Testing Transition State Theory on Kac-Zwanzig Model

A variant of the Kac-Zwanzig model is used to test the prediction of transition state theory (TST) and variational transition state theory (VTST). The model describes the evolution of a distinguished particle moving in a double-well external potential and coupled to N free particles through linear springs. While the Kac-Zwanzig model is deterministic, under appropriate choice of the model parameters the evolution of the distinguished particle can be approximated by a two-state Markov chain whose transition rate constants can be computed exactly in suitable limit. Here, these transition rate constants are compared with the predictions of TST and VTST. It is shown that the application of TST with a naive (albeit natural) choice of dividing surface leads to the wrong prediction of the transition rate constants. This is due to crossings of the dividing surface that do not correspond to actual transition events. However, optimizing over the dividing surface within VTST allows one to eliminate completely these spurious crossings, and therefore derive the correct transition rate constants for the model. The reasons why VTST is successful in this model are discussed, which allows one to speculate on the reliability of VTST in more complicated systems.     

Theoretical kinetic study on the decomposition of 1,5‐diaminotetrazole

1,5‐Daminotetrazole (DAT) is of much interest because of the practical significance and the diversity of characteristics. The study on the decomposition pathway and the kinetics of DAT has been performed based on the quantum chemistry theory. The minimum energy path (MEP) calculation has shown that NH₂N₃ and NH₂CN are the initially detected products of DAT. And the structures of reactant, products and transition state were optimized with MP2 methods using 6‐311G** basis sets, and the energies were refined using CCSD(T)/6‐311G** levels of theory. The calculated rate constants were obtained using the conventional transition‐state theory (TST) and the canonical variational transition‐state theory (CVT) methods. The calculation results indicated that the energy barrier of decomposition reaction is 47.98 kcal mol^?1 and the variational effect is small. In addition, the rate constants and the Arrhenius experience formula of DAT decomposition have been obtained between 200 and 2500 K temperature regions. The fitted three‐parameter expressions calculated using the TST and CVT methods are (TST) and (CVT). This work may provide the theoretical support for further experimental synthesis and testing. Copyright © 2015 John Wiley & Sons, Ltd.     

Reaction rate theory: what it was, where is it today, and where is it going?

A brief history is presented, outlining the development of rate theory during the past century. Starting from Arrhenius [Z. Phys. Chem. 4, 226 (1889)], we follow especially the formulation of transition state theory by Wigner [Z. Phys. Chem. Abt. B 19, 203 (1932)] and Eyring [J. Chem. Phys. 3, 107 (1935)]. Transition state theory (TST) made it possible to obtain quick estimates for reaction rates for a broad variety of processes even during the days when sophisticated computers were not available. Arrhenius' suggestion that a transition state exists which is intermediate between reactants and products was central to the development of rate theory. Although Wigner gave an abstract definition of the transition state as a surface of minimal unidirectional flux, it took almost half of a century until the transition state was precisely defined by Pechukas [Dynamics of Molecular Collisions B, edited by W. H. Miller (Plenum, New York, 1976)], but even this only in the realm of classical mechanics. Eyring, considered by many to be the father of TST, never resolved the question as to the definition of the activation energy for which Arrhenius became famous. In 1978, Chandler [J. Chem. Phys. 68, 2959 (1978)] finally showed that especially when considering condensed phases, the activation energy is a free energy, it is the barrier height in the potential of mean force felt by the reacting system. Parallel to the development of rate theory in the chemistry community, Kramers published in 1940 [Physica (Amsterdam) 7, 284 (1940)] a seminal paper on the relation between Einstein's theory of Brownian motion [Einstein, Ann. Phys. 17, 549 (1905)] and rate theory. Kramers' paper provided a solution for the effect of friction on reaction rates but left us also with some challenges. He could not derive a uniform expression for the rate, valid for all values of the friction coefficient, known as the Kramers turnover problem. He also did not establish the connection between his approach and the TST developed by the chemistry community. For many years, Kramers' theory was considered as providing a dynamic correction to the thermodynamic TST. Both of these questions were resolved in the 1980s when Pollak [J. Chem. Phys. 85, 865 (1986)] showed that Kramers' expression in the moderate to strong friction regime could be derived from TST, provided that the bath, which is the source of the friction, is handled at the same level as the system which is observed. This then led to the Mel'nikov-Pollak-Grabert-Hanggi [Mel'nikov and Meshkov, J. Chem. Phys. 85, 1018 (1986); Pollak, Grabert, and Hanggi, ibid. 91, 4073 (1989)] solution of the turnover problem posed by Kramers. Although classical rate theory reached a high level of maturity, its quantum analog leaves the theorist with serious challenges to this very day. As noted by Wigner [Trans. Faraday Soc. 34, 29 (1938)], TST is an inherently classical theory. A definite quantum TST has not been formulated to date although some very useful approximate quantum rate theories have been invented. The successes and challenges facing quantum rate theory are outlined. An open problem which is being investigated intensively is rate theory away from equilibrium. TST is no longer valid and cannot even serve as a conceptual guide for understanding the critical factors which determine rates away from equilibrium. The nonequilibrium quantum theory is even less well developed than the classical, and suffers from the fact that even today, we do not know how to solve the real time quantum dynamics for systems with "many" degrees of freedom.     

Transition state theory: A generalization to nonequilibrium systems with power-law distributions

Transition state theory (TST) is generalized to nonequilibrium systems with power-law distributions. The stochastic dynamics that gives rise to the power-law distributions for the reaction coordinate and momentum is modeled by Langevin equations and corresponding Fokker-Planck equations. It is considered that a system far away from equilibrium does not have to relax to a thermal equilibrium state with Boltzmann-Gibbs distribution, but asymptotically approaches a nonequilibrium stationary state with a power-law distribution. Thus, we obtain a possible generalization of TST rates to nonequilibrium systems with power-law distributions. Furthermore, we derive the generalized TST rate constants for one-dimensional and n-dimensional Hamiltonian systems away from equilibrium, and obtain a generalized Arrhenius rate for systems with power-law distributions.     

A DFT-based microkinetic theory for Fe2O3 reduction by CO in chemical looping

Redox kinetics of oxygen carrier in chemical looping is an important component for material preparation, reactor design and process demonstration. How to bridge the gap between the microscale density functional theory (DFT) and the macroscale redox kinetics and develop a first-principle-based theoretical model is still a challenge in the field of chemical looping. This study addresses this challenge and proposes a DFT-based microkinetic rate equation theory to calculate the heterogeneous kinetics of Fe₂O₃ reduction by CO in chemical looping. Firstly, the DFT calculation is adopted to search the reaction pathways and to obtain the energy barriers of elementary reactions. Secondly, the DFT results are introduced into the transition state theory (TST) to calculate the reaction rate constants and build the rate equations of elementary surface reactions. Finally, by considering the bulk diffusion, a rate equation is developed to bridge the gap between the elementary surface reactions and the grain conversion. In the theory, the reaction mechanism obtained from DFT and kinetic rate constants obtained from TST are directly implemented into the rate equation to predict the reduction kinetics of oxygen carriers without fitting experimental data. The accuracy of the developed theory is validated by experimental data of two Fe₂O₃ oxygen carriers obtained from the thermogravimetric analyzer (TGA). The microkinetic rate equation theory is based on the first principles calculation and can predict directly the redox kinetics of oxygen carriers without depending on the experimental kinetic data, therefore, it provides a powerful theoretical tool to screen the oxygen carrier materials and optimize the microstructure of oxygen carriers.     

Buckled nano rod – a two state system: quantum effects on its dynamics

We consider a suspended elastic rod under longitudinal compression. The compression can be used to adjust potential energy for transverse displacements from the harmonic to the double well regime. The two minima in potential energy curve describe two possible buckled states. Using transition state theory (TST) we have calculated the rate of conversion from one state to other. If the strain ? = 4? _c the simple TST rate diverges. We suggest a method to correct this divergence for quantum calculations. We also find that zero point energy contributions can be quite large so that single mode calculations can lead to large errors in the rate.     

Pressure effects on thermal isomerizations in highly viscous media. The first clear-cut example of viscosity-induced retardation of “slow” thermal reactions

Abstract

Kinetic effects of pressure on thermal Z/E isomerizations of 4-(dimethylamino)-4′-nitroazo-benzene (DMNAB) and N-[4-(dimethylamino)benzylidene]-4-nitroaniline (DMBNA) were studied by flash photolysis in three viscous solvents; glycerol triacetate (GTA), 2-methyl-2,4-pentanediol (MPD) and “Traction Fluid B” (TFB). In all cases studied, the pressure effects observed at the beginning of pressurization were qualitatively similar to the ones observed in less viscous solvents. The results strongly suggest that the conventional understandings of the kinetic effects of pressure based on the transition state theory (TST) are valid in these thermal unimolecular reactions. At higher pressures, however, pressure-induced viscosity increase resulted in strong retardation of both of the isomerizations. The diffusion-controlled rate constants obtained by substituting the observed and the TST-expected rate constants to I/k_obs = l/k_TST + l/k_dif showed inverse fractional dependence on the solvent viscosity.     

Predicted diffusion rates on fcc (001) metal surfaces for adsorbate/substrate combinations of Ni, Cu, Rh, Pd, Ag, Pt, Au

We investigate the diffusion of a single metal atom on the surface of a fcc (001) metal. Two points concerning the application of kinetic models to diffusion were considered. First, we test the assumption of kinetic models that diffusion occurs via a sequence of uncorrelated jumps. Second, when kinetic models are applicable we predict reasonable values of the kinetic rate constants.

Direct molecular dynamics (MD) simulations were performed for Ag on Ag(001) and Rh on Rh(001) systems. Diffusion was found to obey an Arrhenius-type dependence on temperature in both systems. The barriers and prefactors extracted from the MD results agree with estimates made from transition state theory (TST) and the experimental values for the Rh system. We conclude that kinetic models are applicable to diffusion on fcc (001) surfaces.

Transition state theory was then used to estimate diffusion parameters for all other adsorbate/ substrate combinations of the metals Ni, Cu, Rh, Pd, Ag, Pt, and Au. These results indicate that the characteristics of diffusion are primarily a property of the adsorbate. We also predict Ag atoms to have an anomalously low diffusion barrier on all of the substrates in this study. We use the accurate many-body density functional based MD/MC-CEM potential energy surface which allows us to consistently treat these multi-component systems.     

Theoretical study on the mechanism and kinetics of atmospheric reactions NH2OH + OOH and NH2CH3 + OOH

Mechanism and kinetics of NH₂OH + OOH and NH₂CH₃ + OOH reactions were studied at the B3LYP and M062X levels of theory using the 6-311++G(3df, 3pd) basis set. The NH₂OH + OOH and NH₂CH₃ + OOH reactions proceed through different paths which lead to different products. Transition state structure and activation energy of each path were calculated. The calculated activation energies of hydrogen abstraction reactions were smaller than 25 kcal/mol and of substitution reactions are in the range of 50–70 kcal/mol. The rate constants were calculated using transition state theory (TST) modified for tunneling effect at 273–2000 K.     

Kinetics of C<Subscript>10</Subscript>H<Subscript>7</Subscript>Br Pyrolysis

The temperature and pressure-dependent rate constants for the process C₁₀H₇Br ? C₁₀H₇+Br were evaluated using the variable reaction coordinate transition state theory VRC-TST. The calculated rate constants and computational fluid dynamics (CFD) calculations were employed to estimate the pyrolysis efficiency of 2-bromonaphthalene in the resistively-heated SiC high-temperature “chemical reactor” at the temperature of about 1500 K. The observed 40% pyrolysis efficiency is reproduced by CFD calculations if the value of the calculated rate constant for the C₁₀H₇Br pyrolysis is increased by a factor of 2.     

Theoretical investigation of the transition states leading to HCI elimination in 2-chloropropene

This paper describes ab initio electronic structure calculations on the planar transition states of 2-chloropropene leading to HCI elimination in the ground electronic state to form either propyne or allene as the cofragment. The calculations provide optimized geometries of the transition states for these two reaction channels, together with vibrational frequencies, barrier heights, and reaction endothermicities. The calculated barrier heights for the two distinct four-centre HCI elimination transition states, one leading to HCI and propyne and the other leading to HCI and allene, are 72.5kcalmol^?1 (77.8kcalmol^?1 without zero-point correction) and 73.2kcalmol^?1 (78.7kcalmol^?1) at the MP2/6-311G(d, p) level, 71.Okcalmol^?1 (76.3kcalmol^?1) and 70.5kcalmol^?1 (76.0kcalmol^?1) at the QCISD(T)/6-311 +G(d, p)//MP2/6-311G(d, p) level, and 66.9kcalmol^?1 (71.7kcalmol^?1) and 67.3kcalmol^?1 (72.1kcalmol¹) at the G3//B3LYP level of theory. Calculated harmonic vibrational frequencies at the B3LYP/6-31G(d) level along with transition state barrier heights from the G3//B3LYP level of theory are used to obtain RRKM reaction rate constants for each transition state, which determine the branching ratio between the two HCI elimination channels. Even at internal energies well above both HCI elimination barriers, the HCI elimination leading to propyne is strongly favoured. The smaller rate constant for the HCI elimination leading to allene can be attributed to the strong hindrance of the methyl rotor in the corresponding transition state.     

Linear and nonlinear optical properties of hydrated and dehydrated silica micro-spheres under an electric bias

The linear refractive indices and nonlinear second-order susceptibility of hydrated and dehydrated silica micro-spheres are studied using attenuated total reflectance (ATR) and the second harmonic generation (SHG) method in direct transmission, respectively. A dramatic change of the effective dielectric constant of silica suspension under an electric bias was observed, which is attributed to particle redistribution in the fluid. Dielectric constants of dehydrated silica spheres change slightly under an electric field due to Pockels effect, for which we measure a linear electro-optical coefficient of r₃₃ ∼3.4±0.7 pm/V. The transmission second harmonic generation comes from the third-order susceptibility χ⁽³⁾, which is a coupling of two photons and the electrostatic field induced by the surface –OH charges as characterized by the Gouy-Chapman model. The SH signal from the dehydrated silica vanishes because of the loss of –OH groups on the particle surfaces. Dehydration of silica beads is irreversible. The optical properties of dried silica spheres do not recover their original hydrated state when distilled water is added.     

Ultrasonic studies of aluminium-substituted Bi(Pb)-2223 superconductors

The compositional dependence of elastic properties of Al³⁺-substituted Bi(Pb)-2223 superconducting system with the general formula Bi_1.7−x Al_xPb_0.3Sr₂Ca₂Cu₃ O_y (x = 0.0, 0.1, 0.2 and 0.3) have been studied by means of ultrasonic pulse transmission (UPT) technique at 1 MHz (300 K). The elastic moduli of the specimens are computed and corrected to zero porosity. The observed variation of elastic constants with aluminium substitution has been explained on the basis of the strength of interatomic bonding. The applicability of heterogeneous metal mixture rule for estimating elastic constants and transition temperature has been tested.     

Prediction of ion channel transport from Grote—Hynes and Kramers theories

Generalized Langevin equation based Grote—Hynes (GH) theory and Langevin equation based Kramers theory are used to calculate the transmission coefficient for K⁺ diffusion through a model of the biological potassium ion channel IRK1, which contains a high potential barrier in the selectivity filter. The ion friction kernel is determined from a molecular dynamics (MD) simulation of the force on a stationary ion at the barrier top. The GH and Kramers estimates of the transmission coefficient are compared with those obtained from MD simulations of ion diffusion at the barrier top of the IRK1 channel. It is found that the GH estimate agrees with the value determined by rigorous MD, but the Kramers estimate is about 40% too small. The success or failure of GH and Kramers theories for various other systems is discussed and compared with these results.     

Kinetics of the H + NCO reaction

Ab initio transition state theory (TST) based master equation simulations are used to predict the temperature and pressure dependence of the H + NCO reaction rate and product branching. The barrierless entrance channels to form singlet HNCO and NCOH are studied with variable reaction coordinate TST employing a potential energy surface obtained from multi-reference configuration interaction ab initio calculations. The remaining channels, including reactions on the triplet surface, are studied with standard TST methods employing high level electronic structure results. The energy transfer parameters for the master equation simulations arise from a fit to the experimentally observed HNCO dissociation rate. The lowest energy threshold to formation of bimolecular products, ³NH + CO, lies well below the reactants. The bottleneck for intersystem crossing, which precedes the formation of ³NH + CO from the singlet adducts, becomes the dominant bottleneck for that channel at quite low energies relative to reactants. The effect of this bottleneck is studied with model calculations designed to reproduce detailed experimental observations of photolysis branching ratios. This bottleneck greatly reduces the flux from H + NCO to ³NH + CO via the singlet adducts. As a result, stabilization and reaction on solely the triplet surface are significant components of the overall rate. The present predictions for the high pressure and collisionless limit rate coefficients are accurately reproduced over the 200-2500 K range by the expressions, 1.53 × 10⁻⁵T^−1.86exp(−399/T) + 1.07 × 10³T^−3.15exp(−15219/T) and 5.62 × 10⁻¹²T^0.493exp(148/T) cm³ molecule⁻¹ s⁻¹, respectively, where T is in K. These predictions are in reasonably satisfactory agreement with the somewhat discordant experimental rate measurements.     

Rovibrational quenching of BH in ultracold 3He collisions

The interaction potential of a He-BH complex is investigated by the coupled-cluster single-double plus pertur-bative triples (CCSD (T)) method and an augmented correlation consistent polarized valence (aug-cc-pV)5Z basis set extended with a set of (3s3p2d1f1g) midbond functions. Using the five two-dimensional model potentials, the first three-dimensional interaction potential energy surface is constructed by interpolating along (r–r e ) by using a fourth-order polynomial. The cross sections for the rovibrational relaxation of BH in cold and ultracold collisions with 3 He atom are calculated based on the three-dimensional potential. The results show that the Δv =-1 transition is more efficient than the Δv =-2 transition, and that the process of relaxation takes place mainly between rotational energy levels with the same vibration state and the Δj =-1 transition is the most efficient. The zero temperature quenching rate coefficient is finite as predicted by Wigner’s law. The resonance is found to take place around 0.1–1 cm-1 translational energy, which gives rise to a step in the rate coefficients for temperatures around 0.1–1 K. The final rotational distributions in the state v = 0 resulting from the quenching of state (v = 1, j = 0) at three energies corresponding to the three different regimes are also given.     

Photoconductivity of CdS under high excitation - indicating no homogeneous Mott transition

Excitation spectra of photoconductivity in CdS crystal at He temperatures do not show the expected decrease of many order of magnitude in the excitonic region under intensities above 10 kW cm^-2. Agreement with the rate equations permits us to estimate the exciton-exciton ionization coefficient as c = 2 × 10^-10cm³s^-1. No indication of a homogeneous Mott transition exists up to intensities at which emission spectra are electron-hole plasma (or liquid) like.     

Influence of the nuclear bulk properties and the MIT bag constant on the phase transition to the quark gluon plasma

We consider the influence of the bulk properties of nuclear matter, namely the ground state incompressibility and the effective nucleon mass, and of the MIT bag constant on the phase transition from hadron matter to quark gluon plasma. It is mainly the effective nucleon mass which determines the stiffness of the equation of state and therefore also the behaviour of the phase transition curves. The energy densities in the coexistence region are found to increase for finite chemical potentials and softer equations of state up to 10 GeV/fm³. For small bag constants and for softer nuclear equations of state the phase boundary exhibits unusual deformations, due to the fact that the phase transition sets in already at pressures not too far from the saturation value. Although this would increase the experimental possibility to create the QGP, it is more likely that one must regard bag constants in the range of the original MIT value as not producing a realistic behaviour of the quark-hadron matter phase transition in the context of an MIT bag equation of state for the quark side.     

Quantum dynamics and kinetics of the abstraction reactions by H atoms of primary and secondary hydrogens in C3H8

The abstraction reaction of H atoms with propane molecules presents two concurrent channels. In this work we have determined the specific rate constants and the product branching ratios (BRs) between the two channels using quantum chemistry calculations and reduced dimensionality quantum dynamics. The potential energy surfaces were computed by treating explicitly the forming and breaking bonds during the reaction, and optimizing the geometries of all the remaining degrees of freedom. In this way, the dynamics of the reaction occurs on an effective reduced dimensionality hyper-surface accounting for the zero-point energy of the optimized degrees of freedom. Energies are calculated with the CCSD(T) method and the cc-pVTZ basis set, while frequencies are calculated with the MP2 method and the same basis set. The calculations give barrier heights of 0.46 (0.36) eV and the reactions are exothermic by 0.13 (0.25) eV for primary (secondary) hydrogens in C3H8. At room temperature, quantum tunnelling and zero-point effects are found to contribute more than one order of magnitude to the rate constants, when compared to purely classical transition state theory (TST) computations. The branching ratios show the importance of abstraction of secondary hydrogen in propane more significantly at a lower temperature in accord with experimental investigations.