Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si)

Detailed quasiclassical dynamics of the F- + SiH3Cl multi-channel reaction

We report a detailed quasiclassical trajectory study on the F- + SiH3Cl multi-channel reaction using a full-dimensional ab initio analytical potential energy surface. Reaction probabilities, cross sections, initial attack and scattering angle distributions as well as product relative translational, internal, vibrational, and rotational energy distributions are obtained in the collision energy range of 1-40 kcal mol-1 for the following channels: SiH3F + Cl-, SiH2Cl- + HF, SiH2F- + HCl, SiH2FCl + H-, SiH2 + FHCl-, and SiHFCl- + H2. All the channels are translationally cold indicating indirect mechanisms, except proton transfer (SiH2Cl- + HF), which shows mixed direct-indirect character. The angular distributions vary depending on collision energy and inversion/retention for SiH3F + Cl-. In the case of SiH2Cl- + HF front-side/back-side attack backward-forward/forward scattering preference is found at low/high collision energy. SiH2F- + HCl is formed with isotropic scattering and the preferred angle of attack is similar to the SiH3F + Cl- channel. SiH2FCl + H-/SiH2 + FHCl- favors back-side attack and isotropic/backward scattering, whereas SiHFCl- + H2 does not show significant angular preference.

Exploring borderline SN1-SN2 mechanisms: the role of explicit solvation protocols in the DFT investigation of isopropyl chloride

Nucleophilic substitution at saturated carbon is a crucial class of organic reactions, playing a pivotal role in various chemical transformations that yield valuable compounds for society. Despite the well-established SN1 and SN2 mechanisms, secondary substrates, particularly in solvolysis reactions, often exhibit a borderline pathway. A molecular-level understanding of these processes is fundamental for developing more efficient chemical transformations. Typically, quantum-chemical simulations of the solvent medium combine explicit and implicit solvation methods. The configuration of explicit molecules can be defined through top-down approaches, such as Monte Carlo (MC) calculations for generating initial configurations, and bottom-up methods that involve user-dependent protocols to add solvent molecules around the substrate. Herein, we investigated the borderline mechanism of the hydrolysis of a secondary substrate, isopropyl chloride (iPrCl), at DFT-M06-2X/aug-cc-pVDZ level, employing explicit and explicit + implicit protocols. Top-down and bottom-up approaches were employed to generate substrate-solvent complexes of varying number (n = 1, 3, 5, 7, 9, and 12) and configurations of H2O molecules. Our findings consistently reveal that regardless of the solvation approach, the hydrolysis of iPrCl follows a loose-SN2-like mechanism with nucleophilic solvent assistance. Increasing the water cluster around the substrate in most cases led to reaction barriers of ΔH‡ ≈ 21 kcal mol-1, with nine water molecules from MC configurations sufficient to describe the reaction. The More O'Ferrall-Jencks plot demonstrates an SN1-like character for all transition state structures, showing a clear merged profile. The fragmentation activation strain analyses indicate that energy barriers are predominantly controlled by solvent-substrate interactions, supported by the leaving group stabilization assessed through CHELPG atomic charges.

Phosphorus-centered ion-molecule reactions: benchmark ab initio characterization of the potential energy surfaces of the X- + PH2Y [X, Y = F, Cl, Br, I] systems

In the present work we determine the benchmark relative energies and geometries of all the relevant stationary points of the X- + PH2Y [X, Y = F, Cl, Br, I] identity and non-identity reactions using state-of-the-art electronic-structure methods. These phosphorus-centered ion-molecule reactions follow two main reaction routes: bimolecular nucleophilic substitution (SN2), leading to Y- + PH2X, and proton transfer, resulting in HX + PHY- products. The SN2 route can proceed through Walden-inversion, front-side-attack retention, and double-/multiple-inversion pathways. In addition, we also identify the following product channels: H--formation, PH2-- and PH2-formation, 1PH- and 3PH-formation, H2-formation and HY + PHX- formation. The benchmark classical relative energies are obtained by taking into account the core-correlation, scalar relativistic, and post-(T) corrections, which turn out to be necessary to reach subchemical (<1 kcal mol-1) accuracy of the results. Classical relative energies are augmented with zero-point-energy contributions to gain the benchmark adiabatic energies.

Exploring the versatile reactivity of the F- + SiH3Cl system on a full-dimensional coupled-cluster potential energy surface

We develop a full-dimensional analytical potential energy surface (PES) for the F- + SiH3Cl reaction using Robosurfer for automatically sampling the configuration space, the robust [CCSD-F12b + BCCD(T) - BCCD]/aug-cc-pVTZ composite level of theory for computing the energy points, and the permutationally invariant polynomial method for fitting. Evolution of the fitting error and the percentage of the unphysical trajectories are monitored as a function of the iteration steps/number of energy points and polynomial order. Quasi-classical trajectory simulations on the new PES reveal rich dynamics resulting in high-probability SN2 (SiH3F + Cl-) and proton-transfer (SiH2Cl- + HF) products as well as several lower-probability channels, such as SiH2F- + HCl, SiH2FCl + H-, SiH2 + FHCl-, SiHFCl- + H2, SiHF + H2 + Cl-, and SiH2 + HF + Cl-. The Walden-inversion and front-side-attack-retention SN2 pathways are found to be competitive, producing nearly racemic products at high collision energies. The detailed atomic-level mechanisms of the various reaction pathways and channels as well as the accuracy of the analytical PES are analyzed along representative trajectories.

Effect of Linker Structure and Functionalization on Secondary Gas Formation in Metal-Organic Frameworks

Rare-earth terephthalic acid (BDC)-based metal-organic frameworks (MOFs) are promising candidate materials for acid gas separation and adsorption from flue gas streams. However, previous simulations have shown that acid gases (H₂O, NO₂, and SO₂) react with the hydroxyl on the BDC linkers to form protonated acid gases as a potential degradation mechanism. Herein, gas-phase computational approaches were used to identify the formation energies of these secondary protonated acid gases across multiple BDC linker molecules. Formation energies for secondary protonated acid gases were evaluated using both density functional theory (DFT) and correlated wave function methods for varying BDC-gas reaction mechanisms. Upon validation of DFT to reproduce wave function calculation results, rotated conformational linkers and chemically functionalized BDC linkers with -OH, -NH₂, and -SH were investigated. The calculations show that the rotational conformation affects the molecule stability. Double-functionalized BDC linkers, where two functional groups are substituted onto BDC, showed varied reaction energies depending on whether the functional groups donate or withdraw electrons from the aromatic system. Based on these results, BDC linker design must balance adsorption performance with degradation via linker dehydrogenation for the design of stable MOFs for acid gas separations.

Iridium-Catalyzed Chemo-, Diastereo-, and Enantioselective Allyl-Allyl Coupling: Accessing All Four Stereoisomers of (E)-1-Boryl-Substituted 1,5-Dienes by Chirality Pairing

Here, we report a highly chemo-, diastereo-, and enantioselective allyl-allyl coupling between branched allyl alcohols and α-silyl-substituted allylboronate esters, catalyzed by a chiral iridium complex. The α-silyl-substituted allylboronate esters can be chemoselectively coupled with allyl electrophiles, affording a diverse set of enantioenriched (E)-1-boryl-substituted 1,5-dienes in good yields, with excellent stereoselectivity. By permuting the chiral iridium catalysts and the substrates, we efficiently and selectively obtained all four stereoisomers bearing two consecutive chiral centers. Mechanistic studies via density functional theory calculations revealed the origins of the diastereo- and chemoselectivities, indicating the pivotal roles of the steric interaction, the β-silicon effect, and a rapid desilylation process. Additional synthetic modifications for preparing a variety of enantioenriched compounds containing contiguous chiral centers are also included.

Accelerated Quantum Mechanics/Molecular Mechanics Simulations via Neural Networks Incorporated with Mechanical Embedding Scheme

A powerful tool to study the mechanism of reactions in solutions or enzymes is to perform the ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. However, the computational cost is too high due to the explicit electronic structure calculations at every time step of the simulation. A neural network (NN) method can accelerate the QM/MM-MD simulations, but it has long been a problem to accurately describe the QM/MM electrostatic coupling by NN in the electrostatic embedding (EE) scheme. In this work, we developed a new method to accelerate QM/MM calculations in the mechanic embedding (ME) scheme. The potentials and partial point charges of QM atoms are first learned in vacuo by the embedded atom neural networks (EANN) approach. MD simulations are then performed on this EANN/MM potential energy surface (PES) to obtain free energy (FE) profiles for reactions, in which the QM/MM electrostatic coupling is treated in the mechanic embedding (ME) scheme. Finally, a weighted thermodynamic perturbation (wTP) corrects the FE profiles in the ME scheme to the EE scheme. For two reactions in water and one in methanol, our simulations reproduced the B3LYP/MM free energy profiles within 0.5 kcal/mol with a speed-up of 30-60-fold. The results show that the strategy of combining EANN potential in the ME scheme with the wTP correction is efficient and reliable for chemical reaction simulations in liquid. Another advantage of our method is that the QM PES is independent of the MM subsystem, so it can be applied to various MM environments as demonstrated by an S_N2 reaction studied in water and methanol individually, which used the same EANN PES. The free energy profiles are in excellent accordance with the results obtained from B3LYP/MM-MD simulations. In future, this method will be applied to the reactions of enzymes and their variants.

Predicting Solvent Effects on SN2 Reaction Rates: Comparison of QM/MM, Implicit, and MM Explicit Solvent Models

Solvents are one of the key variables in the optimization of a synthesis yield or properties of a synthesis product. In this paper, contemporary solvent models are applied to predict the rates of S_N2 reactions in a range of aqueous and non-aqueous solvents. High-level CCSD(T)/CBS//M06-2X/6-31+G(d) gas phase energies were combined with solvation free energies from SMD, SM12, and ADF-COSMO-RS continuum solvent models, as well as molecular mechanics (MM) explicit solvent models with different atomic charge schemes to predict the rate constants of three S_N2 reactions in eight protic and aprotic solvents. It is revealed that the prediction of rate constants in organic solvents is not necessarily less challenging than in water and popular solvent models struggle to predict their rate constants to within 3 log units of experimental values. Among the continuum solvent models, the ADF-COSMO-RS model performed the best in predicting absolute rate contants while the SM12 model was best at predicting relative rate constants with an average accuracy of about 1.5 and 0.8 log units, respectively. The use of computationally more demanding MM explicit solvent models did not translate to improvements in absolute rate constants but was quite effective at predicting relative rate constants due to systematic error cancellation. Free energy barriers obtained from umbrella sampling with explicit solvent QM/MM simulations led to excellent agreement with experimental values, provided that a validated level of theory is used to treat the QM region.

A multiscale ONIOM study of the buckminsterfullerene (C60) Diels-Alder reaction: from model design to reaction path analysis

The hybrid ONIOM (Our own N-layered Integrated molecular Orbital and molecular Mechanics) formalism is employed to investigate the Diels-Alder reaction of the buckminsterfullerene C₆₀. Our computations suggest that the ONIOM2(M06-2X/6-31G(d): SVWN/STO-3G) model, enclosing both the diene and the pyracyclene fragment of C60 in the higher-layer, provides a reasonable trade-off between accuracy and computational cost as it comes to predicting reaction energetics. Moreover, the frontier molecular orbital (FMO) theory and activation strain model (ASM) are jointly relied on to rationalize the effect of -OH and -CN substituents on the activation barrier of this reaction. Finally, reaction paths are scrutinized to get insight into the various forces underpinning the process of cycloadduct formation.

Investigating the competing E2 and SN2 mechanisms for the microsolvated HO-(H2O)n=0-4 + CH3CH2X (X = Cl, Br, I) reactions

We characterized the anti-E2, syn-E2, inv-S_N2, and ret-S_N2 reaction channels for the reaction of microsolvated HO^-(H₂O)_n anions with CH₃CH₂X (X = Cl, Br, I), using the CCSD(T)/PP/t//MP2/ECP/d level method, to understand how a solvent influences the competing E2 and S_N2 reactions. The calculated sequence of barrier for the four channels is ret-S_N2 > syn-E2 > anti-E2 > inv-S_N2. The barrier heights increase with incremental hydration as the system transfers from the gas phase to microsolvation, and to bulk solvation (using the PCM implicit solvent model). As the degree of hydration n increases, good correlations have been found between barrier heights and several thermodynamic, geometric and charge parameters, including the reaction enthalpy, proton/ethyl-cation affinity of the hydrated nucleophile, geometric looseness (%L^‡) and asymmetry (%AS^‡) and charge asymmetry (Δq(X-O)) of the transition structures. Under a molecular orbital scheme, the HOMOs of nucleophiles are stabilized by stepwise hydration, explaining the rise in the barriers. Considering the effect of the leaving group, the barrier heights exhibit linear correlation with the halogen electronegativity and H-acidity of substrate CH₃CH₂X. In terms of E2/S_N2 competition, the barrier difference, , first increases then decreases as the number of explicit water molecules increases, under both microsolvation and bulk solvation conditions, but the inv-S_N2 pathway is always favored over the anti-E2 pathway. Energy decomposition analysis attributes the increase of barrier difference to the greater geometric distortion in the anti-E2 transition structure.

Parameter free evaluation of SN2 reaction rates for halide substitution in halomethane

We estimate the kinetic constants of a series of archetypal S_N2 reactions, i.e., the nucleophilic substitutions of halides in halomethane. A parameter free, multiscale approach recently developed [Campeggio et al., Phys. Chem. Chem. Phys., 2020, 22, 3455] is employed. The protocol relies on quantum mechanical calculations for the description of the energy profile along the intrinsic reaction coordinate, which is then mapped onto a reaction coordinate conveniently built for the reactive process. A Kramers-Klein equation is used to describe the stochastic time evolution of the reaction coordinate and its velocity; friction is parameterized using a hydrodynamic model and Kramers theory is used to derive the rate constant of the reaction. The method is here applied to six S_N2 reactions in water at 295.15 K, which differ in the nucleophile and the leaving group. The computed reaction rates are in good agreement with the experimental data and correlate well with the trends observed for the activation energies.

High-Level Systematic Ab Initio Comparison of Carbon- and Silicon-Centered SN2 Reactions

We characterize the stationary points along the Walden inversion, front-side attack, and double-inversion pathways of the X^– + CH₃Y and X^– + SiH₃Y [X, Y = F, Cl, Br, I] S_N2 reactions using chemically accurate CCSD(T)-F12b/aug-cc-pVnZ [n = D, T, Q] levels of theory. At the carbon center, Walden inversion dominates and proceeds via prereaction (X^–···H₃CY) and postreaction (XCH₃···Y^–) ion-dipole wells separated by a usually submerged transition state (X–H₃C–Y)⁻, front-side attack occurs over high barriers, double inversion is the lowest-energy retention pathway for X = F, and hydrogen- (F^–···HCH₂Y) and halogen-bonded (X^–···YCH₃) complexes exist in the entrance channel. At the silicon center, Walden inversion proceeds through a single minimum (X–SiH₃–Y)⁻, the front-side attack is competitive via a usually submerged transition state separating pre- and postreaction minima having X–Si–Y angles close to 90°, double inversion occurs over positive, often high barriers, and hydrogen- and halogen-bonded complexes are not found. In addition to the S_N2 channels (Y^– + CH₃X/SiH₃X), we report reaction enthalpies for proton abstraction (HX + CH₂Y^–/SiH₂Y^–), hydride substitution (H^– + CH₂XY/SiH₂XY), XH···Y^– complex formation (XH···Y^– + ¹CH₂/¹SiH₂), and halogen abstraction (XY + CH₃^–/SiH₃^– and XY^– + CH₃/SiH₃).

The SN2 reaction and its relationship with the Walden inversion, the Finkelstein and Menshutkin reactions together with theoretical calculations for the Finkelstein reaction

This communication gives an overview of the relationships between four reactions that although related were not always perceived as such: SN2, Walden, Finkelstein, and Menshutkin. Binary interactions (SN2 & Walden, SN2 & Menshutkin, SN2 & Finkelstein, Walden & Menshutkin, Walden & Finkelstein, Menshutkin & Finkelstein) were reported. Carbon, silicon, nitrogen, and phosphorus as central atoms and fluorides, chlorides, bromides, and iodides as lateral atoms were considered. Theoretical calculations provide Gibbs free energies that were analyzed with linear models to obtain the halide contributions. The M06-2x DFT computational method and the 6-311++G(d,p) basis set have been used for all atoms except for iodine where the effective core potential def2-TZVP basis set was used. Concerning the central atom pairs, carbon/silicon vs. nitrogen/phosphorus, we reported here for the first time that the effect of valence expansion was known for Si but not for P. Concerning the lateral halogen atoms, some empirical models including the interaction between F and I as entering and leaving groups explain the Gibbs free energies.

TSNet: predicting transition state structures with tensor field networks and transfer learning

Transition states are among the most important molecular structures in chemistry, critical to a variety of fields such as reaction kinetics, catalyst design, and the study of protein function. However, transition states are very unstable, typically only existing on the order of femtoseconds. The transient nature of these structures makes them incredibly difficult to study, thus chemists often turn to simulation. Unfortunately, computer simulation of transition states is also challenging, as they are first-order saddle points on highly dimensional mathematical surfaces. Locating these points is resource intensive and unreliable, resulting in methods which can take very long to converge. Machine learning, a relatively novel class of algorithm, has led to radical changes in several fields of computation, including computer vision and natural language processing due to its aptitude for highly accurate function approximation. While machine learning has been widely adopted throughout computational chemistry as a lightweight alternative to costly quantum mechanical calculations, little research has been pursued which utilizes machine learning for transition state structure optimization. In this paper TSNet is presented, a new end-to-end Siamese message-passing neural network based on tensor field networks shown to be capable of predicting transition state geometries. Also presented is a small dataset of S_N2 reactions which includes transition state structures - the first of its kind built specifically for machine learning. Finally, transfer learning, a low data remedial technique, is explored to understand the viability of pretraining TSNet on widely available chemical data may provide better starting points during training, faster convergence, and lower loss values. Aspects of the new dataset and model shall be discussed in detail, along with motivations and general outlook on the future of machine learning-based transition state prediction.

On the Role of Hydrogen Bonding in Gas-Phase SN2 Reactions at Silicon

The shape of the potential energy surface (PES) of gas-phase S_N2 reactions at silicon is determined by the type of nucleophile, the leaving group, and substituents which remain bonded to silicon. In this study, we present PES scans along the reaction coordinate of six symmetrical S_N2 reactions: X^- + SiR₃X → XSiR₃ + X^-, where X = Cl or F and R = H, Me, or OMe. While the fluorine systems and the ClSiH₃Cl system only give single-well PESs, ClSiMe₃Cl and ClSi(OMe)₃Cl give triple- and double-well PESs with stable pre- and post-reaction complexes. A complementary bonding analysis (energy decomposition analysis, quantum theory of atoms in molecules, and natural bond orbitals) reveals that the leaving group (X^-) is stabilized by hydrogen bonding in the XSiMe₃X and XSi(OMe)₃X systems. It is shown that this so far neglected stabilizing contribution, along with σ-hole bonding, is responsible for the shapes of the PESs of ClSiMe₃Cl and ClSi(OMe)₃Cl in the gas phase.

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.

Ambident Nucleophilic Substitution: Understanding Non-HSAB Behavior through Activation Strain and Conceptual DFT Analyses

The ability to understand and predict ambident reactivity is key to the rational design of organic syntheses. An approach to understand trends in ambident reactivity is the hard and soft acids and bases (HSAB) principle. The recent controversy over the general validity of this principle prompted us to investigate the competing gas-phase SN 2 reaction channels of archetypal ambident nucleophiles CN- , OCN- , and SCN- with CH3 Cl (SN 2@C) and SiH3 Cl (SN 2@Si), using DFT calculations. Our combined analyses highlight the inability of the HSAB principle to correctly predict the reactivity trends of these simple, model reactions. Instead, we have successfully traced reactivity trends to the canonical orbital-interaction mechanism and the resulting nucleophile-substrate interaction energy. The HOMO-LUMO orbital interactions set the trend in both SN 2@C and SN 2@Si reactions. We provide simple rules for predicting the ambident reactivity of nucleophiles based on our Kohn-Sham molecular orbital analysis.

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.

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.

Complementary bonding analysis of the N–Si interaction in pentacoordinated silicon compounds using quantum crystallography

The unique combination of quantum crystallography and complementary bonding analysis is used to investigate the bonding of pentacoordinated silicon atoms.

Hydrolysis of trialkoxysilanes catalysed by the fluoride anion. Nucleophilic vs. basic catalysis

A DFT study showed competition between basic and nucleophilic catalysis of alkoxysilane hydrolysis by the fluoride ion.

Nucleophilic Substitution (SN 2): Dependence on Nucleophile, Leaving Group, Central Atom, Substituents, and Solvent

The reaction potential energy surface (PES), and thus the mechanism of bimolecular nucleophilic substitution (SN 2), depends profoundly on the nature of the nucleophile and leaving group, but also on the central, electrophilic atom, its substituents, as well as on the medium in which the reaction takes place. Here, we provide an overview of recent studies and demonstrate how changes in any one of the aforementioned factors affect the SN 2 mechanism. One of the most striking effects is the transition from a double-well to a single-well PES when the central atom is changed from a second-period (e. g. carbon) to a higher-period element (e.g, silicon, germanium). Variations in nucleophilicity, leaving group ability, and bulky substituents around a second-row element central atom can then be exploited to change the single-well PES back into a double-well. Reversely, these variations can also be used to produce a single-well PES for second-period elements, for example, a stable pentavalent carbon species.

Nucleophilic Substitution in Solution: Activation Strain Analysis of Weak and Strong Solvent Effects

We have quantum chemically studied the effect of various polar and apolar solvents on the shape of the potential energy surface (PES) of a diverse collection of archetypal nucleophilic substitution reactions at carbon, silicon, phosphorus, and arsenic by using density functional theory at the OLYP/TZ2P level. In the gas phase, all our model SN 2 reactions have single-well PESs, except for the nucleophilic substitution reaction at carbon (SN 2@C), which has a double-well energy profile. The presence of the solvent can have a significant effect on the shape of the PES and, thus, on the nature of the SN 2 process. Solvation energies, charges on the nucleophile or leaving group, and structural features are compared for the various SN 2 reactions in a spectrum of solvents. We demonstrate how solvation can change the shape of the PES, depending not only on the polarity of the solvent, but also on how the charge is distributed over the interacting molecular moieties during different stages of the reaction. In the case of a nucleophilic substitution at three-coordinate phosphorus, the reaction can be made to proceed through a single-well [no transition state (TS)], bimodal barrier (two TSs), and then through a unimodal transition state (one TS) simply by increasing the polarity of the solvent.

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.

Revealing Electron-Electron Interactions within Lewis Pairs in Chemical Systems

The so-called "Lewis pair" is a ubiquitous phenomenon in chemistry and is often used as an intuitive construct to predict and rationalize chemical structure and behavior. Concepts from the very general Valence Shell Electron Pair Repulsion (VSEPR) model to the most esoteric reaction mechanism routinely rely on the notion that electrons tend to exist in pairs and that these pairs can be thought of as being localized to a particular region of space. It is precisely this localization that allows one to intuit how these pairs might behave, generally speaking, so that reasonable predictions may be made regarding molecular structure, intermolecular interactions, property trends, and reaction mechanisms, etc. Of course, it is rather unfortunate that the Lewis model is entirely qualitative and yields no information regarding how any specific electron pair is distributed. Here we demonstrate a novel electronic structure analysis technique that predicts and analyzes precise quantitative details about the relative and absolute distribution of individual electron pairs. This Single Electron Pair Distribution Analysis (SEPDA) reveals quantitative details about the distribution of the well-known Lewis pairs, such as how they are distributed in space and how their relative velocities change in various chemical contexts. We show that these distributions allow one to image the explicitly pairwise electronic behavior of bonds and lone pairs. We further demonstrate how this electronic behavior changes with several conditions to explore the nature of the covalent chemical bond, non-covalent interactions, bond formation, and exotic 3-center-2-electron species. It is shown that indications of the strength of bonded and non-bonded interactions may also be gleaned from such distributions and SEPDA can be used as a tool to differentiate between interaction types. We anticipate that SEPDA will be of broad utility in a wide variety of chemical contexts because it affords a very detailed, visual and intuitive analysis technique that is generally applicable.

Microsolvation effects on the reactivity of oxy-nucleophiles: the case of gas-phase SN2 reactions of YO-(CH3OH) n=1,2 towards CH3Cl

The modified G4(MP2) method was applied to explore microsolvation effects on the reactivity of four solvated normal oxy-nucleophiles YO^-(CH₃OH) _n=1,2 (Y = CH₃, C₂H₅, FC₂H₄, ClC₂H₄), and five α-oxy-nucleophiles YO^-(CH₃OH) _n=1,2 (Y = HO, CH₃O, F, Cl, Br), in gas-phase S_N2 reactions towards the substrate CH₃Cl. Based on a Brønsted-type plot, our calculations reveal that the overall activation barriers of five microsolvated α-oxy-nucleophiles are obviously smaller than the prediction from the correlation line constructed by four normal microsolvated ones to different degrees, and clearly demonstrate the existence of an α-effect in the presence of one or two methanol molecule(s). Moreover, it was found that the α-effect of the mono-methanol microsolvated α-nucleophile is stronger than that of the monohydrated α-nucleophile. However, the α-effect of YO^-(CH₃OH)₂ becomes weaker for Y = HO and CH₃O, whereas it becomes stronger for Y = F, Cl, Br than that of YO^-(H₂O)₂, which can be explained by analyses of the activation strain model in the two cases. It was also found that the rationale about the low ionization energy of α-nucleophile inducing the α-effect was not widely significant. Graphical abstract Variation of alpha-effect in the gas-phase S_N2 reaction with the microsolvation.

Mechanistic Insight into the Oxidation of Organic Phenylselenides by H2 O2

The oxidation of organic phenylselenides by H₂ O₂ is investigated in model compounds, namely, n-butyl phenyl selenide (PhSe(nBu)), bis(phenylselanyl)methane (PhSeMeSePh), diphenyl diselenide (PhSeSePh), and 1,2-bis(phenylselanyl)ethane (PhSeEtSePh). Through a combined experimental (¹ H and ⁷⁷ Se NMR) and computational approach, we characterize the direct oxidation of monoselenide to selenoxide, the stepwise double oxidation of PhSeMeSePh that leads to different diastereomeric diselenoxides, the complete oxidation of the diphenyldiselenide that leads to selenium-selenium bond cleavage, and the subsequent formation of the phenylseleninic product. The oxidation of PhSeEtSePh also results in the formation of phenylseleninic acid along with 1-(vinylseleninyl)benzene, which is derived from a side elimination reaction. The evidence of a direct mechanism, in addition to an autocatalytic mechanism that emerges from kinetic studies, is discussed. By considering our observations of diselenides with chalcogen atoms that are separated by alkyl spacers of different length, a rationale for the advantage of diselenide versus monoselenide catalysts is presented.

Activation Strain Analysis of SN2 Reactions at C, N, O, and F Centers

Fundamental principles that determine chemical reactivity and reaction mechanisms are the very foundation of chemistry and many related fields of science. Bimolecular nucleophilic substitutions (S_N2) are among the most common and therefore most important reaction types. In this report, we examine the trends in the S_N2 reactions with respect to increasing electronegativity of the reaction center by comparing the well-studied backside S_N2 Cl^– + CH₃Cl with similar Cl^– substitutions on the isoelectronic series with the second period elements N, O, and F in place of C. Relativistic (ZORA) DFT calculations are used to construct the gas phase reaction potential energy surfaces (PES), and activation strain analysis, which allows decomposition of the PES into the geometrical strain and interaction energy, is employed to analyze the observed trends. We find that S_N2@N and S_N2@O have similar PES to the prototypical S_N2@C, with the well-defined reaction complex (RC) local minima and a central barrier, but all stationary points are, respectively, increasingly stable in energy. The S_N2@F, by contrast, exhibits only a single-well PES with no barrier. Using the activation strain model, we show that the trends are due to the interaction energy and originate mainly from the decreasing energy of the empty acceptor orbital (σ*_A–Cl) on the reaction center A in the order of C, N, O, and F. The decreasing steric congestion around the central atom is also a likely contributor to this trend. Additional decomposition of the interaction energy using Kohn–Sham molecular orbital (KS-MO) theory provides further support for this explanation, as well as suggesting electrostatic energy as the primary reason for the distinct single-well PES profile for the FCl reaction.

Ion-Pair SN 2 Substitution: Activation Strain Analyses of Counter-Ion and Solvent Effects

The ion-pair SN 2 reactions of model systems MnF(n-1) +CH3Cl(M(+) =Li(+), Na(+), K(+), and MgCl(+); n=0, 1) have been quantum chemically explored by using DFT at the OLYP/6-31++G(d,p) level. The purpose of this study is threefold: 1) to elucidate how the counterion M(+) modifies ion-pair SN 2 reactivity relative to the parent reaction F(-) +CH3Cl; 2) to determine how this influences stereochemical competition between the backside and frontside attacks; and 3) to examine the effect of solvation on these ion-pair SN2 pathways. Trends in reactivity are analyzed and explained by using the activation strain model (ASM) of chemical reactivity. The ASM has been extended to treat reactivity in solution. These findings contribute to a more rational design of tailor-made substitution reactions.

E2 and SN2 Reactions of X(-) + CH3CH2X (X = F, Cl); an ab Initio and DFT Benchmark Study

We have computed consistent benchmark potential energy surfaces (PESs) for the anti-E2, syn-E2, and SN2 pathways of X(-) + CH3CH2X with X = F and Cl. This benchmark has been used to evaluate the performance of 31 popular density functionals, covering local-density approximation, generalized gradient approximation (GGA), meta-GGA, and hybrid density-functional theory (DFT). The ab initio benchmark has been obtained by exploring the PESs using a hierarchical series of ab initio methods [up to CCSD(T)] in combination with a hierarchical series of Gaussian-type basis sets (up to aug-cc-pVQZ). Our best CCSD(T) estimates show that the overall barriers for the various pathways increase in the order anti-E2 (X = F) < SN2 (X = F) < SN2 (X = Cl) ∼ syn-E2 (X = F) < anti-E2 (X = Cl) < syn-E2 (X = Cl). Thus, anti-E2 dominates for F(-) + CH3CH2F, and SN2 dominates for Cl(-) + CH3CH2Cl, while syn-E2 is in all cases the least favorable pathway. Best overall agreement with our ab initio benchmark is obtained by representatives from each of the three categories of functionals, GGA, meta-GGA, and hybrid DFT, with mean absolute errors in, for example, central barriers of 4.3 (OPBE), 2.2 (M06-L), and 2.0 kcal/mol (M06), respectively. Importantly, the hybrid functional BHandH and the meta-GGA M06-L yield incorrect trends and qualitative features of the PESs (in particular, an erroneous preference for SN2 over the anti-E2 in the case of F(-) + CH3CH2F) even though they are among the best functionals as measured by their small mean absolute errors of 3.3 and 2.2 kcal/mol in reaction barriers. OLYP and B3LYP have somewhat higher mean absolute errors in central barriers (5.6 and 4.8 kcal/mol, respectively), but the error distribution is somewhat more uniform, and as a consequence, the correct trends are reproduced.

A density functional theory model of mechanically activated silyl ester hydrolysis

To elucidate the mechanism of the mechanically activated dissociation of chemical bonds between carboxymethylated amylose (CMA) and silane functionalized silicon dioxide, we have investigated the dissociation kinetics of the bonds connecting CMA to silicon oxide surfaces with density functional calculations including the effects of force, solvent polarizability, and pH. We have determined the activation energies, the pre-exponential factors, and the reaction rate constants of candidate reactions. The weakest bond was found to be the silyl ester bond between the silicon and the alkoxy oxygen atom. Under acidic conditions, spontaneous proton addition occurs close to the silyl ester such that neutral reactions become insignificant. Upon proton addition at the most favored position, the activation energy for bond hydrolysis becomes 31 kJ mol(-1), which agrees very well with experimental observation. Heterolytic bond scission in the protonated molecule has a much higher activation energy. The experimentally observed bi-exponential rupture kinetics can be explained by different side groups attached to the silicon atom of the silyl ester. The fact that different side groups lead to different dissociation kinetics provides an opportunity to deliberately modify and tune the kinetic parameters of mechanically activated bond dissociation of silyl esters.

Assessment of density-functionals for describing the X(-) + CH3ONO2 gas-phase reactions with X = F, OH, CH2CN

The energetics of the ECO2, SN2@C and SN2@N channels of X(-) + CH3ONO2 (X = F, OH, CH2CN) gas-phase reactions were computed using the CCSD(T)/CBS method. This benchmark extends a previous study with X = OH [M. A. F. de Souza et al., J. Am. Chem. Soc., 2012, 134, 19004] and was used to ascertain the accuracy and robustness of nineteen density-functionals for describing these potential energy profiles (PEP) as well as the kinetic product distributions obtained from RRKM calculations. Assessments were based on the mean unsigned error (MUE), the mean signed error (MSE), the #best : #worst (BW) criterion and the statistical confidence interval (CI) for the MSE. In general, double-hybrid (DH) functionals perform better than the range-separated ones, and both are better than the global-hybrid functionals. Based on the MUE and CI criteria the B2GPPLYP, B2PLYP, M08-SO, BMK, ωB97X-D, CAM-B3LYP, M06, M08-HX, ωB97X and B97-K functionals show the best performance in the description of these PEPs. Within this set, the B2GPPLYP functional is the most accurate and robust. The RRKM results indicate that the DHs are the best for describing the selectivities of these reactions. Compared to CCSD(T), the B2PLYP method has a relative error of only ca. 1% for the selectivity and the accuracy to provide the correct conclusion concerning the nonstatistical behavior of these reactions.

Homologation of boronic esters with organolithium compounds: a computational assessment of mechanism

Ab initio calculations are reported for the reaction of methyl boronic ester with organolithium reagents with α-leaving groups. The best calculations rely on density functional theory prediction of structures and coupled-cluster theory calculation of accurate potential energies. The results provide strong confirmation of the feasibility of a two-step mechanism with rapid initial formation of a boron-ate complex followed by slower migration of methyl from boron to carbon with loss of the leaving group. The calculated free energy of activation is consistent with observed kinetic behavior, and the calculations provide a framework for exploring substituent and other effects on reactivity. Obtaining reasonable agreement with experiment in this way is not trivial and requires careful treatment of level of theory (density functional theory calculations tend to yield inaccurate results), of conformational complexity, especially for the ate complexes, and of the nature of the microscopic model of reactants and solvent. The methodological challenges and possible pitfalls, many of which are relevant more broadly to computational modeling of organic reaction mechanisms, are discussed in detail.

Mechanism and selectivity of methyl and phenyl migrations in hypervalent silylated iminoquinones

Chlorosilanes R(X)(Y)SiCl (R = Me, Ph; X, Y = Me, Ph, Cl) have been reported to react with Pb(ONO(Q))2 (ONO(Q) = 3,5-di-tert-butyl-1,2-quinone-(3,5-di-tert-butyl-2-oxy-1-phenyl)imine) to give five-coordinate (X)(Y)Si(ON[R]O), in which the R group has migrated from silicon to nitrogen. This migration is intramolecular, as confirmed by the lack of crossover between (CH3)3SiCl and (CD3)3SiCl in their reaction with Pb(ONO(Q))2. Reaction of PhSiMeCl2 takes place with high kinetic stereoselectivity to produce isomer Ph(Cl)Si(ON[Me]O) in which the phenyl is axial in the trigonal bipyramid, which subsequently isomerizes to the thermodynamic isomer with axial chlorine. This indicates that migration takes place preferentially from the stereoisomer of the octahedral intermediate, κ(3)-Ph(CH3)(Cl)Si(ONO(Q)), in which the phenyl and methyl groups are mutually trans, indicating that the observed complete selectivity for methyl over phenyl migration is due to intrinsic differences in migratory aptitude. DFT calculations suggest that migration takes place from this isomer not because it undergoes migration faster than other possible stereoisomers, but because it is formed most rapidly, and migration occurs faster than isomerization.