Reaction Coordinates and the Transition-Vector Approximation to the IRC

Substitution Effects in Aryl Halides and Amides into the Reaction Mechanism of Ullmann-Type Coupling Reactions

In this article, we present a comprehensive computational investigation into the reaction mechanism of N-arylation of substituted aryl halides through Ullmann-type coupling reactions. Our computational findings, obtained through DFT ωB97X-D/6-311G(d,p) and ωB97X-D/LanL2DZ calculations, reveal a direct relation between the previously reported experimental reaction yields and the activation energy of haloarene activation, which constitutes the rate-limiting step in the overall coupling process. A detailed analysis of the reaction mechanism employing the Activation Strain Model indicates that the strain in the substituted iodoanilines is the primary contributor to the energy barrier, representing an average of 80% of the total strain energy. Additional analysis based on conceptual Density Functional Theory (DFT) suggests that the nucleophilicity of the nitrogen in the lactam is directly linked to the activation energies. These results provide valuable insights into the factors influencing energetic barriers and, consequently, reaction yields. These insights enable the rational modification of reactants to optimize the N-arylation process.

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.

How Bases Catalyze Diels-Alder Reactions

We have quantum chemically studied the base-catalyzed Diels-Alder (DA) reaction between 3-hydroxy-2-pyrone and N-methylmaleimide using dispersion-corrected density functional theory. The uncatalyzed reaction is slow and is preceded by the extrusion of CO₂ via a retro-DA reaction. Base catalysis, for example, by triethylamine, lowers the reaction barrier up to 10 kcal mol^-1 , causing the reaction to proceed smoothly at low temperature, which quenches the expulsion of CO₂ , yielding efficient access to polyoxygenated natural compounds. Our activation strain analyses reveal that the base accelerates the DA reaction via two distinct electronic mechanisms: i) by the HOMO-raising effect, which enhances the normal electron demand orbital interaction; and ii) by donating charge into 3-hydroxy-2-pyrone which accumulates in its reactive region and promotes strongly stabilizing secondary electrostatic interactions with N-methylmaleimide.

Understanding the Reactivity of Combination Reactions of Intramolecular Geminal Group 13 Element/Phosphorus and Gallium/Group 15 Element Frustrated Lewis Pairs with CS2

The reactions of CS₂ captured by intramolecular geminal G13/P-based (G13 = group 13 elements) and Ga/G15-based (G15 = group 15 elements) frustrated Lewis pairs have been theoretically examined by using density functional theory (DFT) computations. With regard to the nine FLP-related compounds, our DFT calculated results reveal that only Al/P-Rea and Ga/P-Rea can kinetically and thermodynamically precede the energetically feasible combination reactions with CS₂ to form the five-membered heterocyclic adducts. Our activation strain model analyses on the nine aforementioned model molecules indicate that the atomic radius of the Lewis acceptor (G13) and the Lewis donor (G15) plays a role in controlling their barrier heights to obtain good orbital overlaps among G13/P-Rea, Ga/G15-Rea, and CS₂. Our theoretical observations based on the energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) approach strongly indicate that the donor-acceptor bonding (i.e., singlet-singlet bonding) rather than the electron-sharing bonding (i.e., triplet-triplet bonding) plays a central role in determining the bonding conditions of the transition states, G13/P-TS and Ga/G15-TS. In addition, the theoretical evidence obtained by the frontier molecular orbital theory and EDA-NOCV analyses reveals that the best description for the bonding natures of the combination reactions of intramolecular geminal G13/P-Rea and Ga/G15-Rea with CS₂ is the lone pair(G15) → p-π*(C) interaction rather than the p-π*(G13) ← p-π(S) interaction. Moreover, our present DFT computations concerning the calculated structures and corresponding relative energetics of the stationary points connected with the aforementioned sophisticated approaches are in accordance with the Hammond postulate.

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.

SN2 versus SN2' Competition

We have quantum chemically explored the competition between the S_N2 and S_N2' pathways for X^- + H₂C═CHCH₂Y (X, Y = F, Cl, Br, I) using a combined relativistic density functional theory and coupled-cluster theory approach. Bimolecular nucleophilic substitution reactions at allylic systems, i.e., C^γ═C^β-C^α-Y, bearing a leaving-group at the α-position, proceed either via a direct attack at the α-carbon (S_N2) or via an attack at the γ-carbon, involving a concerted allylic rearrangement (S_N2'), in both cases leading to the expulsion of the leaving-group. Herein, we provide a physically sound model to rationalize under which circumstances a nucleophile will follow either the aliphatic S_N2 or allylic S_N2' pathway. Our activation strain analyses expose the underlying physical factors that steer the S_N2/S_N2' competition and, again, demonstrate that the concepts of a reaction's "characteristic distortivity" and "transition state acidity" provide explanations and design tools for understanding and predicting reactivity trends in organic synthesis.

An ETS-NOCV-based computational strategies for the characterization of concerted transition states involving CO2

Due to the presence of both a slightly acidic carbon and a slightly basic oxygen, carbon dioxide is often involved in concerted transition states (TSs) with two (or more) different molecular events interlaced in the same step. The possibility of isolating and quantitatively evaluating each molecular event would be important to characterize and understand the reaction mechanism in depth. This could be done, in principle, by measuring the relevant distances in the optimized TS, but often distances are not accurate enough, especially in the presence of many simultaneous processes. Here, we have applied the Extended Transition State‐Natural Orbital for Chemical Valence‐method (ETS‐NOCV), also in combination with the Activation Strain Model (ASM) and Energy Decomposition Analysis (EDA), to separate and quantify these molecular events at the TS of both organometallic and organic reactions. For the former, we chose the decomposition of formic acid to CO₂ by an iridium catalyst, and for the latter, a CO₂‐mediated transamidation and its chemical variations (hydro‐ and aminolysis of an ester) as case studies. We demonstrate that the one‐to‐one mapping between the “molecular events” and the ETS‐NOCV components is maintained along the entire lowest energy path connecting reactants and products around the TS, thus enabling a detailed picture on the relative importance of each interacting component. The methodology proposed here provides valuable insights into the effect of different chemical substituents on the reaction mechanism and promises to be generally applicable for any concerted TSs.

Origin of the α-Effect in SN 2 Reactions

The α-effect is a term used to explain the dramatically enhanced reactivity of α-nucleophiles (R-Y-X:- ) compared to their parent normal nucleophile (R-X:- ) by deviating from the classical Brønsted-type reactivity-basicity relationship. The exact origin of this effect is, however, still heavily under debate. In this work, we have quantum chemically analyzed the α-effect of a set of anionic nucleophiles, including O-, N- and S-based normal and α-nucleophiles, participating in an SN 2 reaction with ethyl chloride using relativistic density functional theory at ZORA-OLYP/QZ4P. Our activation strain and Kohn-Sham molecular orbital analyses identified two criteria an α-nucleophile needs to fulfill in order to show α-effect: (i) a small HOMO lobe on the nucleophilic center, pointing towards the substrate, to reduce the repulsive occupied-occupied orbital overlap and hence (steric) Pauli repulsion with the substrate; and (ii) a sufficiently high energy HOMO to overcome the loss of favorable HOMO-LUMO orbital overlap with the substrate, as a consequence of the first criterion, by reducing the HOMO-LUMO orbital energy gap. If one of these two criteria is not fulfilled, one can expect no α-effect or inverse α-effect.

Switch From Pauli-Lowering to LUMO-Lowering Catalysis in Brønsted Acid-Catalyzed Aza-Diels-Alder Reactions

Brønsted acid-catalyzed inverse-electron demand (IED) aza-Diels-Alder reactions between 2-aza-dienes and ethylene were studied using quantum chemical calculations. The computed activation energy systematically decreases as the basic sites of the diene progressively become protonated. Our activation strain and Kohn-Sham molecular orbital analyses traced the origin of this enhanced reactivity to i) "Pauli-lowering catalysis" for mono-protonated 2-aza-dienes due to the induction of an asynchronous, but still concerted, reaction pathway that reduces the Pauli repulsion between the reactants; and ii) "LUMO-lowering catalysis" for multi-protonated 2-aza-dienes due to their highly stabilized LUMO(s) and more concerted synchronous reaction path that facilitates more efficient orbital overlaps in IED interactions. In all, we illustrate how the novel concept of "Pauli-lowering catalysis" can be overruled by the traditional concept of "LUMO-lowering catalysis" when the degree of LUMO stabilization is extreme as in the case of multi-protonated 2-aza-dienes.

How metallylenes activate small molecules

We have studied the activation of dihydrogen by metallylenes using relativistic density functional theory (DFT). Our detailed activation strain and Kohn-Sham molecular orbital analyses have quantified the physical factors behind the decreased reactivity of the metallylene on going down Group 14, from carbenes to stannylenes. Along this series, the reactivity decreases due to a worsening of the back-donation interaction between the filled lone-pair orbital of the metallylene and the σ*-orbital of H2, which, therefore, reduces the metallylene-substrate interaction and increases the reaction barrier. As the metallylene ligand is varied from nitrogen to phosphorus to arsenic a significant rate enhancement is observed for the activation of H2 due to (i) a reduced steric (Pauli) repulsion between the metallylene and the substrate; and (ii) less activation strain, as the metallylene becomes increasingly more predistorted. Using a rationally designed metallylene with an optimal Group 14 atom and ligand combination, we show that a number of small molecules (i.e. HCN, CO2, H2, NH3) may also be readily activated. For the first time, we show the ability of our H2 activated designer metallylenes to hydrogenate unsaturated hydrocarbons. The results presented herein will serve as a guide for the rational design of metallylenes toward the activation of small molecules and subsequent reactions.

Computational Analysis of the Selective Formation of the C4α-C8' Bond in the Intermolecular Coupling of Catechin Derivatives

Procyanidin B3 is a natural flavonoid composed of two catechins connected via a C4α-C8' bond. The couplings of catechin derivatives, promoted by Lewis acids, have been widely applied to the syntheses of procyanidin B3 and related flavonoids because the reactions construct the C4α-C8' bond in a highly stereo- and regioselective manner. However, the structural complexity of the catechin derivatives has complicated the exploration of a detailed mechanism for this selectivity. Here, we report the results of a computational study to provide plausible origins for the selective C4α-C8' bond formation of catechin derivatives 1 and 2 by using models 5 and 7. Although a systematic search did not provide S_N2-like transition states, we successfully identified transition states TS-A, TS-B, and TS-C for the S_N1-type C4α-C8', C4β-C8', and C4α-C6' bond formations, respectively, from a total of 233 transition states to justify the stereo- and regioselectivity of the experimental results. The analysis of these structures by NCIPLOT mapping and the distortion/interaction strain model suggests that the eclipsed interaction at the forming C-C bond between the electrophile and the nucleophile destabilizes TS-B, while the strain of the electrophile destabilizes TS-C. Consequently, the C4α-C8' bond is formed via the lowest energy transition state TS-A.

Theoretical Study of the Mechanism of Catalytic Enanteoselective N-H and O-H Insertion Reactions

Theoretical density functional theory (DFT) calculations were carried out to study bond insertion reactions using a copper(I)-Box-carbenoid as a bond activator. In order to understand the reaction mechanism where N-H and O-H bonds actively participate, the reaction force (RF) and activation strain model (ASM) were used. Results indicate that the first step of the reaction is barrierless for both bond insertions (N-H and O-H), and the second step of the insertion reaction in the phenol (O-H bond) is favored kinetically and thermodynamically with regard to the aniline substrate (N-H bond). The enantioselectivity is driven by the ligand of the catalyst by steric repulsion, favoring the formation of the R isomer. The analysis of the reaction force and ASM exhibited that the higher energy barrier in aniline is mainly due to a higher W₂ contribution together with repulsive interactions, which hinders the insertion process.

Activation Strain Analyses of Counterion and Solvent Effects on the Ion-Pair SN 2 Reaction of NH 2 - and CH3 Cl

We have computationally studied the bimolecular nucleophilic substitution (S_N 2) reactions of M_n NH₂ ^(n-1) + CH₃ Cl (M⁺  = Li⁺ , Na⁺ , K⁺ , and MgCl⁺ ; n = 0, 1) in the gas phase and in tetrahydrofuran solution at OLYP/6-31++G(d,p) using polarizable continuum model implicit solvation. We wish to explore and understand the effect of the metal counterion M⁺ and of solvation on the reaction profile and the stereochemical preference, that is, backside (S_N 2-b) versus frontside attack (S_N 2-f). The results were compared to the corresponding ion-pair S_N 2 reactions involving F^- and OH^- nucleophiles. Our analyses with an extended activation strain model of chemical reactivity uncover and explain various trends in S_N 2 reactivity along the nucleophiles F^- , OH^- , and NH 2 - , including solvent and counterion effects. © 2019 Wiley Periodicals, Inc.

PyFrag 2019-Automating the exploration and analysis of reaction mechanisms

We present a substantial update to the PyFrag 2008 program, which was originally designed to perform a fragment-based activation strain analysis along a provided potential energy surface. The original PyFrag 2008 workflow facilitated the characterization of reaction mechanisms in terms of the intrinsic properties, such as strain and interaction, of the reactants. The new PyFrag 2019 program has automated and reduced the time-consuming and laborious task of setting up, running, analyzing, and visualizing computational data from reaction mechanism studies to a single job. PyFrag 2019 resolves three main challenges associated with the automated computational exploration of reaction mechanisms: it (1) computes the reaction path by carrying out multiple parallel calculations using initial coordinates provided by the user; (2) monitors the entire workflow process; and (3) tabulates and visualizes the final data in a clear way. The activation strain and canonical energy decomposition results that are generated relate the characteristics of the reaction profile in terms of intrinsic properties (strain, interaction, orbital overlaps, orbital energies, populations) of the reactant species. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Dual Activation of Aromatic Diels-Alder Reactions

The unusually fast Diels-Alder reactions of [5]cyclophanes were analyzed by DFT at the BLYP-D3(BJ)/TZ2P level of theory. The computations were guided by an integrated activation-strain and Kohn-Sham molecular orbital analysis. It is revealed why both [5]metacyclophane and [5]paracyclophane exhibit a significant rate enhancement compared to their planar benzene analogue. The activation strain analyses revealed that the enhanced reactivity originates from 1) predistortion of the aromatic core resulting in a reduced activation strain of the aromatic diene, and/or 2) enhanced interaction with the dienophile through a distortion-controlled lowering of the HOMO-LUMO gap within the diene. Both of these physical mechanisms and thus the rate of Diels-Alder cycloaddition can be tuned through different modes of geometrical distortion (meta versus para bridging) and by heteroatom substitution in the aromatic ring. Judicious choice of the bridge and heteroatom in the aromatic core enables effective tuning of the aromatic Diels-Alder reactivity to achieve activation barriers as low as 2 kcal mol-1 , which is an impressive 35 kcal mol-1 lower than that of benzene.

Structural Distortion of Cycloalkynes Influences Cycloaddition Rates both by Strain and Interaction Energies

The reactivities of 2‐butyne, cycloheptyne, cyclooctyne, and cyclononyne in the 1,3‐dipolar cycloaddition reaction with methyl azide were evaluated through DFT calculations at the M06‐2X/6‐311++G(d)//M06‐2X/6‐31+G(d) level of theory. Computed activation free energies for the cycloadditions of cycloalkynes are 16.5–22.0 kcal mol⁻¹ lower in energy than that of the acyclic 2‐butyne. The strained or predistorted nature of cycloalkynes is often solely used to rationalize this significant rate enhancement. Our distortion/interaction–activation strain analysis has been revealed that the degree of geometrical predistortion of the cycloalkyne ground‐state geometries acts to enhance reactivity compared with that of acyclic alkynes through three distinct mechanisms, not only due to (i) a reduced strain or distortion energy, but also to (ii) a smaller HOMO–LUMO gap, and (iii) an enhanced orbital overlap, which both contribute to more stabilizing orbital interactions.

Factors Controlling the Diels-Alder Reactivity of Hetero-1,3-Butadienes

We have quantum chemically explored the Diels-Alder reactivities of a systematic series of hetero-1,3-butadienes with ethylene by using density functional theory at the BP86/TZ2P level. Activation strain analyses provided physical insight into the factors controlling the relative cycloaddition reactivity of aza- and oxa-1,3-butadienes. We find that dienes with a terminal heteroatom, such as 2-propen-1-imine (NCCC) or acrolein (OCCC), are less reactive than the archetypal 1,3-butadiene (CCCC), primarily owing to weaker orbital interactions between the more electronegative heteroatoms with ethylene. Thus, the addition of a second heteroatom at the other terminal position (NCCN and OCCO) further reduces the reactivity. However, the introduction of a nitrogen atom in the backbone (CNCC) leads to enhanced reactivity, owing to less Pauli repulsion resulting from polarization of the diene HOMO in CNCC towards the nitrogen atom and away from the terminal carbon atom. The Diels-Alder reactions of ethenyl-diazene (NNCC) and 1,3-diaza-butadiene (NCNC), which contain heteroatoms at both the terminal and backbone positions, are much more reactive due to less activation strain compared to CCCC.

Modeling of Multicolor Single-Molecule Förster Resonance Energy-Transfer Experiments on Protein Folding

Using a coarse-grained, C_α-model of BBL protein, a multicolor single-molecule Förster resonance energy transfer (FRET) experiment is modeled. Three fluorophores are introduced, which, for simplicity, are associated with C_α beads. Two fluorophores are placed at the ends of protein chain and the third one at the middle of the chain. The free-energy surfaces (FESs) depending on the interfluorophore distances and on the FRET efficiencies corresponding to these distances have been constructed and compared with the FESs depending on the conventional collective variables, such as the fraction of native contacts and radius of gyration. It has been found that multicolor experiments can successfully resolve all essential BBL states that are revealed by the conventional FESs. The resolution of these states with the FRET-efficiency histogram is found to be successful if the energy transfer is measured between the fluorophores at the BBL ends. We also show that, although the present model construct of BBL is very simple, it captures some characteristic features of the single-molecule FRET experiments, such as the pattern of the FRET-efficiency histograms and their evolution with the denaturant concentration.

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.

Ion-Pair SN 2 Reaction of OH- and CH3 Cl: Activation Strain Analyses of Counterion and Solvent Effects

We have theoretically studied the non-identity S_N 2 reactions of M_n OH^(n-1) +CH₃ Cl (M⁺ =Li⁺ , Na⁺ , K⁺ , and MgCl⁺ ; n=0, 1) in the gas phase and in THF solution at the OLYP/6-31++G(d,p) level using polarizable continuum model (PCM) implicit solvation. We want to explore and understand the effect of the metal counterion M⁺ and solvation on the reaction profile and the stereoselectivity of these processes. To this end, we have explored the potential energy surfaces of the backside (S_N 2-b) and frontside (S_N 2-f) pathways. To explain the computed trends, we have carried out analyses with an extended activation strain model (ASM) of chemical reactivity that includes the treatment of solvation effects.

Fluorine substituent effect on the stereochemistry of catalyzed and non-catalyzed Diels–Alder reactions. The case of R-butenone with cyclopentadiene: a computational assessment of the mechanism

A semiquantitative prediction of stereoselectivity due to substitutions of dienophile is obtained.

Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model

The activation strain or distortion/interaction model is a tool to analyze activation barriers that determine reaction rates. For bimolecular reactions, the activation energies are the sum of the energies to distort the reactants into geometries they have in transition states plus the interaction energies between the two distorted molecules. The energy required to distort the molecules is called the activation strain or distortion energy. This energy is the principal contributor to the activation barrier. The transition state occurs when this activation strain is overcome by the stabilizing interaction energy. Following the changes in these energies along the reaction coordinate gives insights into the factors controlling reactivity. This model has been applied to reactions of all types in both organic and inorganic chemistry, including substitutions and eliminations, cycloadditions, and several types of organometallic reactions.

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.

The activation strain model and molecular orbital theory

The activation strain model is a powerful tool for understanding reactivity, or inertness, of molecular species. This is done by relating the relative energy of a molecular complex along the reaction energy profile to the structural rigidity of the reactants and the strength of their mutual interactions: ΔE(ζ) = ΔE_strain(ζ) + ΔE_int(ζ). We provide a detailed discussion of the model, and elaborate on its strong connection with molecular orbital theory. Using these approaches, a causal relationship is revealed between the properties of the reactants and their reactivity, e.g., reaction barriers and plausible reaction mechanisms. This methodology may reveal intriguing parallels between completely different types of chemical transformations. Thus, the activation strain model constitutes a unifying framework that furthers the development of cross-disciplinary concepts throughout various fields of chemistry. We illustrate the activation strain model in action with selected examples from literature. These examples demonstrate how the methodology is applied to different research questions, how results are interpreted, and how insights into one chemical phenomenon can lead to an improved understanding of another, seemingly completely different chemical process. WIREs Comput Mol Sci 2015, 5:324-343. doi: 10.1002/wcms.1221.

Driving and retarding forces in a chemical reaction

The reaction force F(ξ) is the negative gradient of the potential energy of a chemical process along the intrinsic reaction coordinate ξ. We extend the rigorous concept of F(ξ) to the "activation strain model" of Bickelhaupt et al., to formulate the "strain" force Fstr(ξ) that retards a reaction and the "interaction" force Fint(ξ) that drives it. These are investigated for a group of Diels-Alder cycloadditions. The results fully support the interpretation of the minimum of F(ξ) as defining the beginning of the transition from deformed reactants to eventual products.

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.

The activation strain model of chemical reactivity

Herein, we provide an account of the activation strain model of chemical reactivity and its recent applications. In this model, the potential energy surface DeltaE(zeta) along the reaction coordinate zeta is decomposed into the strain DeltaE(strain)(zeta) of the increasingly deformed reactants plus the interaction DeltaE(int)(zeta) between these deformed reactants, i.e., DeltaE(zeta) = DeltaE(strain)(zeta) + DeltaE(int)(zeta). The purpose of this fragment-based approach is to arrive at a qualitative understanding, based on accurate calculations, of the trends in activation barriers and transition-state geometries (e.g., early or late along the reaction coordinate) in terms of the reactants' properties. The usage of the activation strain model is illustrated by a number of concrete applications, by us and others, in the fields of catalysis and organic chemistry.