Optimizing the Structures of Minimum and Transition State on the Free Energy Surface

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Abstract
Presented here is the application of a scheme for optimizing the structures of minima and transition states on the free energy surface (FES) for a path along a fixed reaction coordinate with the aid of ab initio molecular dynamics (AIMD) simulation. In the direction of the reaction coordinate, the values corresponding to the stationary points were optimized using the quasi-Newton method, in which the gradient of the free energy along the reaction coordinate was obtained by a constraint AIMD method, and the Bofill Hessian update scheme was used. The equilibrium values for the other directions were taken as the corresponding averages in the dynamic simulation. This scheme was applied to several elementary bimolecular addition reactions: (A) BH3 + H2O → H2O·BH3; (B) BF3 + NH3 → FB3·NH3; (C) SO3 + NH3 → O3S·NH3; (D) C2H4 + CCl2 → H4C2·CCl2; (E) Ni(NH2)2 + PH3 → (NH2)2Ni·PH3; (F) W(CO)5 + CO → W(CO)6. For reactions A, B, C, and F, no transition state (TS) exists on the potential energy surface (PES). However there is a TS on the FES. This stems from the curvature difference of the PES and −TΔS as a function of the reaction coordinate. For all reactions, it is found that the TS shifts toward the complexation product with increasing temperature because of the curvature increase of −TΔS. The equilibrium bond distances for the inactive coordinates perpendicular to the reaction coordinate always increase with temperature, which is due to the thermal excitation and anharmonicity of the PES.