title: Projection of the Dynamics of Electron Transfer Reaction in Dual Space onto the One-Dimensional Slower Reaction Coordinate Axis.
abstract: We have derived here for the first time an exact dynamical equation within the domain of classical mechanics for the time dependent density distribution function of one-dimensional reaction coordinate (RC) in the condensed phase for electron transfer reaction by projecting the dynamics of slower modes in multidimensional Liouville space starting with a given set of coordinates of the faster modes. After the faster modes were ensemble averaged, the dynamics of the whole system solely depends on the slower RC. To simplify the complicated equation into a tractable form, benchmark approximations are employed to reduce the formally exact equation into an equation similar to the Smoluchowski equation with a delocalized sink term. As a test case, a Hamiltonian for the solute-solvent system modeled by quadratic functions for fast-relaxing vibrational and slow-relaxing polarization modes, respectively, has been considered. Interestingly, our simplified kinetic equation corresponding to this model Hamiltonian is transformed into the well-known phenomenological Sumi-Marcus equation.
authors.affiliation: Center for Materials Theory, Rutgers University , Piscataway, New Jersey 08854, United States.|Theoretical Chemistry Section, Bhabha Atomic Research Centre , Mumbai 400085, India.
authors.forename: Aniket
authors.initials: A
authors.lastname: Patra
authors.affiliation: Center for Materials Theory, Rutgers University , Piscataway, New Jersey 08854, United States.|Theoretical Chemistry Section, Bhabha Atomic Research Centre , Mumbai 400085, India.
authors.forename: Kanagala Ajay
authors.initials: KA
authors.lastname: Acharya
authors.affiliation: Center for Materials Theory, Rutgers University , Piscataway, New Jersey 08854, United States.|Theoretical Chemistry Section, Bhabha Atomic Research Centre , Mumbai 400085, India.
authors.forename: Alok
authors.initials: A
authors.lastname: Samanta