arXiv subjects

David Z. Goodson

Publications and source records attributed to David Z. Goodson.

2 recordsLinked to original sources

arXiv1997

A Simple Method for Calculating Quantum Effects on the Temperature Dependence of Bimolecular Reaction Rates: An Application to $CH_4 + H \to CH_3 + H_2$

The temperature dependence of the rate of the reaction CH_4+H \to CH_3+H_2 is studied using classical collision theory with a temperature-dependent effective potential derived from a path integral analysis. Analytical expressions are obtained for the effective potential and for the rate constant. The rate constant expressions use a temperature-dependent activation energy. They give better agreement with the available experimental results than do previous empirical fits. Since all but one of the parameters in the present expressions are obtained from theory, rather than by fitting to experimental reaction rates, the expressions can be expected to be more dependable than purely empirical expressions at temperatures above 2000 K or below 350 K, where experimental results are not available.

physics.chem-ph↗

arXiv1997

Dimensional perturbation theory for vibration-rotation spectra of linear triatomic molecules

A very efficient large-order perturbation theory is formulated for the nuclear motion of a linear triatomic molecule. To demonstrate the method, all of the experimentally observed rotational energies, with values of $J$ almost up to 100, for the ground and first excited vibrational states of CO$_2$ and for the ground vibrational states of N$_2$O and of OCS are calculated. All coupling between vibration and rotation is included. The perturbation expansions reported here are rapidly convergent. The perturbation parameter is $D^{-1/2}$, where $D$ is the dimensionality of space. Increasing $D$ is qualitatively similar to increasing the angular momentum quantum number $J$. Therefore, this approach is especially suited for states with high rotational excitation. The computational cost of the method scales only as $JN_v^{5/3}$, where $N_v$ is the size of the vibrational basis set.

physics.chem-ph↗