem to be ensured by a large value of W3. The chemical events that define the forward reactions are basically the breaking of the H-H bond and the forming of two C-H bonds; the reverse reaction involves the opposite events, namely two C-H bonds breaking and the H-H bond forming. It is our experience that forming processes lead to exothermic reactions, whereas breaking ones lead to endothermic reactions. In this context, reversibility of reactions R1-R4 is not possible because the reverse reactions are overall a net breaking process. In principle, one can argue that the addition of external species, as a metallic center, could help bond forming processes thus lowering W3 to facilitate the formation of the hydrogen molecule.42 A nice illustration of the above idea is the catalytic dehydrogenation of ammonia-borane,43 where a nickel N-heterocyclic carbene (NHC) catalysts releases free NHC into the reaction media to facilitate the release of H2. 4.2. Chemical Potential and Reaction Electronic Flux. Taking into account that the cyclic systems have shown a similar behavior to its acyclic analogues and the observed changes in reaction and activation energies are mostly due to substitution of a methyl group by an amino group, hereafter only acyclic systems, reactions R1 and R3, will be discussed in detail. For these systems, the profiles of μ(ξ) and J(ξ), which have been calculated using eqs 6 and 7, are shown in Figure 3. It can be noticed that in both reactions, the chemical potential is relatively constant in the reactant region. Afterward, a broad peak in the transition state region sets in, and remains until the product region. In order to explore in depth the electronic processes that take place along the reaction coordinate the REF, J(ξ), was calculated. During the first part of the reactant region, the REF presents a similar trend in both reactions, practically following a zero flux regime, thus providing clear evidence that at this stage the

Figure 3. Profile of chemical potential (in kcal/mol) and reaction electronic flux for reactions R1 and R3 (in kcal/[mol ξ]). 3054

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Figure 4. REF decomposition: profiles of polarization and electron transfer flux for the H2 activation reactions R1 and R3.

structural changes associated to the approaching of the two fragments are predominant and determine the first part of the activation energy W1. Afterward, entering the TS region of R1 and of R3, a spontaneous electronic activity with J(ξ) > 0 thus associated to bond strengthening processes begins to emerge. A closer view shows that in R3, a first maximum flux is reached at the reaction force minimum, while in R1 it is observed later, just before the transition state. After the maximum, at the TS region, both reactions begin to display some differences in the REF profiles. In R1, J(ξ) is positive until the TS configuration, where it is zero (J(ξTS) = 0). Then a broad negative peak shows up at the TS region becoming positive at the product region. In R3, J(ξ) becomes negative before the TS configuration where it is a minimum, then it shows a narrow positive peak at the product region. It seems that in R1 a spontaneous process that can be associated with polarization of the carbene moiety allows to reach the TS configuration. In R3 this effect comes together with the H-H bond breaking and the weakening of the C 3 3 3 N — bond, indicating that an electron transfer process is also necessary. These processes mostly take place before the TS configuration. For both reactions, a negative flux regime characteristic of bond breaking processes dominates the transition state region in a non spontaneous electronic reordering. To confirm the above finding and to elucidate the origin of the REF at different points along the reaction coordinate, fragmentation of the supermolecule was made setting H2 and the carbene units as the molecular fragments all along the reaction coordinate. The results for polarization and transfer fluxes, obtained through eqs 9, 10, and 12, are displayed in Figure 4. It shows for each reaction the contributions Jp(ξ) and Jt(ξ) to J(ξ) (left panels) and the fragment contributions to Jp(ξ) (right panels). It can be noticed that polarization and charge transfer processes occur quite simultaneously along the reaction coordinate, with polarization effects being spontaneous Jp(ξ) > 0 and most

electronic transfer effects being nonspontaneous along the reaction coordinate. At the first stage, the positive REF (J(ξ) > 0) observed in R1 mainly comes from the polarization of the carbene center due to the interaction with the hydrogen molecule, at this point electronic transfer activity is almost absent. It only becomes dominant at the transition state region, with a global minimum in the second part of the TS region. A different behavior of the REF is observed for R3 where the main contribution to the initial REF peak comes from electronic transfer Jt(ξ), showing a local maximum value at the minimum of the reaction force, with a smaller contribution from polarization. Then, during the first part of the TS region, Jt(ξ) decreases constantly reaching its minimum at the TS geometry. Thus, showing that the major charge transfer between the two fragments are more intensive in the first part of the TS region. It can be noted that in both reactions, polarization of the carbene molecule increases along the reaction coordinate, which is not only due to the polarized carbon center but also due to the electronic reordering over the C-N bond(s). At the product region, both systems show a positive peak which is again originated by the polarization of the carbene fragment, here the pyramidization on the NH2 group from the planar structure, coupled with other structural rearrangements in the system results in a spontaneous electronic reordering (J(ξ) > 0) that leads to the product state. In summary, after the zero flux regime observed for both systems at the reactant region, the activation process of each one occurs in different ways. In R1, a spontaneous polarization flux (Jp(ξ) > 0), which start at the end of the reactant region, activates the reaction and the subsequent nonspontaneous electronic transfer flux (Jt(ξ) < 0) at the TS region. Here, the electron transfer activity is mainly located in the second part of the TS region. However, in R3 the activation process is mainly triggered by a spontaneous electron transfer processes, with a smaller contribution from polarization, then a nonspontaneous (Jt(ξ) < 0) 3055

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Figure 5. Dual descriptor along the reaction force profile of the H2 activation reactions R1 and R3.

electronic transfer flux drive the process in order to reach the TS structure. Finally, at the product region the polarization process begins to dominate in both systems and comes together with the structural relaxations to reach the corresponding product of the reactions. In Section 4.4 the observed electronic activity will be related to the dual descriptor, adding some valuable information in order to support the electronic flux analysis. 4.3. REF and Potential Energy. The zero flux regime observed in the reactant region of both reactions confirms that W1 is mainly due to the structural preparation of the reactants to produce the chemical change. The polarization observed within the TS region in R1 is mainly responsible for W2. In short, the activation energy of R1 is about 70% associated to structural rearrangement, and the remaining 30% is mainly due to polarization effects on carbene with some electronic transfer (see Figure 4). In R3, the electron transfer peak emerges within the reactant region, thus indicating that W1 contains some electronic activity. W2 is mainly due to electron transfer with a smaller contribution from polarization activity. In summary, the previous analysis confirms that the reactant region predominantly involves structural effects, whereas in the TS region, the electronic effects are predominant. R1 is activated mainly through electron polarization at the carbene center while R3 is mostly activated by electronic transfer effects featuring an early electron transfer activity that shows up before leaving the reactant region.

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4.4. Nucleophilic and Electrophilic Character of Carbenes. Since the philicity of the carbene has been suggested to be one of the factors that determine the reaction's mechanism, in this section the evolution of the dual descriptor Δf(r) along the reaction coordinate is discussed. Δf(r) functions have been calculated at the five key points along the reaction coordinate: reactants, force minimum, transition state, force maximum, and products. In Figure 5, we display the dual descriptor at these points along the reaction force profiles for R1 and R3; threedimensional maps of the nucleophilic/electrophilic behavior of the different sites within the composite systems are shown; areas in yellow are electrophilic sites with Δf(r) > 0, whereas red areas display nucleophilic sites with Δf(r) < 0. First, at the reactants, it is possible to note that in R1 the carbene center is biphilic because it features both electrophilic (yellow) and nucleophilic (red) character, the nucleophilic character is primarily due to the π-donating nature of the amino substituent bonded to the carbene atom while the electrophilic character has its origin in the divalent carbon nucleus. Additionally, it can be checked out that the nitrogen atom has an important electrophilic character. In R3, the carbene center is markedly nucleophilic and the nitrogen atoms show a very small electrophilic character. The feasibility of the H2 activation reaction is closely related to the electrophilic capability of the carbene center, this is observed in R1 from the very beginning of the reaction, whereas in R3 it is acquired through the structural rearrangements that initiate the reaction. Eventually, a very small electrophilic character emerges at the carbene center in R3 by the force minimum and increases within the transition state region. It is interesting to point out that at the reaction force minimum the nucleophilic power of the carbene in R3 is partially transferred to the hydrogen molecule, thus indicating an “early” electron transfer from carbene center to one hydrogen atom, in agreement with our previous observations in the R3 REF profiles. In contrast, the nucleophilic behavior of the hydrogen in R1 emerges only at the TS configuration, where the electron transfer process start to dominate. The biphilic behavior of the carbene center of R1 indicates that it may mimic a metallic center thus facilitating the activation of H-H bond. In contrast to this, in R3 the dual behavior is observed well entered the transition state region, making R3 much less feasible than R1, thus explaining the much low energy barrier in R1 in comparison to that of R3, see the energetic data in Table 1. The transition state configuration of R1 still presents a carbene center featuring both nucleophilic and electrophilic behavior, whereas in R3 the electrophilic character largely predominates over the nucleophilic power. Finally, once reached the reaction force maximum systems evolve similarly, in both reactions the products show that the nucleophilic character is exclusively localized on the nitrogen atoms, while the central carbon atom exhibit a neutral behavior. It is this neutrality over the carbon center which causes the irreversibility of the process, as indicated by the high W3 values. Eventually, reversibility can be forced by inducing an electrophilic behavior in that center through the action of external agents such as external fields or catalysts. The qualitative analysis of the relative orientation of the dual descriptors lobules of carbene and hydrogen, may throw more light on the reaction mechanisms. Figure 5 can be used for such a qualitative analysis keeping in mind that the dual descriptor of Figure 5 is that of carbene, whereas the dual descriptor of H2 features a nucleophilic lobule along the H-H bond and two electrophilic lobules pointing out on the same axis. It can be seen 3056

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Figure 6. Wiberg bond order evolution and transition state complex for the H2 activation reactions R1 and R3.

that at the reactant structure, the orientation of the hydrogen molecules is the same in both reaction, with one of the electrophilic lobules in H2 oriented to the electrophilic lobule centered in C1. As the reaction moves forward, the hydrogen molecule starts to be orientated in such way that the nucleophilic lobule centered in H-H bond interacts with the carbene center. In R1, this interaction is clearly visible at the minimum of the force, where the electrophilic lobule centered in C1 interacts with the nucleophilic lobule of H-H, while the lone pair centered in C1 interacts with the electrophilic one of the hydrogen molecule. This interaction is increased at the transition state, in line with the observation of a synchronous activation process (see next section). However, at the minimum of the force the electrophilic lobule centered in C1 of R3 does not interact with the nucleophilic lobule centered in H-H bond. At the TS structure even when the carbene center shows an electrophilic character, it is not enough to allow an optimal overlap with the nucleophilic lobule over H-H bond. A consequence of this mismatch in the orientation might be the delay on the formation of the second C-H bond for bis(amino) systems, which could explain the inertness of this system under experimental conditions. 4.5. Natural Bond Analysis. Figure 6 displays the evolution of the Wiberg bond order along the reaction coordinate for the critical bonds defining the main chemical events that takes place during the reaction. It can be seen that the H4-H5 and C1-Hn (n = 4,5) bonds begin to change before reaching the transition state region; these changes, together with the constant polarized charges observed in H2, reveal that at the beginning of the transition state a electron transfer (earlier in R3) and polarization takes place which is characterized by a positive flux. Note in R1 that along the reaction coordinate the C1-C2 bond remain fairly constant, thus indicating that the methyl substituent acts only as

spectator of the electronic processes that are taking place. However, the C—N bond order remains practically constant within the reactant region at a value that suggests a double bond character with a planar NH2 group. This bond evolves toward a single C—N bond at the product region where the NH2 group become pyramidal; as expected, the main changes of the C—N bonds are observed at the TS region and are in part responsible of the increase in the polarization flux. In the transition state region, the charge transfer and bond breaking/forming processes take place. In R1, the H4—H5 bond breaks and the C1—Hn bonds form in a quite synchronous process, with the electron transfer processes mostly centered in the second part of the TS region. This synchronicity is in agreement with the previously discussed biphilic nature of the carbene. In R3, the C1—Hn bonds forming processes are asynchronous, in this case the C1—H4 bond has been almost completely formed at the TS point, while the C1—H5 bond achieve formation later. At the transition state, only a 40% of the C1—H5 bond formation has been achieved, compared with the 80% formation of the C1—H4 bond. This asynchronous process is featured in the REF profile, where an early electron transfer process takes place at the beginning of the TS region, indicating the first bond forming process. Then, at the end of the transition state a shoulder due to charge transfer processes is again observed (see Figure 3). 4.6. The Effect of Substituents. One of the keys for the isolations and enhanced reactivity of the carbenes capable to mimic the behavior of metal systems lay in the recognition that they require very large substituents to prevent secondary reactions such as dimerization.3 In order to understand the influence they have over the whole activation process, we have carried out the study of hydrogen activation by tert-butyl diisopropylamino 3057

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Figure 7. Energy profile (in kcal/mol) and reaction electronic flux (in kcal/[mol ξ]) for the H2 activation processes R10 and R30 .

carbene (R10 ) and Bis(diisopropylamino)carbene (R30 ), which are actually the compounds used in the experimental H2 activation reaction.8 The energy and reaction electronic flux profile for both systems (Figure 7) are in very good agreement with previous results for the model reactions; the activation and reaction energies follow the previously observed trends, see Table 1. The energy barriers are lower in comparison with the R1 and R3 model reactions. The catalytic effect of the substituents is observed at both stages of the reaction, showing a marked decrease of both W1 and W2, although in R30 the catalytic effect is emphasized at the transition state region where W2 decreases by a factor of 1.9 with respect to the value of R3. However, it is interesting to note that W3 is still large, being the leading term of the reverse energy barriers. The reaction electronic flux also follows the pattern encountered in R1 and R3, a polarization process at the beginning of the transition state region is followed by a negative peak featuring electron transfer processes. However, the polarization processes due to relaxation observed at the product region are less intensive in the new systems, it appears that the use of bulky substituents makes the NR2 group more planar, this leads to a less intensive structural relaxation process to reach the product, this can be confirmed through the values of W4.

5. CONCLUSIONS In the present work, a comprehensive study of the H2 activation reaction by (amino)carbene systems has been performed. It was found that the electronic activity in alkyl(amino)carbene reactions is initiated by spontaneous polarization, followed by a non-spontaneous electronic transfer. Bi(mino) carbene systems feature an early electron transfer activity that shows up before leaving the reactant region. It has been found that in all cases, the activation energy is mostly due to structural

rearrangements. However, the electronic processes that take place after that are different. R1 is activated mainly through electron polarization at the carbene center, while R3 is mostly activated due to electronic transfer effects. Biphilic behavior of the carbene center of alkyl(amino)carbenes lead to a positive overlap between the carbene center and the H-H bond. It indicates that these systems may mimic a metallic center thus facilitating the activation of H-H bond. It is this biphilic character that allows an optimal polarization and help to the synchronicity in the bond formation processes. Contrarily, nucleophilic carbene centers lead to an early electronic transfer and an asynchronous bond formation process. The irreversibility for this process stems from the high values of W3, associated with the breaking process of the C-H bonds. We propose that external agents could help lower the reverse activation energy to produce H2.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]

’ ACKNOWLEDGMENT This work was supported by Fondecyt through project 1090460. F.D. wishes to thank CONICYT for Doctoral and Apoyo de Tesis fellowships and to L’OREAL-UNESCO for Women in Science 2009 award. We also thank the referee for helpful suggestions. ’ REFERENCES (1) Kubas, G. Chem. Rev. 2007, 107, 4152. (2) Siegbahn, P. Adv. Inorg. 2004, 56, 101. (3) Power, P. Nature 2010, 463, 171. 3058

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