Polanyi Rules Research Articles

Direct dynamics trajectory study of vibrational effects: can polanyi rules be generalized to a polyatomic system?

We present an ab initio direct dynamics trajectory study of the hydrogen abstraction reaction: H2CO+ + CD4 --> H2COD+ + CD3, with methane excited in two different distortion modes (nu4 and nu2). The trajectory simulations were able to reproduce experimental results and for the first time show how vibrational enhancement originates in reaction of small polyatomic species. Roughly equal contributions from two vibrational enhancement mechanisms were found. The "distortion" mechanism correlates the vibrational effects with vibration-induced reactant distortions, and the "velocity" mechanism correlates vibrational effects with vibrational velocities of the constituent atoms. This reaction has a reactant-like transition state and, thus, would correspond to an "early" barrier system in the context of the well-known Polanyi rules for predicting effects of vibration and collision energy. Straightforward application of these rules would predict that vibration should be ineffective in driving reaction, in disagreement with both experiment and trajectory results. Using the trajectories for guidance, we were able to construct a two-dimensional cut through the reaction potential energy surface that does suggest a predictive, Polanyi-type rule.

Trajectory study of the effect of energy barrier location on the energy disposal for the reaction O(3P) + Cl2 → OCl + Cl

The mode of partitioning of total energy available in the reaction O(3P) + Cl2 → OCl + Cl is investigated as a function of the initial collision energy, in correlation with Polanyi's adiabaticity rules, using a series of related LEPS-type potential energy functions. All surfaces possess a classical energy barrier of similar height located in the entrance valley of the reaction, but present a small, gradual displacement of the top of the barrier to later positions along the approach coordinate. Quasiclassical trajectory calculations on these surfaces indicate marked differences in the disposal of total energy and the dynamical behaviour of the reaction. Also the effect of excess reagent vibration is investigated.

Polanyi rules for ultrafast unimolecular reactions: simulations for HCo(CO)4(1E)* .fwdarw. hydrogen atom + cobalt tetracarbonyl

The traditional Polanyi rules for control of bimolecular reactions by selective investment of energy, e.g. preferentially translational, not vibrational energy for early-downhill reactions on attractive potential energy surfaces, are extended to ultrafast unimolecular reactions. Specifically, we consider photodissociations of the metal-hydrogen bond of HCo(CO) 4 ( 1 E), occurring on a time scale of approximately 20 fs, much faster than competing intramolecular vibrational energy redistribution (IVR). Here the reaction path toward the products H+Co(CO) 4 is hindered by a barrier located in the H+Co(CO) 4 exit valley of the potential energy surface

Molecular Orbital Approach to Antioxidant Mechanisms of Phenols by an Ab Initio Study

Abstract An ab initio molecular orbital theory has been applied to a study of the hydrogen abstractions of phenolic antioxidants in the chain process of autoxidation. The optimum structures of phenols, of peroxides, and of those compounds in the transition states were obtained with a Hartree–Fock/STO-3G basis set. From the values of enthalpy (ΔH) and activation energy (Ea) obtained, it was found that the rates of the reaction of peroxyl radical with phenolic antioxidant were faster than those with organic substrate in the propagation, and that the effect of the aromatic ring of the antioxidants not only stabilized a product state but also decreased an energy level in the transition state. The para-substituent effect that an electron-releasing substituent increased the antioxidant activity, whereas an electron-withdrawing one decreased it, was recognized. The relationship between ΔH and Ea values followed the Evans–Polanyi rule. The transition states in the hydrogen abstractions with lower Ea values prefer reactant-like structures, whereas those with higher Ea values prefer product-like ones.

What can gas phase reactions tell us about solution reactions?

Much of the behavior of simple gas phase reaction dynamics can be understood in terms of simple pictures based on the shapes of the underlying potential energy surfaces and the masses of the reagent atoms. Our aim here is to investigate to what extent such gas phase models can be used to understand properties of solution reactions. In particular, we examine for a solution reaction the validity of the Evans–Polanyi rule that an early potential barrier favors translational excitation of the reactants and vibrational excitation of the products, with the converse holding true for a late barrier. The test is performed by using molecular dynamics simulations for an asymmetric linear transition state A+BC→AB+C atom exchange reaction in argon solvent. We calculate for both gas and solution reactions the partitioning among translational, rotational, and vibrational energy during the reaction process. We find that for a short time period (−65 to 65 fs where t=0 is at the barrier top), in which the forces from the intrinsic gas phase potential dominate, the Evans–Polanyi rule can be carried over into the solution reaction. The gas phase vibrational energy distributions persist in solution over a much longer period. In particular, this calculation illustrates for an early barrier linear transition state potential in solution that a solvent induced fluctuation in the reagent translational energy is considerably more effective than a fluctuation in vibrational energy in prompting reaction. The resulting reaction products are formed highly vibrationally excited. For the reverse late barrier reaction, a solvent induced fluctuation in vibrational energy is needed for reaction and the resulting products are initially highly translationally excited. We expect that on the proper time scale, many other gas phase reaction dynamics rules will also carry over to solution reactions, particularly in cases in which the reagent–solvent interaction is weak.

On the dynamics of exothermic triatomic exchange reactions

Analytic expressions are derived for the population of vibrational states for triatomic exchange reactions. The predictions are in good accord with the so-called ’’Polanyi rules.’’ The results are expressed in terms of the masses, frequencies, exothermicity, interaction length, and the attractive part of the potential A⊥E*. Comparison with exact quantum-mechanical calculations is made for a series of light-heavy-heavy (LHH) reactions. An almost linear relation between the attractive part of the potential and the product vibrational energy is obtained. For the LHH-mass combination the slope is almost one. For other mass combinations like HHL, HLL, or HLH the final vibrational energy is relatively insensitive to A⊥, showing always strong population inversion. The width of the vibrational energy distribution is smallest for the HLH mass combination.

Qualitative interpretation of the dynamics of collinear exchange reactions

The many-channel resonance scattering theory is adapted for the purpose of investigation of the dynamics of collinear chemical exchange reactions. A general expression for the scattering matrix is presented which appears to be useful for developing a simple algebraic procedure of calculation of the parameters needed for various resonance expansions. The case of weak nonadabatic coupling between vibrational levels is studied in detail by means of a version of perturbational treatment that is valid for a resonance situation. This approach is then applied to account for the qualitative peculiarities observed in recent experimental and numerical investigations of reactive collosions A + BC → AB + C. The Polanyi rules are formulated in terms of the accessibility of a transition zone region for adiabatic channel functions. Several mechanisms of product population inversion are discussed. That of them occurring at low kinetic energies in the transition zone is supposed to arise due to the resonance scattering caused by the wells of dynamic adjabatic potentials, which have been revealed by Wu, Johnson and Levine. The estimations for Breit-Wigner reduced width amplitudes are given in framework of weak coupling approximation. They are shown to provide a meaningful background for understanding of resonance phenomena found in quantum calculations.

Evaluation of Activation Energy for Addition Reactions of Radicals to Vinyl Compounds

Evaluation of activation energy for the reactions of radical additions to vinyl compounds was studied as an extension of the theory employing two Morse functions for the initial and the final systems. The π-bond dissociation energies of vinyl compounds in the initial system were estimated by using the localization energy method. The difference between the a′Δr* values of the Morse functions of the initial and the final systems in the transition state was empirically determined as a function, af′Δrf*−aπ′Δrπ*=ωΔH, of the reaction heat ΔH. Based on the above finding, an empirical equation for evaluation of the activation energies of the radical addition reactions was derived, and its propriety was checked in comparison with the observed values. An approximate formula of the empirical equation was introduced in order to facilitate calculations of the activation energies. The Evans–Polanyi and Semenov rules, the Hammett-type rule and the Q–e scheme in the radical copolymerizations were derived by using this approximate formula and are discussed in detail.

Anodic methoxylation of alkylbenzenes

Anodic reactions of three kinds of alkylbenzene, toluene, ethylbenzene and cumene, in methanolic solution are described. Voltammetric measurements showed that alkylbenzenes examined here do not participate in the charge- transfer reaction so that the various aromatic derivatives appearing in the solution after electrolysis are the products of subsidiary chemical reactions induced by the primary product of the electrode reaction. This was confirmed by a comparative experiment in which ethylbenzene was reacted with molecular bromine in methanolic solution with no current passing. Among several products obtained by electrolysis, the formation of the α-substituted methyl ether was mainly studied. Coulombic efficiency of the methyl ether formation was affected greatly by the supporting electrolyte. This finding has been explained by Polanyi's rule assuming that the hydrogen abstraction reaction from the hydrocarbon is the rate-determining step. It has also been shown that the ether formation reaction is a heterogeneous surface reaction occurring on the platinum electrode surface.

Kinetics of radical polymerization—XVI. II. Polycondensed aromatic hydrocarbons

An account is given of the inhibition kinetic examination of some aromatic hydrocarbons which act as retarders for the polymerization of vinyl acetate. The dependence of the reactivity on parameters characterizing the structure of aromatic hydrocarbons is discussed in detail. It is shown that the aromatic molecules are attacked by radicals not only at the points of maximum reactivity but also, with appropriately reduced probability, at their less reactive points. In calculating theoretical values of the reactivity and the stoichiometric coefficient, these facts have been taken into account. The activation energy of elementary inhibition reactions is also discussed. It is shown that only a small part of the modification of reactivity can be ascribed to changes in activation energy; modification of the pre-exponential factor is of much greater significance. Consequently, radical reactions of aromatic hydrocarbons cannot be directly interpreted according to Polanyi's rule.