We give a detailed description of the use of explicit as well as implicit solvation treatments to compute the reduction potentials of biomolecules in a medium. The explicit solvent method involves quantum mechanical/molecular mechanics (QM/MM) treatment of the solvated moiety followed by a Monte-Carlo (MC) simulation of the primary solvent layer. The QM task for considerably large biomolecules is normally carried out by density functional treatment (DFT) along with the MM-assisted evaluation of the most stable configuration for the primary layer and biomolecule complex. The MC simulation accounts for the dynamics of the associated solvent molecules. Contributions of the solvent molecules of the bulk towards the absolute free energy change of the reductive process are incorporated in terms of the Born energy of ion-dielectric interaction, the Onsager energy of dipole-dielectric interaction and the Debye-Hückel energy of ion-ionic cloud interaction. In the implicit solvent treatment, one employs the polarizable continuum model (PCM). Thus the contribution of all the solvent molecules towards the free energy change are incorporated by considering the whole solvent as a dielectric continuum.

As an example, the QM(DFT)/MM/MC-Born/Onsager/Debye-Hückel corrections yielded the oneelectron reduction potential of Pheophytin-a in the solvent DMF as $−0.92 \pm 0.27$ V and the two-electron reduction potential as $−1.34 \pm 0.25$ V at 298.15 K while the DFT-DPCM method yielded the corresponding values as $−1.03 \pm 0.17$ V and $−1.30 \pm 0.17$ V, respectively. The calculated values more or less agree with the observed mid-point potentials of −0.90 V and −1.25 V, respectively. Moreover, a numerical finite difference Poisson-Boltzmann solution along with the DFT-DPCM methodology was employed to calculate the reduction potential of Pheophytin-a within the thylakoid membrane. The calculated reduction potential value of −0.58 V is in agreement with the reported value of −0.61 V that appears in the socalled 𝑍-scheme and is considerably different from the value in vitro.

Both implicit solvation method (dielectric polarizable continuum model, DPCM) and hybrid solvation method (cluster-continuum model) were adopted to calculate the $pK_a$ of mono-protonated form of $13^2$-(demethoxycarbonyl) pheophytin 𝑎 (Pheo) in methanol. In the cluster-continuum model calculations, we considered only 1 solvent molecule attached explicitly and others treated implicitly whereas in the DPCM calculations all the solvent molecules were treated implicitly. DPCM calculations were carried out on Pheo, PheoH+, Pheo-CH₃OH and PheoH⁺-CH₃OH in methanol solution. The aim of these calculations was to determine the free energy changes involved in the deprotonation of PheoH⁺ ($\Delta G_{\text{sol}}$) and finally to obtain the corresponding $pK_a$ value. DPCM calculations were carried out employing the restricted open-shell density functional treatment (ROB3LYP) using the 6-31G(𝑑) basis set to determine the free energy of solvation of bare Pheo and PheoH+ and of the clusters, Pheo-CH₃OH and PheoH⁺-CH₃OH in methanol. In-vacuo geometries of all the species were obtained by performing optimizations at ROB3LYP level using the 6-31G(𝑑) basis. Electronic energies of all the species were then obtained by carrying out single point DFT calculations using 6-311+G(2𝑑, 2𝑝) basis set on the respective optimized geometries. Differences in thermal energy and molecular entropy were calculated by carrying out frequency calculations at ROB3LYP/STO-3G level on the optimized geometries of the truncated models. The optimized geometries of the clusters display intermolecular hydrogen bonding interactions. The $pK_a$ values of PheoH⁺ calculated by DFT-DPCM and cluster-continuum methods are 6.12 and 4.70 respectively while the observed value is 4.14. The hydrogen bonding interaction between the solute and the solvent can be attributed for the good performance of the cluster-continuum model over pure continuum model.