Harmonic Rate Constants Research Articles

Anharmonic effect of the decomposition reaction of the CF3CCl2O radical

The rate constant of the unimolecular decomposition reaction of the CF3CCl2O radical was calculated by using the method proposed by Yao and Lin (YL method). Two important channels of decomposition occurring via C–C and C–Cl bond scission were investigated. The results show that C–Cl bond scission is the dominant channel during the decomposition of the CF3CCl2O radical. Especially, the reasonable anharmonic effect on the decomposition reaction was investigated. The results show that the harmonic rate constants are higher than those of the anharmonic case in both microcanonical and canonical systems. The anharmonic effect is more evident with increasing energy.

Anharmonic effect of the dissociation rate constant of the unimolecular reactions of CH2XCHFO (X = H, F)

This study examines six unimolecular reactions of CH2XCHFO (X = H, F). The geometries of the reactions are optimized with Gaussian 03. The calculated barrier heights show that bond C–C′ scission, CH2XCHFO (X = H, F) → CH2X + CHFO (R1), dominates the decomposition of CH2XCHFO. For X = H and X = F, the barrier heights of (R1) are 13.37 and 9.67 kcal mol−1, respectively. The YL (Yao and Lin) method is used to calculate the anharmonic and harmonic rate constants of the unimolecular reactions. The results clearly demonstrate the anharmonic effect of these reactions. In the microcanonical case, for (R1) (X = H), the total energy is from 42.78 to 144.84 kcal mol−1. The corresponding anharmonic rate constants are from 1.57 × 1012 to 2.52 × 1013 s−1 and the harmonic rate constants are from 1.52 × 1012 to 2.52 × 1013 s−1.

Anharmonic effect of dissociation rate constant of the ethoxy radical

The anharmonic effect of rate constants is studied in regard to the unimolecular dissociation reaction of ethoxy radical. Due to the high strain energy of the isomerization transition states of ethoxy radical, the present Letter only deals with two dissociation channels, the C–C bond and the C–H bond scission, with the YL method. Our results show that the calculated harmonic rate constants are in reasonable agreement with the values from earlier theoretical studies. It turns out in particular that the anharmonic effect is not evident at either low energy or low temperature, while it becomes prominent with increasing energy and temperature.

Anharmonic RRKM Calculation for the Dissociation of (H2O)2H+ and Its Deuterated Species (D2O)2D+

Investigations on the dissociation kinetics of hydrated protonium ions, (H(2)O)(2)H(+) and their deuterated species (D(2)O)(2)D(+), are reported based on the harmonic and anharmonic oscillator model using the transition state theory and ab initio calculations. We find that the dissociation of (H(2)O)(2)H(+) and (D(2)O)(2)D(+) exhibits a distinct threshold behavior due to the existence of activation energies. Moreover, the deviation between the harmonic and anharmonic dissociation rate constants becomes larger in the high energy or temperature range, with the rate constants becoming unreasonably large under the harmonic oscillator model. The isotope effect is found to become more distinct but only in the case of the anharmonic oscillator model. These results show that the anharmonic Rice-Ramsperger-Kassel-Marcus (RRKM) theory can provide a reasonably good description for the dissociation of (H(2)O)(2)H(+) and (D(2)O)(2)D(+). Furthermore, a theoretical model to demonstrate the principle of vibrational predissociation spectroscopy (VPS) is established from the viewpoint of RRKM theory and applied in determining the experimental conditions and understanding the role of the dissociation rate constant k(E) played in the VPS experiment, using (H(2)O)(2)H(+) and (D(2)O)(2)D(+) as examples.

ANHARMONIC EFFECT OF UNIMOLECULAR REACTION:HCO2→H+CO2WITH RRKM THEORY

Anharmonic and harmonic rate constants were calculated in the unimolecular reaction HCO2→ H + CO2with Yao and Lin (YL) method. In microcanonical case, the total number of states and density of states increase reasonably with the increasing of the total energy and the temperature. Both in microcanonical and canonical cases, the harmonic rate constants are much higher than those for anharmonic cases, especially in the case of high total energy and temperature, which indicates that anharmonic effect of the reaction is so significant that it is not negligible. The results obtained in this research show that the YL method works well for such unimolecular reactions.

Dissociation Rate Constant of the Hydrogen Fluoride Dimer by the ab Initio Anharmonic RRKM Theory

The dissociation rate constants for hydrogen fluoride dimers are calculated using the YL method, proposed by Yao and Lin (Yao, L.; Mebel, A. M.; Lu, H. F.; Neusser, H. J.; Lin, S. H. J. Phys. Chem. A 2007, 111, 6722). The dividing surface method and RRKM theory are also used to obtain pseudo-transition states and rate constants, respectively. For the dissociation of HF dimers, the anharmonic rate constants are around 3.02 x 10(10) to 3.46 x 10(12) s(-1), while the harmonic rate constants are in the range of 2.93 x 10(10) to 1.66 x 10(13) s(-1), at a temperature range of 243-1000 K, for the canonical case. For the microcanonical case, the anharmonic rate constants are in the range of 1.91 x 10(12) to 1.32 x 10(13) s(-1) and the harmonic rate constants are in the range of 1.89 x 10(12) to 4.93 x 10(13) s(-1), with a total energy range of 1338-4500 cm(-1). Both harmonic and anharmonic rate constants are only comparable to the experimental results 0.5 x 10(10) s(-1) and 1 x 10(11) s(-1) in an inert gas bath at room temperature. In this case the harmonic and anharmonic rate constants show similar results in this calculation. The results of this paper indicate that the YL method is suitable for calculating dissociation rate constants of small flexible HF dimers and the anharmonic effect should be included.

Anharmonic Semiclassical Variational Transition-State Theory Rate Constant Model for H Atom Association with Different Sites on the Diamond {111} Surface

Canonical variational transition-state theory (CVTST) rate constants, for H atom association to terrace and ledge sites on the diamond {111} surface, are calculated using anharmonic energy levels for the transitional modes orthogonal to the reaction path. The reaction path and transitional modes, required for the calculation, are defined by the reaction path Hamiltonian. A separable Einstein−Brillouin−Keller (EBK) semiclassical quantization model is used to determine anharmonic energy levels for the transitional modes. The free energy, calculated from these anharmonic levels, has multiple maxima along the reaction path, which become more pronounced as the temperature is increased. CVTST association rate constants, calculated from the highest maxima, are somewhat larger than the harmonic CVTST rate constants. A canonical unified statistical theory (UST), which incorporates the effect of the multiple free energy maxima and minima, gives association rate constants in remarkably good agreement with those determined from quasiclassical trajectory calculations. The rate constant for the terrace site is significantly larger than those for the ledge sites. The multiple maxima and minima in the free energy curve result from strong couplings between the transitional bending and surface modes, which changes the eigenvectors for the transitional modes as the reactive system moves along the reaction path. This work illustrates the possible importance of coupling between transitional and conserved modes in VTST calculations for barrierless association reactions.

Harmonic and anharmonic rate constants and transmission coefficients obtained from ab initio data

Recent ab initio information of Kraka and Dunning on the reaction OH+H2→H2O+H is used to construct a potential energy surface in the vicinity of the reaction path. The resultant energy surface reproduces the ab initio reactant and product properties and provides a good fit to the ab initio data in the interaction region. Anharmonic vibrational energy levels involving the bound degrees of freedom orthogonal to the reaction coordinate are obtained using perturbation theory through second order for cubic terms and first order for quartic terms, with resonance effects removed. These energy levels are used in the calculation of transmission coefficients and thermal rate constants over the temperature range from 200 to 2400 K. The results are compared with those obtained from harmonic vibrational energy levels.

Reaction-path dynamics with harmonic vibration frequencies in curvilinear internal coordinates: H+trans-N2H2→N2H+H 2

This paper presents a general method for treating doubly degenerate bending vibrations of bonds with 180 deg bond angles in curvilinear coordinates along a reaction path. The new treatment improves the generalized normal mode frequencies needed for rate constant calculations with variational transition state theory and for multidimensional semiclassical tunneling calculations. We apply this method to calculate harmonic vibrational frequencies and rate constants for the reaction H+trans-N2H2→N2H+H2. The new results are compared to earlier calculations employing rectilinear Cartesian coordinates in order to evaluate the sensitivity of the calculations to the coordinate system chosen.

Comparison of quantum and semiclassical variational transition state models for the HO2→H+O2 microcanonical rate constant

Comparisons, for J=0, are made between HO2→H+O2 reaction path anharmonic energy levels, variational transition states, and unimolecular rate constants determined by three different semiclassical models and a quantum mechanical model. The semiclassical models are based on the reaction path Hamiltonian. However, to determine anharmonic energy levels, the harmonic potential of this Hamiltonian is replaced by the actual anharmonic DMBE IV potential for the HO2 system. Two of the semiclassical models use Einstein–Brillouin–Keller (EBK) quantization to determine energy levels for motion orthogonal to the reaction path; i.e., one model neglects anharmonic coupling between modes, while the other retains all the coupling. The third semiclassical model is based on a quartic expansion of the potential and second-order perturbation theory to determine the energy levels. A comparison of the results of these three semiclassical models shows that anharmonic coupling between modes orthogonal to the reaction path is unimportant for HO2 dissociation. The separable EBK model gives a RRKM rate constant versus energy in very good agreement with that obtained from a quantum mechanical calculation which retains full coupling between modes in determining the reaction path energy levels. If anharmonicity is treated, the reaction path Hamiltonian and its vibrator transition state give accurate RRKM rate constants for HO2 dissociation. Rate constants calculated with the flexible transition states model are in very good agreement with those of the semiclassical and quantum vibrator transition state models, if the O2 stretch conserved mode is treated as an anharmonic oscillator in the flexible model. However, in contrast to the vibrator transition state models, ‘‘steps’’ are not observed in the rate constants for the flexible model, since the transitional mode is treated classically. Harmonic and anharmonic rate constants are compared for both the vibrator and flexible transition state models.