Computational Strategies for Redox Processes in Condensed Phase : Both Explicit and Implicit Solvation Treatments

We provide a detailed account of the theory of solvation models, especially those involved in the calculation of the reduction potentials of biomolecules in a solvent or a membrane. The explicit solvation model involves a hybrid quantum mechanical-molecular mechanical (QM/MM) treatment of the solvated biomolecule and a dynamical treatment of the primary solvent layer through either Molecular dynamics (MD) or Monte-Carlo (MC) simulations. Contributions of the solvent molecules in the bulk to the free energy change of the reduction process is incorporated in the form of the Born free energy of ion-dielectric interaction, the Onsager energy of dipole-dielectric interaction and the Debye-Huckel energy of ion-ionic cloud interaction. The implicit solvation treatment employs the dielectric polarisable continuum model (DPCM) where all the solvent molecules together are represented as a continuum with a fixed dielectric constant. Whereas the implicit model only accounts for an average molecule-medium interaction, the explicit model also considers fluctuations of the medium molecules from their average coordinates in thermal equilibrium. The theory and the models are exemplified by calculations on three biomolecules in different environments. The QM/MM method could successfully reproduce the standard reduction potential of plastocyanin in water. The QM/MM/MD + Born/Onsager/Debye-Huckel procedure was used to obtain the standard oxidation and reduction potentials of Chlorophyll-a in acetonitrile. The QM/MM/MC + Born/Onsager/Debye-Huckel technology was adopted to determine the one- and two-electron reduction potentials of Pheophytin-a in DMF. The implicit solvation model along with density functional treatment (DFT-DPCM method) was also used to this end. A finite difference Poisson-Boltzmann solver along with the DFT-DPCM method was utilized to calculate the reduction potential of Pheophytin-a within the thylakoid membrane. These examples amply demonstrate the soundness of the explicit and implicit models of molecule-medium interaction