Mechanistic Insights into the Proton Transfer and Substitution Dynamics of N-Atom Center Reactions: A Study of CH3O- with NH2Cl

Bimolecular substitution reactions involving N as the central atom have continuously improved our understanding of substitution dynamics. This work used chemical dynamics simulations to investigate the dynamics of NH2Cl with N as the central atom and the multiatomic nucleophile CH3O- and compared these results with the F- + NH2Cl reaction. The most noteworthy difference is in the competition between proton transfer (PT) and the SN2 pathways. Our results demonstrate that, for the CH3O- + NH2Cl system, the PT pathway is considerably more favorable than the SN2 pathway. In contrast, no PT pathway was observed for the F- + NH2Cl system at room temperature. This can be attributed to the exothermic reaction of the PT pathway for the CH3O- + NH2Cl reaction and is coupled with a more stable transition state compared to the substitution pathway. Furthermore, the bulky nature of the CH3O- group impedes its participation in SN2 reactions, which enhances both the thermodynamic and the dynamic advantages of the PT reaction. Interestingly, the atomic mechanism reveals that the PT pathway is primarily governed by indirect mechanisms, similar to the SN2 pathway, with trajectories commonly trapped in the entrance channel being a prominent feature. These trajectories are often accompanied by prolonged and frequent proton exchange or proton abstraction processes. This current work provides insights into the dynamics of N-centered PT reactions, which are useful in gaining a comprehensive understanding of the dynamics behavior of similar reactions.

Alternating Stereospecificity upon Central-Atom Change: Dynamics of the F- +PH2 Cl SN 2 Reaction Compared to its C- and N-Centered Analogues

Central-atom effects on bimolecular nucleophilic substitution (SN 2) reactions are well-known in chemistry, however, the atomic-level SN 2 dynamics at phosphorous (P) centers has never been studied. We investigate the dynamics of the F- +PH2 Cl reaction with the quasi-classical trajectory method on a novel full-dimensional analytical potential energy surface fitted on high-level ab initio data. Our computations reveal intermediate dynamics compared to the F- +CH3 Cl and the F- +NH2 Cl SN 2 reactions: phosphorus as central atom leads to a more indirect SN 2 reaction with extensive complex-formation with respect to the carbon-centered one, however, the title reaction is more direct than its N-centered pair. Stereospecificity, characteristic at C-center, does not appear here either, due to the submerged front-side-attack retention path and the repeated entrance-channel inversional motion, whereas the multi-inversion mechanism discovered at nitrogen center is also undermined by the deep Walden-well. At low collision energies, 6 % of the PH2 F products form with retained configuration, mostly through complex-mediated mechanisms, while this ratio reaches 24 % at the highest energy due to the increasing dominance of the direct front-side mechanism and the smaller chance for hitting the deep Walden-inversion minimum. Our results suggest pronounced central-atom effects in SN 2 reactions, which can fundamentally change their (stereo)dynamics.

Effects of Methyl Substitution and Leaving Group on E2/SN2 Competition for Reactions of F- with RY (R = CH3, C2H5, iC3H7, tC4H9; Y = Cl, I)

The competition between base-induced elimination (E2) and bimolecular nucleophilic substitution (SN2) is of significant importance in organic chemistry and is influenced by many factors. The electronic structure calculations for the gas-phase reactions of F- + RY (R = CH3, C2H5, iC3H7, tC4H9, and Y = Cl, I) are executed at the MP2 level with aug-cc-pVDZ or ECP/d basis set to investigate the α-methyl substitution effect. The variation in barrier height, reaction enthalpy, and competition of SN2/E2 as a function of methyl-substitution and leaving group ability has been emphasized. And the nature of these rules has been explored. As the degree of methyl substitution on α-carbon increases, the E2 channel becomes more competitive and dominant with R varying from C2H5, iC3H7, to tC4H9. Energy decomposition analysis offers new insights into the competition between E2 and SN2 processes, which suggests that the drop in interaction energy with an increasing degree of substitution cannot compensate for the rapid growth of preparation energy, leading to a rapid increase in the SN2 energy barrier. By altering the leaving group from Cl to I, the barriers of both SN2 and E2 monotonically decrease, and, with the increased number of substituents, they reduce more dramatically, which is attributed to the looser transition state structures with the stronger leaving group ability. Interestingly, ∆E0‡ exhibits a positive linear correlation with reaction enthalpy (∆H) and halogen electronegativity. With the added number of substituents, the differences in ∆E0‡ and ∆H between Y = Cl and I likewise exhibit good linearity.

Theoretical studies on the kinetics and dynamics of the BeH+ + H2O reaction: comparison with the experiment

The reaction of BeH+ with background gaseous H2O may play a role in qubit loss for quantum information processing with Be+ as trapped ions, and yet its reaction mechanism has not been well understood until now. In this work, a globally accurate, full-dimensional ground-state potential energy surface (PES) for the BeH+ + H2O reaction was constructed by fitting a total of 170 438 ab initio energy points at the level of RCCSD(T)-F12/aug-cc-pVTZ using the fundamental invariant-neural network method. The total root-mean-square error of the final PES was 0.178 kcal mol-1. For comparison, quasi-classical trajectory calculations were carried out on the PES at an experimental temperature of 150 K. The obtained thermal rate constant and product branching ratio of the BeD+ + H2O reaction agreed quite well with experimental results. In addition, the vibrational state distributions and energy disposals of the products were calculated and rationalized using the sudden vector projection model.

Reaction mechanism conversion induced by the contest of nucleophile and leaving group

Direct dynamic simulations have been employed to investigate the OH^- + CH₃Cl reaction with the chosen B3LYP/aug-cc-pVDZ method. The calculated rate coefficient for the bimolecular nucleophilic substitution reaction (S_N2), 1.0 × 10^-9 cm³ mol^-1 s^-1 at 300 K, agrees well with the experimental result of (1.3-1.6) × 10^-9 cm³ mol^-1 s^-1. The simulations reveal that the majority of the S_N2 reactions are temporarily trapped in the hydrogen-bonded complex at E_coll = 0.89 kcal mol^-1. Importantly, the influences of the leaving group and nucleophile have been discussed by comparisons of X^- + CH₃Y (X = F, OH; Y = Cl, I) reactions. For the X = F^- reactions, the reaction probability of S_N2 increases along the increased leaving group ability Cl < I, suggesting that the thermodynamic factor plays a key role. The indirect mechanisms were found to be dominant for both reactions. In contrast, for X = OH^-, the fraction of S_N2 drops with the enhanced leaving group ability. In particular, a dramatic transition occurs for the dominant atomic reaction mechanisms, i.e., from complex-mediated indirect to direct, implying an interesting contest between the leaving group and the nucleophile and the importance of the dynamic factors, i.e., the dipole moment, steric hindrance, and electronegativity.

Atomic-Level Mechanism, Solvent Effect, and Potential of the Mean Force of the F- + CH3CH2Cl SN2 Reaction in Aqueous Solution

We investigate the bimolecular nucleophilic substitution (S_N2) reaction of F^- with CH₃CH₂Cl in aqueous solution using combined multilevel quantum mechanism (ML-QM) theories with molecular mechanics (MM). The synchronized, atomic-level structural and charge evolutions are analyzed along the reaction path. The potential mean force along the reaction path in water is calculated at high-accuracy CCSD(T)/aug-cc-pVTZ/MM level of theory with a free energy barrier of 16.8 kcal/mol and a free energy of reaction of -9.7 kcal/mol. The water solvent hinders the reactivity by raising its reaction barrier by 15.1 kcal/mol, of which 13.6 kcal/mol comes from solvent energy contribution and 1.5 kcal/mol comes from the polarization effect. This indicates that the water solvent plays an essential role on this reaction in aqueous solution. We also predict the potential mean force profile based on the gas-phase reaction path and the solvation free energies of the stationary points; the comparison between our calculated result at CCSD(T)/MM level shows an excellent agreement with the predicted one with the free energy barrier at 16.2 kcal/mol and the free energy of reaction at -8.3 kcal/mol.

Unexpected steric hindrance failure in the gas phase F- + (CH3)3CI SN2 reaction

Base-induced elimination (E2) and bimolecular nucleophilic substitution (S_N2) reactions are of significant importance in physical organic chemistry. The textbook example of the retardation of S_N2 reactivity by bulky alkyl substitution is widely accepted based on the static analysis of molecular structure and steric environment. However, the direct dynamical evidence of the steric hindrance of S_N2 from experiment or theory remains rare. Here, we report an unprecedented full-dimensional (39-dimensional) machine learning-based potential energy surface for the 15-atom F⁻ + (CH₃)₃CI reaction, facilitating the reliable and efficient reaction dynamics simulations that can reproduce well the experimental outcomes and examine associated atomic-molecular level mechanisms. Moreover, we found surprisingly high “intrinsic” reactivity of S_N2 when the E2 pathway is completely blocked, indicating the reaction that intends to proceed via E2 transits to S_N2 instead, due to a shared pre-reaction minimum. This finding indicates that the competing factor of E2 but not the steric hindrance determines the small reactivity of S_N2 for the F⁻ + (CH₃)₃CI reaction. Our study provides new insight into the dynamical origin that determines the intrinsic reactivity in gas-phase organic chemistry.

Base-induced elimination (E2) and bimolecular nucleophilic substitution (SN2) are of significant importance in physical organic chemistry. Here, the authors show that the competing factor of E2 as opposed to steric hindrance determines the low reactivity of SN2 in the F⁻ + (CH₃)₃CI reaction.

Free-Energy Landscape of the SN2 Reaction CH3Br + Cl- → CH3Cl + Br- in Different Liquid Environments

This work describes in detail the reaction path of the well-known S_N2 reaction CH₃Br + Cl^- → CH₃Cl + Br^-, whose reaction rate has a huge variation with the solvent in the gas phase and in protic and aprotic liquid environments. We employed the ASEC-FEG method to optimize for minima (reactants and products) and saddle points (transition states) in the in-solution free-energy hypersurface. The method takes atomistic details of the solvent into account. A polarizable continuum model (PCM) has also been employed for comparison. The most perceptive structural changes are noted in aqueous solution by using the ASEC-FEG approach. The activation energies in all solvents, estimated by means of free-energy perturbation calculations, are in good agreement with the experimental data. The total solute-solvent hydrogen bonds play an important role in the increased barrier height observed in water and are therefore crucial to explain the huge decrease in the kinetic constant. It is also found that the hydration shell around the ions breaks itself spontaneously to accommodate the molecule, thus forming minimum energy complexes.

Reaction mechanism of an intracluster SN2 reaction induced by electron capture

Bimolecular nucleophilic substitution (S_N2) reactions have been widely investigated from both experimental and theoretical points of view because they represent one of the simplest organic reactions. Most studies on S_N2 reactions have been focused on bimolecular collision. In contrast, information on intracluster S_N2 reactions is limited. In this study, an intracluster S_N2 reaction of NF₃-CH₃Cl triggered by electron attachment was investigated using a direct ab initio molecular dynamics (AIMD) method. In the structure of NF₃-CH₃Cl, the N-F bond in NF₃ is oriented collinearly toward the carbon atom of CH₃Cl. After electron capture by NF₃-CH₃Cl, the F^- ion that is generated from the (NF₃)^- moiety collides with the carbon atom of CH₃Cl. The intracluster S_N2 reaction occurs as follows: (NF₃-CH₃Cl)^- (electron capture state) → NF₂-(F^-)-CH₃Cl (pre-reaction complex) → transition state (TS) → NF₂-CH₃F-Cl^- (post-reaction complex) → NF₂ + CH₃F + Cl^- (product state). The reaction energy is efficiently transferred to the translational mode of Cl^-, and the Cl^- ion with a high translational energy is then removed from the system. This energy is significantly larger than that of Cl^- formed in the bimolecular S_N2 reaction (F^- + CH₃Cl). The reaction mechanism is discussed based on the theoretical results.

Kinetic and dynamic studies of the NH2+ + H2 reaction on a high-level ab initio potential energy surface

The dynamics and kinetics of the NH2+ + H2 reaction are investigated on a newly developed ab initio potential energy surface using the quasi-classical trajectory method.

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).

Detailed quasiclassical dynamics of the F- + CH3Br reaction on an ab initio analytical potential energy surface

Dynamics and mechanisms of the F^- + CH₃Br(v = 0) → Br^- + CH₃F (S_N2 via Walden inversion, front-side attack, and double inversion), F^- + inverted-CH₃Br (induced inversion), HF + CH₂Br^- (proton abstraction), and FH⋯Br^- + ¹CH₂ reactions are investigated using a high-level global ab initio potential energy surface, the quasiclassical trajectory method, as well as non-standard configuration- and mode-specific analysis techniques. A vector-projection method is used to identify inversion and retention trajectories; then, a transition-state-attack-angle-based approach unambiguously separates the front-side attack and the double-inversion retention pathways. The Walden-inversion S_N2 channel becomes direct rebound dominated with increasing collision energy as indicated by backward scattering, initial back-side attack preference, and the redshifting of product internal energy peaks in accord with CF stretching populations. In the minor retention and induced-inversion pathways, almost the entire available energy transfers into product rotation-vibration, and retention mainly proceeds with indirect, slow double inversion following induced inversion with about 50% probability. Proton abstraction is dominated by direct stripping (evidenced by forward scattering) with CH₃-side initial attack preference, providing mainly vibrationally ground state products with significant zero-point energy violation.

Study on the kinetics and dynamics of the H2 + NH2- reaction on a high-level ab initio potential energy surface

Gas-phase ion-molecule reactions play major roles in many fields of chemistry and physics. The reaction of an amino radical anion with a hydrogen molecule is one of the simplest proton transfer reactions involving anions. A globally accurate full-dimensional potential energy surface (PES) for the NH₂^- + H₂ reaction is developed by the fundamental invariant-neural network method, resulting in a root mean square error of 0.116 kcal mol^-1. Quasi-classical trajectory calculations are then carried out on the newly developed PES to give integral cross sections, differential cross sections and thermal rate coefficients. This reaction has two reaction channels, proton transfer and hydrogen exchange. The reactivity of the proton transfer channel is about one or two orders of magnitude stronger than that of the hydrogen exchange channel in the energy range studied. Vibrational excitation of H₂ promotes the proton transfer reaction, while fundamental excitation of each vibrational mode of NH₂^- has a negligible effect. In addition, the theoretical rate coefficients of the proton transfer reaction on the PES show inverse temperature dependence from 150 to 750 K, in accordance with the available experimental results.

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.

Fifty years of nucleophilic substitution in the gas phase

Bimolecular nucleophilic substitution ( S N 2 ) reactions have become a model system for the investigation of structure-reactivity relationships, stereochemistry, solvent influences, and detailed atomistic dynamics. In this review, the progress during five decades of experimental and theoretical research on gas phase S N 2 reactions is discussed. Many advancements of the employed methods have led to a tremendous increase in our understanding of the properties and the dynamics of these reactions. For reactions involving six atoms a quantitative agreement of the differential reactive scattering cross sections has already been achieved, in the future it is expected that even larger polyatomic reactions systems become tractable. Furthermore, studies with higher precision, improved reactant control, and a more accurate theoretical treatment of quantum effects are envisioned.

First-Principles Reaction Dynamics beyond Six-Atom Systems

Moving beyond the six-atomic benchmark systems, we discuss the new age and future of first-principles reaction dynamics, which investigates complex, multichannel chemical reactions. We describe the methodology starting from the benchmark ab initio characterization of the stationary points, followed by full-dimensional potential energy surface (PES) developments and reaction dynamics computations. We highlight our composite ab initio approach providing benchmark stationary-point properties with subchemical accuracy, the Robosurfer program system enabling automatic PES development, and applications for the Cl + C2H6, F + C2H6, and OH- + CH3I post-six-atom reactions focusing on ab initio issues and their solutions as well as showing the excellent agreement between theory and experiment.

Facilitated inversion complicates the stereodynamics of an SN2 reaction at nitrogen center

Bimolecular nucleophilic substitution (S_N2) reactions at carbon center are well known to proceed with the stereospecific Walden-inversion mechanism. Reaction dynamics simulations on a newly developed high-level ab initio analytical potential energy surface for the F⁻ + NH₂Cl nitrogen-centered S_N2 and proton-transfer reactions reveal a hydrogen-bond-formation-induced multiple-inversion mechanism undermining the stereospecificity of the N-centered S_N2 channel. Unlike the analogous F⁻ + CH₃Cl S_N2 reaction, F⁻ + NH₂Cl → Cl⁻ + NH₂F is indirect, producing a significant amount of NH₂F with retention, as well as inverted NH₂Cl during the timescale within the unperturbed NH₂Cl molecule gets inverted with only low probability, showing the important role of facilitated inversions via an FH…NHCl⁻-like transition state. Proton transfer leading to HF + NHCl⁻ is more direct and becomes the dominant product channel at higher collision energies.

Multiple-inversion, the analogue of the double-inversion pathway recently revealed for S_N2@C, is the key mechanism in S_N2 at N center undermining stereospecificity.

Investigating the role of halogen-bonded complexes in microsolvated Y−(H2O)n + CH3I SN2 reactions

A halogen-bonded complex pathway is computed for Y⁻(H₂O)_n + CH₃I (Y = HO, F, Cl, Br, and I) ion–molecule nucleophilic substitution reactions and is compared with back-side and front-side attack pathways.

On the development of a gold-standard potential energy surface for the OH− + CH3I reaction

We develop the first accurate full-dimensional ab initio PES for the OH⁻ + CH₃I S_N2 and proton-transfer reactions treating the failure of CCSD(T) at certain geometries.

Benchmark ab initio and dynamical characterization of the stationary points of reactive atom + alkane and SN2 potential energy surfaces

We review composite ab initio and dynamical methods and their applications to characterize stationary points of atom/ion + molecule reactions.

A global ab initio potential energy surface and dynamics of the proton-transfer reaction: OH− + D2 → HOD + D−

The reaction mechanisms of OH⁻ + D₂ → HOD + D⁻ were first revealed by theory, based on an accurate full-dimensional PES.

Multilevel Quantum Mechanics and Molecular Mechanics Study of the Double-Inversion Mechanism at Nitrogen: F- + NH2Cl in Aqueous Solution

We employ a multilevel quantum mechanics and molecular mechanics method to investigate the double-inversion mechanism of the nucleophilic substitution reaction at the N center: the F^- + NH₂Cl reaction in aqueous solution. We find that the structures of the stationary points along the reaction path are quite different from the ones in the gas phase owing to the hydrogen-bond interactions between the solute and the surrounding water molecules. The atomic-level evolutions of the structures and charge transfer along the reaction path show that this double-inversion mechanism consists of an upside-down proton inversion process and a Walden-inversion process. The computed potential of mean force at the coupled-cluster singles and doubles with perturbative triples (CCSD(T))/molecular mechanics (MM) level of theory has the two-inversion barrier heights, and reaction free energy at 11.7, 29.6, and 12.6 kcal/mol, agreeing well with the predicted ones at 12.6, 32.5, and 12.2 kcal/mol obtained on the basis of the gas-phase reaction path and the solvation free energies of the stationary points.

Theoretical study of the F(2P) + NH3→ HF + NH2 reaction on an accurate potential energy surface: dynamics and kinetics

The highly exothermic hydrogen abstraction reaction of the F atom with NH₃ is investigated using the quasi-classical trajectory method on a newly developed potential energy surface (PES) for the ground electronic state. The full-dimensional PES is constructed by fitting 41 282 ab initio energy points at the level of UCCSD(T)-F12/aug-cc-pVTZ. The flexible fundamental invariant-neural network method is applied in the fitting, resulting in a total root mean square error of 0.13 kcal mol^-1. On one hand, the calculated differential cross sections agree reasonably well with the experimental results and indicate that the reaction is dominated by the direct abstraction and stripping mechanisms while a considerable amount of reaction takes place by the indirect "yo-yo" mechanism. The product energy partition also reproduces well the experimental result, which can be understood according to the geometry change along the minimum energy path. On the other hand, the obtained vibrational state distribution of the product HF follows P_νHF=2≈P_νHF=1 > P_νHF=0 > P_νHF=3, less consistent with the scattered experimental results. In addition, the calculated thermal rate coefficients have practically no temperature dependence within the statistical errors.

Pronounced changes in atomistic mechanisms for the Cl- + CH3I SN2 reaction with increasing collision energy

In a previous direct dynamics simulation of the Cl- + CH3I → ClCH3 + I- SN2 reaction, predominantly indirect and direct reaction was found at collision energies Erel of 0.20 and 0.39 eV, respectively. For the work presented here, these simulations were extended by studying the reaction dynamics from Erel of 0.15 to 0.40 eV in 0.05 eV intervals. A transition from a predominantly indirect to direct reaction is found for Erel of 0.27-0.28 eV, a finding consistent with experiment. The simulation results corroborate the understanding that in experiments indirect reaction is characterized by small product translational energies and isotropic scattering, while direct reaction has higher translational energies and anisotropic scattering. The traditional statistical theoretical model for the Cl- + CH3I SN2 reaction assumes the Cl--CH3I pre-reaction complex (A) is formed, followed by barrier crossing, and then formation of the ClCH3-I- post-reaction complex (B). This mechanism is seen in the dynamics, but the complete atomistic dynamics are much more complex. Atomistic SN2 mechanisms contain A and B, but other dynamical events consisting of barrier recrossing (br) and the roundabout (Ra), in which the CH3-moiety rotates around the heavy I-atom, are also observed. The two most important mechanisms are only formation of A and Ra + A. The simulation results are compared with simulations and experiments for Cl- + CH3Cl, Cl- + CH3Br, F- + CH3I, and OH- + CH3I.

Rethinking the X− + CH3Y [X = OH, SH, CN, NH2, PH2; Y = F, Cl, Br, I] SN2 reactions

Explicitly-correlated ab initio computations reveal novel inversion and retention pathways for several S_N2 reactions with different nucleophiles and leaving groups.

Calculation of VS,max and Its Use as a Descriptor for the Theoretical Calculation of pKa Values for Carboxylic Acids

The theoretical calculation of pKa values for Brønsted acids is a challenging task that involves sophisticated and time-consuming methods. Therefore, heuristic approaches are efficient and appealing methodologies to approximate these values. Herein, we used the maximum surface electrostatic potential (V_S,max) on the acidic hydrogen atoms of carboxylic acids to describe the H-bond interaction with water (the same descriptor that is used to characterize σ-bonded complexes) and correlate the results with experimental pKa values to obtain a predictive model for other carboxylic acids. We benchmarked six different methods, all including an implicit solvation model (water): Five density functionals and the Møller–Plesset second order perturbation theory in combination with six different basis sets for a total of thirty-six levels of theory. The ωB97X-D/cc-pVDZ level of theory stood out as the best one for consistently reproducing the reported pKa values, with a predictive power of 98% correlation in a test set of ten other carboxylic acids.

Mode-Specific Quasiclassical Dynamics of the F- + CH3I SN2 and Proton-Transfer Reactions

Mode-specific quasiclassical trajectory computations are performed for the F^- + CH₃I( v _k = 0, 1) S_N2 and proton-transfer reactions at nine different collision energies in the range of 1.0-35.3 kcal/mol using a full-dimensional high-level ab initio analytical potential energy surface with ground-state and excited CI stretching ( v₃), CH₃ rocking ( v₆), CH₃ umbrella ( v₂), CH₃ deformation ( v₅), CH symmetric stretching ( v₁), and CH asymmetric stretching ( v₄) initial vibrational modes. Millions of trajectories provide statistically definitive mode-specific cross sections, opacity functions, scattering angle distributions, and product internal energy distributions. The excitation functions reveal slight vibrational S_N2 inversion inhibition/enhancement at low/high collision energies ( E_coll), whereas large decaying-with- E_coll vibrational enhancement effects for the S_N2 retention (double inversion) and proton-transfer channels. The most efficient vibrational enhancement is found by exciting the CI stretching (high E_coll) for S_N2 inversion and the CH stretching modes (low E_coll) for double inversion and proton transfer. Mode-specific effects do not show up in the scattering angle distributions and do blue-shift the hot/cold S_N2/proton-transfer product internal energies.

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.

Benchmark ab Initio Characterization of the Complex Potential Energy Surfaces of the X- + NH2Y [X, Y = F, Cl, Br, I] Reactions

We report a comprehensive high-level explicitly correlated ab initio study on the X^- + NH₂Y [X,Y = F, Cl, Br, I] reactions characterizing the stationary points of the S_N2 (Y^- + NH₂X) and proton-transfer (HX + NHY^-) pathways as well as the reaction enthalpies of various endothermic additional product channels such as H^- + NHXY, XY^- + NH₂, XY + NH₂^-, and XHY^- + NH. Benchmark structures and harmonic vibrational frequencies are obtained at the CCSD(T)-F12b/aug-cc-pVTZ(-PP) level of theory, followed by CCSD(T)-F12b/aug-cc-pVnZ(-PP) [n = Q and 5] and core correlation energy computations. In the entrance and exit channels we find two equivalent hydrogen-bonded C₁ minima, X^-···HH'NY and X^-···H'HNY connected by a C_s first-order saddle point, X^-···H₂NY, as well as a halogen-bonded front-side complex, X^-···YNH₂. S_N2 reactions can proceed via back-side attack Walden inversion and front-side attack retention pathways characterized by first-order saddle points, submerged [X-NH₂-Y]^- and high-energy [H₂NXY]^-, respectively. Product-like stationary points below the HX + NHY^- asymptotes are involved in the proton-transfer processes.

Indirect dynamics in SN2@N: insight into the influence of central atoms

Central atoms have a significant influence on the reaction kinetics and dynamics of nucleophilic substitution (S_N2). Herein, atomistic dynamics of a prototype S_N2@N reaction F^- + NH₂Cl is uncovered employing direct dynamics simulations that show strikingly distinct features from those determined for a S_N2@C congener F^- + CH₃Cl. Indirect scattering is found to prevail, which proceeds predominantly through a hydrogen-bonded F^--HNHCl complex in the reactant entrance channel. This unexpected finding of a pronounced contribution of indirect reaction dynamics, even at a high collision energy, is in strong contrast to a general evolution from indirect to direct dynamics with enhanced energy that characterizes S_N2@C. This result suggests that the relative importance of different atomic-level mechanisms may depend essentially on the interaction potential of reactive encounters and the coupling between inter- and intramolecular modes of the pre-reaction complex. For F^- + NH₂Cl the proton transfer pathway is less competitive than S_N2. A remarkable finding is that the more favorable energetics for NH₂Cl proton transfer, as compared to that for CH₃Cl, does not manifest itself in the reaction dynamics. The present work sheds light on the underlying reaction dynamics of S_N2@N, which remain largely unclear compared to well-studied S_N2@C.

A new, double-inversion mechanism of the F- + CH3Cl SN2 reaction in aqueous solution

Atomic-level, bimolecular nucleophilic substitution reaction mechanisms have been studied mostly in the gas phase, but the gas-phase results cannot be expected to reliably describe condensed-phase chemistry. As a novel, double-inversion mechanism has just been found for the F^- + CH₃Cl S_N2 reaction in the gas phase [Nat. Commun., 2015, 6, 5972], here, using multi-level quantum mechanics methods combined with the molecular mechanics method, we discovered a new, double-inversion mechanism for this reaction in aqueous solution. However, the structures of the stationary points along the reaction path show significant differences from those in the gas phase due to the strong influence of solvent and solute interactions, especially due to the hydrogen bonds formed between the solute and the solvent. More importantly, the relationship between the two double-inversion transition states is not clear in the gas phase, but, here we revealed a novel intermediate complex serving as a "connecting link" between the two transition states of the abstraction-induced inversion and the Walden-inversion mechanisms. A detailed reaction path was constructed to show the atomic-level evolution of this novel double reaction mechanism in aqueous solution. The potentials of mean force were calculated and the obtained Walden-inversion barrier height agrees well with the available experimental value.

Conservation of direct dynamics in sterically hindered SN2/E2 reactions

Nucleophilic substitution (S_N2) and base-induced elimination (E2), two indispensable reactions in organic synthesis, are commonly assumed to proceed under stereospecific conditions. Understanding the way in which the reactants pre-orient in these reactions, that is its stereodynamics, is essential in order to achieve a detailed atomistic picture and control over such processes. Using crossed beam velocity map imaging, we study the effect of steric hindrance in reactions of Cl^- and CN^- with increasingly methylated alkyl iodides by monitoring the product ion energy and scattering angle. For both attacking anions the rebound mechanism, indicative of a direct S_N2 pathway, is found to contribute to the reaction at high relative collision energies despite being increasingly hindered. An additional forward scattering mechanism, ascribed to a direct E2 reaction, also contributes at these energies. Inspection of the product energy distributions confirms the direct and fast character of both mechanisms as opposed to an indirect reaction mechanism which leads to statistical energy redistribution in the reaction complex. This work demonstrates that nonstatistical dynamics and energetics govern S_N2 and E2 pathways even in sterically hindered exchange reaction systems.

Dynamics and Novel Mechanisms of SN2 Reactions on ab Initio Analytical Potential Energy Surfaces

We describe a novel theoretical approach to the bimolecular nucleophilic substitution (S_N2) reactions that is based on analytical potential energy surfaces (PESs) obtained by fitting a few tens of thousands high-level ab initio energy points. These PESs allow computing millions of quasi-classical trajectories thereby providing unprecedented statistical accuracy for S_N2 reactions, as well as performing high-dimensional quantum dynamics computations. We developed full-dimensional ab initio PESs for the F^- + CH₃Y [Y = F, Cl, I] systems, which describe the direct and indirect, complex-forming Walden-inversion, the frontside attack, and the new double-inversion pathways as well as the proton-transfer channels. Reaction dynamics simulations on the new PESs revealed (a) a novel double-inversion S_N2 mechanism, (b) frontside complex formation,

Deciphering Front-Side Complex Formation in SN2 Reactions via Dynamics Mapping

Due to their importance in organic chemistry, the atomistic understanding of bimolecular nucleophilic substitution (S_N2) reactions shows exponentially growing interest. In this publication, the effect of front-side complex (FSC) formation is uncovered via quasi-classical trajectory computations combined with a novel analysis method called trajectory orthogonal projection (TOP). For both F^- + CH₃Y [Y = Cl,I] reactions, the lifetime distributions of the F^-···YCH₃ front-side complex revealed weakly trapped nucleophiles (F^-). However, only the F^- + CH₃I reaction features strongly trapped nucleophiles in the front-side region of the prereaction well. Interestingly, both back-side and front-side attack show propensity to long-lived FSC formation. Spatial distributions of the nucleophile demonstrate more prominent FSC formation in case of the F^- + CH₃I reaction compared to F^- + CH₃Cl. The presence of front-side intermediates and the broad spatial distribution in the back-side region may explain the indirect nature of the F^- + CH₃I reaction.

Imaging dynamic fingerprints of competing E2 and SN2 reactions

The competition between bimolecular nucleophilic substitution and base-induced elimination is of fundamental importance for the synthesis of pure samples in organic chemistry. Many factors that influence this competition have been identified over the years, but the underlying atomistic dynamics have remained difficult to observe. We present product velocity distributions for a series of reactive collisions of the type X⁻ + RY with X and Y denoting the halogen atoms fluorine, chlorine and iodine. By increasing the size of the residue R from methyl to tert-butyl in several steps, we find that the dynamics drastically change from backward to dominant forward scattering of the leaving ion relative to the reactant RY velocity. This characteristic fingerprint is also confirmed by direct dynamics simulations for ethyl as residue and attributed to the dynamics of elimination reactions. This work opens the door to a detailed atomistic understanding of transformation reactions in even larger systems.

The competition between chemical reactions critically affects our natural environment and the synthesis of new materials. Here, the authors present an approach to directly image distinct fingerprints of essential organic reactions and monitor their competition as a function of steric substitution.

Effects of microsolvation on a SN2 reaction: indirect atomistic dynamics and weakened suppression of reactivity

Systematic studies of microsolvation in the gas phase have enriched our knowledge of solvent effects. Here, the dynamics of a prototype S_N2 reaction of a hydrated fluoride ion with methyl iodide is uncovered employing direct dynamics simulations that show strikingly distinct features from those determined for an unsolvated system. An indirect scattering is found to prevail, which occurs dominantly by forming hydrated F^-(H₂O)-HCH₂I and F^-(H₂O)-CH₃I pre-reaction complexes at low energies, but proceeds through their water-free counterparts at higher energies. This finding is in strong contrast to a general evolution from indirect to direct dynamics with enhancing energy for the unsolvated substitution reactions, and this discrepancy is understood by the substantial steric hindrance introduced by a water molecule. As established in experiments, solvation suppresses the reactivity, whereas we find that this depression is remarkably frustrated upon raising the energy given that collision-induced dehydration essentially diminishes the water block for reactive collisions. The present study sheds light on how solute-solvent interactions affect the underlying dynamics at a deeper atomic level, thereby promoting our understanding of the fundamental solvent effects on chemical reactions in solution.

High-level ab initio potential energy surface and dynamics of the F- + CH3I SN2 and proton-transfer reactions

Bimolecular nucleophilic substitution (S_N2) and proton transfer are fundamental processes in chemistry and F^- + CH₃I is an important prototype of these reactions. Here we develop the first full-dimensional ab initio analytical potential energy surface (PES) for the F^- + CH₃I system using a permutationally invariant fit of high-level composite energies obtained with the combination of the explicitly-correlated CCSD(T)-F12b method, the aug-cc-pVTZ basis, core electron correlation effects, and a relativistic effective core potential for iodine. The PES accurately describes the S_N2 channel producing I^- + CH₃F via Walden-inversion, front-side attack, and double-inversion pathways as well as the proton-transfer channel leading to HF + CH₂I^-. The relative energies of the stationary points on the PES agree well with the new explicitly-correlated all-electron CCSD(T)-F12b/QZ-quality benchmark values. Quasiclassical trajectory computations on the PES show that the proton transfer becomes significant at high collision energies and double-inversion as well as front-side attack trajectories can occur. The computed broad angular distributions and hot internal energy distributions indicate the dominance of indirect mechanisms at lower collision energies, which is confirmed by analyzing the integration time and leaving group velocity distributions. Comparison with available crossed-beam experiments shows usually good agreement.

Variational Flooding Study of a SN2 Reaction

We have studied the reaction dynamics of a prototypical organic reaction using a variationally optimized truncated bias to accelerate transitions between educt and product reactant states. The asymmetric S_N2 nucleophilic substitution reaction of fluoromethane and chloromethane CH₃F + Cl^- ⇌ CH₃Cl + F^- is considered, and many independent biased molecular dynamics simulations have been performed at 600, 900, and 1200 K, collecting several hundred transitions at each temperature. The transition times and relative rate constants have been obtained for both reaction directions. The activation energies extracted from an Arrhenius plot compare well with standard static calculations.

Imaging the dynamics of ion–molecule reactions

A range of ion–molecule reactions have been studied in the last years using the crossed-beam ion imaging technique, from charge transfer and proton transfer to nucleophilic substitution and elimination.

Mode-specific multi-channel dynamics of the F- + CHD2Cl reaction on a global ab initio potential energy surface

We report a detailed quasiclassical trajectory study for the dynamics of the ground-state and CH/CD stretching-excited F^- + CHD₂Cl(v_CH/CD = 0, 1) → Cl^- + CHD₂F, HF + CD₂Cl^-, and DF + CHDCl^- S_N2, proton-, and deuteron-abstraction reactions using a full-dimensional global ab initio analytical potential energy surface. The simulations show that (a) CHD₂Cl(v_CH/CD = 1), especially for v_CH = 1, maintains its mode-specific excited character prior to interaction, (b) the S_N2 reaction is vibrationally mode-specific,

Dynamical Bifurcation in Gas-Phase XH- + CH3 Y SN 2 Reactions: The Role of Energy Flow and Redistribution in Avoiding the Minimum Energy Path

The gas-phase reactions of XH^- (X=O, S) + CH₃ Y (Y=F, Cl, Br) span nearly the whole range of S_N 2 pathways, and show an intrinsic reaction coordinate (IRC) (minimum energy path) with a deep well owing to the CH₃ XH⋅⋅⋅Y^- (or CH₃ S^- ⋅⋅⋅HF) hydrogen-bonded postreaction complex. MP2 quasiclassical-type direct dynamics starting at the [HX⋅⋅⋅CH₃ ⋅⋅⋅Y]^- transition-state (TS) structure reveal distinct mechanistic behaviors. Trajectories that yield the separated CH₃ XH+Y^- (or CH₃ S^- +HF) products directly are non-IRC, whereas those that sample the CH₃ XH⋅⋅⋅Y^- (or CH₃ S^- ⋅⋅⋅HF) complex are IRC. The IRCIRC/non-IRC ratios of 90:10, 40:60, 25:75, 2:98, 0:100, and 0:100 are obtained for (X, Y)=(S, F), (O, F), (S, Cl), (S, Br), (O, Cl), and (O, Br), respectively. The properties of the energy profiles after the TS cannot provide a rationalization of these results. Analysis of the energy flow in dynamics shows that the trajectories cross a dynamical bifurcation, and that the inability to follow the minimum energy path arises from long vibration periods of the X-C⋅⋅⋅Y bending mode. The partition of the available energy to the products into vibrational, rotational, and translational energies reveals that if the vibrational contribution is more than 80 %, non-IRC behavior dominates, unless the relative fraction of the rotational and translational components is similar, in which case a richer dynamical mechanism is shown, with an IRC/non-IRC ratio that correlates to this relative fraction.