Transition-state optimization by the free energy gradient method: Application to aqueous-phase Menshutkin reaction between ammonia and methyl chloride

Peierls Barrier of Screw Dislocation in bcc Iron at Finite Temperature

“…14,15) This method is known as the constraint method. Although the constraint method is simple, it can be used to obtain a unique FEG.…”

Structure Optimization of Solute Molecules via Free Energy Gradient Method

“…In MD simulation, forces acting on each atom of the solute molecule by all solvent molecules are always calculated every time step. By timeaveraging these forces, the "force" on FES, i.e., a minus of FEG, is obtained as a function of the solute molecular structure q s as follows, 4,[7][8][9] (1) (2) where V is the whole potential of solution, under the condition that the solute molecular structure is restricted to be q s and q B denotes the solvent coordinates as a whole. For structure optimization, in the FEG method with the steepest-descent-path following procedure, the i+1th reactant structure is taken to be…”

“…8 As explained in the subsection III-B, the solutesolvent system was described by a hybrid QM/MM method. 8 The TS thus obtained (Figure 4(b)) was found earlier than that in the gas phase (Figure 4(a)), which is in accord with the Hammond postulate. As a result, the reaction path in water was found to deviate largely from that in the gas phase.…”

“…As a result, the reaction path in water was found to deviate largely from that in the gas phase. 8 One can understand therefore that, in aqueous solution, the reaction should proceed accompanied with such a structural deformation to enhance the charge separation. It is concluded that, in such a reaction including charge separation, TS structure optimization on an FES is inevitable for obtaining valid information about a TS in polar solution.…”

“…1 To obtain a stationary point on a multi-dimensional free energy surface (FES), 1 e.g., stable state (SS) or transition state (TS) in solution chemical reaction, a new TS optimization method, the free energy gradient (FEG) method, has been developed. [2][3][4][5][6][7][8][9] Analogous to the method for the BornOppenheimer (BO) potential energy surface using ab initio molecular orbital (MO) calculation, the FEG method utilizes force and hessian on the FES, which can be calculated by molecular dynamics (MD) method and the free energy perturbation (FEP) theory. 10,11 Furthermore, on the basis of the method, we have proposed the definition of the intrinsic reaction coordinate (IRC) on the FES.…”