Roger L. Wilkins

Monte Carlo Calculations of Reaction Rates and Energy Distributions Among Reaction Products. I. F+H2→HF+H

A three‐dimensional, classical trajectory calculation is made of the collision dynamics of the reaction F+H2(v, J)→HF(v′, J′)+H by means of the London‐Eyring‐Polanyi‐Sato (LEPS) potential energy surface. Monte Carlo procedures are used to start each collision trajectory. A discussion is presented of the temperature dependence of the relative rates of formation of vibrationally excited hydrogen fluoride. By means of this calculation, it can be predicted that 71% of the mean fraction of available energy will become vibration in HF, 10.5% will become rotation in HF, and 18.5% will become translation in the product. The probability that direct chemical reaction between atomic fluorine and molecular hydrogen will lead to the formation of the product HF molecule in the ground vibrational state v′=0 was found to be zero. The ratio k(v′=3)/k(v′=2) appears to be independent of temperature and has a value of 0.49, which is in excellent agreement with available experimental data. The ratio k(v′=2)/k(v′=1) has a slig...

Monte Carlo calculations of reaction rates and energy distribution among reaction products. II. H+HF(v) → H2 (v′) + F and H+HF(v) → HF(v′) + H

Rate constants are calculated for the reactions of atomic hydrogen with vibrationally excited hydrogen fluoride by analyzing the results of classical trajectories on a semiempirical London‐Eyring‐Polanyi‐Sato (LEPS) potential energy surface. Monte Carlo procedures are used to start each collision trajectory. Reaction rate constants are presented for direct reactions into specific vibrational states of the product H2 and HF molecules. By means of this calculation, it is predicted for the reactant HF molecule in the ν = 3 state that 11.3% of the mean fraction of available energy will become vibrational energy in H2, 1.2% will become rotational energy in H2, and 87.5% will become translational energy in the products. As the vibrational energy of the reactant HF molecule increases, the mean fraction of available energy which becomes vibrational energy of the product H2 molecule increases. For example, if the reactant molecule HF is in the v = 6 state, it is found that the mean fraction of available energy that will become vibrational energy in H2 is 35.1%, 8% will become rotational in H2, and 56.9% will become translational energy in the products. For the reactant HF molecule in the v = 3 state, 45% of the mean fraction of available energy will become vibrational energy in the product HF molecule, 0.4% will become rotational energy in HF, and 54.8% will become translational energy in the products. The de‐excitation of HF by H atoms is due to vibration‐translation energy transfer. Results of this trajectory calculation, indicate that (1) multiple quantum jumps are significant in the reactions of H atoms with vibrationally excited HF, and (2) chemical effects provide an important mechanism for the efficient relaxation of vibrationally excited HF by H atoms. Both theory and experiment indicate that the rate of deactivation of vibrationally excited HF by H atoms is very fast. Rate constants are provided for many reactions that have not been measured experimentally.

Mechanisms of Energy Transfer in Hydrogen Fluoride Systems.

Rate coefficients are calculated for the energy‐transfer processes that ocuur when HF(v1,J1) molecules collide with HF(v2, J2) molecules. Three‐dimensional classical trajectories of the collision dynamics of these energy‐transfer processes were calculated by means of a potential energy surface, which consists of a London–Eyring–Polanyi–Sato (LEPS) potential function for the short‐range interactions and a partial‐point‐charge, dipole–dipole function for long‐range interactions. This energy surface was used to predict an equilibrium geometry of the HF dimer. From the trajectory calculations it was predicted that the v→v energy‐transfer processes occur by means of Δv=±1 transitions and that the rate coefficients for the processes HF(v)+HF(v=0) →HF(v−1)+HF(v=1) decrease with increasing vibrational quantum number v. A calculation of the v→v rate for the reaction HF(v=1)+HF(v=1) →HF(v=0)+HF(v=2) indicates a value of 1.2×1013 cm3 mol−1 s−1 at 300 K. This process corresponds to near‐resonant vibration‐to‐vibratio...

Monte Carlo calculations of reaction rates and energy distributions among reaction products. III. H+F2→ HF+F and D+F2→ DF+F

A three‐dimensional classical trajectory calculation is made of the collision dynamics of the exothermic reactions H+F2(v, J)→ HF(v′, J′)+F and D+F2(v, J)→ DF(v′, J′)+F by means of a modified London‐Eyring‐Polanyi‐Sato (LEPS) potential energy surface. Trajectory calculations are used to establish the anti‐Morse parameters for a modified LEPS potential‐energy surface which produce the best agreement with previous experimental measurements of reaction rates and energy distributions among reaction products. Very good agreement is obtained with the experimental overall rate constant, the experimental prediction that the maximum vibrational level population of HF (v′) is achieved in v′ = 5, and the mean fraction of available energy entering vibration of the newly formed HF bond. The maximum vibrational level population of DF (v′) is achieved in v′ = 8. The mean fractions (fv′=Ev′/Etotal and fR′=EJ′/Etotal) of the total available energy entering vibration plus rotation are (1) for H+F2, fv′+fR′=(0.54+0.02)=...

Flow‐tube studies of vibrational energy transfer in HF(v)+HF, DF(v)+HF, and DF(v)+D2 systems

A medium‐pressure (1 Torr), large‐diameter (10 cm) flow tube has been used to measure rate coefficients at 298 °K for (a) total relaxation (sum of vibrational–vibrational and vibrational–rotational, translational processes) of HF(v=1, 2, 3, 4, and 5) by HF, (b) relaxation of DF(1, 2, 3, and 4) by HF, and (c) over‐all relaxation of DF(v=1, 2, 3, and 4) by D2. The chemically produced vibrationally excited HF or DF species have been studied by monitoring their vibrational–rotational emission in a fast‐flow system. The rate coefficient for the relaxation of HF(1) by HF is 5.3×104 sec−1⋅Torr−1. The measured rate coefficients for the deexcitation of HF(v=2, 3, 4, and 5) by HF are 5.3×105, 8.5×105, 8.8×105, and 2.8×105 sec−1⋅Torr−1, respectively. The rate coefficients for the vibrational–rotational, translational deexcitation from the upper vibrational levels of DF(v) by HF are found to have a nonlinear vibrational dependence. The rate coefficient for the relaxation of DF(v=1) by D2 is 1.35×104 sec−1⋅Torr−1.

Monte Carlo calculations of reaction rates and energy distributions among reaction products. IV. F+HF(ν) → HF(ν′)+F and F+DF(ν) → DF(ν′)+F

Rate constants are calculated for the vibrational relaxation HF(ν) and DF(ν) molecules by F atoms with ν = 1, 2, 3, and 6. Three‐dimensional classical trajectories of the collision dynamics of these reactions were calculated by means of a modified London‐Eyring‐Polanyi‐Sato (LEPS) potential energy surface used to calculate rate constants for the reactions between H atoms and F2 molecules, and D atoms and F2 molecules. The Monte Carlo procedure is used to start each collision trajectory. By means of this calculation, it is predicted for the reactant HF molecule in the ν = 2, J = 8 state that 13.3% of the mean fraction of available energy will become rotation in the product HF, 80.7% will become vibrational energy in the product HF, and 6% will become relative translational energy of the products. As the vibrational energy of the reactant HF molecule increases the mean fraction of available energy that becomes rotational energy increases slightly. For example, if the reactant molecule HF is in the ν = 6, J ...

Reaction rates and energy distributions among reaction products for the H+Cl2 and Cl+H2 reactions

Rate coefficients have been calculated for the bimolecular exchange reactions of H with Cl2 and Cl with H2. Three‐dimensional classical trajectories of the collision dynamics of these reactions have been calculated using London–Eyring–Polanyi–Sato (LEPS) potential energy surfaces. The results of this trajectory study are as follows. For the H+Cl2 reaction at room temperature, the relative rate coefficients for formation of HCl into specific vibrational states are: k (v′=1) =0.01, k (v′=2) =0.65, [k (v′=3) =1.0], k (v′=4) =0.10, and k (v′=5) ?0. The symbol v′ indicates the product HCl vibrational state. The relative rate coefficient k (v′=2)/k (v′=3) has a slight temperature dependence, and the other relative rate coefficients k (v′≠2)/k (v′=3) are temperature dependent. The mean fraction (?v′=Ev′/ Etotal and ?J′=EJ′/Etotal) of the total energy entering vibration plus rotation is ?v′+?J′= (0.46+0.05) =0.51. For the Cl+H2 (v=0) reaction, ?v′+?J′= (0.37+0.16) =0.53; and for Cl+H2(v=1), ?v′+?J′ = (0.57+0.11) ...

Temperature dependence of vibrational relaxation from the upper vibrational levels of HF and DF

A kinetic model of infrared laser‐induced fluorescence experiments has been used to simulate quenching coefficients between 300 and 2400 K for the vibrational relaxation of HF(v1) and DF(v1) by HF(v2=0) and DF(v2=0). This rotational nonequilibrium model is based on the predicted energy‐transfer mechanisms in hydrogen–fluoride and deuterium–fluoride systems reported earlier by Wilkins. The deactivation rates for the V→R processes for HF(v1)+HF(v2=0) and their isotopic analogs are predicted to scale as vn with n varying from 2.3 to 1.6 as v varies from 2 to 6. These quenching coefficients for V→R processes from the upper vibrational levels are predicted to have a temperature dependence very similar to that for V→R relaxation from the v=1 level. The results are discussed in relation to V→V energy transfer and V→R intramolecular energy conversion.

Flow tube measurements of H + HF(V) deactivation rates

Abstract : A medium-pressure flow tube is used to determine the rate constants for vibrational deactivation of HF(v = 1, 2, 3) by H-atoms by monitoring the HF vibration-rotation emission. The deactivation of HF(v) by H-atoms is found to be a very efficient energy-transfer process. The experimental results are compared with available theoretical data of Wilkins.

Temperature dependence of HF(v1=1)+HF(v2=0) vibrational relaxation

A kinetics model of infrared laser‐induced fluorescence experiments has been used to simulate the experimental quenching rate coefficients reported between 300 and 4000 K for the vibrational relaxation of HF(v1=1) by HF. This rotational nonequilibrium model is based on the predicted energy‐transfer mechanisms in hydrogen fluoride systems reported in a trajectory study by Wilkins. This model includes v→R, R→v, R→ (R′, T′), and (R′, T′) →R energy‐transfer processes. A key process is vibrational‐to‐rotational intramolecular energy transfer in which HF(v1=1,J1) terminates on high J′ 1 states ofv′1=0. The calculated temperature‐ dependent quenching rate coefficient for self relaxation of HF(v1=1) at temperatures between 300 and 2000 K is dependent on v→R andR→v energy‐transfer processes, and beyond 2000 K only on v→R processes. The temperature dependence observed for HF(v1=1) vibrational relaxation by HF(v2=0) is explained by this model. For the high roational states in the v′ 1=0 manifold, this model predicts...