Canonical Rate Constants Research Articles

NAST: Nonadiabatic Statistical Theory Package for Predicting Kinetics of Spin-Dependent Processes.

We present a nonadiabatic statistical theory (NAST) package for predicting kinetics of spin-dependent processes, such as intersystem crossings, spin-forbidden unimolecular reactions, and spin crossovers. The NAST package can calculate the probabilities and rates of transitions between the electronic states of different spin multiplicities. Both the microcanonical (energy-dependent) and canonical (temperature-dependent) rate constants can be obtained. Quantum effects, including tunneling, zero-point vibrational energy, and reaction path interference, can be accounted for. In the limit of an adiabatic unimolecular reaction proceeding on a single electronic state, NAST reduces to the traditional transition state theory. Because NAST requires molecular properties at only a few points on potential energy surfaces, it can be applied to large molecular systems, used with accurate high-level electronic structure methods, and employed to study slow nonadiabatic processes. The essential NAST input data include the nuclear Hessian at the reactant minimum, as well as the nuclear Hessians, energy gradients, and spin-orbit coupling at the minimum energy crossing point (MECP) between two states. The additional computational tools included in the NAST package can be used to extract the required input data from the output files of electronic structure packages, calculate the effective Hessian at the MECP, and fit the reaction coordinate for more advanced NAST calculations. We describe the theory, its implementation, and three examples of application to different molecular systems.

Unimolecular dissociation dynamics of C6H6–C6Cl6 complex and the effect of anharmonicity

Chemical dynamics simulations are performed to study the unimolecular dissociation of C6H6–C6Cl6 (Bz-HCB) complex at a temperature range of 1000–2000 K. The intramolecular and intermolecular potential energy parameters are optimized to reproduce the experimental frequencies, equilibrium energy and the minimum energy geometry of the complex. The microcanonical and canonical rate constants are fit to the harmonic classical Rice–Ramsperger–Kassel–Marcus (RRKM) and transition state theory (TST) equations, respectively. The role of anharmonicity on the dissociation of the complex is examined by considering the modified TST equation with the inclusion of an exponential anharmonic correction. The requirement of such a correction in analyzing the dissociation dynamics of Bz-HCB complex is validated by a Monte Carlo based calculation.

Calculations on the unimolecular decomposition of the nerve agent VX.

It is very difficult to perform experiments on the physical parameters for the thermal decomposition of chemical nerve agents such as VX and computations, therefore, are useful. The reaction dynamics of the gas-phase pericyclic hydrogen transfer of the nerve agent VX is studied computationally. The geometries of the stationary structures are calculated at M06-2X/jul-cc-pVTZ level of theory. Single point energy calculations are carried out at the CBS/QB3 level to correct the energy barriers. Canonical reaction rate constants are calculated as a function of temperature. The one-dimensional semiclassical transition state theory is used to analyse the quantum tunneling effects. A reduced-dimensional hindered rotor model is proposed, tested, and applied to calculate the vibrational partition functions. It is found that the ester (O-side) and thioester (S-side) side chains of VX undergo pericyclic H-transfer reactions that result in decomposition of the molecule. The S-side reaction is favoured both kinetically and thermodynamically and dominates the pyrolysis over the temperature range from 600 K to 1000 K. It is predicted that VX completely decomposes in 2 s at temperatures above 750 K.

Eyringpy: A program for computing rate constants in the gas phase and in solution

AbstractEyringpy is a modular program for calculating thermochemical properties and rate constants for reactions in the gas phase and in solution. The code is written in Python and it has a user‐friendly interface and a simple input format. Unimolecular and bimolecular reactions with one and two products are supported. Thermochemical properties are estimated through canonical ensemble and rate constants are computed according to the transition state theory. One‐dimensional Wigner and Eckart tunneling corrections are also available. Rate constants of bimolecular reactions involving the formation of pre‐reactive complexes are also estimated. To compute rate constants in solution, Eyringpy uses the Collins–Kimball theory to include the diffusion‐limit, the Marcus theory for electron transfer processes, and the molar fractions to account for the solvent pH effect.

Predicted Chemical Activation Rate Constants for HO2 + CH2NH: The Dominant Role of a Hydrogen-Bonded Pre-reactive Complex.

The reaction of methanimine (CH2NH) with the hydroperoxy (HO2) radical has been investigated by using a combination of ab initio and density functional theory (CCSD(T)/CBSB7//B3LYP+Dispersion/CBSB7) and master equation calculations based on transition state theory (TST). Variational TST was used to compute both canonical (CVTST) and microcanonical (μVTST) rate constants for barrierless reactions. The title reaction starts with the reversible formation of a cyclic prereactive complex (PRC) that is bound by ∼11 kcal/mol and contains hydrogen bonds to both nitrogen and oxygen. The reaction path for the entrance channel was investigated by a series of constrained optimizations, which showed that the reaction is barrierless (i.e., no intrinsic energy barrier along the path). However, the variations in the potential energy, vibrational frequencies, and rotational constants reveal that the two hydrogen bonds are formed sequentially, producing two reaction flux bottlenecks (i.e., two transition states) along the reaction path, which were modeled using W. H. Miller's unified TST approach. The rate constant computed for the formation of the PRC is pressure-dependent and increases at lower temperatures. Under atmospheric conditions, the PRC dissociates rapidly and its lifetime is too short for it to undergo significant bimolecular reaction with other species. A small fraction isomerizes via a cyclic transition state and subsequent reactions lead to products normally expected from hydrogen abstraction reactions. The kinetics of the HO2 + CH2NH reaction system differs substantially from the analogous isoelectronic reaction systems involving C2H4 and CH2O, which have been the subjects of previous experimental and theoretical studies.

A new ab initio based global HOOH(13A″) potential energy surface for the O(3P) + H2O(X1A1) ↔ OH(X2Π) + OH(X2Π) reaction

An accurate global potential energy surface is developed for the title reaction by fitting more than 36,000 of ab initio points at the CCSD(T)∕AVTZ level using the permutation invariant polynomial method. The canonical rate constants for both the forward and reverse directions of the title reaction are determined on the new potential energy surface and the agreement with experiment is satisfactory. In addition, the dynamics of the forward reaction is investigated with the quasi-classical trajectory method. It is found that this direct abstraction reaction has a backward bias in its product angular distribution, consistent with a direct rebound mechanism. The OH product newly formed by the reaction exhibits a bimodal rotational state distribution, due apparently to secondary collisions with the slowly recoiling spectator OH product.

N-Acylated Dipeptide Tags Enable Precise Measurement of Ion Temperature in Peptide Fragmentation

Peptide fragmentations into b- and y-type ions are useful for the identification of proteins. The b ion, having the structure of a N-protonated oxazolone, dissociates to the a-type ion with loss of CO. This CO-loss process affords the possibility of characterizing the temperature of the b ion. Herein, we used N-acylated dipeptide tags, isobaric tags originally developed for protein quantification, as internal standards for the measurement of the ion temperature in peptide fragmentation. Amine-reactive dipeptide tags were attached to the N-termini of sample peptides. Collision-induced dissociation (CID) of the tagged peptides yielded a b-type quantitation signal (b(S)) from the tag, which subsequently dissociated into the a(S) ion with CO-loss. As the length of alkyl side chain on the dipeptide tag was extended from C(1) to C(8), the yield of a(S) ion gradually increased for the 4-alkyl-substituted oxazolone ion but decreased for the 2-alkyl-substituted one. To gain insights into the unimolecular dissociation kinetics, we obtained the potential energy surface from ab initio calculations. Theoretical study suggested that the 4-alkyl substitution on N-protonated oxazolone decreased the enthalpy of activation by stabilizing the productlike transition state, whereas the 2-alkyl substitution increased it by stabilizing the reactant. Resulting potential energy surfaces were used to calculate the microcanonical and canonical rate constants as well as the a(S)-ion yield. Arrhenius plots of canonical rate constants provided activation energies and pre-exponential factors for the CO-loss processes in the 600-800 K range. Comparison of experimental a(S)-ion yields with theoretical values led to precise determination of the temperature of b(S) ion. Thus, the b(S)-ion temperature of tagged peptide can be measured simply by combining kinetic parameters provided here and a(S)-ion yields obtained experimentally. Although the b-type fragment patterns varied with the chain length and position of alkyl substituent on the N-protonated oxazolone, the y-type fragment patterns were almost identical under these conditions. Furthermore, b(S)-ion temperatures were nearly the same with only a few degrees K difference. Our results demonstrate a novel use of N-acylated dipeptide tags as internal temperature standards, which enables the reproducible acquisition of peptide fragment spectra.

Implementation of a variational code for the calculation of rate constants and application to barrierless dissociation and radical recombination reactions: CH3OH = CH3 + OH

AbstractHere, a new implementation for calculating canonical variational rate constants is introduced and tested against methanol dissociation rate constants and the (high pressure) radical recombination reaction, CH3 + OH → CH3OH. Reaction paths are described at the CASSCF level, with energy corrections at MRMP2. Molecular properties for both stationary and non‐stationary points along the reaction path are used for the calculation of rate constants. Different models for the low vibrational frequencies are discussed: harmonic oscillator and free rotor models. The CH3 + OH → CH3OH recombination rate constants are determined from dissociation rate constants and equilibrium constants. Our calculated rate constants agree with previously reported data for these reactions, suggesting the good performance of our implemented code in calculating canonical variational rate constants. The rate expressions are suggested: as: kdis (T) = 8.42 × 10+16 × e−96.18/RT and krec (T) = 2.05 × 10−10 × (T/298)−0.24 × e−0.30/RT, in units s−1 and cm3 molecule−1 s−1, respectively, and over the temperature range 300–2000 K, with activation energies in kcal/mol. © 2012 Wiley Periodicals, Inc.

Path integral approach to the calculation of reaction rates for a reaction coordinate coupled to a dual harmonic bath

AbstractWe present a new method for the numerical calculation of canonical reaction rate constants in complex molecular systems, which is based on a path integral formulation of the flux–flux correlation function. Central is the partitioning of the total system into a relevant part coupled to a dual bath. The latter consists of two parts: First, there is a set of strongly coupled harmonic modes, describing, for example, intramolecular degrees of freedom. They are treated on the basis of a reaction surface Hamiltonian approach. Second, there is a set of bath modes mimicking an unspecific environment modeled by means of a continuous spectral density. After deriving general equations expressing the canonical rate constant in terms of appropriate influence functionals, several approximations are introduced to provide an efficient numerical implementation. Results for an initial application to the H‐transfer in 6‐aminofulvene‐1‐aldimine are discussed. © 2011 Wiley Periodicals, Inc.

Semiclassical instanton approach to calculation of reaction rate constants in multidimensional chemical systems

The semiclassical instanton approximation is revisited in the context of its application to the calculation of chemical reaction rate constants. An analytical expression for the quantum canonical reaction rate constants of multidimensional systems is derived for all temperatures from the deep tunneling to high-temperature regimes. The connection of the derived semiclassical instanton theory with several previously developed reaction rate theories is shown and the numerical procedure for the search of instanton trajectories is provided. The theory is tested on seven different collinear symmetric and asymmetric atom transfer reactions including heavy-light-heavy, light-heavy-light and light-light-heavy systems. The obtained thermal rate constants agree within a factor of 1.5-2 with the exact quantum results in the wide range of temperatures from 200 to 1500 K.

A practical implementation of semi-classical transition state theory for polyatomics

An algorithm is described for computing rate constants with semi-classical transition state theory (SCTST) formulated by Miller and coworkers. SCTST incorporates non-separable coupling among all degrees of freedom and multi-dimensional quantum mechanical tunneling along the curved reaction path. The algorithm, which is practical for reactants containing dozens of atoms, predicts both microcanonical and canonical rate constants. In addition, the quantum chemistry code CFOUR has been extended to efficiently compute fully-coupled vibrational anharmonicities for transition states at the CCSD(T) level of theory. The new methods are demonstrated for the H 2 + OH reaction and the ‘tail-biting’ isomerization of acetylperoxyl radical.

Anharmonic Effect on Unimolecular Reactions with Application to the Photodissociation of Ethylene

The importance of anharmonic effect on dissociation of molecular systems, especially clusters, has been noted. In this paper, we shall present a theoretical approach that can carry out the first principle calculations of anharmonic canonical and microcanonical rate constants of unimolecular reactions within the framework of transition state theory. In the canonical case, it is essential to calculate the partition function of anharmonic oscillators; for convenience, the Morse oscillator potential will be used for demonstration in this paper. In the microcanical case, which involves the calculation of the total number of states for the activated complex and the density of states for the reactant, we make use of the fact that both the total number of states and the density of states can be expressed in the inverse Laplace transformation of the partition functions and that the inverse Laplace transformation can in turn be carried out by using the saddle-point method. We shall also show that using the theoretical approach presented in this paper the total number of states and density of states can be determined from thermodynamic properties and the difference between the method used in this paper and the thermodynamic model used by Krems and Nordholm will be given. To demonstrate the application of our theoretical approach, we chose the photodissociation of ethylene at 157 and 193 nm as an example.

Quantum Mechanical Rate Constants for H + O2 ↔ O + OH and H + O2 → HO2 Reactions

Canonical rate constants for both the forward and reverse H + O(2) <--> O + OH reactions were calculated using a quantum wave packet-based statistical model on the DMBE IV potential energy surface of Varandas and co-workers. For these bimolecular reactions, the results show reasonably good agreement with available experimental and theoretical data up to 1500 K. In addition, the capture rate for the H + O(2) --> HO(2) addition reaction at the high-pressure limit was obtained on the same potential using a time-independent quantum capture method. Excellent agreement with experimental and quasi-classical trajectory results was obtained except for at very low temperatures, where a reaction threshold was found and attributed to the centrifugal barrier of the orbital motion.

Evaluation of canonical and microcanonical nonadiabatic reaction rate constants by using the Zhu–Nakamura formulas

We consider a problem of calculating both thermal and microcanonical rate constants for nonadiabatic chemical reactions. Instead of using the conventional transition state theory, we use a generalized seam surface and introduce a concept of a coordinate dependent effective nonadiabatic transition probability based on the Zhu-Nakamura theory which can treat the nonadiabatic tunneling properly. The present approach can be combined with Monte Carlo method so as to be applicable to chemical reactions in complicated systems. The method is demonstrated to work well in wide energy and temperature range. Numerical tests also show that it is very essential for accurate evaluation of the thermal rate constant to use the generalized seam surface and take into account the nonadiabatic tunneling effect.

Crystals of binary Lennard-Jones solids

We present crystalline structures for 60-, 256-, and 320-atom supercells of binary Lennard-Jones solids. These structures, based on cubic close packing, are much lower in energy than the disordered structures usually considered for this model glass former. We present a disconnectivity graph for a database of minima and transition states for the 320-atom system, which has been simplified using a grouping technique based on the canonical rate constants.

The Transition State: A Theoretical Approach Edited by Takayuki Fueno (Osaka University and Aichi Institute of Technology). Kodansha: Tokyo and Gordon Breach Publishers: Amsterdam. 1999. xvi + 328 pp. $120.00. ISBN 90-5699-216-3

The transition state is the critical configuration of a reaction system situated at the highest point of the most favorable reaction path on the potential-energy surface, its characteristics governing the dynamic behavior of reacting systems decisively. This text presents an accurate survey of current theoretical investigations of chemical reactions, with a focus on the nature of the transition state. Its scope ranges from general basic theories associated with the transition states, to their computer-assisted applications, through to a number of reactions in a state-of-the-art fashion. It covers various types of gas-phase elementary reactions, as well as some specific types of chemical processes taking place in the liquid phase. Also investigated is the recently developing transition state spectroscopy. Chapter 1. Introduction; Chapter 2. Determination of Transition State Structures on Potential Energy Surfaces; Chapter 3. Molecular Symmetry and Transition State; Chapter 4. Transition State Theoretical Calculations of the Canonical Rate Constants for Bimolecular Reactions; Chapter 5. Development of the Microcanonical Statistical Rate Theory for Unimolecular Reactions; Chapter 6. Intracluster Reaction Dynamics of Ar{sub 4}{sup +}; Chapter 7. Transition State for Chemical Reactions in Solution; Chapter 8. Structures and Reactions of Compounds Containing Heavier Main Group Elements; Chapter 9. Transition States in Organometallicmore » Reactions; Chapter 10. Chemical Reaction Dynamics and Potential Ridge: Beyond the Transition State; Chapter 11. Differential Geometry in Chemical Reaction Dynamics; Chapter 12. Toward Transition State Spectroscopy: Experimental Approaches Using Weakly Bonded Clusters; Chapter 13. Relativistic Effects on Transition State Structures and Properties: Transition State Spectroscopy of IHI and BrHI; Chapter 14. A Time-Dependent Theoretical Approach to Transition State Spectroscopy; Chapter 15. Scattering Theory for Photodetachment and Molecular Dissociation as a Direct Probe of Transition State.« less

“Direct” and “Correct” Calculation of Canonical and Microcanonical Rate Constants for Chemical Reactions

Theoretical approaches for calculating rate constants of chemical reactionseither the microcanonical rate for a given total energy k(E) or the canonical rate for a given temperature k(T)are described that are both “direct”, i.e., bypass the necessity of having to solve the complete state-to-state quantum reactive scattering problem, yet also “correct”, i.e., in principle exact (given a potential energy surface, assuming nonrelativistic quantum mechanics, etc.) Applications to a variety of reactions are presented to illustrate the methodology for various dynamical situations, e.g., transition-state-theory-like dynamics where the system moves directly through the interaction (transition-state) region and reactions that form long-lived collision complexes. It is also shown how this rigorous quantum theory can be combined with the Lindemann mechanism for describing the effects of collisions with a bath gas, so as to be able to treat recombination reactions and other effects of pressure. Finally, several ways ...

Theoretical investigation of the mechanism and kinetics for HCO + HCN ⇄ HCHO + CN

The mechanism and kinetics for HCO + HCN ⇄ HCNO + CN have been studied theoretically. The potential energy profile along the intrinsic reaction coordinate (IRC) has been obtained at ab initio QCISD/6-31G ∗∗//UHF/6-31G ∗∗ and CCSD/6-31G ∗∗//UHF/6-31G ∗∗ levels. The forward activation barriers are about 136.45 adn 140.94 kJ mol −1 at these levels, respectively, and the reverse barriers are 2.71 and 1.26 kJ mol −1, respectively. The canonical rate constants for the forward and reverse reactions have been calculated by using statistical theory.

Theoretical Calculation on the Canonical Rate Constants for the Addition Reaction of 1,3-cyclohexa-diene with Propylene

Theoretical Calculation on the Canonical Rate Constants for the Addition Reaction of 1,3-cyclohexa-diene with Propylene

Comparisons between statistics, dynamics, and experiment for the H+O2→OH+O reaction

The accuracy of the variable reaction coordinate (VRC) implementation of transition state theory (TST) is investigated for the bimolecular reaction of H with O2 via direct comparisons with quantum scattering theory for J=0, classical trajectory simulations for a wide range of J, and experimental canonical rate constants. The DMBE IV potential energy surface of Varandas and co-workers is employed in each of the theoretical calculations. The first two comparisons indicate that the VRC-TST approach overestimates the cumulative reaction probability (CRP) for this reaction by a factor of 2.3, roughly independent of E and J for moderate energies. The trajectory simulations further indicate that this failure of TST is primarily the result of the rapid redissociation of a large fraction of the initially formed HO2. An estimate for the quantum CRP on the basis of the combined dynamical and statistical results is seen to provide a useful alternative to the more standard quasiclassical trajectory estimates. A thermal averaging over the E and J-dependence of the TST estimates for the CRP provides canonical rate constants, k(T), which, when corrected for the above-mentioned overestimate, are still a factor of 1.7–2.0 times greater than the experimental data. This discrepancy is most likely the result of either (i) inaccuracies in the DMBE IV surface and/or (ii) an overestimate of the contribution to the reactive flux from the nearly degenerate first excited state in the exit channel region.