Ab initio benchmark study for the oxidative addition of CH4 to Pd: Importance of basis-set flexibility and polarization

Rational design of iron catalysts for C-X bond activation

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.

Palladium-catalyzed activation of HnA–AHn bonds (AHn = CH3, NH2, OH, F)

We have quantum chemically studied activation of HnA–AHn bonds (AHn = CH3, NH2, OH, F) by PdLn catalysts with Ln = no ligand, PH3, (PH3)2, using relativistic density functional theory at ZORA-BLYP/TZ2P. The activation energy associated with the oxidative addition step decreases from H3C–CH3 to H2N–NH2 to HO–OH to F–F, where the activation of the F–F bond is barrierless. Activation strain and Kohn–Sham molecular orbital analyses reveal that the enhanced reactivity along this series of substrates originates from a combination of (i) reduced activation strain due to a weaker HnA–AHn bond; (ii) decreased Pauli repulsion as a result of a difference in steric shielding of the HnA–AHn bond; and (iii) enhanced backbonding interaction between the occupied 4d atomic orbitals of the palladium catalyst and σ* acceptor orbital of the substrate.

C−X Bond Activation by Palladium: Steric Shielding versus Steric Attraction

The C−X bond activation (X = H, C) of a series of substituted C(n°)−H and C(n°)−C(m°) bonds with C(n°) and C(m°) = H₃C− (methyl, 0°), CH₃H₂C− (primary, 1°), (CH₃)₂HC− (secondary, 2°), (CH₃)₃C− (tertiary, 3°) by palladium were investigated using relativistic dispersion‐corrected density functional theory at ZORA‐BLYP‐D3(BJ)/TZ2P. The effect of the stepwise introduction of substituents was pinpointed at the C−X bond on the bond activation process. The C(n°)−X bonds become substantially weaker going from C(0°)−X, to C(1°)−X, to C(2°)−X, to C(3°)−X because of the increasing steric repulsion between the C(n°)‐ and X‐group. Interestingly, this often does not lead to a lower barrier for the C(n°)−X bond activation. The C−H activation barrier, for example, decreases from C(0°)−X, to C(1°)−X, to C(2°)−X and then increases again for the very crowded C(3°)−X bond. For the more congested C−C bond, in contrast, the activation barrier always increases as the degree of substitution is increased. Our activation strain and matching energy decomposition analyses reveal that these differences in C−H and C−C bond activation can be traced back to the opposing interplay between steric repulsion across the C−X bond versus that between the catalyst and substrate.

C(spn)-X (n = 1-3) Bond Activation by Palladium

We have studied the palladium-mediated activation of C( sp n )-X bonds (n = 1-3 and X = H, CH 3 , Cl) in archetypal model substrates H 3 C-CH 2 -X, H 2 C=CH-X and HC≡C-X by catalysts PdL n  with L n  = no ligand, Cl - , and (PH 3 ) 2 , using relativistic density functional theory at ZORA-BLYP/TZ2P. The oxidative addition barrier decreases along this series, even though the strength of the bonds increases going from C( sp 3 )-X, to C( sp 2 )-X, to C( sp )-X. Activation strain and matching energy decomposition analyses reveal that the decreased oxidative addition barrier going from  sp 3  to  sp 2  to  sp , originates from a reduction in the destabilizing steric (Pauli) repulsion between catalyst and substrate. This is the direct consequence of the decreasing coordination number of the carbon atom in C( sp n )-X, which goes from four, to three, to two along this series. The associated net stabilization of the catalyst-substrate interaction dominates the trend in strain energy which indeed becomes more destabilizing along this same series as the bond becomes stronger from C( sp 3 )-X to C( sp )-X.

Chalcogen bonds: Hierarchical ab initio benchmark and density functional theory performance study

We have performed a hierarchical ab initio benchmark and DFT performance study of D2 Ch•••A- chalcogen bonds (Ch = S, Se; D, A = F, Cl). The ab initio benchmark study is based on a series of ZORA-relativistic quantum chemical methods [HF, MP2, CCSD, CCSD(T)], and all-electron relativistically contracted variants of Karlsruhe basis sets (ZORA-def2-SVP, ZORA-def2-TZVPP, ZORA-def2-QZVPP) with and without diffuse functions. The highest-level ZORA-CCSD(T)/ma-ZORA-def2-QZVPP counterpoise-corrected complexation energies (ΔECPC ) are converged within 1.1-3.4 kcal mol-1 and 1.5-3.1 kcal mol-1 with respect to the method and basis set, respectively. Next, we used the ZORA-CCSD(T)/ma-ZORA-def2-QZVPP (ΔECPC ) as reference data for analyzing the performance of 13 different ZORA-relativistic DFT approaches in combination with the Slater-type QZ4P basis set. We find that the three-best performing functionals are M06-2X, B3LYP, and M06, with mean absolute errors (MAE) of 4.1, 4.2, and 4.3 kcal mol-1 , respectively. The MAE for BLYP-D3(BJ) and PBE amount to 8.5 and 9.3 kcal mol-1 , respectively.

Dual catalytic enantioselective desymmetrization of allene-tethered cyclohexanones

The construction of enantioenriched azabicyclo[3.3.1]nonan-6-one heterocycles via an enantioselective desymmetrization of allene-linked cyclohexanones, enabled through a dual catalytic system, that provides synchronous activation of the cyclohexanone with a chiral prolinamide and the allene with a copper(i) co-catalyst to deliver the stereodefined bicyclic core, is described. Successful application to oxygen analogues was also achieved, thereby providing a new enantioselective synthetic entry to architecturally complex bicyclic ethereal frameworks. The mechanistic pathway and the origin of enantio- and diastereoselectivities has been uncovered using density functional theory (DFT) calculations.

Understanding chemical reactivity using the activation strain model

Understanding chemical reactivity through the use of state-of-the-art computational techniques enables chemists to both predict reactivity and rationally design novel reactions. This protocol aims to provide chemists with the tools to implement a powerful and robust method for analyzing and understanding any chemical reaction using PyFrag 2019. The approach is based on the so-called activation strain model (ASM) of reactivity, which relates the relative energy of a molecular system to the sum of the energies required to distort the reactants into the geometries required to react plus the strength of their mutual interactions. Other available methods analyze only a stationary point on the potential energy surface, but our methodology analyzes the change in energy along a reaction coordinate. The use of this methodology has been proven to be critical to the understanding of reactions, spanning the realms of the inorganic and organic, as well as the supramolecular and biochemical, fields. This protocol provides step-by-step instructions-starting from the optimization of the stationary points and extending through calculation of the potential energy surface and analysis of the trend-decisive energy terms-that can serve as a guide for carrying out the analysis of any given reaction of interest within hours to days, depending on the size of the molecular system.

Cooperative Catalysis of Chiral Guanidine and Rh2(OAc)4 in Asymmetric O-H Insertion of Carboxylic Acid: A Theoretical Investigation

We reported a mechanistic study on asymmetric O-H insertion reaction of α-diazoester with carboxylic acid using Rh₂(OAc)₄/chiral guanidine-amide as the cocatalyst by density functional theory [B3LYP-D3(BJ)/def2-TZVP//B3LYP-D3(BJ)/[6-31G**, SDD] (SMD, Et₂O)]. The catalytic reaction included two stages: (i) formation of Rh-carbene species, subsequently by the construction of C-O bond forming enol and (ii) chiral guanidinium salt-assisted H-transfer to the enol. In cooperative catalysis, Rh₂(OAc)₄ helped to form an enol intermediate via high-reactivity Rh-carbene species, while the in situ-formed guanidium carboxylate acted as a chiral proton shuttle to construct a hydrogen bonding net for the stereo-determinant protonation. The repulsions between the phenyl group of the enol intermediate and the cyclohexyl as well as the ortho-substituted isopropyl group of chiral guanidine played important roles in controlling stereoselectivity. A disadvantageous steric arrangement in si-face attack weakened the stabilizing electrostatic and orbital interaction of reacting species in the H-transfer step, enhancing the pathway to form a predominant product with R-configuration in the two competing pathways. A model was proposed to explain the asymmetric induction of chiral guanidine-amide in protonation.

Arylic C-X Bond Activation by Palladium Catalysts: Activation Strain Analyses of Reactivity Trends

We have quantum chemically explored arylic carbon-substituent bond activation via oxidative insertion of a palladium catalyst in C₆H₅X + PdL_n model systems (X = H, Cl, CH₃; L_n = no ligand, PH₃, (PH₃)₂, PH₂C₂H₄PH₂) using relativistic density functional theory at ZORA-BLYP/TZ2P. Besides exploring reactivity trends and comparing them to aliphatic C-X activation, we aim at uncovering the physical factors behind the activity and selectivity. Our results show that barriers for arylic C-X activation are lower than those for the corresponding aliphatic C-X bonds. However, trends along bonds or upon variation of ligands are similar. Thus, bond activation barriers increase along C-Cl < C-H < C-C and along Pd < Pd(PH₃) or Pd(PH₂C₂H₄PH₂) < Pd(PH₃)₂. Activation strain analyses in conjunction with quantitative molecular orbital theory trace these trends to the rigidity and bonding capability of the various C-X bonds, model catalysts, and ligands.

Catalytic Carbon-Halogen Bond Activation: Trends in Reactivity, Selectivity, and Solvation

We have theoretically studied the oxidative addition of all halomethanes CH3X (with X = F, Cl, Br, I, At) to Pd and PdCl(-), using both nonrelativistic and zeroth-order-regular-approximation-relativistic density functional theory at BLYP/QZ4P. Our study covers the gas phase as well as the condensed phase (water), where solvent effects are described with the conductor-like screening model. The activation of the C*-X bond may proceed via two stereochemically different pathways:  (i) direct oxidative insertion (OxIn) which goes with retention of the configuration at C* and (ii) an alternative SN2 pathway which goes with inversion of the configuration at C*. In the gas phase, for Pd, the OxIn pathway has the lowest reaction barrier for all CH3X's. Anion assistance, that is, going from Pd to PdCl(-), changes the preference for all CH3X's from OxIn to the SN2 pathway. Gas-phase reaction barriers for both pathways to C-X activation generally decrease as X descends in group 17. Two striking solvent effects are (i) the shift in reactivity of Pd + CH3X from OxIn to SN2 in the case of the smaller halogens, F and Cl, and (ii) the shift in reactivity of PdCl(-) + CH3X in the opposite direction, that is, from SN2 to OxIn, in the case of the heavier halogens, I and At. We use the activation strain model to arrive at a qualitative understanding of how the competition between OxIn and SN2 pathways is determined by the halogen atom in the activated C-X bond, by anion assistance, and by solvation.

Selective C-H and C-C Bond Activation: Electronic Regimes as a Tool for Designing d(10) MLn Catalysts

We wish to understand how a transition-metal catalyst can be rationally designed so as to selectively activate one particular bond in a substrate, herein, C-H and C-C bonds in ethane. To this end, we quantum chemically analyzed the activity and selectivity of a large series of model catalysts towards ethane and, for comparison, methane, by using the activation strain model and quantitative molecular orbital theory. The model catalysts comprise d(10) MLn complexes with coordination numbers n=0, 1, and 2; metal centers M=Co(-), Rh(-), Ir(-), Ni, Pd, Pt, Cu(+), Ag(+), and Au(+); and ligands L=NH3, PH3, and CO. Our analyses reveal that rather subtle electronic differences between bonds can be exploited to induce a lower barrier for activating one or the other, depending, among other factors, on the catalysts electronic regime (i.e., s-regime versus d-regime catalysts). Interestingly, the concepts and design principles emerging from this work can also be applied to the more challenging problem of differentiating between activation of the C-H bonds in ethane versus those in methane.

Indenyl effect due to metal slippage? Computational exploration of rhodium-catalyzed acetylene [2+2+2] cyclotrimerization

The mechanism of CpRh (Cp=cyclopentadienyl) and IndRh (Ind=indenyl)-catalyzed acetylene [2+2+2] cyclotrimerization has been revisited aiming at finding an explanation for the better performance of the latter catalyst found experimentally. The hypothesis that an ancillary ligand of the precatalyst remains bonded to the metal center throughout the whole catalytic cycle, based on the experimental evidence that the nature of this ligand can exert some control in cocyclotrimerization of different alkynes, is considered. Strong hapticity variations occur in both the CpRh- and IndRh-catalyzed processes. As the Ind ligand undergoes a more facile slippage than Cp, the energy profile is far smoother in the IndRh-catalyzed cyclotrimerization. This difference in the energetics of the process translates into an enhanced activity of the IndRh catalyst, in nice agreement with experiment.

In silico design of heteroaromatic half-sandwich RhI catalysts for acetylene [2+2+2] cyclotrimerization: evidence of a reverse indenyl effect

A mechanistic density functional theory study of acetylene [2+2+2] cyclotrimerization to benzene catalyzed by Rh(I) half metallocenes is presented. The catalyst fragment contains a heteroaromatic ligand, that is, the 1,2-azaborolyl (Ab) or the 3a,7a-azaborindenyl (Abi) anions, which are isostructural and isoelectronic to the hydrocarbon cyclopentadienyl (Cp) and indenyl (Ind) anions, respectively, but differ from the last ones on having two adjacent carbon atoms replaced with a boron and a nitrogen atom. The better performance of either the classic hydrocarbon or the heteroaromatic catalysts is found to depend on the different mechanistic paths that can be envisioned for the process. The present analyses uncover and explain general structure-reactivity relationships that may serve as rational design principles. In particular, we provide evidence of a reverse indenyl effect.

Benchmark study of the performance of density functional theory for bond activations with (ni,pd)-based transition-metal catalysts

The performance of 23 density functionals, including one LDA, four GGAs, three meta-GGAs, three hybrid GGAs, eight hybrid meta-GGAs, and ten double-hybrid functionals, was investigated for the computation of activation energies of various covalent main-group single bonds by four catalysts: Pd, PdCl⁻, PdCl₂, and Ni (all in the singlet state). A reactant complex, the barrier, and reaction energy were considered, leading to 164 energy data points for statistical analysis. Extended Gaussian AO basis sets were used in all calculations. The best functional for the complete benchmark set relative to estimated CCSD(T)/CBS reference data is PBE0-D3, with an MAD value of 1.1 kcal mol⁻¹ followed by PW6B95-D3, the double hybrid PWPB95-D3, and B3LYP-D3 (1.9 kcal mol⁻¹ each). The other tested hybrid meta-GGAs perform less well (M06-HF: 7.0 kcal mol⁻¹; M06-2X: 6.3 kcal mol⁻¹; M06: 4.9 kcal mol⁻¹) for the investigated reactions. In the Ni case, some double hybrids show larger errors due to partial breakdown of the perturbative treatment for the correlation energy in cases with difficult electronic structures (partial multi-reference character). Only double hybrids either with very low amounts of perturbative correlation (e.g., PBE0-DH) or that use the opposite-spin correlation component only (e.g., PWPB95) seem to be more robust. We also investigated the effect of the D3 dispersion correction. While the barriers are not affected by this correction, significant and mostly positive results were observed for reaction energies. Furthermore, six very recently proposed double-hybrid functionals were analyzed regarding the influence of the amount of Fock exchange as well as the type of perturbative correlation treatment. According to these results, double hybrids with <50–60 % of exact exchange and ∼30 % perturbative correlation perform best.

Nonlinear d(10)-ML2 Transition-Metal Complexes

We have investigated the molecular geometries of a series of dicoordinated d(10)-transition-metal complexes ML2 (M=Co(-), Rh(-), Ir(-), Ni, Pd, Pt, Cu(+), Ag(+), Au(+); L=NH3, PH3, CO) using relativistic density functional theory (DFT) at ZORA-BLYP/TZ2P. Not all complexes have the expected linear ligand-metal-ligand (L-M-L) angle: this angle varies from 180° to 128.6° as a function of the metal as well as the ligands. Our main objective is to present a detailed explanation why ML2 complexes can become bent. To this end, we have analyzed the bonding mechanism in ML2 as a function of the L-M-L angle using quantitative Kohn-Sham molecular orbital (MO) theory in combination with an energy decomposition analysis (EDA) scheme. The origin of bent L-M-L structures is π backdonation. In situations of strong π backdonation, smaller angles increase the overlap of the ligand's acceptor orbital with a higher-energy donor orbital on the metal-ligand fragment, and therefore favor π backdonation, resulting in additional stabilization. The angle of the complexes thus depends on the balance between this additional stabilization and increased steric repulsion that occurs as the complexes are bent.

Theoretical study on the gas-phase reaction mechanism between palladium monoxide and methane

The gas-phase reaction mechanism between palladium monoxide and methane has been theoretically investigated on the singlet and triplet state potential energy surfaces (PESs) at the CCSD(T)/AVTZ//B3LYP/6-311+G(2d, 2p), SDD level. The major reaction channel leads to the products PdCH(2) + H(2)O, whereas the minor channel results in the products Pd + CH(3)OH, CH(2)OPd + H(2), and PdOH + CH(3). The minimum energy reaction pathway for the formation of main products (PdCH(2) + H(2)O), involving one spin inversion, prefers to start at the triplet state PES and afterward proceed along the singlet state PES, where both CH(3)PdOH and CH(3)Pd(O)H are the critical intermediates. Furthermore, the rate-determining step is RS-CH(3) PdOH → RS-2-TS1cb → RS-CH(2)Pd(H)OH with the rate constant of k = 1.48 × 10(12) exp(-93,930/RT). For the first C-H bond cleavage, both the activation strain ΔE(≠)(strain) and the stabilizing interaction ΔE(≠)(int) affect the activation energy ΔE(≠), with ΔE(≠)(int) in favor of the direct oxidative insertion. On the other hand, in the PdCH(2) + H(2) O reaction, the main products are Pd + CH(3)OH, and CH(3)PdOH is the energetically preferred intermediate. In the CH(2)OPd + H(2) reaction, the main products are Pd + CH(3)OH with the energetically preferred intermediate H(2)PdOCH(2). In the Pd + CH(3)OH reaction, the main products are CH(2)OPd + H(2), and H(2)PdOCH(2) is the energetically predominant intermediate. The intermediates, PdCH(2), H(2) PdCO, and t-HPdCHO are energetically preferred in the PdC + H(2), PdCO + H(2), and H(2)Pd + CO reactions, respectively. Besides, PdO toward methane activation exhibits higher reaction efficiency than the atom Pd and its first-row congener NiO.

Steric nature of the bite angle. A closer and a broader look

The bite angle (ligand-metal-ligand angle) is known to greatly influence the activity of catalytically active transition-metal complexes towards bond activation. Here, we have computationally explored how and why the bite angle has such effects in a wide range of prototypical C-X bonds and palladium complexes, using relativistic density functional theory at ZORA-BLYP/TZ2P. Our model reactions cover the substrates H(3)C-X (with X = H, CH(3), Cl) and, among others, the model catalysts, Pd[PH(2)(CH(2))(n)PH(2)] (with n = 2-6) and Pd[PR(2)(CH(2))(n)PR(2)] (n = 2-4 and R = Me, Ph, t-Bu, Cl), Pd(PH(3))X(-) (X = Cl, Br, I), as well as palladium complexes of chelating and non-chelating N-heterocyclic carbenes. The purpose is to elaborate on an earlier finding that bite-angle effects have a predominantly (although not exclusively) steric nature: a smaller bite angle makes more room for coordinating a substrate by bending away the ligands. Indeed, the present results further consolidate this steric picture by revealing its occurrence in this broader range of model reactions and by identifying and quantifying the exact working mechanism through activation strain analyses.

Pd-catalyzed N-arylation of secondary acyclic amides: catalyst development, scope, and computational study

We report the efficient N-arylation of acyclic secondary amides and related nucleophiles with aryl nonaflates, triflates, and chlorides. This method allows for easy variation of the aromatic component in tertiary aryl amides. A new biaryl phosphine with P-bound 3,5-(bis)trifluoromethylphenyl groups was found to be uniquely effective for this amidation. The critical aspects of the ligand were explored through synthetic, mechanistic, and computational studies. Systematic variation of the ligand revealed the importance of (1) a methoxy group on the aromatic carbon of the "top ring" ortho to the phosphorus and (2) two highly electron-withdrawing P-bound 3,5-(bis)trifluoromethylphenyl groups. Computational studies suggest the electron-deficient nature of the ligand is important in facilitating amide binding to the LPd(II)(Ph)(X) intermediate.

Bond activation by group-11 transition-metal cations

We have computationally explored C–X bond activation by the group-11 transition-metal cations Cu+, Ag+, and Au+, and, for comparison, Pd, using relativistic density functional theory (DFT) at ZORA-BLYP/TZ2P. Oxidative insertion of the second-row transition-metal species Ag+ and Pd leads, for a given bond, to the highest overall reaction barriers. On the other hand, if we compare the different bonds oxidative insertion into the C–F bond is associated with (one of the) highest overall barriers whereas insertion into the C–Cl bond leads to the lowest overall barrier for any transition metal. The main trends in reactivity are rationalized using the activation strain model of chemical reactivity, which is an extension of the fragment approach to reaction profiles. In this model, the shape of the reaction profile ΔE(ζ) and the height of the overall reaction barrier ΔE≠ = ΔE(ζ=ζTS) are interpreted in terms of the strain energy ΔEstrain(ζ) associated with deforming the reactants along the reaction coordinate ζ plus the interaction energy ΔEint(ζ) between these deformed reactants: ΔE(ζ) = ΔEstrain(ζ) + ΔEint(ζ).

Frontside versus Backside S(N)2 substitution at group 14 atoms: origin of reaction barriers and reasons for their absence

We have theoretically studied the gas-phase nucleophilic substitution at group-14 atoms (S(N)2@A) in the model reactions of Cl(-)+AH(3)Cl (A=C, Si, Ge, Sn, and Pb) using relativistic density functional theory (DFT) at ZORA-OLYP/TZ2P. Firstly, we wish to explore and understand how the reaction coordinate zeta, and potential energy surfaces (PES) along zeta, vary as the center of nucleophilic attack changes from carbon to the heavier group-14 atoms. Secondly, a comparison between the more common backside reaction (S(N)2-b) and the frontside pathway (S(N)2-f) is performed. The S(N)2-b reaction is found to have a central barrier for A=C, but none for the other group-14 atoms, A=Si-Pb. Relativistic effects destabilize reactant complexes and transition species by up to 10 kcal mol(-1) (for S(N)2-f@Pb), but they do not change relative heights of barriers. We also address the nature of the transformation in the frontside S(N)2-f reactions in terms of turnstile rotation versus Berry-pseudorotation mechanism.