Correction: Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance.

Correction for 'Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance' by Pascal Vermeeren et al., Phys. Chem. Chem. Phys., 2022, 24, 18028-18042, https://doi.org/10.1039/D2CP02234F.

Understanding chemistry with the symmetry-decomposed Voronoi deformation density charge analysis.

The symmetry-decomposed Voronoi deformation density (VDD) charge analysis is an insightful and robust computational tool to aid the understanding of chemical bonding throughout all fields of chemistry. This method quantifies the atomic charge flow associated with chemical-bond formation and enables decomposition of this charge flow into contributions of (1) orbital interaction types, that is, Pauli repulsive or bonding orbital interactions; (2) per irreducible representation (irrep) of any point-group symmetry of interacting closed-shell molecular fragments; and now also (3) interacting open-shell (i.e., radical) molecular fragments. The symmetry-decomposed VDD charge analysis augments the symmetry-decomposed energy decomposition analysis (EDA) so that the charge flow associated with Pauli repulsion and orbital interactions can be quantified both per atom and per irrep, for example, for σ, π, and δ electrons. This provides detailed insights into fundamental aspects of chemical bonding that are not accessible from EDA.

The Origin of Catalysis and Regioselectivity of Lewis Acid-Catalyzed Diels-Alder Reactions with Tropone.

We have studied the uncatalyzed and Lewis acid (LA)-catalyzed cycloaddition reaction between tropone and 1,1-dimethoxyethene using dispersion-corrected relativistic density functional theory (DFT). The LA catalysts BF3 , B(C6 H5 )3 , and B(C6 F5 )3 efficiently accelerate both the competing [4+2] and [8+2] cycloaddition reactions by lowering the activation barrier up to 12 kcal mol-1 compared to the uncatalyzed reaction. Our study reveals that the LA catalyst promotes both cycloaddition reaction pathways by LUMO-lowering catalysis and demonstrates that Pauli-lowering catalysis is not always the operative catalytic mechanism in cycloaddition reactions. Judicious choice of the LA catalyst can effectively impart regiocontrol of the cycloaddition: B(C6 H5 )3 furnishes the [8+2] adduct while B(C6 F5 )3 yields the [4+2] adduct. We discovered that the regioselectivity shift finds its origin in the ability of the LA to absorb distortion by adopting a trigonal pyramidal geometry around the boron atom.

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.

SN 2 versus E2 Competition of Cyclic Ethers.

We have quantum chemically studied the influence of ring strain on the competition between the two mechanistically different SN 2 and E2 pathways using a series of archetypal ethers as substrate in combination with a diverse set of Lewis bases (F- , Cl- , Br- , HO- , H3 CO- , HS- , H3 CS- ), using relativistic density functional theory at ZORA-OLYP/QZ4P. The ring strain in the substrate is systematically increased on going from a model acyclic ether to a 6- to 5- to 4- to 3-membered ether ring. We have found that the activation energy of the SN 2 pathway sharply decreases when the ring strain of the system is increased, thus on going from large to small cyclic ethers, the SN 2 reactivity increases. In contrast, the activation energy of the E2 pathway generally rises along this same series, that is, from large to small cyclic ethers. The opposing reactivity trends induce a mechanistic switch in the preferred reaction pathway for strong Lewis bases from E2, for large cyclic substrates, to SN 2, for small cyclic substrates. Weak Lewis bases are unable to overcome the higher intrinsic distortivity of the E2 pathway and, therefore, always favor the less distortive SN 2 reaction.

How Ionization Catalyzes Diels-Alder Reactions.

The catalytic effect of ionization on the Diels-Alder reaction between 1,3-butadiene and acrylaldehyde has been studied using relativistic density functional theory (DFT). Removal of an electron from the dienophile, acrylaldehyde, significantly accelerates the Diels-Alder reaction and shifts the reaction mechanism from concerted asynchronous for the neutral Diels-Alder reaction to stepwise for the radical-cation Diels-Alder reaction. Our detailed activation strain and Kohn-Sham molecular orbital analyses reveal how ionization of the dienophile enhances the Diels-Alder reactivity via two mechanisms: (i) by amplifying the asymmetry in the dienophile's occupied π-orbitals to such an extent that the reaction goes from concerted asynchronous to stepwise and thus with substantially less steric (Pauli) repulsion per reaction step; (ii) by enhancing the stabilizing orbital interactions that result from the ability of the singly occupied molecular orbital of the radical-cation dienophile to engage in an additional three-electron bonding interaction with the highest occupied molecular orbital of the diene.

How Ionization Catalyzes Diels-Alder Reactions.

Invited for the cover of this issue are Pascal Vermeeren, Trevor A. Hamlin, and F. Matthias Bickelhaupt of the TheoCheM group at the Vrije Universiteit Amsterdam. The cover art depicts how ionizing the dienophile lowers the Diels-Alder reaction barrier between 1,3-butadiene and acrylaldehyde by reducing the destabilizing steric Pauli repulsion and enhancing the stabilizing orbital interactions. Read the full text of the article at 10.1002/chem.202200987.

SN2 versus SN2' Competition.

We have quantum chemically explored the competition between the SN2 and SN2' 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., Cγ═Cß-Cα-Y, bearing a leaving-group at the α-position, proceed either via a direct attack at the α-carbon (SN2) or via an attack at the γ-carbon, involving a concerted allylic rearrangement (SN2'), 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 SN2 or allylic SN2' pathway. Our activation strain analyses expose the underlying physical factors that steer the SN2/SN2' 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.

Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance.

Hierarchical, convergent ab initio benchmark computations were performed followed by a systematic analysis of DFT performance for five pericyclic reactions comprising Diels-Alder, 1,3-dipolar cycloaddition, electrocyclic rearrangement, sigmatropic rearrangement, and double group transfer prototypes. Focal point analyses (FPA) extrapolating to the ab initio limit were executed via explicit quantum chemical computations with electron correlation treatments through CCSDT(Q) and correlation-consistent Gaussian basis sets up to aug'-cc-pV5Z. Optimized geometric structures and vibrational frequencies of all stationary points were obtained at the CCSD(T)/cc-pVTZ level of theory. The FPA reaction barriers and energies exhibit convergence to within a few tenths of a kcal mol-1. The FPA benchmarks were used to evaluate the performance of 60 density functionals (eight dispersion-corrected), covering the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. The meta-hybrid M06-2X functional provided the best overall performance [mean absolute error (MAE) of 1.1 kcal mol-1] followed closely by the double-hybrids B2K-PLYP, mPW2K-PLYP, and revDSD-PBEP86 [MAE of 1.4-1.5 kcal mol-1]. The regularly used GGA functional BP86 gave a higher MAE of 5.8 kcal mol-1, but it qualitatively described the trends in reaction barriers and energies. Importantly, we established that accurate yet efficient meta-hybrid or double-hybrid DFT potential energy surfaces can be acquired based on geometries from the computationally efficient and robust BP86/DZP level.

How Oriented External Electric Fields Modulate Reactivity.

A judiciously oriented external electric field (OEEF) can catalyze a wide range of reactions and can even induce endo/exo stereoselectivity of cycloaddition reactions. The Diels-Alder reaction between cyclopentadiene and maleic anhydride is studied by using quantitative activation strain and Kohn-Sham molecular orbital theory to pinpoint the origin of these catalytic and stereoselective effects. Our quantitative model reveals that an OEEF along the reaction axis induces an enhanced electrostatic and orbital interaction between the reactants, which in turn lowers the reaction barrier. The stronger electrostatic interaction originates from an increased electron density difference between the reactants at the reactive center, and the enhanced orbital interaction arises from the promoted normal electron demand donor-acceptor interaction driven by the OEEF. An OEEF perpendicular to the plane of the reaction axis solely stabilizes the exo pathway of this reaction, whereas the endo pathway remains unaltered and efficiently steers the endo/exo stereoselectivity. The influence of the OEEF on the inverse electron demand Diels-Alder reaction is also investigated; unexpectedly, it inhibits the reaction, as the electric field now suppresses the critical inverse electron demand donor-acceptor interaction.

Bifunctional Hydrogen Bond Donor-Catalyzed Diels-Alder Reactions: Origin of Stereoselectivity and Rate Enhancement.

The selectivity and rate enhancement of bifunctional hydrogen bond donor-catalyzed Diels-Alder reactions between cyclopentadiene and acrolein were quantum chemically studied using density functional theory in combination with coupled-cluster theory. (Thio)ureas render the studied Diels-Alder cycloaddition reactions exo selective and induce a significant acceleration of this process by lowering the reaction barrier by up to 7 kcal mol-1 . Our activation strain and Kohn-Sham molecular orbital analyses uncover that these organocatalysts enhance the Diels-Alder reactivity by reducing the Pauli repulsion between the closed-shell filled π-orbitals of the diene and dienophile, by polarizing the π-orbitals away from the reactive center and not by making the orbital interactions between the reactants stronger. In addition, we establish that the unprecedented exo selectivity of the hydrogen bond donor-catalyzed Diels-Alder reactions is directly related to the larger degree of asynchronicity along this reaction pathway, which is manifested in a relief of destabilizing activation strain and Pauli repulsion.

Not Carbon s-p Hybridization, but Coordination Number Determines C-H and C-C Bond Length.

A fundamental and ubiquitous phenomenon in chemistry is the contraction of both C-H and C-C bonds as the carbon atoms involved vary, in s-p hybridization, along sp3 to sp2 to sp. Our quantum chemical bonding analyses based on Kohn-Sham molecular orbital theory show that the generally accepted rationale behind this trend is incorrect. Inspection of the molecular orbitals and their corresponding orbital overlaps reveals that the above-mentioned shortening in C-H and C-C bonds is not determined by an increasing amount of s-character at the carbon atom in these bonds. Instead, we establish that this structural trend is caused by a diminishing steric (Pauli) repulsion between substituents around the pertinent carbon atom, as the coordination number decreases along sp3 to sp2 to sp.

Lewis Acid-Catalyzed Diels-Alder Reactions: Reactivity Trends across the Periodic Table.

The catalytic effect of various weakly interacting Lewis acids (LAs) across the periodic table, based on hydrogen (Group 1), pnictogen (Group 15), chalcogen (Group 16), and halogen (Group 17) bonds, on the Diels-Alder cycloaddition reaction between 1,3-butadiene and methyl acrylate was studied quantum chemically by using relativistic density functional theory. Weakly interacting LAs accelerate the Diels-Alder reaction by lowering the reaction barrier up to 3 kcal mol-1 compared to the uncatalyzed reaction. The reaction barriers systematically increase from halogen

How Lewis Acids Catalyze Ring-Openings of Cyclohexene Oxide.

We have quantum chemically studied the Lewis acid-catalyzed epoxide ring-opening reaction of cyclohexene epoxide by MeZH (Z = O, S, and NH) using relativistic dispersion-corrected density functional theory. We found that the reaction barrier of the Lewis acid-catalyzed epoxide ring-opening reactions decreases upon ascending in group 1 along the series Cs+ > Rb+ > K+ > Na+ > Li+ > H+. Our activation strain and Kohn-Sham molecular orbital analyses reveal that the enhanced reactivity of the Lewis acid-catalyzed ring-opening reaction is caused by the reduced steric (Pauli) repulsion between the filled orbitals of the epoxide and the nucleophile, as the Lewis acid polarizes the filled orbitals of the epoxide more efficiently away from the incoming nucleophile. Furthermore, we established that the regioselectivity of these ring-opening reactions is, aside from the "classical" strain control, also dictated by a hitherto unknown mechanism, namely, the steric (Pauli) repulsion between the nucleophile and the substrate, which could be traced back to the asymmetric orbital density on the epoxide. In all, this work again demonstrates that the concept of Pauli-lowering catalysis is a general phenomenon.

Origin of asynchronicity in Diels-Alder reactions.

Asynchronicity in Diels-Alder reactions plays a crucial role in determining the height of the reaction barrier. Currently, the origin of asynchronicity is ascribed to the stronger orbital interaction between the diene and the terminal carbon of an asymmetric dienophile, which shortens the corresponding newly formed C-C bond and hence induces asynchronicity in the reaction. Here, we show, using the activation strain model and Kohn-Sham molecular orbital theory at ZORA-BP86/TZ2P, that this rationale behind asynchronicity is incorrect. We, in fact, found that following a more asynchronous reaction mode costs favorable HOMO-LUMO orbital overlap and, therefore, weakens (not strengthens) these orbital interactions. Instead, it is the Pauli repulsion that induces asynchronicity in Diels-Alder reactions. An asynchronous reaction pathway also lowers repulsive occupied-occupied orbital overlap which, therefore, reduces the unfavorable Pauli repulsion. As soon as this mechanism of reducing Pauli repulsion dominates, the reaction begins to deviate from synchronicity and adopts an asynchronous mode. The eventual degree of asynchronicity, as observed in the transition state of a Diels-Alder reaction, is ultimately achieved when the gain in stability, as a response to the reduced Pauli repulsion, balances with the loss of favorable orbital interactions.

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.

A Unified Framework for Understanding Nucleophilicity and Protophilicity in the SN 2/E2 Competition.

The concepts of nucleophilicity and protophilicity are fundamental and ubiquitous in chemistry. A case in point is bimolecular nucleophilic substitution (SN 2) and base-induced elimination (E2). A Lewis base acting as a strong nucleophile is needed for SN 2 reactions, whereas a Lewis base acting as a strong protophile (i.e., base) is required for E2 reactions. A complicating factor is, however, the fact that a good nucleophile is often a strong protophile. Nevertheless, a sound, physical model that explains, in a transparent manner, when an electron-rich Lewis base acts as a protophile or a nucleophile, which is not just phenomenological, is currently lacking in the literature. To address this fundamental question, the potential energy surfaces of the SN 2 and E2 reactions of X- +C2 H5 Y model systems with X, Y = F, Cl, Br, I, and At, are explored by using relativistic density functional theory at ZORA-OLYP/TZ2P. These explorations have yielded a consistent overview of reactivity trends over a wide range in reactivity and pathways. Activation strain analyses of these reactions reveal the factors that determine the shape of the potential energy surfaces and hence govern the propensity of the Lewis base to act as a nucleophile or protophile. The concepts of "characteristic distortivity" and "transition state acidity" of a reaction are introduced, which have the potential to enable chemists to better understand and design reactions for synthesis.

The Nature of Nonclassical Carbonyl Ligands Explained by Kohn-Sham Molecular Orbital Theory.

When carbonyl ligands coordinate to transition metals, their bond distance either increases (classical) or decreases (nonclassical) with respect to the bond length in the isolated CO molecule. C-O expansion can easily be understood by π-back-donation, which results in a population of the CO's π*-antibonding orbital and hence a weakening of its bond. Nonclassical carbonyl ligands are less straightforward to explain, and their nature is still subject of an ongoing debate. In this work, we studied five isoelectronic octahedral complexes, namely Fe(CO)6 2+ , Mn(CO)6 + , Cr(CO)6 , V(CO)6 - and Ti(CO)6 2- , at the ZORA-BLYP/TZ2P level of theory to explain this nonclassical behavior in the framework of Kohn-Sham molecular orbital theory. We show that there are two competing forces that affect the C-O bond length, namely electrostatic interactions (favoring C-O contraction) and π-back-donation (favoring C-O expansion). It is a balance between those two terms that determines whether the carbonyl is classical or nonclassical. By further decomposing the electrostatic interaction ΔVelstat into four fundamental terms, we are able to rationalize why ΔVelstat gives rise to the nonclassical behavior, leading to new insights into the driving forces behind C-O contraction.

Understanding the 1,3-Dipolar Cycloadditions of Allenes.

We have quantum chemically studied the reactivity, site-, and regioselectivity of the 1,3-dipolar cycloaddition between methyl azide and various allenes, including the archetypal allene propadiene, heteroallenes, and cyclic allenes, by using density functional theory (DFT). The 1,3-dipolar cycloaddition reactivity of linear (hetero)allenes decreases as the number of heteroatoms in the allene increases, and formation of the 1,5-adduct is, in all cases, favored over the 1,4-adduct. Both effects find their origin in the strength of the primary orbital interactions. The cycloaddition reactivity of cyclic allenes was also investigated, and the increased predistortion of allenes, that results upon cyclization, leads to systematically lower activation barriers not due to the expected variations in the strain energy, but instead from the differences in the interaction energy. The geometric predistortion of cyclic allenes enhances the reactivity compared to linear allenes through a unique mechanism that involves a smaller HOMO-LUMO gap, which manifests as more stabilizing orbital interactions.

SN2 versus E2 Competition of F- and PH2- Revisited.

We have quantum chemically analyzed the competition between the bimolecular nucleophilic substitution (SN2) and base-induced elimination (E2) pathways for F- + CH3CH2Cl and PH2- + CH3CH2Cl using the activation strain model and Kohn-Sham molecular orbital theory at ZORA-OLYP/QZ4P. Herein, we correct an earlier study that intuitively attributed the mechanistic preferences of F- and PH2-, i.e., E2 and SN2, respectively, to a supposedly unfavorable shift in the polarity of the abstracted ß-proton along the PH2--induced E2 pathway while claiming that ″...no correlation between the thermodynamic basicity and E2 rate should be expected.″ Our analyses, however, unequivocally show that it is simply the 6 kcal mol-1 higher proton affinity of F- that enables this base to engage in a more stabilizing orbital interaction with CH3CH2Cl and hence to preferentially react via the E2 pathway, despite the higher characteristic distortivity (more destabilizing activation strain) associated with this pathway. On the other hand, the less basic PH2- has a weaker stabilizing interaction with CH3CH2Cl and is, therefore, unable to overcome the characteristic distortivity of the E2 pathway. Therefore, the mechanistic preference of PH2- is steered to the SN2 reaction channel (less-destabilizing activation strain).