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.