Yuri Georgievskii

Predictive theory for the combination kinetics of two alkyl radicals

An ab initio transition state theory based procedure for accurately predicting the combination kinetics of two alkyl radicals is described. This procedure employs direct evaluations of the orientation dependent interaction energies at the CASPT2/cc-pvdz level within variable reaction coordinate transition state theory (VRC-TST). One-dimensional corrections to these energies are obtained from CAS+1+2/aug-cc-pvtz calculations for CH3 + CH3 along its combination reaction path. Direct CAS+1+2/aug-cc-pvtz calculations demonstrate that, at least for the purpose of predicting the kinetics, the corrected CASPT2/cc-pvdz potential energy surface is an accurate approximation to the CAS+1+2/aug-cc-pvtz surface. Furthermore, direct trajectory simulations, performed at the B3LYP/6-31G* level, indicate that there is little local recrossing of the optimal VRC transition state dividing surface. The corrected CASPT2/cc-pvdz potential is employed in obtaining direct VRC-TST kinetic predictions for the self and cross combinations of methyl, ethyl, iso-propyl, and tert-butyl radicals. Comparisons with experiment suggest that the present dynamically corrected VRC-TST approach provides quantitatively accurate predictions for the capture rate. Each additional methyl substituent adjacent to a radical site is found to reduce the rate coefficient by about a factor of two. In each instance, the rate coefficients are predicted to decrease quite substantially with increasing temperature, with the more sterically hindered reactants having a more rapid decrease. The simple geometric mean rule, relating the capture rate for the cross reaction to those for the self-reactions, is in remarkably good agreement with the more detailed predictions. With suitable generalizations the present approach should be applicable to a wide array of radical-radical combination reactions.

Association rate constants for reactions between resonance-stabilized radicals: C3H3 + C3H3, C3H3 + C3H5, and C3H5 + C3H5

Reactions between resonance-stabilized radicals play an important role in combustion chemistry. The theoretical prediction of rate coefficients and product distributions for such reactions is complicated by the fact that the initial complex-formation steps and some dissociation steps are barrierless. In this paper direct variable reaction coordinate transition state theory (VRC-TST) is used to predict accurately the association rate constants for the self and cross reactions of propargyl and allyl radicals. For each reaction, a set of multifaceted dividing surfaces is used to account for the multiple possible addition channels. Because of their resonant nature the geometric relaxation of the radicals is important. Here, the effect of this relaxation is explicitly calculated with the UB3LYP/cc-pvdz method for each mutual orientation encountered in the configurational integrals over the transition state dividing surfaces. The final energies are obtained from CASPT2/cc-pvdz calculations with all pi-orbitals in the active space. Evaluations along the minimum energy path suggest that basis set corrections are negligible. The VRC-TST approach was also used to calculate the association rate constant and the corresponding number of states for the C(6)H(5) + H --> C(6)H(6) exit channel of the C(3)H(3) + C(3)H(3) reaction, which is also barrierless. For this reaction, the interaction energies were evaluated with the CASPT2(2e,2o)/cc-pvdz method and a 1-D correction is included on the basis of CAS+1+2+QC/aug-cc-pvtz calculations for the CH(3) + H reference system. For the C(3)H(3) + C(3)H(3) reaction, the VRC-TST results for the energy and angular momentum resolved numbers of states in the entrance channels and in the C(6)H(5) + H exit channel are incorporated in a master equation simulation to determine the temperature and pressure dependence of the phenomenological rate coefficients. The rate constants for the C(3)H(3) + C(3)H(3) and C(3)H(5) + C(3)H(5) self-reactions compare favorably with the available experimental data. To our knowledge there are no experimental rate data for the C(3)H(3) + C(3)H(5) reaction.

Variable reaction coordinate transition state theory: Analytic results and application to the C2H3+H→C2H4 reaction

A novel derivation is provided for the canonical, microcanonical, and energy E and total angular momentum J resolved reactive flux within the variable reaction coordinate transition state theory (VRC-TST) formalism. The use of an alternative representation for the reaction coordinate velocity yields a new expression for the kinematic factor which better illustrates its dependence on the pivot point location, and which can be straightforwardly evaluated. Also, the use of a geometric approach in place of an earlier algebraic one clarifies the derivation as does the use of Lagrange multiplier methodology for the analytic integration over the total angular momentum. Finally, a quaternion representation for the fragment and line-of-centers orientations is employed in place of the Euler angle or internal/external rotational coordinates used in prior studies. The result is an efficient, and particularly easy to implement, methodology for performing variable reaction coordinate transition state theory calculation...