A comparison of various methods for calculating unimolecular reaction rate constants

A test of the Kassel quantum expressions for unimolecular rate constants and densities of vibrational states is described. Rate constants are calculated for nine reactions previously used in such tests, over a wide range of temperatures and pressures. The Kassel expression using the geometric mean of the molecular vibration frequencies is generally found to give better results than that using the arithmetic mean.     

Comparison between hydrogen-transfer and fluoro-transfer reactions on the microcanonical unimolecular rate constants

The microcanonical rate constants for the hydrogen-transfer process of HCCF (reaction 7) and the fluoro-transfer process of FCCF (reaction 8) are carried out with tunneling correction and curvature correction. The results show that the tunneling effects and curvature effects on the rate constant of reaction 7 is quite different from that of reaction 8. The rate constants for different rotational states are also studied for these reactions.     

Implementation of a microcanonical variational transition state theory for direct dynamics calculations of rate constants

Calculation of microcanonical rate constants has been an important field in chemical dy-namic studies for many years because it can be used not only to give good prediction of rate con-stants in microcanonical assembly, but also to calculate rate constants with certain conserved quantum numbers such as the total angular momentum, and in turn, can be easily converted into thermal rate constants[1—3]. The widely used method for calculating microcanonical rate constants of unimolecular reac-tions…     

氟代乙炔氢迁移反应微正则系综速率常数的计算

以氟代乙炔的氢迁移反应为例, 计算了隧道效应、曲率因子和转动选态对微正则系综单分子反应速率常数的影响。结果表明, 在低能区域, 隧道效应和曲率因子对反应速率有较大影响, 均使反应速率增加, 而在高能区域作用不明显。与此同时还研究了不同对称态下的反应速率常数, 结果表明, 本例中的两对称态(A'态和A"态)的反应速率常数在能量较低时差异较大, 随能量升高, 两者趋于相等。     

Improved Whitten-Rabinovitch approximation for the Rice-Ramsperger-Kassel-Marcus calculation of unimolecular reaction rate constants for proteins

The Whitten-Rabinovitch (WR) approximation used in the semi-classical calculation of the Rice-Ramsperger-Kassel-Marcus (RRKM) unimolecular reaction rate constant was improved for reliable application to protein reactions. The state sum data for the 10-mer of each amino acid calculated by the accurate Beyer-Swinehart (BS) algorithm were used to obtain the residue-specific correction functions (w). The correction functions were obtained down to a much lower internal energy range than reported in the original work, and the cubic, rather than quadratic, polynomial was used for data fitting. For a specified sequence of amino acid residues in a protein, an average was made over these functions to obtain the sequence-specific correction function to be used in the rate constant calculation. Reliability of the improved method was tested for dissociation of various peptides and proteins. Even at low internal energies corresponding to the RRKM rate constant as small as 0.1 s-1, the rate constant calculated by the present method differed from the accurate BS result by 60% only. In contrast, the result from the original WR calculation differed from the accurate result by a factor of 3000. Compared to the BS method, which is difficult to use for proteins, the main advantage of the present method is that the RRKM rate constant can be calculated instantly regardless of the protein mass.     

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.     

A metropolis Monte Carlo method for computing microcanonical statistical rate constants

A new method of computing microcanonical statistical rate constants is presented. The method utilizes the Metropolis Monte Carlo algorithm in a manner which circumvents some of the numerical inefficiency associated with other Metropolis and “shot-gun” Monte Carlo based schemes. It is therefore expected to be useful in studies of many degree of freedom systems where numerical efficiency is crucial. Optimization of the method efficiency with respect to its adjustable parameters is examined in detail, both theoretically and in a numerical study of the T-shaped Ar₃ “inversion” process. The energy dependence of the T-shaped Ar₃ inversion rate is studied in a sample application of the method. An application to full three dimensional Ar₃ will be presented in a future study.     

Evaluation of unimolecular rate constants for some outer-sphere electrochemical reactions

Unimolecular rate constants, k_et (s^?1), and transfer coefficients, α_cet, for the outer-sphere electroreduction of several Co(III) ammine and ethylenediamine complexes have been evaluated by electrostatically adsorbing the reactants at silver electrodes coated with chloride or bromide monolayers. Sufficiently strong diffuse-layer adsorption is thereby produced so to enable k_cet and α_cet to be determined by means of linear sweep voltammetry, employing sufficiently fast sweep rates (10–100 V s^?1) and dilute reactant concentrations (≤ 50 μM) so that the bulk solution reactant contributes negligibly to the observed faradaic transients. Comparison with corresponding rate constants and transfer coefficients for the solution reactants enables the influence of precursor-state stability upon the latter rate parameters to be assessed.     

Molecular beam measurements of small specific rate constants for unimolecular reactions

The investigation of unimolecular reactions with small rate constants is difficult owing to competing processes (inelastic collisions and bimolecular reactions) and the diffusion of reactant and product molecules out of the detection volume. For this reason, a new experimental approach for the measurement of specific rate constants in a molecular beam experiment has been exploited; instead of monitoring the temporal change of intensity as in a cell experiment, we monitor the spatial change along the molecular beam axis after laser excitation. For a given particle velocity the flight path between excitation and detection region defines the reaction time. By varying the distance the specific rate constant can be determined directly both from the decrease in the number density of reactant molecules as well as from the increase in product molecules. As a model system, the laser-induced (λ = 193 nm) photodissociation of mesitylene (trimethylbenzene) is studied. Previous experiments on the specific rate constant of mesitylene at this excitation energy differ between each other by about a factor of ten. By combining the new results with measurements at higher excitation energies, rate constants over a range of two orders of magnitude are now available for this reaction. The differences between the various experimental results are discussed within the framework of a statistical theory.     

A general computer approach for calculating rate constants from near-equilibrium kinetic studies

A general computer approach for estimating rate constants from relaxation times is described. The programme CORNEK is essentially a least-squares refinement programme applied to non-linear systems. It uses directly the differential forms of the first derivatives of mass-balance and rate equations, thus avoiding the time-consuming derivations of near-equilibrium rate equations. The programme has been tested for binary systems such as Cu-histamine, Cu-serine, and the ternary system Cu-histamine-serine.     

Intramolecular conversions. V. Rational rate constants for reversible unimolecular reactions

The available RRKM programs which cover the full pressure range (high → low-pressure limits) were written for nonreversible reactions. For reversible reactions the correct shapes of the fall-off curves can be estimated by applying a correction factor to the RRKM bimolecular rate constant, which depends on a ratio of state densities at the potential maximum. It is proposed that the analysis of such systems in terms of relaxation kinetics provides a more rational treatment, free of the ambiguities associated with specifying a “transition state.”     

An efficient solution of weak-collision master equations in thermal unimolecular reaction rate theory

A new finite-basis-set method of solving the weak-collision master equation of thermal unimolecular reactions in the general pressure regime is presented. Consecutive sections of the equilibrium probability density are used as basis functions. Significant advantages in terms of efficiency and applicability are obtained. Representative calculations are performed to illustrate the method's convergence properties and storage requirements. Calculations of collisional efficiency factors in the low-pressure limit β₀ and weak-collision broadening factors F^WC(ω) are performed to offer a simple concise representation of weak-collision effects. It is noted that weak-collision effects can be incorporated into fall-off curves with an accuracy of within an order of magnitude by simple scaling of the strong-collision fall-off curves. However, for accurate representation of weak-collision effects the weak-collision broadening must be taken into account.     

An analytic model for the optical properties of gold

A simple analytic model for the optical properties of gold is proposed. The model includes a minimum set of parameters necessary to represent the complex dielectric function of gold in the visible and near-uv regions. Explicit values for the parameters to reproduce the Johnson and Christy data [Phys. Rev. B 6, 4370 (1972)] on the optical properties of gold are provided.     

A novel method for calculating rate constants of diffusion-influenced reactions

In the present work we suggest a method for calculating rate constants of chemical processes affected by mobility of reactants. The method is based on the encounter theory. Unlike the widely accepted model of collision complexes it provides a general formal solution for practically arbitrary reaction scheme.     

An analytic model for the excess properties of binary liquid mixtures

A model has been devised to analyse excess property data for binary liquid mixtures. The model embodies the concept of the segmentation of the total composition range into three distinct regions. Results are given for the analyses of Δ$\text{V}$, Δ$\text{H}$ and Δν for the acetonitrile-water and dimethylsulfoxide-water systems.     

An improved computer program for calculating formation constants of ligand complexes from pH data

Several improvements are made to available computer programs for calculating formation constants from pH data. The most important features are wide portability of program among computers, ability to optimize any parameter in the model equations and to fix any parameters (including stepwise formation constants) to a constant, and options to allow for variations in thermodynamic activity of ions and to fit pH after fitting the volume of added reagent. The latter feature was used with synthetic data to explore the effects of random errors in either reagent volume or pH or both. Whereas fits to reagent volume will usually be more accurate for systems with pK_a values near 7, this is not the case for systems with pK_a values which differ by > 2.0 from 7.     

An analytic model for atomic clusters

The paper presents an analytic model which is based on approximation of the catchment basins in cluster potential energy surface by structures of ash-tray type. In order to see how the quantities to be specified relate to those obtained by means of numerical computation, predictions for the Ar₁₃ caloric curve are made and they are compared with computer simulation data.     

Direct measurement of near-threshold rate constants for unimolecular dissociation of CF3I after IR multiphoton excitation

Excited-state populations of CF₃I after IR multiphoton excitation were monitored by time-resolved hot-band UV absorption spectroscopy. Using a calibration of the spectrum by shock-wave experiments, the absorption changes during the laser pulse are analyzed with respect to excited-state populations and dissociation at higher excitation energies. Dissociation of molecules near threshold is detected under collision-free conditions by absorption changes after the laser pulse. At higher pressures, absorption signals after the pulse are markedly influenced by energy transfer between excited and cold molecules. The measured dissociation rate constants near threshold are consistent with statistical calculations of k(E,J), showing pronounced rotational dependence.