Palladium-Catalyzed Activation of Carbon–Halogen Bonds: Electrostatics-Controlled Reactivity

We have quantum chemically studied the palladium-mediated activation of C( sp n ) (cid:0) X bonds (n = 1–3; X = F, Cl, Br, I) in the archetypal model substrates H 3 C (cid:0) CH 2 (cid:0) X, H 2 C = CH (cid:0) X, and HC � C (cid:0) X by a model bare palladium catalyst, using relativistic density functional theory at ZORA-BLYP/TZ2P. The bond activation reaction barrier decreases, for all sp -hybridized carbon centers, when the substituent X of the substrate is changed from X = F to I. Activation strain and energy decomposition analyses reveal that the enhanced reactivity along this series originates from (i) a less destabilizing activation strain due to an intrinsically weaker C( sp n ) (cid:0) X bond; and (ii) an increasingly more stabilizing electrostatic interaction between the catalyst and the substrate. The latter is a direct consequence of the more diffuse electron density and higher nuclear charge of the X atom in the C( sp n ) (cid:0) X bond when going from X = F to I, which, in turn, engages in a more favorable electrostatic attraction with the nucleus and electrons, respectively, of the palladium catalyst.


Introduction
Transition metal catalysis plays a key role in many industrial processes, as well as in the synthesis of various biologically active compounds. [1]An important class of catalytic processes is constituted by palladium-catalyzed cross-coupling reactions which furnish new carbon-carbon bonds (Scheme 1). [2]The first and, commonly, the rate-determining step in the catalytic cycle of this archetypical cross-coupling reaction is the activation of a carbon-element bond (C(sp n )À X) by oxidative addition to the palladium center of the catalyst. [3]This reaction step plays an essential role in the selectivity and efficiency of the overall catalytic cycle.The oxidative addition is followed by a transmetalation step, whereby substituent A on the palladium metal center is replaced by hydrocarbon R. In the last step, the original palladium catalyst is regenerated by a reductive elimination step (the reverse of oxidative addition), yielding the new C(sp n )À R bond.In a typical homogenous catalytic reaction, as mentioned earlier, the oxidative addition step is rate-limiting, and as such, has been the focus of extensive experimental [4] and theoretical studies. [5,6]Considering the importance of oxidative addition, a deep understanding of the underlying mechanism is crucial to designing new catalysts and improving the existing ones.
To understand the effect of varying the substituent X of C(sp n )À X (n = 1-3; X = F, Cl, Br, I) in the bond activation process, we have quantum chemically explored the potential energy surface (PES) of the oxidative addition reaction of C(sp n )À X by a model bare Pd catalyst, using relativistic density functional theory at ZORA-BLYP/TZ2P (Scheme 2).To this end, we have chosen to represent common motifs of reactants in palladiumcatalyzed reactions through archetypal model C(sp n )À X substrates, with C(sp n ) = H 3 CÀ CH 2 À (sp 3 ), H 2 C=CHÀ (sp 2 ), HC�CÀ (sp).Recently, we have found that key reactivity trends are already nicely captured with bare Pd and that the addition of ligands to the catalyst results, independent of the nature of the CÀ X bond that is being activated, in an increase of the activation energy. [6]The activation strain model (ASM) [7] in combination with quantitative Kohn-Sham molecular orbital (KS-MO) theory [8] and a matching energy decomposition analysis (EDA) scheme [9] were employed to unravel the trends in reactivity and provide quantitative insights into the effect of variating the substituent X on the C(sp n )À X bond activation.This computational methodology provides deep physical insight into the factors controlling reactivity and has proven useful for the understanding of, among others, oxidative addition reactions. [6]mputational Methods

Computational details
All calculations were executed with the Amsterdam Density Functional (ADF) program. [10]The generalized gradient approximation (GGA) functional BLYP [11] was used for the optimizations of all stationary points and subsequent analyses.The basis set used, denoted TZ2P, [12] is of triple-ζ quality and is augmented with two sets of polarization functions on each atom.Scalar relativistic effects were taken into account using the zeroth-order regular approximation (ZORA). [13]This level of theory is denoted as ZORA-BLYP/TZ2P and has been widely tested with several ab initio reference benchmarks up until the coupled cluster CCSD(T). [14]15b,c] Through vibrational analysis, all stationary points were confirmed to be either equilibrium structures (zero imaginary frequencies) or transition states (one single imaginary frequency). [16]urthermore, the normal mode character associated with the imaginary frequency was analyzed to ensure that the correct transition state was found.The potential energy surfaces (PESs) of the studied oxidative addition reactions were obtained by utilizing intrinsic reaction coordinate (IRC) calculations. [17]The obtained PESs were further analyzed using the PyFrag 2019 program. [18]All stationary-point structures were illustrated using CYLview. [19]

Activation strain model and energy decomposition analysis
The activation strain model (ASM, [7] also known as the distortion/ interaction model [20] ) is a fragment-based approach to understand the energy profile of a chemical process in terms of the original reactants, which are the model bare palladium catalyst and the substrate C(sp n )À X.It considers their rigidity and the extent to which the reactants must deform during the reaction plus their capability to interact as the reaction proceeds.In this model, we decompose the total energy, ΔE(ζ), into the strain and interaction energy, ΔE strain (ζ) and ΔE int (ζ), respectively, along the IRC which is projected onto a reaction coordinate ζ that is critically involved in the reaction [Eq.( 1)].
In this equation, the strain energy, ΔE strain (ζ), is the energy required to deform the reactants from their equilibrium structure to the geometry they acquire during the reaction at an arbitrary point ζ of the reaction coordinate.On the other hand, the interaction energy, ΔE int (ζ), accounts for all the mutual interactions that occur between the deformed fragments along the reaction coordinate.
The interaction energy between the deformed reactants is further analyzed with the help of our canonical energy decomposition analysis (EDA) scheme. [9]The EDA decomposes the ΔE int (ζ) into the following three energy terms [Eq.( 2)]: From this equation, ΔV elstat (ζ) is the quasi-classical electrostatic interaction between the unperturbed charge distributions of the deformed reactants.The ΔV elstat (ζ) can be further divided into four components [Eq.( 3)]: dr 1 dr 2 (3) Where A and B stand for the catalyst Pd and the substrate C(sp n )À X.The first term is the electrostatic repulsion between the nuclei of fragments A and B. The second and third terms are the electrostatic attraction between the nuclei of fragment A and the electron density of fragment B and vice versa; while the last term is the electrostatic repulsion between the electron densities of fragments A and B.
The Pauli repulsion, ΔE Pauli (ζ), emerges from the destabilizing interaction between occupied orbitals (more precisely, electrons of same spin) on either of the fragments due to Pauli's exclusion principle.Lastly, the orbital interaction energy, ΔE oi (ζ), accounts for charge transfer (e. g., HOMO-LUMO interactions) and polarization between the fragments.A detailed, step-by-step guide on how to perform and interpret the ASM and EDA can be found in ref. [7c].
In this work, the activation strain and energy decomposition analyses were carried out along the intrinsic reaction coordinate (IRC) projected onto the stretch of the activated C(sp n )•••X bond which is a critical geometry parameter of the reaction. [21]This particular geometric parameter undergoes a well-defined change during the reaction going from the reactant complex via the transition state to the product complex and has been shown to be a useful reaction coordinate for studying oxidative addition reactions. [6]

Results and Discussion
The substrates investigated in this work follow the series C(sp n )À X; where C(sp n ) = H 3 CÀ CH 2 À (sp 3 ), H 2 C=CHÀ (sp 2 ), HC�CÀ (sp) and X = F, Cl, Br, I. We begin by first discussing the bond lengths and strengths of these C(sp n )À X bonds in the substrates, which is a critical aspect of the overall bond activation process (vide infra).Table 1 contains the computed bond lengths and bond dissociation enthalpies at ZORA-BLYP/TZ2P.Two primary trends emerge, first the C(sp n )À X bond becomes, for all sphybridized carbon atom centers, weaker and longer as X varies from F to I.For example, along the H 2 C=CHÀ X (sp 2 ) series, the bond strength and length go from 129.5 kcal mol À 1 and 1.370 Å for H 2 C=CHÀ F to 65.0 kcal mol À 1 and 2.131 Å for H 2 C=CHÀ I. Blokker et al. have shown that this trend in bond strength on going down Group 17 does not originate from the decreasing electronegativity difference, but, instead, due to the increasing Pauli repulsion across the C(sp n )À X bond for the larger halogen atoms. [23]Second, the C(sp n )À X bond becomes stronger, and shorter when the sp-hybridization of the carbon center changes from sp 3 to sp 2 to sp, while keeping the substituent X constant, e. g., from 117.7 kcal mol À 1 and 1.426 Å for H 3 CÀ CH 2 À F to 137.3 kcal mol À 1 and 1.294 Å for HC�CÀ F. Recently, we have shown that the underlying physical mechanism behind this structural trend is the reduction of steric congestion around the C(sp n ) atom, that is, the reduction in the destabilizing Pauli repulsion between the C(sp n ) fragment and the substituent X as the number of substituents around the pertinent C(sp n ) atom goes down from 4, to 3, to 2, along sp 3 to sp 2 to sp hybridization. [24]he results of our computed ZORA-BLYP/TZ2P reaction profiles for the studied C(sp n )À X bond activation reactions are collected in Table 2 and Figure 1 and Figure S1.The reactions proceed via a reactant complex (RC) and a transition state (TS), towards the product complex (PC).Note, that the overall activation energy ΔE � , that is, the energy difference between the TS and the infinitely separated reactants (Pd and C(sp n )À X), can be negative if a substantially stabilized reactant complex is formed.For a more detailed discussion on the various types of reaction potential energy surfaces, see, for example, Reference [25].Based on the reaction profiles, two distinct reactivity trends can be discerned from this data.First, the overall activation energy for the oxidative addition process decreases, for all sp-hybridized substrates, upon going down in Group 17 from X = F to I, e. g., the activation energy goes down from 5.3 kcal mol À 1 for H 2 C=CHÀ F to À 28.5 kcal mol À 1 for H 2 C=CHÀ I. Second, changing the sp-hybridization of the carbon atom constituting the C(sp n )À X bond from sp 3 to sp 2 to sp while keeping the substituent X constant leads, in general, to a lowering of the reaction barrier.For example, for C(sp n )À F, the reaction barrier goes from 17.6 kcal mol À 1 for H 3 CÀ CH 2 À F to 0.1 kcal mol À 1 for HC�CÀ F. There is, however, one exception, namely, HC�CÀ I has a slightly higher reaction barrier than H 2 C=CHÀ I (À 28.4 kcal mol À 1 versus À 28.5 kcal mol À 1 , respectively).

Substrate
Bond type The latter reactivity trend, that is what happens when one varies the sp-hybridization of the carbon atom of C(sp n )À X bond from sp 3 to sp 2 to sp while keeping the substituent X constant has recently been studied by our group. [26]We have found that the reaction barrier decreases along C(sp 3 )À X to C(sp 2 )À X to C(sp)À X, even though the bond becomes substantially stronger and hence requires consistently more energy to break during the oxidative addition process.This reactivity trend is, in fact, established by the reduction of Pauli repulsion between the Pd catalyst and the substrate.Going from C(sp 3 )À X to C(sp 2 )À X to C(sp)À X, the number of substituents around the pertinent carbon atom goes down from 4 to 3 to 2, causing less steric interactions between occupied orbitals of the Pd catalyst and the occupied orbitals with amplitude on the substituents of the substrate.The reactivity trend becomes reinforced by an increasingly more stabilizing π-backbonding interaction, which is the result of a smaller catalyst-substrate HOMO-LUMO gap between the d π and σ* C(spn)À X orbitals, as the orbital energy of the substrate σ* C(spn)À X orbital drops along sp 3 to sp 2 to sp. [24] To gain quantitative insight into the physical factors governing the bond activation trend when changing the substituent X, we applied the activation strain model (ASM) of chemical reactivity. [7]Figure 2 shows the activation strain diagrams (ASDs) of the C(sp 2 )À X bond activation by the model bare Pd catalyst along the IRC are projected on the C(sp 2 )•••X bond stretch (see the Computational Methods for more details).The ASDs of all other substrates, i. e., C(sp 3 )À X and C(sp)À X, possess the same features and are provided in Figures S2 and  S3 of the Supporting Information.As found in Table 2, the reaction barrier goes down from C(sp 2 )À F to C(sp 2 )À I, which can be traced back to both a less destabilizing strain energy and a more stabilizing interaction energy along this series (Figure 2b and Figure 2c).The trend in strain energy originates from the increasingly weaker, and longer, C(sp 2 )À X bond going from X = F to I (vide supra; Table 1).The weaker the C(sp 2 )À X bond, the easier it becomes to break, and hence it generates less activation strain during the oxidative addition process.
Next, we turn to the energy decomposition analysis (EDA) to get a better understanding of why the interaction energy becomes more stabilizing from C(sp 2 )À F to C(sp 2 )À I. Interestingly, and in contrast to our previous studies on palladiummediated bond activation trends, [6] the enhanced interaction energy upon going from C(sp 2 )À F to C(sp 2 )À I is exclusively determined by the electrostatic interaction (Figure 2d).The least stabilizing electrostatic interaction is found for the Pd insertion into the C(sp 2 )À F bond and this effect becomes increasingly more stabilizing when going down Group 17 for atom X in C(sp 2 )À X.The Pauli repulsion and orbital interactions (Figure 2e and Figure 2f), on the other hand, are significantly less important or show even an opposite trend.
Finally, to get a more detailed insight into the origin of the reactivity trend, we decompose the electrostatic interaction into the repulsive and attractive electrostatic contributions according to Equation 3 at consistent geometries obtained from the IRC with a C(sp 2 )•••X bond stretch of 0.335 Å (Table 3, see Tables S2 and S3 for other substrates).7b] As seen in Figure 2d, the electrostatic interactions become more stabilizing upon going down in Group 17 for substituent X, namely, from À 114.0 kcal mol À 1 for C(sp 2 )À F to À 155.0 kcal mol À 1 for C(sp 2 )À I.a,b] Substrate Repulsive electrostatic interactions [c] Attractive electrostatic interactions [d] Total electrostatic interactions C(sp 2 )À F 311806.4 À 311920.4À 114.0 C(sp 2 )À Cl 398457.3À 398596.2À 138.9 C(sp 2 )À Br 597485.0À 597632.6À 147.7 C(sp 2 )À I 775514.0À 775669.0À 155.0 [a] Analyses at consistent geometries obtained from the IRC with a C(sp 2 )•••X bond stretch of 0.335 Å at ZORA-BLYP/TZ2P.[b] The interacting reactants are the bare palladium model catalyst and the substrate C(sp 2 )À X.
[c] Repulsive electrostatic interactions are the sum of the nuclear Pd -nuclear C(sp2)À X and electron Pd -electron C(sp2)À X repulsion.[d] Attracctive electrostatic interactions are the sum of the nuclear Pd -electron C(sp2)À X and electron Pd -nuclear C(sp2)À X attraction.
The attractive electrostatic interactions between Pd and C(sp 2 )À X become more stabilizing from X = F to I, due to (i) a more diffuse electron density; and (ii) a higher nuclear charge of the larger atom X.In Figure 3, we plot the electron density of the palladium catalyst (red) and C(sp 2 )À X (blue) at consistent geometries obtained from the IRC with a C(sp 2 )•••X bond stretch of 0.335 Å (see Figures S4 and S5 for other substrates).When going down Group 17, the electron density on atom X naturally increases and expands and hence overlaps better with the nucleus of the Pd catalyst, even though the distance between X•••Pd increases from 2.243 Å for X = F to 2.779 Å for X=I, resulting in a more favorable nuclear Pd -electron C(sp2)À X attraction.In addition, the nuclear charge on atom X also increases along the studied series from Z C(sp2)À X = 9 for C(sp 2 )À F to Z C(sp2)À X = 53 for C(sp 2 )À I, leading to a more attractive electron Pd -nuclear C(sp2)À X interaction upon going down in Group 17.These two enhanced electrostatic attractions, ultimately, result in the more stabilizing interaction energy and hence a lower reaction barrier for the bond activation of C(sp 2 )À F compared to C(sp 2 )À I by the palladium catalyst.The repulsive electrostatic interactions, on the other hand, become more destabilizing from C(sp 2 )À F to C(sp 2 )À I and, therefore, partly but not completely, counteract the trend dictated by the attractive electrostatic interactions.Interestingly, a similarly decisive role, and mechanism, of electrostatic interactions was found before in a quite different context, namely, in the trend in the preferred conformation of α-halocarbonyl compounds. [27]

Conclusions
Our computational study quantifies the reactivity trends of the oxidative addition reaction between Pd and C(sp n )À X (n = 1-3 and X = F, Cl, Br, I) in archetypal model substrates H 3 CÀ CH 2 À X (sp 3 ), H 2 C=CHÀ X (sp 2 ), and HC�CÀ X (sp), using relativistic density functional theory.We have found that the reaction barrier of C(sp n )À X bond activation systematically decreases, for all sp nhybridized carbon atoms along the series C(sp n )À F > C(sp n )À Cl > C(sp n )À Br > C(sp n )À I.
Our activation strain and energy decomposition analyses reveal that the decreased oxidative addition reaction barrier of C(sp n )À X by Pd going down Group 17 from X = F to Cl to Br to I originates from two factors: (i) a less destabilizing activation strain; and (ii) a more favorable electrostatic attraction between the catalyst and the substrate.Going down Group 17, the C(sp n )À X bond becomes weaker, as explained by Blokker et al. [23] The weaker the bond, the easier it is to break and hence the less activation strain it generates during the oxidative addition reaction.
The electrostatic interaction between the catalyst and substrate also becomes more favorable when changing the substrate from C(sp n )À F to C(sp n )À I.The larger X atom has a more diffuse and electron-rich density and a higher nuclear charge, which, in turn, can engage in more favorable electrostatic attraction with the palladium nucleus and electron density, respectively.This effect makes the oxidative addition reaction involving the C(sp n )À X bond with a larger X atom correspond to a more stabilizing interaction and hence lower reaction barrier.These findings will equip experimentalists with the mechanistic insight to understand and predict the trends in reactivity of palladium-mediated oxidative addition reactions.

Figure 2 .
Figure 2. Activation strain analyses: a) total energy, b) strain energy, c) interaction energy; and energy decomposition analyses: d) electrostatic interaction, e) Pauli repulsion, and f) orbital interactions, for the oxidative addition of Pd into the C(sp 2 )À X bond (X = F, Cl, Br, I), where the transition states are indicated with a dot and the energy terms along the IRC are projected on the C(sp 2 )•••X bond stretch.Computed at ZORA-BLYP/TZ2P.

:
Activation strain model • Bond activation • Density functional calculations • Homogeneous catalysis • Oxidative addition

Figure 3 .
Figure 3. Density contours from À 0.095 to 0.099 Bohr À 3 for the oxidative addition of Pd into the C(sp 2 )À X bond (X = F, Cl, Br, I; electron density of Pd in red; electron density of C(sp 2 )À X substrate in blue; distances in Å) at consistent geometries along the IRC with a C(sp 2 )•••X bond stretch of 0.335 Å, computed at ZORA-BLYP/TZ2P.Atom colors: C = gray, F = green, Cl = red, Br = blue, I = black, Pd = orange.
* and X * radical.The last term, Δ(