Catalytic Mechanism of H2 Activation by a Carbenoid Aluminum

Article pubs.acs.org/JPCC

Catalytic Mechanism of H2 Activation by a Carbenoid Aluminum Complex Nery Villegas-Escobar, Soledad Gutiérrez-Oliva,* and Alejandro Toro-Labbé* Nucleus Millennium Chemical Processes and Catalysis (CPC), Laboratorio de Química Teórica Computacional (QTC), Facultad de Química, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile S Supporting Information *

ABSTRACT: The catalytic mechanism of H2 activation by a carbenoid aluminum compound is analyzed in great detail. On the basis of the reaction force analysis, the electronic activity that takes place during the chemical reaction was identified and characterized through the reaction electronic flux and rationalized in terms of chemical events that drive the reaction. Successive transformation of the nucleophilic or electrophilic character of the reagents along the reaction coordinate monitored through the dual descriptor allows us to obtain a very complete and detailed description of the reaction mechanism that proceeds through a two-stage mechanism in a one-kinetic-step process.

1. INTRODUCTION More than a decade ago Roesky and coworkers characterized the first stable monomeric aluminum compound, analogue to carbene,1 and they carried out the synthesis and characterization of a stable singlet carbenoid Al(I) center coordinated to the diiminoacetylacetonate ligand NacNac (NacNac = [ArNC(Me)CHC(Me)NAr]− and Ar = 2,6-iPr2C6H3). The importance of this compound is stressed by the fact that only a few low-valence aluminum compounds have been isolated. Although there are some examples in which aluminum centers exhibit valence +2,2−6 Al1+ centers are not thermodynamically stable. For this reason, it is interesting to learn about the behavior and nature of this kind of compound and the mechanism of the reactions in which they are involved. Recently, Nikonov and coworkers used the NacNacAl(I) compound toward the activation of σ-bonds, using H−X bonds (X = H, Si, B, Al, C, etc.) through oxidative addition of Al(I).7 The activation of σ-bonds by metallic centers can be carried out in two ways: (a) formation of σ-complexes [M−(σ···H−X)]8,9 and (b) oxidative addition [MH(X)].10,11 The activation of σbonds has been for a long time an exclusive feature of transition metals as a part of catalytic cycles. However, Nikonov7 and other authors12,13 have shown that σ-bond activation by main group elements is possible, allowing their use in catalytic applications. The main goal of this study is to analyze the mechanism of oxidative addition of H2 to the Al(I) complex displayed in Figure 1 through the use of the reaction force,14,15 reaction electronic flux,16,17 and dual descriptor.18 © 2015 American Chemical Society

Figure 1. Oxidative addition of the Al(I) carbenoid complex toward H2 activation. It should be noted that we used NacNac = [ArNC(Me)CHC(Me)NAr]− with Ar = Ph.

2. THEORETICAL BACKGROUND 2.1. Reaction Force. The reaction force14,15 is a rigorously defined approach to analyze chemical processes, and it gives relevant information about changes that occur when reactants (R) are transformed into product (P) passing through a transition state (TS).19 The reaction force is defined as the negative derivative of the potential energy E(ξ) with respect to the intrinsic reaction coordinate (IRC = ξ) F (ξ ) = −

dE(ξ) dξ

(1)

Received: September 14, 2015 Revised: November 1, 2015 Published: November 2, 2015 26598

DOI: 10.1021/acs.jpcc.5b08957 J. Phys. Chem. C 2015, 119, 26598−26604

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The Journal of Physical Chemistry C

the discontinuity of N, the total number of electrons of the system, the chemical potential can be estimated using the finite difference approximation and the Koopmans’ theorem as follows26,27

When F(ξ) is negative, it is a retarding force that opposes the process. The latter means that energy is required to overcome it. Furthermore, the retarding force is then associated with the activation process.20 On the other hand, a positive reaction force drives the formation of the product of the reaction, and energy is being released; therefore F(ξ) > 0 is associated with relaxation processes,20 and F(ξ) = 0 at the reactant, TS, and product, ξR, ξTS, and ξP, respectively. Critical points of F(ξ) are found at ξ1, a minimum before the transition state, and ξ2, a maximum after the transition state. Using these critical points, the reaction coordinate can be divided into reaction regions. For a single-step reaction three reaction regions are defined. The reactant region located between ξR and ξ1, i.e., from R to the force minimum. Here the reaction force is negative, and structural changes prepare the reactants for the following steps of the reaction. The transition state region is located from ξ1 to ξ2, and it is mostly dominated by intensive electronic reordering. Most bond formation/breaking occurs in this region. Within the TS region the reaction force is negative before the transition state and positive after it. The product region is located between ξ2 and ξP. Within this region the reaction force is positive, and energy is released through structural relaxation to reach the product structure (P). All three reaction regions are specific regions in which different mechanisms might be operating.14,20 The complete and partial integration of the force profile produces interesting information, in particular on reaction and activation energies, ΔE° and ΔE⧧, respectively. Reaction works are energies associated with specific reaction regions21 W1 = −

ξ1

∫ξ

F(ξ)dξ > 0

R

W3 = −

∫ξ

ξ2

W2 = −

∫ξ

ξTS

1 1 μ ≈ − (IP + EA) ≈ (ϵH + ϵL) 2 2

where IP is the first ionization potential; EA is the electron affinity; and ϵH and ϵL are the energies of the highest occupied and the lowest unoccupied molecular orbitals, HOMO and LUMO, respectively. The use of the frontier molecular orbital (FMO) energies, ϵH and ϵL, as an approximation of IP and EA is also supported by Janak’s Theorem.28 Furthermore, the connection of the Kohn− Sham HOMO eigenvalue to −IP and the physical meaning of the Kohn−Sham LUMO are well stablished.23,29−33 In this context, we have found that the negative of Hartree−Fock and Kohn−Sham HOMO orbitals define upper and lower limits, respectively, for experimentally obtained values of IP.34 In addition, we have confirmed that the use of FMO energies produces a trend for μ along the IRC similar to finite difference approximation. To characterize the electronic activity that takes place during a chemical reaction, the reaction electronic flux (REF) has been introduced, and it is defined as16,17

⎛ dμ ⎞ J (ξ ) = − ⎜ ⎟ ⎝ dξ ⎠

TS

W4 = −

∫ξ

ξP

F(ξ)dξ < 0

2

Note that W2 and W3 are defined in the TS region; therefore, W2 and W3 represent the energy associated with electronic activity, whereas W1 and W4 would be associated with structural reordering taking place during the reaction. An important feature of the reaction force is that it produces a rational partition of both reaction and activation energies. The reaction energy has the following form ΔE° = [E(ξP) − E(ξR )] = W1 + W2 + W3 + W4

(2)

indicating that the thermodynamics of the reaction can be understood in terms of structural and electronic effects. On the other hand activation energy can be expressed as ⧧

ΔE = [E(ξTS) − E(ξR )] = W1 + W2

⎛ ∂ρ( r )⃗ ⎞ ⎟ f ( r )⃗ = ⎜ ⎝ ∂N ⎠v(r)⃗

(3)

allowing us to rationalize the activation energy in terms of structural and electronic contributions.22 2.2. Reaction Electronic Flux. The electronic chemical potential (μ), extracted from density functional theory (DFT),23 represents the escaping tendency of electrons from an equilibrium distribution. It is a key property to understand the changes of the electronic structure during a chemical reaction.23,24 Chemical potential is defined as μ=

⎛ ∂E ⎞ ⎜ ⎟ ≅ −χ ⎝ ∂N ⎠v( r ⃗)

(6)

In analogy with the thermodynamic concept, positive REF values account for spontaneous changes in the electronic density which are driven by bond strengthening or forming processes. On the other hand, negative REF values indicate nonspontaneous changes in the electronic density that are driven by bond weakening or breaking processes.16,17,22,35 Moreover, since spontaneous processes are associated with expansion work, we should expect that when J(ξ) > 0 the electronic density expands, thus leading to a decrease of the density measured at any point r⃗. For nonspontaneous electronic activity characterized by J(ξ) < 0 the electronic density should contract. 2.3. Dual Descriptor f(2)(r)⃗ . The Fukui function, f(r⃗), was introduced by Parr and Yang36 as the derivative of the chemical potential with respect to the external potential v(r⃗), or equivalently as the derivative of the total electron density ρ(r⃗) upon changes in the total number of electrons

F(ξ)dξ > 0

1

F(ξ)dξ < 0

(5)

(7)

f(r⃗) 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 electrons, two Fukui functions have been introduced through the finite difference approximation:37 f +(r⃗) that measures the electrophilic power at point r⃗ in the molecule and f−(r⃗) which governs the nucleophilic power. When they are expanded through the use of the Kohn−Sham orbitals, one obtains38

(4)

HOMO − 1 −

f ( r )⃗ = ρHOMO ( r )⃗ +

One important characteristic of μ is its link with classical structural chemistry through the electronegativity χ.25 Due to

∑ i=1

26599

⎛ ∂|ϕ( r )⃗ |2 ⎞− ⎜⎜ i ⎟⎟ ⎝ ∂N ⎠v(r)⃗

(8)


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The Journal of Physical Chemistry C HOMO

f + ( r )⃗ = ρLUMO ( r )⃗ +

∑ i=1

⎛ ∂|ϕ( r )⃗ |2 ⎞+ ⎜⎜ i ⎟⎟ ⎝ ∂N ⎠v(r)⃗

(9)

The first term in each equation represents the HOMO and LUMO densities, and the second terms correspond to the orbital relaxation due to removal or addition of an electron. The dual descriptor, f(2)(r⃗), was defined by Morell et al.18 with the aim to understand the reactivity in chemical systems through the simultaneous knowledge of electrophilic and nucleophilic sites in the molecule. The dual descriptor (DD) can be calculated, discarding the orbital relaxation terms, as LUMO f (2) ( r )⃗ ≃ [f + ( r )⃗ − f − ( r )] ( r )⃗ − ρ HOMO ( r )] ⃗ ≃ [ρ ⃗

(10) (2)

The f (r⃗) characterizes the electrophilic and nucleophilic regions within a molecule simultaneously; it will be positive (f(2)(r⃗) > 0) in electrophilic regions and negative (f(2)(r⃗) < 0) in nucleophilic regions.39 Furthermore, extensions of the usual DD (eq 10) have been proposed, for instance, for the generation of state-specific dual descriptors by using the densities of the electronic excited states.40−42 It has been useful to get a complete picture of the local reactivity when the use of frontier molecular orbitals fails.

Figure 2. Energy (blue line) and reaction force (red line) profiles for the oxidative addition of Al(I): toward the activation of H2 computed at the B3LYP/6-311++G(d,p) level of theory.

Table 1. Activation and Reaction Energies Obtained with Each Functional Using the 6-311++G(d, p) Basis Seta

3. COMPUTATIONAL METHODS Calculations along the reaction coordinate ξ were performed with the Becke-3 for exchange43 and the correlation of Lee− Yang−Parr44−46 functionals, along with the 6-311G basis set that was augmented with p and d type polarization and double diffuse functions. With the aim to compare the activation and reaction energies obtained with B3LYP, the minimum energy path was also calculated with the hybrid meta-GGA functional M06-2X developed by Zhao and Truhlar.47,48 The reaction profiles were obtained through the IRC procedure,49,50 previously optimizing the transition state structure characterized by a single imaginary frequency with the same methodologies. Stationary points were identified by frequency analysis using analytic second derivatives. Tight convergence to find TS structures was employed (RMS forces ≤1× 10−5 Eha−1 0 ). The REF and DD were computed from the frontier molecular orbitals obtained through single-point calculations on the previously optimized geometries obtained from the IRC procedure at the B3LYP/6-311++G(d,p) level of theory. Natural bond order (NBO)51 analysis was carried out using the Mayer’s bond order52,53 to explain the evolution of REF along the reaction coordinate. All calculations were performed using the Gaussian 09 software package.54

a

functional

ΔE⧧

ΔE°

B3LYP M06-2X

36.7 40.6

−34.4 −31.9

Values reported in kcal mol−1.

−34.4 kcal mol−1, respectively. M06-2X results predict higher activation energy and a lower exothermicity of the reaction. The activation energies obtained from both B3LYP and M062X functionals suggest that the activation of H2 by the carbenoid aluminum complex would take place rather slowly (k ∼ 6.8 × 10−13 s−1) in agreement with the experimental data of Nikonov and coworkers. They showed that the reaction of LAl (L = [ArNC(Me)CHC(Me)NAr]− and Ar = 2,6-iPr2C6H3) with hydrogen takes place cleanly and slowly at T = 70 °C.7 On the other hand, it is interesting to note that the reaction energies obtained through both calculations, B3LYP and M062X, are in good agreement with the sum of experimental dissociation bond energies (D°0,rxn) associated with the primary chemical events taking place during the reaction. These are the breaking of the H2 bond (D°0,H2 = 104.20 kcal mol−1)55 and the formation of two Al−H bonds (D°0,AlH= −68.09 kcal mol−1).56 These gave D°0,rxn = D°0,H2 + 2 D°0,AlH = −31.98 kcal mol−1 that can be directly compared with the obtained reaction energies displayed in Table 1, thus confirming the reliability of the theoretical method used to characterize the H2 activation reaction. Figure 2 displays the energy and reaction force profiles along with the partition of the reaction coordinate into reaction regions. In Table 2 are quoted all the chemical events involved in the reaction and the energetic cost associated with them. As already mentioned, in the reactant region the main events are the polarization of the H−H bond, which is promoted by the nucleophilic attack of the aluminum to the H+ moiety. Structural energy W1 = 30.8 kcal mol−1 is associated with this couple of events. Then, entering the TS region, near ξ = −0.6,

4. RESULT AND DISCUSSION 4.1. Energy and Force Profiles. The oxidative addition of H2 on aluminum(I) carbenoid (R) to activate the H2 bond occurs as a one-kinetic-step reaction to lead the dihydride (P), in which are merged the following main chemical events: (1) polarization of H2 bond (H+···H−), (2) nucleophilic attack of Al: to the H+ moiety, and (3) the hydride attack H− to AlH to produce the AlH2 complex (see Figure 1). Figure 2 displays the energy and force profiles computed at the B3LYP/6-311+ +G(d,p) level of theory, and Table 1 displays the energetic data obtained using the B3LYP and M06-2X functionals. Both functionals show that the oxidative addition exhibits a high energy barrier and a highly exo-energetic character. At the B3LYP level, the activation and reaction energies are 36.7 and 26600


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The Journal of Physical Chemistry C Table 2. Primary (p) and Secondary (s) Events Driving the Reactiona main chemical events

region

H2 weakening bond

R

Al: nucleophilic attack to H+

oxidative addition

TS

P

primary/secondary events H(38)−H(39) bond weakening (s) Al:−H+(38) bond formation (p) Al:−H+(38) bond formation (p) Al−H(38) bond strengthening (s) Al−H−(39) bond formation (p) AlH−H−(39) bond formation (p) AlH−H(39) bond strengthening (s)

Table 3. TS Main Bond Distances (BDs) and Bond Orders of the Reaction Calculated Using the Wiberg (WBO) and Mayer (MBO) Definitions at the B3LYP/6-311++G(d, p) Level of Theory

Wi W1 = 30.80

W2 = 5.95 W3 = −23.12

bond

BD

WBO

MBO

Al−H(38) Al−H(39) H(38)−H(39)

1.59 1.94 1.27

0.74 0.71 0.21

0.67 0.35 0.24

which contain in their definition the overlap integral52,53 between the atoms involved in the bond, causes the difference between the two bonds to emerge. Therefore, WBOs seem not to be consistent with the calculated bond distances displayed in Figure 3, whereas the MBOs show that at the transition state Al−H(38) is stronger than Al−H(39), thus suggesting the reaction presents an important degree of asynchronicity. Since the synchronicity of the reaction depends upon the relative formation rate of the Al−H bonds, bond orders may help to characterize synchronicity of bond formations. In this context the synchronicity of the reaction can be estimated through

W4 = −48.10

Reaction works quoted in the last column are given in kcal mol−1. Values computed using B3LYP/6-311++G(d,p). a

the bond between Al: and H+ moiety starts to develop. The formation and strengthening of this bond take place until reaching the TS structure. Figure 3 displays the transition state structure with the main bond distances calculated through B3LYP and M06-2X/6-311+

ΘS =

(BO)β (BO)α

(11)

where (BO)β corresponds to the bond order of the last bond getting formed, i.e., Al−H(39), and (BO)α corresponds to the bond order of the first bond getting formed, i.e., Al−H(38). Since 0 ≤ ΘS ≤ 1, it permits us to characterize the nature of the process. When ΘS tends to unity, the process is completely synchronous and concerted. When ΘS has values between 0.5 < ΘS < 1, the process becomes asynchronous. However, when ΘS ≃ 0.5 the reaction proceeds in a two-stage process. Finally, when ΘS → 0 the reaction will be stepwise, and the two chemical events take place concerted and sequentially: the first is formation of one bond and then the second one in a twokinetic-steps process. In this case the two bonds that define the synchronicity of the reaction are Al−H(38) and Al−H(39), corresponding to (BO)α and (BO)β, respectively. The value of ΘS calculated using the Mayer bond orders is 0.52, thus indicating that the reaction proceeds in two stages. The use of Wiberg bond orders wrongly leads to a synchronous formation of the bonds. In summary, bond distances and MBOs indicate that the reaction occurs in a two-stage process: the nucleophilic attack occurs first, and it is then followed by the oxidative addition. At the transition state structure, the H(38)−H(39) bond is almost completely broken exhibiting a distance of 1.27 Å with a MBO of 0.24. Note that this process, from ξ = −0.6 to ξ = 0, needs W2= 5.95 kcal mol−1 which is mainly attributed to electronic reordering. Using eq 3 to analyze the activation energy, we note that the main process responsible for W1 and W2 is the H2 weakening followed by the Al: nucleophilic attack and formation of Al−H(38). From ξ = 0 to ξ2 the Al−H(38) bond strengthening takes place, and the oxidative addition (H−(39) to AlH) emerges, associating to this couple of events an energy W3 = −23.12 kcal mol−1. Entering to the product region (ξ > ξ2), the AlH−H(39) bond strengthens, and the energy associated is W4 = −48.10 kcal mol−1. In this way, the reaction force analysis provides crucial information about the energy cost at each step of the reaction. 4.2. Reaction Electronic Flux, Dual Descriptor, and Natural Bond Order Analysis. The electronic activity that

Figure 3. TS structure which is symmetric with respect to the σ plane that passes through Al(13)−H(38)−H(39) atoms. Selected bond distances are given in Angstroms (Å). In parentheses are given the distances computed with the M06-2X functional.

+G(d, p) levels of theory. It is interesting to note that both functionals predict similar TS structure and a remarkable match in bond lengths. Since bond distances are related to bond orders, to have a complete characterization of the TS structure, NBO bond orders, as defined by Wiberg57 and Mayer,52,53 will be used, and they are quoted in Table 3. Note that Wiberg bond orders (WBOs) for Al−H(38) and Al−H(39) are quite similar. In contrast to this, the Mayer bond orders (MBOs), 26601


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Figure 4. REF profile and dual descriptor calculated at six key points along the reaction coordinate. Areas in red show nucleophilic sites (f(2)(r⃗) < 0), and yellow areas display electrophilic behavior ( f(2)(r⃗) > 0).

Figure 5. Bond length and Mayer bond order of relevant bonds along the reaction coordinate. Distances are given in Å.

takes place along the reaction path is captured by the REF and displayed in Figure 4. At the beginning of the reaction the REF shows the electronic activity in an equilibrium state (J(ξ) = 0), and then as the reaction gets activated by the approach of the reacting species to each other, electronic polarization shows up in the REF profile with negative values most probably associated with the polarization and simultaneous weakening of the H−H bond. The REF decreases until reaching a broad negative peak in the reactant region (see Figure 4). This nonspontaneous electronic activity is associated with the H−H bond weakening into H+···H− due to the approach of the carbene Al complex. H2 bond polarization is clearly activated by the approach of the nucleophilic aluminum center. This is a quite remarkable effect since the H−H bond distance remains quite constant all along

the reactant region and starts to change only entering the transition state region; within the reactant region, polarization effects promote the subsequent heterolytic cleavage that takes place within the TS region. A spontaneous electronic activity entering the transition state region is observed, and a narrow positive peak indicates the carbenoid aluminum attack on the polarized H+···H−. A second positive peak leaving the transition region is observed which is due to the oxidative addition of the hydride to the AlH already formed. The two separate positive peaks of the REF show that the H2 addition reaction occurs in a two-stage process: formation of Al−H(38) followed by Al− H(39). Finally, the electronic activity decreases toward a zero flux regime to give the dihydride (see P in Figure 1). To help explain the mechanism, the dual descriptor was computed at the reaction force’s five key points along the 26602



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reaction coordinate: reactants (R), force minimum (1), transition state (TS), force maximum (2), and product (P). The DD color code displayed in Figure 4 is red for nucleophilic sites, f(2)(r⃗) < 0, and yellow for electrophilic sites, f(2)(r⃗) > 0. It can be noticed that the aluminum complex corresponds to a biphilic reagent. A large nucleophilic site over the aluminum atom is observed, while some electrophilic sites over the ligand are also evidenced. The dual descriptor (Figure 4) confirms the bond polarization of H2 that emerges as an ionic pair H+···H− in the reactant region. The nucleophilic character of the Al center allows the capture of H+ leading to the first Al−H bond, and the prominent increase in the nucleophilic character on the remaining H atom confirms the hydride formation. Note that the nucleophilic character on the aluminum atom has disappeared, and the complex becomes an electrophilic species, thus promoting a viable oxidative addition. At the force maximum, structure 2, the hydride attack on the now electrophilic AlH species is carried out. At the product structure P, the chemical system turns again as a biphilic reagent; however, positive and negative f(2)(r⃗) functions are evidenced just in the NacNac ligand. The REF findings are confirmed by the evolution of bond distances and bond orders along the reaction coordinate, and these are displayed in Figure 5(a) and 5(b), respectively. It can be noticed that whereas the H−H distance remains unchanged the Al−H distances decrease monotonically until reaching their final value (∼1.59 Å). Note in Figure 5(b) that the H−H bond order decreases slightly until ξ ≈ −3. Then, it decreases sharply until reaching its minimum, and constant values are observed leaving the transition region. It is interesting to note that Al− H(39) (green line) and H−H (blue line) bond orders start to change almost at the same time. Furthermore, the bond order between the aluminum center and H(38) (purple line) starts to change early in the reaction, promoting from the very beginning of the reaction the polarization of the H2 molecule. On the other hand, note that both positive peaks depicted in the REF profile fade out at ξ ≈ 5, where Al−H(38) and Al− H(39) MBOs reach their highest values. Figure 5 confirms that the reaction proceeds in an asynchronous fashion.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b08957. Cartesian coordinates for transition state structure at the B3LYP/6-311++G(d,p) and M06-2X/6-311++G(d,p) levels of theory (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +56(2) 354 4746. Fax: +56(2) 354 4744. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the financial support of the Nucleus Millennium “Chemical Processes and Catalysis” NC 120082 and the project FONDECYT Grants No.1130072 and No.1141098. N.V.E. wishes to thank Abigail Ulloa for her help in the confection of the figures of this work.

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REFERENCES

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5. CONCLUSIONS In the present work, a comprehensive study of the oxidative addition of carbenoid aluminum(I) complex has been performed through the use of the reaction force, reaction electronic flux, dual descriptor, and Mayer bond orders. It was found that the activation process occurs in a two-stages, onestep process. The reaction takes place as follows: first, the approaching of both molecules produces a strong polarization on H2, thus leading to an ionic pair H+···H−. Then, the nucleophilic carbenoid aluminum attacks the polarized H+···H− species and captures the proton. Afterward, the oxidative addition of the hydride to the electrophilic AlH already formed is achieved in a second stage of the mechanism. Chemical events along the reaction coordinate were fully characterized in terms of electronic activity through the REF and Mayer bond orders, and they gave reliable and consistent results. On the other hand, the dual descriptor helped to understand the reactivity in terms of electrophilic or nucleophilic sites studied at key points along the reaction coordinate. 26603


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Catalytic Mechanism of H2 Activation by a Carbenoid Aluminum

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