Dielectric relaxation dynamics of water and methanol solutions associated with the ionization of N,N-dimethylaniline: Theoretical analyses

Abstract

The solvation dynamics associated with the ionization of N,N‐dimethylaniline (DMA) in water and methanol solutions has been studied theoretically. Potential energy surfaces of DMA and DMA⁺ were computed by ab initio molecular orbital (MO) methods. Intermolecular pair potential functions between DMA and H₂O were developed with the aid of the electron distributions of DMA and H₂O and the results of MO calculations for the DMA–H₂O system. Potential functions between DMA and MeOH were also determined empirically using the parameters for DMA–H₂O interaction. Equilibrium and nonequilibrium molecular dynamics calculations were carried out for the DMA–water and DMA–methanol solutions. The simulation results were analyzed comparing two solvents in order to obtain a realistic molecular model for the solvation dynamics of DMA in polar solvents. The solvation coordinate was defined by the potential energy difference between neutral and cation states and free energy curves along it were constructed using the umbrella sampling method. They were found to be well described by parabolas and nonlinear effects such as the dielectric saturation were not observed. The fluctuation–dissipation relation was also examined. It was found that the present systems follow the linear response to a reasonable approximation. In order to provide a kinematic foundation for the choice of the solvation coordinate, the generalized Langevin equation (GLE) for the motion along the solvation coordinate is derived utilizing the reaction path model originally developed to describe photochemical processes in the gas phase. The mechanism of the dielectric relaxation dynamics was discussed on the basis of the quantities in the GLE deduced from the molecular dynamics (MD) calculations.