In this paper, we have proposed a first-principles methodology to screen transition metal complexes against a particular organic solvent and organic solvents against a particular transition metal complex based on their solubility information without the knowledge of heat of fusion and melting temperature. The energy density of a non-aqueous redox flow cell directly depends on the solubility of the redox active species in the non-aqueous medium. We have used the "COSMOSAC-LANL" activity coefficient model (A. Karmakar, R. Mukundan, P. Yang and E. R. Batista, RSC Adv., 2019, 18506-18526; A. Karmakar and R. Mukundan, Phys. Chem. Chem. Phys., 2019, 19667-19685) which is based on first-principles COSMO calculations where the microscopic information is passed to the macroscopic world via a dielectric continuum solvation model, followed by a post-statistical thermodynamic treatment of the self-consistent properties of the solute particle to calculate the solubility. To model the activity coefficient at infinite dilution for the binary mixtures, a 3-suffix Margules (3sM) function is introduced for the quantitative estimation of the asymmetric interactions and, for the combinatorial term, the Staverman-Guggenheim (SG) form is used. The new activity coefficient model is separately called the "LANL" activity coefficient model. The metal complex and the organic solvent have been treated as a simple binary mixture. The present model has been applied to a set of 14 different organic solvents and 16 different transition metal complexes. Using the new LANL activity coefficient model in combination with the ADF-COSMOSAC-2013 model, we have shown how one can improve the solubility of a transition metal complex in an organic solvent. We applied our model to screen 84 binary mixtures to predict the compatible pair of redox active species and organic solvent to increase the energy density. The solvation mechanism of the transition metal complexes in the organic solvents was obtained using the new model. The results have been compared with the experimental and theoretical results where they are available.