Rational design of iron catalysts for C–X bond activation

Abstract We have quantum chemically studied the iron‐mediated C—X bond activation (X = H, Cl, CH3) by d8‐FeL4 complexes using relativistic density functional theory at ZORA‐OPBE/TZ2P. We find that by either modulating the electronic effects of a generic iron‐catalyst by a set of ligands, that is, CO, BF, PH3, BN(CH3)2, or by manipulating structural effects through the introduction of bidentate ligands, that is, PH2(CH2) n PH2 with n = 6–1, one can significantly decrease the reaction barrier for the C—X bond activation. The combination of both tuning handles causes a decrease of the C—H activation barrier from 10.4 to 4.6 kcal mol−1. Our activation strain and Kohn‐Sham molecular orbital analyses reveal that the electronic tuning works via optimizing the catalyst–substrate interaction by introducing a strong second backdonation interaction (i.e., “ligand‐assisted” interaction), while the mechanism for structural tuning is mainly caused by the reduction of the required activation strain because of the pre‐distortion of the catalyst. In all, we present design principles for iron‐based catalysts that mimic the favorable behavior of their well‐known palladium analogs in the bond‐activation step of cross‐coupling reactions.

iron-and palladium-based model catalysts. In all cases, we found that Fe-catalysts follow a significantly lower reaction barrier for the oxidative addition. Hence, iron-based catalysts can potentially mimic the favorable behavior of their well-known palladium analogs in the bondactivation step of cross-coupling reactions.
The design of efficient catalysts usually proceeds via a trial-anderror approach by systematically varying the metal, ligands, reaction conditions, and solvent, in the hope of finding an optimal combination. 2,[42][43][44][45][46][47][48][49] With the ever-increasing power of quantum-chemical methods, chemists can now, not only, quickly compute a large set of molecular systems and chemical processes with sufficient accuracy, 50,51 but also obtain quantitative insights into the factors controlling the reactivity in these chemical systems. 41,52,53 Here, we provide a quantum chemical protocol for rationally tuning the activity of iron-d 8 -based 1 FeL 4 catalysts for C X bond activation in crosscoupling reactions. To demonstrate our approach, we have developed a new arsenal of iron-based catalysts that mimic the behavior of their well-known palladium analogs.
To achieve this, we have explored the electronic and structural effects for the iron-mediated C X bond activation of model system FeCO 4 + H 3 C X (X = H, Cl, CH 3 ) using relativistic density functional theory at ZORA-OPBE/TZ2P. Note that the active Fe (CO) 4 catalyst will form from the more stable but not active precatalyst Fe(CO) 5 [69][70][71][72][73][74][75][76] with the frozen core approximation, set to small. Our early work 41 and extensive benchmarking 77,78 have shown this approach to be well suited for the systems of interest. Relativistic effects were accounted for by using the zeroth-order regular approximation (ZORA). The basis set used, denoted TZ2P, is of triple-ζ quality for all atoms and has been improved by two sets of polarization functions. 77 The accuracies of the fit scheme (Zlm fit) and the integration grid (Becke grid) were, for all calculations, set to VERYGOOD. 79,80 Geometries were optimized without any symmetry constraint. All stationary points were confirmed by vibrational analysis. [81][82][83] For equilibrium structures, all normal modes have real frequencies, whereas transition states have one normal mode with an imaginary frequency. The character of the normal mode associated with the imaginary frequency was analyzed to ensure that the correct transition state was found. The potential energy surfaces (PES) of the studied reactions were obtained by performing intrinsic reaction coordinate (IRC) calculations, [84][85][86] which, in turn, were analyzed using the PyFrag program. 87,88 We focused in this study on the electronic energies of the molecular systems, as our previous study showed that trends in Gibbs free activation barriers remain unchanged compared with trends in electronic energies. 41 The optimized structures were illustrated using CYLview. 89

| Activation strain and energy decomposition analysis
The activation strain model (ASM) of chemical reactivity, 54 also known as the distortion/interaction model, 90,91 is a fragment-based approach in which the PES can be described with respect to, and understood in terms of the characteristics of the reactants. It considers the rigidity of the reactants and to which extent they need to deform during the reaction, plus their capability to interact with each other as the reaction proceeds. Using this model, one can decompose the total energy, ΔE(ζ), into the strain and interaction energy, ΔE strain (ζ) and ΔE int (ζ), respectively, and project these values onto the reaction coordinate ζ (Equation (1)).
In this equation, the strain energy, ΔE strain (ζ), is the penalty that needs to be paid in order to deform the reactants from their equilibrium to the geometry they adopt during the reaction at the point ζ of the reaction coordinate. On the other hand, the interaction energy, ΔE int (ζ), accounts for all the chemical interactions that occur between these two deformed reactants along the reaction coordinate. The total strain energy can, in turn, be further decomposed into the strain energies corresponding to the deformation of the substrate, ΔE strain,sub (ζ), and the catalyst, ΔE strain,cat (ζ) (Equation (2)).
The interaction energy between the deformed reactants can be further analyzed in terms of quantitative Kohn-Sham molecular orbital (KS-MO) 55 theory together with a canonical energy decomposition analysis (EDA). 56,57 The EDA decomposes the ΔE int (ζ) into the following three energy terms (Equation (3)): Herein, ΔV elstat (ζ) is the classical electrostatic interaction between the unperturbed charge distributions of the (deformed) reactants, and is usually attractive. The Pauli repulsion, ΔE Pauli (ζ), includes the destabilizing interaction between the fully occupied orbitals of both fragments due to the Pauli principle. The orbital interaction energy, ΔE oi (ζ), accounts for, among others, charge transfer between the fragments, such as HOMO-LUMO interactions.
In the herein presented activation strain and accompanied energy decomposition diagrams, the intrinsic reaction coordinate (IRC) is projected onto the C X bond stretch. This critical reaction coordinate undergoes a well-defined change during the reaction from the reactant (complex) via the transition state to the product and is shown to be a valid reaction coordinate for studying C X activation reactions. 41,68,92 3 | RESULTS AND DISCUSSION

| Ligand tuning
First, we have investigated the influence of the electronic effects of the Fe-catalyst through ligand variation. Table 1 and Figure 1 summarize the computed potential energy surfaces of the C X (X = H, Cl, CH 3 ) bond activation of H 3 C X substrates by the model catalyst Fe(CO) 3 L 1 with L 1 = CO, BF, PH 3 , BN(CH 3 ) 2 and the previously obtained data 41 for the Pd(CO) 2 catalyst (see Figure S1 and Table S2 in the Supporting Information for structural information and coordinates of all computed systems). In line with previous findings, 93,94 most ligands considered, that is, L 1 = CO, PH 3 , and BN(CH 3 ) 2 , can only occupy an axial position in Fe(CO) 3 L 1 . In contrast, BF can only adopt an equatorial position. 95 In general, the bond activation proceeds via a reactant complex (RC), followed by a transition state (TS), and a final product (P). Note, that in the gas phase, the overall reaction barrier, ΔE ‡ , corresponds to the energy difference between the TS and the infinitely separated reactants. 96 Several apparent trends can be found by analyzing the reaction profiles (Table 1). In the first place, the reaction barriers for all studied Fe-catalysts for the C X bond activation decrease along with the series C C > C Cl > C H. For instance, for reference Fe(CO) 4 , the barrier decreases from 48.0, to 25.5, to 10.4 kcal mol À1 for C C, C Cl, and C H, respectively. This reactivity trend is in line with other metals (e.g., palladium). 97 102 In Figure 2, we focus on the C H bond activation by Fe(CO) 4 as our parent model Fe-catalyst (black curves) and Fe(CO) 3 BN(CH 3 ) 2 (red curves) as our most efficient catalyst by electronic tuning. The ASM results of the other ligands show the same characteristics and are depicted in Figure S2 and Table S1 in the Supporting Information. As can be seen in Figure 2A, the reaction barrier is significantly lower for Fe(CO) 3   an energy decomposition analysis (EDA). 56 The EDA decomposes the ΔE int into the following three chemically intuitive energy terms: ΔV elstat , ΔE Pauli , and ΔE oi . Our canonical EDA analysis shows that Fe(CO) 3 BN(CH 3 ) 2 engages both a more stabilizing electrostatic (ΔV elstat ) and orbital interaction (ΔE oi ) with the substrate, in which the latter one is more important ( Figure 2B). The origin of the more stabilizing orbital interaction for Fe(CO) 3 BN(CH 3 ) 2 with the substrate is further explored by performing a Kohn-Sham molecular orbital analysis. 55 In line with our previous work, 41 we find that in general, Fecomplexes feature a relatively small HOMO-LUMO gap due to the incomplete d 8 shell of iron, which goes with both, a high-energy d π HOMO and a low-energy d σ LUMO, that can participate in both a strong π-backdonation and σ-donation ( Figure 4B,C). This is a characteristic difference compared with, for instance, Pd-complexes, which in general have a filled d-shell providing also a high-energy HOMO that can be deployed for strong π-backdonation. However, the LUMO of Pd-complex is a higher-energy Pd-5s derived orbital which is less capable of entering into a favorable σ-donation interaction. 41,42 In-depth analyses of the catalyst-substrate interactions revealed that the Fe(CO) 3  show that the HOMO-LUMO gap of the Fe-catalyst remains notably constant ( Figure 4A), which is the case for all studied ligands (see T A B L E 2 Electronic energies (in kcal mol À1 ) relative to reactants for the oxidative addition by Fe(CO) 2 L 2 (L 2 = PH 2 (CH 2 ) n PH 2 ; n = 6-1) to C X bonds (X = H, Cl, and CH 3 ) F I G U R E 5 Structures and key distances (in Å) and dihedral angles (in ) of stationary points of the C H bond activation by FeCO 2 P 3 P computed at ZORA-OPBE/TZ2P (C = gray, H = white, O = red, Fe = cyan) Figure S3b and Table S1 for all studied catalysts). Indeed, as expected, the more electron-donating ligand BN(CH 3 ) 2 (see Figure S3a) pushes up the orbitals more, but this electronic mechanism affects both the filled and empty orbitals ( Figure 3A). This results in an enhanced π-backdonation ( Figure 4B) due to the higher-lying HOMO orbital of FeCO 3 BN(CH 3 ) 2 . In contrast, the σ-donation ( Figure 4C) becomes substantially less stabilizing due to the higher-lying LUMO of FeCO 3 BN(CH 3 ) 2 . The weaker σ-donation cancels the enhanced π-backdonation and, therefore, these two key interactions cannot explain the higher reactivity found for

| Structural tuning
Next, the influence of the structural effects was systematically investigated for our iron-d 8 catalysts. These structural effects are dictated to a large extent by the ligand-metal-ligand angle, that is, the bite angle. In general, a smaller bite angle pre-distorts the catalyst and reduces the required deformation of the catalyst to react, which lowers the reaction barrier. In this way, the ligands do not need to be significantly bent away from the approaching substrate, a process that occurs in linear complexes to relieve (steric) Pauli repulsion between substrate and ligands.  Decreasing the n in PH 2 (CH 2 ) n PH 2 directly leads to a short tethered chain that pulls the two ligands closer and decreases the bite angle and effectively pre-distorts the catalyst. Similarly with Pd catalysts, this increase of the pre-distortion of the catalyst as the bite angle of Fe(CO) 2 P n P decreases from 111 to 91 going from n = 6 to n = 3, causes a decrease of the reaction barrier for C H activation from 14.4 to 5.2 kcal mol À1 , respectively. However, if the bite angle is reduced to very small values in our computed iron-d 8 catalysts, as in the case for Fe(CO) 2 P 2 P (87 ) and Fe(CO) 2 P 1 P (76 ), the reaction barrier for C H activation does not continue to decrease, but actually begins to increase going from 5.2 to 5.4 to 10.2 kcal mol À1 along n = 3, 2, 1 (see Table 2). This remarkable finding is in sharp contrast to Pd-based catalysts of the type d 10 -PdL 2 , where a smaller bite angle, in general, leads to lower barriers. 103 These reactivity trends are also found for C Cl and C C activation.
In order to understand the effects at play when decreasing the bite angle in our iron-d 8 catalysts, we further analyzed the PES by performing activation strain analyses ( Figure 6). Figure 6A shows the ASM results for Fe(CO) 2 P 6 P with a bite angle of 111 (black) and Fe(CO) 2 P 3 P (green) with a bite angle of 91 . The ASM results for model catalysts Fe(CO) 2 P 5 P and Fe(CO) 2 P 4 P with intermediate bite angles show the same characteristics and are depicted in Figure S4 (activation strain diagrams) and Figure S5 (structures).
The reduction in reaction barrier for Fe(CO) 2 P 3 P can be solely ascribed to the less destabilizing strain, which is a direct result of the pre-distortion of the catalyst. The pre-distortion of the catalyst results in less deformation along the reaction path, and thus, causes a less destabilizing strain energy. In contrast, very small bite angles for our computed iron-d 8 catalysts do not always lead to lower barriers F I G U R E 6 Activation strain analysis of C H bond activation along the reaction coordinate projected onto the CÁ Á ÁH stretch (A) by Fe(CO) 2 P 6 P (black) and Fe(CO)P 3 P (green); and (B) by Fe(CO) 2 P 3 P (green) and Fe(CO)P 1 P (red). Transition states are indicated with dots.
(C) Energy decomposition analysis for the C H bond activation by Fe(CO)P 3 P (green) and Fe(CO)P 1 P (red). Computed at ZORA-OPBE/TZ2P ( Figure 6B). This seemingly counterintuitive finding can be understood by analyzing the ASM/EDA results for Fe(CO) 2 P 3 P (green) with a bite angle of 91 and Fe(CO) 2 P 1 P (red) with a bite angle of 67 . We find that for these systems the reduction in destabilizing strain energy going to smaller bite angles, that is, Fe(CO) 2 P 3 P to Fe(CO) 2 P 1 P is not present. In contrast, Fe(CO) 2 P 1 P, with the smaller bite angle, does engage in a weaker interaction with the substrate compared to Fe(CO) 2 P 3 P. The energy decomposition analysis (EDA) in Figure 6C shows that the weaker interaction energy can be traced back to the more destabilizing (steric) Pauli repulsion between the catalyst and the substrate. To verify if the EDA results are not skewed by the distance between the catalyst and the substrate, we performed an additional ASM/EDA, in which we artificially constrained the FeÁ Á ÁH and FeÁ Á ÁC bond lengths of Fe(CO) 2 P 1 P + H 3 C H to that of Fe(CO) 2 P 3 P + H 3 C H, while keeping the CÁ Á ÁH bond stretch constant (see Table 3). This reinforces that, indeed, the more destabilizing (steric) Pauli repulsion between Fe(CO) 2 P 1 P and the substrate causes the weaker interaction energy compared to Fe(CO) 2 P 3 P. This can be traced back to the two CO ligands, which cannot efficiently bend away in Fe(CO) 2 P 1 P from the substrate because the bidentate ligand blocks space in the area to which they have to bend, which is illustrated by the distance between the hydrogen of the activated C H bond and the carbon of the CO (P 3 P = 2.06 Å; P 1 P = 2.02 Å).

| Rational tuning of Fe catalysts
Lastly, we combine both design handles (i.e., electronic and structural properties) for rationally optimizing the activity of a novel Fe-catalyst for C X bond activation. To this end, we turn to the optimal ligands identified in our analyses outlined above, in terms of barrier lowering capacity, namely BN(CH 3 ) 2 and P 3 P. This results in an enhanced π-backdonation (HOMO cat -LUMO sub ) and a weaker σ-donation (LUMO cat -HOMO sub ) for all catalysts, which practically cancel each other. Note that this "ligand-assisted" interaction is maximized for the C H bond activation due to the reduced steric demand of this process compared to the C C and C Cl bond activation.
The lowering of the reaction barrier by reducing the bite angle of the chelate complex Fe(CO) 2 (PH 2 (CH 2 ) n PH 2 ) catalyst works in a similar way as in the case of palladium chelate complexes: In the case of smaller bite angles, that is, as the polymethylene bridge gets shorter, ligands do not need to bend away so much to make room for the substrate during the reaction because the catalyst is already accordingly pre-distorted. Thus, less catalyst deformation strain is building up which results in a lower barrier. Interestingly, and in contrast to the behavior of Pd-based analogs, we find that overly bending the bite angle, to very small values, does not necessarily lead to a further lowering of C X bond-activation barriers for our ironbased model catalyst. This reveals the existence of a hitherto undiscovered "sweet-spot" in terms of bite angle for the studied ironbased catalysts. The increase in reaction barrier upon "overbending" is the result of a more destabilizing steric (Pauli) repulsion between catalyst and substrate. This steric repulsion in the case of a too small bite angle of Fe(CO) 2 (PH 2 (CH 2 ) n PH 2 ) (n < 3) originates from the two CO ligands which can no longer efficiently bend away from the substrate because the bidentate ligand blocks space in the area to which they would otherwise bend.