Quantum chemical and conventional TST calculations of rate constants for the OH + alkane reaction

Reactions of OH with methane, ethane, propane, i-butane, and n-butane have been modeled using ab initio (MP2) and hybrid DFT (BHandHLYP) methods, and the 6-311G(d,p) basis set. Furthermore, single-point calculations at the CCSD(T) level were carried out at the optimized geometries. The rate constants have been calculated using the conventional transition-state theory (CTST). Arrhenius equations are proposed in the temperature range of 250–650 K. Hindered Internal Rotation partition functions calculations were explicitly carried out and included in the total partition functions. These corrections showed to be relevant in the determination of the pre-exponential parameters, although not so important as in the NO₃ + alkane reactions [G. Bravo-Pérez, J.R. Alvarez-Idaboy, A. Cruz-Torres, M.E. Ruíz, J. Phys. Chem. A 106 (2002) 4645]. The explicit participation of the tunnel effect has been taken into account. The calculated rate coefficients provide a very good agreement with the experimental data. The best agreement for the overall alkane + OH reactions seemed to occur when the BHandHLYP geometries and partition functions are used. For propane and i-butane, in addition to the respective secondary and tertiary H-abstraction channels, the primary one has been considered. These pathways are confirmed to be significant in spite of the large differences in activation energies between primary and secondary or primary and tertiary channels, respectively of propane and i-butane reactions and should not be disregarded.     

Semiclassical calculation of nonadiabatic thermal rate constants: application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.     

Evaluation of the rate constants in chemical reactions

This article is concerned with the application of a new method to recover the rate constants in chemical reactions. The method is based on treating the unknown parameters as time dependent. With appropriate experimental data the unknown rate constants are guided from an arbitrary initial condition to their true value at a final time. An explicit equation describing the time evolution of the parameters is obtained by minimizing the error along the trajectory. The method leads to an iterative algorithm which is described in detail. Numerical results with the method indicate that accurate estimates of the rate constants can be obtained directly from experimental data. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 151–159, 1998.     

A semiclassical reactive flux method for the calculation of condensed phase activated rate constants

A semi classical reactive flux algorithm for calculating thermally activated rate constants is presented which is based on a semi-classical transition state theory due to Chapman, Garrett and Miller [J. Chem. Phys. 63 (1975) 2710]. This reactive flux technique, when combined with the semiclassical TST, enables one to describe dynamical recrossings of the transition state on the same footing as tunneling effects. Most importantly, the method is readily applied to nonlinear multidimensional systems over a wide range of temperatures. It will be shown that the method works very well for a variety of existing models.     

Path-integral calculations of heavy atom kinetic isotope effects in condensed phase reactions using higher-order Trotter factorizations

A convenient approach to compute kinetic isotope effects (KIEs) in condensed phase chemical reactions is via path integrals (PIs). Usually, the primitive approximation is used in PI simulations, although such quantum simulations are computationally demanding. The efficiency of PI simulations may be greatly improved, if higher-order Trotter factorizations of the density matrix operator are used. In this study, we use a higher-order PI method, in conjunction with mass-perturbation, to compute heavy-atom KIE in the decarboxylation of orotic acid in explicit sulfolane solvent. The results are in good agreement with experiment and show that the mass-perturbation higher-order Trotter factorization provides a practical approach for computing condensed phase heavy-atom KIE.     

Intermolecular force constants of hcn in the condensed phase

A simple theory of linear lattice is applied to the hydrogen bonded linear chain system of HCN to calculate the intermolecular force constants at different temperatures in the condensed phase. The strong CN bond is assumed to remain unperturbed in the hydrogen bond formation. The sharp change in intermolecular force constant while passing from the crystalline to the liquid phase is interpreted as a characteristic of this phase transition (fusion).     

Calculation of the rate constants of diffusion-controlled chemical reactions for reagents of arbitrary shape

A method of describing small-size reactant diffusion in the presence of any amount of arbitrary located sinks is developed. The propagation function of mobile reagent (MR) in such a system is found. The developed method was used to calculate rate constants of bimolecular reactions of MRs with absorbents (traps) having arbitrary shape. The procedure of calculation of the rate constant has been reduced to integral equation for flux density towards a trap which is MRs' absorber. If small parameters exist, the expansion in powers of these parameters is possible. The bimolecular rates were calculated for traps of different shape. The equation was obtained which permits to determine the asymptotic time dependence of rate constants.     

Comparison between the Landau-Teller and flux-flux methods for computing vibrational energy relaxation rate constants in the condensed phase

The calculation of vibrational energy relaxation (VER) rate constants in the condensed phase is usually based on the Landau-Teller formula, which puts them in terms of the Fourier transform, at the vibrational frequency, of the autocorrelation function of the force exerted on the relaxing mode by the bath modes. An alternative expression for the VER rate constant puts it in terms of the autocorrelation function of the vibrational energy flux. In this paper, we compare the predictions obtained via those two methods in the case of iodine in liquid xenon. We find that the computational cost underlying both methods is comparable and that they predict similar VER rates. However, while the calculation of the VER rate via the Landau-Teller formula is somewhat more direct, the predictions obtained via the flux-flux formula are in somewhat better agreement with the VER rates obtained from nonequilibrium molecular dynamics simulations.     

Radical-olefin addition reactions in condensed phase

A study has been made of the rate constant for the reaction The states of the product have quasilevels E_n — i_n, which, depending on the heat of reaction, may be in resonance with the state of the reactants after surmounting the activation barrier. Because of this, there is no monotonic variation of the propagation rate constant, even as a function of the heat of reaction; the behavior of the rate constant has a resonance character. The results obtained in this investigation are in good agreement with experimental data.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 1, pp. 25–32, January–February, 1990.     

Methods for improving models for condensed phase equilibrium calculations

Local composition models like UNIQUAC, NRTL and the UNIFAC group contribution method are used the world over in the synthesis and design of separation processes, as well as for a large number of other applications of industrial interest. They can qualitatively describe the equilibrium behaviour of systems of different complexities but, sometimes, not with the precision required for the design of separation equipment. Regrettably, this precision is not even achieved for the LLE of many conventional type 1 and some type 2 ternary systems. High deviations in correlation results are not rare, thus showing that more capable and flexible models are needed. The analysis of the topology of the Gibbs energy of mixing function, and therefore the knowledge of the geometrical conditions that this function has to fulfil, is a valuable tool that has allowed avoiding inconsistencies in the use of the existing methods, to ascertain their capabilities and limitations to reproduce complex systems and additionally to suggest new models that improve the flexibility and accuracy needed. In this work, a simple equation based on the NRTL model, that takes into account such topological conditions, is proposed and its capabilities are tested with selected systems.     

Point-core approximation effects on quantum chemical calculations of vibrational force constants

Using adequate functions to represent core charge densities, we have developed an expression to compute second derivatives of core-core energy with respect to the intermolecular distance. Thus, it is possible to study the influence of point-core approximation (PCA) on force constants. Corrections to this approximation are analytically expressed, so one can their values in a systematic way. Results for a selected series of bonds between atoms of the first three rows of the periodic table allow us to assess the reliability of PCA within usual internuclear distances.     

Algorithm to evaluate rate constants for polyatomic chemical reactions. II. Applications

A new implementation of the classical reaction path-Liouville algorithm, as developed by the authors in the preceding paper, is tested with several chemical reactions. It results in a simple algorithm, which may be used straightforwardly for the calculation of rate constants, as well as to extract dynamical information of the reactive process. Results for the rate constant have been compared to transition state calculations, confirming that it provides a new lower bound than traditional transition state estimates. In addition, the time-dependence of the kinetic energy stored in vibrational modes has been studied, as a means of characterizing the importance of each normal mode inside the reaction mechanism.     

Estimation of rate constants in nonlinear reactions involving chemical inactivation of oxidation catalysts

Over the last decades, copious work has been devoted to the development of small molecule replicas of the peroxidase enzymes that activate hydrogen peroxide in metabolic and detoxifying processes. TAML activators that are the subject of this study are the first full functional, small molecule peroxidase mimics. As an important feature of the catalytic cycle, TAML reactive intermediates (active catalysts, Ac) undergo suicidal inactivation, compromising the functional catalysis. Herein the relationship between suicidal inactivation and productive catalysis is rigorously addressed mathematically and chemically. We focus on a generalized catalytic cycle in which the TAML inactivation step is delineated by its rate constant $k_{\mathrm{i}}$ where the revealing data is collected in the regime of incomplete conversion of substrate (S) artificially imposed by the use of very low catalyst concentrations. $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} \hbox {Resting catalyst (Rc)} + \hbox {Oxidant} \rightarrow \hbox {Ac} &{} (k_{\mathrm{I}})\\ \hbox {Ac + Substrate (S)}\rightarrow \hbox {Rc}+\hbox {Product} &{} (k_{\mathrm{II}})\\ \hbox {Ac} \rightarrow \hbox {Inactive catalyst} &{} (k_{\mathrm{i}}) \end{array} \right. \end{aligned}$$ The system exhibits a nonlinear conservation law and is modeled via a singular perturbation approach, which is used to obtain closed form relationships between system parameters. A new method is derived that allows to compute all the rate constants in the catalytic cycle, $k_{\mathrm{I}},k_{\mathrm{II}}$ , and $k_{\mathrm{i}}$ , with as little as two linear least squares fits, for the minimal data set collected under any conditions providing that the oxidation of S is incomplete. This method facilitates determination of $k_{\mathrm{i}}$ , a critical rate constant that describes the operational lifetime of the catalyst, and greatly reduces the experimental work required to obtain the important rate constants.The approach was applied to the behavior of a new TAML activator, the synthesis and characterization of which are also described.     

Quantum chemical prediction of pathways and rate constants for reaction of cyanomethylene radical with NO

High-level ab initio calculations have been performed to study the mechanism and kinetics of the reaction of the cyanomethylene radical (HCCN) with the NO. The species involved have been optimized at the B3LYP/6-311++G(3df,2p) level, and their corresponding single-point energies are improved by the CCSD(T)/aug-cc-PVQZ//B3LYP/6-311++G(3df,2p) approach. From the calculated potential energy surface, we have predicted the favorable pathways for the formation of several isomers of a HCCN-NO complex. Barrierless formation of HCN + NCO (P1) is also possible. Formation of HCNO + CN (P3) is endoergic but may become significant at high temperatures. To rationalize the scenario of our calculated results, we also employ the Fukui functions and hard-and-soft acid-and-base (HSAB) theory to seek possible clues. The predicted total rate coefficient, k(total), at He pressure 760 Torr can be represented with the equation k(total) = 1.40 × 10(-7) T(-2.01) exp(3.15 kcal mol(-1)/RT) at T = 298-3000 K in units of cm(3) molecule(-1) s(-1). The predicted total rate coefficients at some available conditions (He pressures of 6, 18, and 30 Torr in the temperature of 298 K) are in reasonable agreement with experimental observation. In addition, the rate constants for key individual product channels are provided in different temperature and pressure conditions.     

Theoretical calculations of the unimolecular canonical rate constants

Microcanonical rate constants k(E) and canonical rate constants k(T) for unimolecular reactions have been obtained through the calculations of cumulative reaction probabilities N(E) with the unsymmetrical Eckart potential tunneling correction. By way of example, the reactions HCN→CNH (I) and FNC→NCF (II) have been employed. For reaction (I), the calculated rate constants are in agreement with the experimental data; for reaction (II), the results are in accordance with the rate constants kCVT/MEPSAG(T) calculated by the common program POLYRATE.     

Linking the historical and chemical definitions of diabatic states for charge and excitation energy transfer reactions in condensed phase

Marcus theory of electron transfer (ET) and Fo?rster theory of excitation energy transfer (EET) rely on the Condon approximation and the theoretical availability of initial and final states of ET and EET reactions, often called diabatic states. Recently [Subotnik et al., J. Chem. Phys. 130, 234102 (2009)], diabatic states for practical calculations of ET and EET reactions were defined in terms of their interactions with the surrounding environment. However, from a purely theoretical standpoint, the definition of diabatic states must arise from the minimization of the dynamic couplings between the trial diabatic states. In this work, we show that if the Condon approximation is valid, then a minimization of the derived dynamic couplings leads to corresponding diabatic states for ET reactions taking place in solution by diagonalization of the dipole moment matrix, which is equivalent to a Boys localization algorithm; while for EET reactions in solution, diabatic states are found through the Edmiston-Ruedenberg localization algorithm. In the derivation, we find interesting expressions for the environmental contribution to the dynamic coupling of the adiabatic states in condensed-phase processes. In one of the cases considered, we find that such a contribution is trivially evaluable as a scalar product of the transition dipole moment with a quantity directly derivable from the geometry arrangement of the nuclei in the molecular environment. Possibly, this has applications in the evaluation of dynamic couplings for large scale simulations.     

Quantitative rate constants for radical reactions in the nanopores of cotton

The understanding of radical reactions in nanostructured materials is important for developing new synthetic procedures and controlling degradation reactions. To develop this area, an easy method for measuring quantitative rate constants of some radical reactions in nanostructures is required. A simple method for measuring the rate constant of dye bleaching, kdye, by organic radicals in such materials is introduced, involving the measurement of microsecond bleaching kinetics by diffuse reflectance spectroscopy, following laser flash creation of the radicals. Using wet and dry cotton as model substrates, we obtained kdye of 2-hydroxy-2-propyl and 1-hydroxy-1-cyclohexyl radicals with reactive red 3 and reactive orange 4 and compared them to solution-phase values. Surprisingly, the reactions in cotton follow simple liquid-phase kinetics and are diffusion-controlled. A cage effect in cotton is also found.     

Ion–molecule reactions by chemical ionization: Determination of rate constants

Tungsten hexacarbonyl was studied by chemical ionization mass spectrometry using carbon monoxide as reagent gas. The variation of the relative abundances of ions as a function of reactant gas pressure was used for evaluating the relative rate constants for consecutive reactions. The results are in agreement with the rate constant ratios obtained from ion trap mass spectrometric data.