MNDO Study of reaction pathways for SN2 reactions. Menschutkin reaction potential energy surfaces

MNDO molecular orbital calculations have been employed to investigate limited reaction pathways and potential energy surfaces for a series of S_N2 reactions. Model calculations for X^? + CH₃X (X = H, F, OH, OCH₃, and CN) indicate that the MNDO method gives qualitative agreement with ab initio studies except for the hydride–CH₄ exchange. Studies involving alkylation of pyridine (Menschutkin reaction) were also carried out. For the reaction of pyridine with CH₃Cl, which involves charge separation, our MNDO studies (which do not include solvation effects) do not produce a characteristic S_N2 pathway. For the reaction of pyridine with trimethyloxonium cation [(CH₃)₃O⁺] as the alkylating agent, a well defined S_N2 reaction pathway was obtained; this reaction involves charge transfer. A potential energy surface for the pyridine–trimethyloxonium cation reaction shows the presence of a saddle point transition state that resembles starting materials, in agreement with the Hammond postulate for this exothermic reaction.     

Activation energy for thermal decomposition of nitric oxide

Variation of the reaction mechanism for homogeneous thermal decomposition of NO into N₂ and O₂ in the temperature range between 1000 and 4000 K is studied. The decomposition always proceeds through an atomic chain mechanism initiated by formation of oxygen atom. However the step of the oxygen atom initiation depends on the reaction condition, i.e., collision between two NO molecules at low conversions (when P_O2/P_NO ratio≪ ≪ 1) and collision between NO and O₂ and/or unimolecular decomposition of O₂ at high conversions (after substantial O₂ has been accumulated from the reaction). In this study, apparent activation energy (E_app) of the decomposition reaction has been theoretically determined on the basis of our proposed mechanisms. The E_app thus determined varies widely (from 254 to 401 kJ mol⁻¹) with the accepted step of initiation. This variation can account for the variations among experimental activation energies for the decomposition reaction in the literature. © 1996 John Wiley & Sons, Inc.     

Extension of the fast multipole method for the rectangular cells with an anisotropic partition tree structure

The fast multipole method (FMM) is an order N method for the numerically rigorous calculation of the electrostatic interactions among point charges in a system of interest. The FMM is utilized for massively parallelized software for molecular dynamics (MD) calculations. However, an inconvenient limitation is imposed on the implementation of the FMM: In three-dimensional case, a cubic MD unit cell is hierarchically divided by the octree partitioning under isotropic periodic boundary conditions along three axes. Here, we extended the FMM algorithm adaptive to a rectangular MD unit cell with different periodicity along the axes by applying an anisotropic hierarchical partitioning. The algorithm was implemented into the parallelized general-purpose MD calculation software designed for a system with uniform distribution of point charges in the unit cell. The partition tree can be a mixture of binary and ternary branches, the branches being chosen arbitrarily with respect to the coordinate axes at any levels. Errors in the calculated electrostatic interactions are discussed in detail for a selected partition tree structure. The extension enables us to execute MD calculations under more general conditions for the shape of the unit cell, partition tree, and boundary conditions, keeping the accuracy of the calculated electrostatic interactions as high as that with the conventional FMM. An extension of the present FMM algorithm to other prime number branches, such as 5 and 7, is straightforward.     

Prediction of LUMO energy and rate constant by comparative molecular field analysis (CoMFA)

We used the comparative molecular field analysis (CoMFA) method to correlate the rate constant (log k) for the S_N2 reaction of benzyl benzenesulfonates and p-methoxybenzylamines. Molecular fields calculated with a C⁺ probe produced a good correlation with a small standard deviation and a high correlation coefficient with cross validation. This study demonstrated that CoMFA is an excellent method in predicting the physicochemical properties of the molecule such as LUMO energy and rate constants. © 1995 by John Wiley & Sons, Inc.     

Kinetic analysis of crude oils by a weighted mean activation energy approach

A weighted mean activation energy method was applied to describe the reactivity and combustibility of crude oils via simultaneous TG/DTG. Thermal experiments were conducted with a non-isothermal method at a heating rate of 10C min^–1 with excess air. Reaction rates increased progressively with increasing temperature. The rate data were fitted to an Arrhenius equation; the plots showed three distinct reaction regions. Weighted mean activation energies (E _wm), of the crude oils were calculated and a correlation was established betweenE _wm, API gravity and peak temperatures during high-temperature oxidation.     

Estimation of the R-H bond energy from the activation energy for the reaction RH + O2 → R· + HO2·

Since the activation energy for the reaction RH + O₂ → R· + HO₂. is very close to its endothermicity, the R-H bond energy can be calculated from the activation energy for free radical formation by the reaction RH + O₂. The relation between E_i and Q_R–H was found empirically after measuring E_i by the method of inhibitors for the oxidation of cyclohexane, n? heptane, and toluene: The values of Q_R–H are calculated from these and earlier experimental data for five hydrocarbons, five phenols, and four aromatic amines.     

Fast multipole method for three-dimensional systems with periodic boundary condition in two directions

We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.     

A fully ab initio potential energy surface for ClH2 reactive system

Anab initio analytical potential energy surface called BW3 for the ClH₂ reactive system is presented. The fit of this surface is based on about 1 200ab initio energy points, computed with multi-reference configuration interaction(MRCI) and scaling external correlation (SEC) method and a very large basis set. The precision in the fit is very high. The BW3 surface could reproduce correctly the dissociation energy of H₂ and HCl, and the endothermicity of the Cl + H₂ abstraction reaction. For the Cl + H₂ abstraction reaction, the saddle point of BW3 lies in collinear geometries, and the barrier height is 32.84 kJ/mol; for the H + ClH exchange reaction, the barrier of BW3 is also linear, with a height of 77.40 kJ/mol.     

Radical-type addition of benzyl bromide to vinyl chloride: the kinetics and activation energy of the process

Radical telomerization of vinyl chloride with benzyl bromide and the competitive reaction of benzyl bromide with vinyl chloride and trimethylvinylsilane have been studied. The relative rate constant for the addition of C₆H₅C · H₂ to vinyl chloride,k _rel (with respect to trimethylvinylsilane), is close to unity, whereas the activation energy of the addition of C₆H₅C^.H₂ to vinyl chloride is considerably lower (by 7 kcal mol^–1) than in the reaction involving trimethylvinylsilane. The possible fragmentation of the radical-adduct C₆H₅CH₂CH₂C^.HCl was suggested as one of the possible reasons of underestimation ofk _rel. The activation energy was estimated by the MPDO/3 method.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 886–888, May, 1993.     

Ab initio Calculations of the potential energy surface of the reaction of singlet methylene with the hydrogen molecule

The potential energy surface for the insertion of singlet methylene into H₂ has been computed on theab initio SCF level as well as with inclusion of electron correlation by means of the CEPA method. The results are compared with those of previous semiempirical,ab initio SCF and CI calculations. The system is a prototype of a reaction where an allowed and a symmetry-forbidden path can compete. The electron correlation energy was found to be very different for different regions of the surface, but did not have much influence on the optimum reaction path. From the computed heat of the reaction, the heat of formation of singlet methylene was estimated to be 101.5 kcal/mol. According to the calculations the reaction does not need any activation energy.     

Correlation energy contributions to reaction heats

New, more accurate, Hartree-Fock limit energies (E_HF) for ethane and ethylene are obtained from SCF total molecular energie using Ermler and Kern's procedure. These results, together with E_HF values for other small closed shell molecules, are employed to calculate correlation energy (E_c) contributions to reaction heats. Cancellation to within 98% of the total E_c involved, and often to more than 99%, is found for a wide variety of chemical reactions, which strongly suggests that there are systematic regularities in the contribution to E_c from the different kinds of electron pairs in the valence shell. Assuming trictly localized pairs occupying orbitals having strongly directional character, E_c for the valence shell is evaluated in terms of E_c per lone pair, E_c per X? H bond, and E_c per X/X shared pair for Ne and for molecules containing first row atoms, where X is C, N, O, and F.     

Multiple‐pathways of carbon dioxide binding by a Lewis acid [B(C6F5)3] and a lewis base [P(tBu)3]: The energy landscape perspective

Using the reaction‐relevant two‐dimensional potential energy surface, an accurate reaction‐pathway mapping and ab inito molecular dynamics, it is shown that CO₂ capture by P(tBu)₃ and B(C₆F₅)₃ species has many nearly degenerate reaction‐routes to take. The explanation of that is in the topography of the transition state (saddle) area. An ensemble of asynchronous reaction‐routes of CO₂ binding is described in fine detail. © 2013 Wiley Periodicals, Inc.     

Z-discrimination avoidance in mass-analysed ion kinetic energy spectral studies performed on an unmodified ZAB-E mass spectrometer

A method is introduced by which mass-analysed ion kinetic energy spectra free from Z-discrimination can be obtained for both collisionally activated (CA) and metastable decomposition reactions. The method, performed on a ZAB-E instrument fitted with a collision cell, but applicable also to the ZAB-2F, involves summation of the ‘height resolved’ contributions (formed by beam collimation in the Z-axis and selected by electrostatic deflection of the incident beam) using the signal averaging facility normally available. Representative results (at 8 or 10 keV energy) are given for the CA (Ar target) reactions [CS₂]²⁺ → [CS]⁺; [CS₂]⁺ → S⁺ and [CH₃OH]⁺ → [m/z = 12–31]⁺, and for the metastable reaction [m/z 45]⁺ → [m/z 29]⁺ in ethanol.     

Negative influence of pKa on activation energy barrier: A case study for double proton transfer reaction in inorganic acid dimers

Strength of acid can be determined by means of pK_a value. Attempts have been made to find a relationship between pK_a and activation energy barrier for a double proton transfer (DPT) reaction in inorganic acid dimers. Negative influence of pK_a is observed on activation energy (E_a) which is contrary to the general convention of pK_a. Four different levels of theories with two different basis sets have been used to calculate the activation energy barrier of the DPT reaction in inorganic acid dimers. A model based on first and second order polynomial has been created to find the relationship between activation energy for DPT reaction. © 2018 Wiley Periodicals, Inc.     

Actual activation energy of electrode process under mixed kinetics conditions

In the case of a single-electron reaction with account for slow diffusion of reagents, equations for actual (experimentally determined) activation energies of two types were derived and analyzed: real energy A f, i.e., the energy measured at a constant electrode polarization value η = const) and formal energy (Ω_f, i.e., the value measured at a constant value of potential vs. an ambiguously chosen reference electrode E = const). It is found that under the conditions of a sufficiently significant deviation from equilibrium, the actual activation energy A _f is the weighted arithmetic mean of the diffusion activation energy and the sum of A ₀ + αFη (where A ₀ is the real activation energy of the discharge stage at polarization of η = 0); herewith, the weighting coefficients are the corresponding values of the current of the discharge stage and the limiting diffusion current. A similar relationship is also obtained for Ω_f. It is found that the A _f, η- and Ω_f, E-curves can in a number of cases feature regions with the negative A _f and Ω_f values in the mixed kinetics range.     

Critical level topology of energy hypersurfaces

Topologies are introduced into the nuclear configuration space R of molecular systems, based upon equipotential contour hypersurfaces on the otential energy hypersurface E. Critical level topologies T _fc and T _fc, based upon the number and distribution of various critical points of E, are of particular importance, since they represent convenient yet rigorous mathematical models for relations between elementary reaction mechanisms, and for relations between open sets of nuclear geometries which are classically accessible at a given total energy.     

Potential energy surface exploration with equilibrial paths. Part II: Application

The results of an exploration of an ab initio potential energy surface of the C₂H₄O system with equilibrial paths are presented. In particular, four minimizers associated with the product of an elimination reaction and 26 saddle points, among these 14 saddle points of first order, have been located. Furthermore, twelve valley–ridge inflection points and seven double bifurcation points have been detected.     

Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998     

Pressure tensor for electrostatic interaction calculated by fast multipole method with periodic boundary condition

A microscopic expression of the pressure tensor using the fast multipole method (FMM) with periodic boundary conditions has been derived. The pressure tensor calculated using this expression has been compared with that obtained using the Ewald method with high accuracy. The precision of the pressure tensor can be controlled as a function of expansion order p of FMM. Using the calculated pressure tensor, the constant pressure molecular dynamics calculation with fully fluctuating cell can be performed for anisotropic systems such as crystals, metals, liquid crystals, glasses, polymers, lipid bilayers, and interfacial regions between two phases. © 2018 Wiley Periodicals, Inc.     

Monte Carlo simulation of the diabatic free energy curves for a dissociative electron transfer reaction in a polar solvent

In the present work we have carried out a Monte Carlo simulation of a dissociative electron transfer reaction in a polar solvent. In particular, we have chosen as a very simple model the electrochemical reduction of hydrogen fluoride to give a hydrogen atom and a fluoride anion in a dipolar solvent. From a classical point of view, the electron transfer occurs at the intersection region S* of the diabatic potential hypersurfaces H_pp and H_ss, corresponding to the precursor and successor complexes, respectively. We have evaluated both diabatic surfaces using potential functions that have been built up with ab initio methods by us. For each of the obtained configurations the parameter ΔE = H_ss – H_pp has been calculated. This parameter is then used as the reaction coordinate for obtaining the diabatic free energy curves of the reaction. Because the activation energy is high, a suitable mapping potential along with the statistical perturbation theory is employed to force the system to evolve toward the intersection region S*. A total of 68,340,000 configurations have been generated. The main conclusion of this article is that Marcus' relationship seems to fail for this kind of inner-sphere processes. © 1992 by John Wiley & Sons, Inc.