Multipath variational transition state theory: rate constant of the 1,4-hydrogen shift isomerization of the 2-cyclohexylethyl radical

We propose a new formulation of variational transition state theory called multipath variational transition state theory (MP-VTST). We employ this new formulation to calculate the forward and reverse thermal rate constant of the 1,4-hydrogen shift isomerization of the 2-cyclohexylethyl radical in the gas phase. First, we find and optimize all the local-minimum-energy structures of the reaction, product, and transition state. Then, for the lowest-energy transition state structures, we calculate the reaction path by using multiconfiguration Shepard interpolation (MSCI) method to represent the potential energy surface, and, from this representation, we also calculate the ground-state vibrationally adiabatic potential energy curve, the reaction-path curvature vector, and the generalized free energy of activation profile. With this information, the path-averaged generalized transmission coefficients <γ> are evaluated. Then, thermal rate constant containing the multiple-structure anharmonicity and torsional anharmonicity effects is calculated using multistructural transition state theory (MS-TST). The final MP-VTST thermal rate constant is obtained by multiplying k(MS-T)(MS-TST) by <γ>. In these calculations, the M06 density functional is utilized to compute the energy, gradient, and Hessian at the Shepard points, and the M06-2X density functional is used to obtain the structures (conformers) of the reactant, product, and the saddle point for computing the multistructural anharmonicity factors.