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

Theoretical investigation of nucleophilic substitution reaction of phenyl carbonyl isothiocyanates with pyridines in gas and polar aprotic solvent

This study focuses on the mutual interaction of substituents in the nucleophile and substrate - cross interaction constant, ρXY, in the uncatalyzed aminolysis by substituting pyridine with phenyl carbonyl isothiocyanate. The mechanism was found to be a stepwise process with a rate-limiting breakdown of the -NCS leaving group. This stepwise reaction mechanism considers the cross-interaction constant (CIC) with rate-limiting breakdown of tetrahedral intermediate in gas and solvent phases. The corresponding Hammett coefficients are related to the substituents associated with (1) the nucleophiles (X), ρX (-1.93 to -6.54 for the gas phase and 10.5 to 18.9 in the solvent model), and with (2) the substituents associated with the phenyl ring of the substrate (Y), ρY (0.41-3.48 for the gas phase and 1.83 to -10.70 for the solvent model). It also includes the Brønsted coefficient with X, βX (0.11-1.52 for the gas phase and -2.57 to 3.96 for the solvent model), and CIC values, ρXY (0.69 for the gas phase and 0.87 for the solvent model). In this work, the NBO analysis, reaction potential, reaction electronic flux (REF), dual descriptor, and the structure-energy relationships were considered in interpreting the mechanistic criteria.

Computational Insights into SN 2 and Proton Transfer Reactions of CH3 O- with NH2 Y and CH3 Y

Bimolecular nucleophilic substitution (SN 2) reactions have been extensively studied in both theory and experiment. While research on C-centered SN 2 reactions (SN 2@C) has been ongoing, SN 2 reactions at neutral nitrogen (SN 2@N) have received increased attention in recent years. To recommend methods for dynamics simulations, the comparison for the properties of the geometries, vibrational frequencies, and energies is done between MP2 and six DFT functional calculations and experimental data as well as the high-level CCSD(T) method for CH3 O- +NH2 Cl/CH3 Cl reactions. The relative energy diagrams at the M06 method for CH3 O- with CH3 Y/NH2 Y reactions (Y=F, Cl, Br, I) in the gas and solution phase are explored to investigate the effects of the leaving groups, different reaction centers, and solvents. We mainly focus on the computational of inv-SN 2 and proton transfer (PT) pathways. The PT channel in the gas phase is more competitive than the SN 2 channel for N-center reactions, while the opposite is observed for C-centered reactions. Solvation completely inhibits the PT channel, making SN 2 the dominant pathway. Our study provides new insight into the SN 2 reaction mechanisms and rich the novel reaction model in gas-phase organic chemistry.

Blueshift in Trifurcated Hydrogen Bonds: A Tradeoff between Tetrel Bonding and Steric Repulsion

We have quantum chemically investigated the origin of the atypical blueshift of the H-C bond stretching frequency in the hydrogen-bonded complex X- •••H3 C-Y (X, Y=F, Cl, Br, I), as compared to the corresponding redshift occurring in Cl- •••H3 N and Cl- •••H3 C-H, using relativistic density functional theory (DFT) at ZORA-BLYP-D3(BJ)/QZ4P. Previously, this blueshift was attributed, among others, to the contraction of the H-C bonds as the H3 C moiety becomes less pyramidal. Herein, we provide quantitative evidence that, instead, the blueshift arises from a direct and strong X- •••C interaction of the HOMO of A- with the backside lobe on carbon of the low-lying C-Y antibonding σ* LUMO of the H3 C-Y fragment. This X- •••C bond, in essence a tetrel bond, pushes the H atoms towards a shorter H-C distance and makes the H3 C moiety more planar. The blueshift may, therefore, serve as a diagnostic for tetrel bonding.

Double Centrosymmetric Si···π Tetrel Bonds as New Synthons─Evidence from Crystal Structures and DFT Calculations

The crystal structure of bis((μ2-ethynylsilyloxo)-dichloro-aluminum), BEDCA, and a few related structures are characterized by the occurrence of tetrel bonds that link molecules. Particularly, centosymmetric dimers in such structures occur that are connected by two equivalent Si···π tetrel bonds. The dimer of BEDCA and dimers of other model species that similarly are linked by two equivalent Si···π tetrel bonds are analyzed theoretically. Some of the complexes calculated here are also characterized by the occurrence of triel bonds. Thus, ωB97XD/aug-cc-pVTZ calculations are performed and these DFT results are further supported by calculations with the use of other theoretical approaches: the quantum theory of atoms in molecules, QTAIM; the natural bond orbital, NBO; the energy decomposition analysis, EDA; and the noncovalent interactions method, NCI. The results show that the tetrel bonds analyzed here are rather weak, and they are not detected by the QTAIM approach; however, they are detected by other approaches, like NBO, for example. On the other hand, the triel bonds that occur in a few complexes discussed here are very strong and possess characteristics of covalent bonds.

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.

Seeking the Optimal Descriptor for SN2 Reactions through Statistical Analysis of Density Functional Theory Results

Bimolecular nucleophilic substitution is one of the fundamental reactions in organic chemistry, yet there is still knowledge to be gained on the role of the nucleophile and the substrate. A statistical treatment of over 600 density functional theory (DFT)-computed barriers for bimolecular nucleophilic substitution at methyl derivatives (S_N2@C) leads to the identification of numerical descriptors that best represent the entering and leaving ability of 26 different nucleophiles. The treatment is based on singular value decomposition (SVD) of a matrix of computed energy barriers. The current work represents the extension to a problem of reactivity of the hidden descriptor methodology that we had previously developed for the thermodynamic problem of bond dissociation energies in transition-metal complexes. The analysis of the results shows that a single descriptor is sufficient. This hidden descriptor has different values for nucleophilic and leaving abilities and, contrary to expectation, does not correlate especially well with either frontier molecular orbital descriptors or solvation descriptors. In contrast, it correlates with other thermodynamic and geometric parameters. This statistical procedure can be in principle extended to additional chemical fragments and other reactions.

Interacting Quantum Atoms Analysis of the Reaction Force: A Tool to Analyze Driving and Retarding Forces in Chemical Reactions

The analysis of the reaction force and its topology has provided a wide range of fruitful concepts in the theory of chemical reactivity over the years, allowing to identify chemically relevant regions along a reaction profile. The reaction force (RF), a projection of the Hellmann-Feynman forces acting on the nuclei of a molecular system onto a suitable reaction coordinate, is partitioned using the interacting quantum atoms approach (IQA). The exact IQA molecular energy decomposition is now shown to open a unique window to identify and quantify the chemical entities that drive or retard a chemical reaction. The RF/IQA coupling offers an extraordinarily detailed view of the type and number of elementary processes that take reactants into products, as tested on two sets of simple reactions.

Energetic Descriptors of Steric Hindrance in Real Space: An Improved IQA Picture*

Steric hindrance (SH) plays a central role in the modern chemical narrative, lying at the core of chemical intuition. As it however happens with many successful chemical concepts, SH lacks an underlying physically sound root, and multiple mutually inconsistent approximations have been devised to relate this fuzzy concept to computationally derivable descriptors. We here argue that being SH related to spatial as well as energetic features of interacting systems, SH can be properly handled if we chose a real space energetic stance like the Interacting Quantum Atoms (IQA) approach. Drawing on previous work by Popelier and coworkers (ChemistryOpen 8, 560, 2019) we build an energetic estimator of SH, referred to as E_ST . We show that the rise in the self-energy of a fragment that accompanies steric congestion is a faithful proxy for the chemist's SH concept if we remove the effect of charge transfer. This can be done rigorously, and the E_ST here defined provides correct sterics even for hydrogen atoms, where the plain use of deformation energies leads to non-chemical results. The applicability of E_ST is validated in several chemical scenarios, going from atomic compressions to archetypal S_N2 reactions. E_ST is shown to be a robust steric hindrance descriptor.

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.

Comparison of Free-Energy Methods to Calculate the Barriers for the Nucleophilic Substitution of Alkyl Halides by Hydroxide

Calculating the free-energy barriers of liquid-phase chemical reactions with explicit solvent is a considerable challenge. Most studies use the energy and entropy of minimized single-point geometries of the reactants and transition state in implicit solvent using normal mode analysis (NMA). Explicit-solvent methods instead make use of the potential of mean force (PMF). Here, we propose a new energy-entropy (EE) method to calculate the Gibbs free energy of reactants and transition states in explicit solvent by combining quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with multiscale cell correlation (MCC). We apply it to six nucleophilic substitution reactions of the hydroxide transfer to methyl and ethyl halides in water, where the halides are F, Cl, and Br. We compare EE-MCC Gibbs free energy barriers using two Hamiltonians, self-consistent charge density functional based tight-binding (SCC-DFTB) and B3LYP/6-31+G* density functional theory (DFT) with respective PMF values, EE-NMA values using B3LYP/6-31+G* and M06/6-31+G* DFT in implicit solvent and experimental values derived via transition state theory. The barriers using SCC-DFTB are found to agree well with the PMF and experiment and previous computational studies, being slightly higher but improving on the lower values obtained for the implicit solvent. Achieving convergence over many degrees of freedom remains a challenge for EE-MCC in explicit-solvent QM/MM systems, particularly for the more expensive B3LYP/6-31+G* and M06/6-31+G* DFT methods, but the insightful decomposition of entropy over all degrees of freedom should make EE-MCC a valuable tool for deepening the understanding of chemical reactions.

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

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

Symmetry-Adapted Perturbation Theory Decomposition of the Reaction Force: Insights into Substituent Effects Involved in Hemiacetal Formation Mechanisms

The decomposition of the reaction force based on symmetry-adapted perturbation theory (SAPT) has been proposed. This approach was used to investigate the substituent effects along the reaction coordinate pathway for the hemiacetal formation mechanism between methanol and substituted aldehydes of the form CX₃CHO (X = H, F, Cl, and Br), providing a quantitative evaluation of the reaction-driving and reaction-retarding force components. Our results highlight the importance of more favorable electrostatic and induction effects in the reactions involving halogenated aldehydes that leads to lower activation energy barriers. These substituent effects are further elucidated by applying the functional-group partition of symmetry-adapted perturbation theory (F-SAPT). The results show that the reaction is largely driven by favorable direct noncovalent interactions between the CX₃ group on the aldehyde and the OH group on methanol.

Dual Geometry Schemes in Tetrel Bonds: Complexes between TF₄ (T = Si, Ge, Sn) and Pyridine Derivatives

When an N-base approaches the tetrel atom of TF₄ (T = Si, Ge, Sn) the latter molecule deforms from a tetrahedral structure in the monomer to a trigonal bipyramid. The base can situate itself at either an axial or equatorial position, leading to two different equilibrium geometries. The interaction energies are considerably larger for the equatorial structures, up around 50 kcal/mol, which also have a shorter R(T··N) separation. On the other hand, the energy needed to deform the tetrahedral monomer into the equatorial structure is much higher than the equivalent deformation energy in the axial dimer. When these two opposite trends are combined, it is the axial geometry which is somewhat more stable than the equatorial, yielding binding energies in the 8–34 kcal/mol range. There is a clear trend of increasing interaction energy as the tetrel atom grows larger: Si < Ge < Sn, a pattern which is accentuated for the binding energies.

Nucleophilic Influences and Origin of the SN 2 Allylic Effect

The potential energy surfaces for the S_N 2 reactions of allyl and propyl chlorides with 21 anionic and neutral nucleophiles was studied by using ωB97X-D/6-311++G(3df,2pd) computations. The "allylic effect" on S_N 2 barriers was observed for all reactions, and compared with propyl substrates, the energy barriers differed by -0.2 to -4.5 kcal mol^-1 in the gas phase. Strong correlations of the S_N 2 net activation barriers with cation affinities, proton affinities, and electrostatic potentials at nuclei demonstrated the powerful influence of electrostatic interactions on these reactions. For the reactions of anionic (but not neutral) nucleophiles with allyl chloride, some of the incoming negative charge (0.2-18 %) migrated into the carbon chains, which would provide secondary stabilization of the S_N 2 transition states. Activation strain analysis provided additional insight into the allylic effect by showing that the energy of geometric distortion for the reactants to reach the S_N 2 transition state was smaller for each allylic reaction than for its propyl analogue. In many cases, the interaction energies between the substrate and nucleophile in this analysis were more favorable for propyl chloride reactions, but this compensation did not overcome the predominant strain energy effect.

Tetrel Bonds with π-Electrons Acting as Lewis Bases-Theoretical Results and Experimental Evidences

MP2/aug-cc-pVTZ calculations were carried out for the ZFH₃-B complexes (Z = C, Si, Ge, Sn and Pb; B = C₂H₂, C₂H₄, C₆H₆ and C₅H₅⁻; relativistic effects were taken into account for Ge, Sn and Pb elements). These calculations are supported by other approaches; the decomposition of the energy of interaction, Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Orbital (NBO) method. The results show that tetrel bonds with π-electrons as Lewis bases are classified as Z···C links between single centers (C is an atom of the π-electron system) or as Z···π interactions where F‒Z bond is directed to the mid-point (or nearly so) of the CC bond of the Lewis base. The analogous systems with Z···C/π interactions were found in the Cambridge Structural Database (CSD). It was found that the strength of interaction increases with the increase of the atomic number of the tetrel element and that for heavier tetrel elements the ZFH₃ tetrahedral structure is more deformed towards the structure with the planar ZH₃ fragment. The results of calculations show that the tetrel bond is sometimes accompanied by the Z-H···C hydrogen bond or even sometimes the ZFH₃-B complexes are linked only by the hydrogen bond interaction.

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.

An interacting quantum atom study of model SN 2 reactions (X- ···CH3 X, X = F, Cl, Br, and I)

The quantum chemical topology method has been used to analyze the energetic profiles in the X-  + CH3 X → XCH3  + X- SN 2 reactions, with X = F, Cl, Br, and I. The evolution of the electron density properties at the BCPs along the reaction coordinate has been analysed. The interacting quantum atoms (IQA) method has been used to evaluate the intra-atomic and interatomic energy variations along the reaction path. The different energetic terms have been examined by the relative energy gradient method and the ANANKE program, which enables automatic and unbiased IQA analysis. Four of the six most important IQA energy contributions were needed to reproduce the reaction barrier common to all reactions. The four reactions considered share many common characteristics but when X = F a number of particularities occur. © 2017 Wiley Periodicals, Inc.

Theoretical Investigation of the Gas-Phase SN2 Reactions of Anionic and Neutral Nucleophiles with Chloramines

The S_N2 reactions at nitrogen center (S_N2@N) play a significant role in organic synthesis, carcinogenesis, and the formation of some environmentally toxic compounds. However, the S_N2@N reactions specifically for neutral compounds as nucleophiles are less known. In this work, reactions of dimethylamine (DMA) and F^- with NH₂Cl were investigated as model reactions to validate an accurate functional from 24 DFT functionals by comparing with the CCSD(T) reference data. M06-2X functional was found to perform best and applied to systematically explore the trends in reactivity for halides (F^- and Cl^-) and simple amines toward the substrates NH₂Cl and NHCl₂ (S_N2@N) as well as CH₃Cl and CH₂Cl₂ (S_N2@C). The computational results show that the backside inversion channel dominates most the S_N2@N reactions except for the case of F^- + NHCl₂, which reacts preferentially via proton transfer. The overall activation free energies (Δ G^‡) of the inversion channel for the S_N2 reactions of F^- and Cl^- with chloramines are negative, whereas those for amines as nucleophiles are around 30-44 kcal/mol. The S_N2@N reactions for all the nucleophiles investigated here are faster than the corresponding S_N2@C. Moreover, amines react faster when they have a higher extent of methyl substitution. Additionally, the energy gap between the HOMO of nucleophile and LUMO of substrate generally correlates well with Δ G^‡ of the corresponding S_N2 reactions, which is consistent with previous results.

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.

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

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