Efficient computer programming of the theoretical model provides a great insight into molecular/cluster systems with different perspectives. These computer-aided simulation techniques have effectively influenced both the basic understanding of atomic/molecular systems and their application in various fields of interest . Despite the advent of more powerful computer systems such as HPC (high-performance computing), the computational capability for solving scientific problems is still facing stiff challenges, especially in the context of the atomic-level study of large molecular systems. For a few decades, first principles (Ab initio) methods, based on quantum mechanics, have emerged as a powerful tool to probe the properties of matter at an atomic scale . The first principles-based density functional theory (DFT) has gained significant popularity because of its capability in providing the ground state properties with good accuracy . Recently, the DFT method has been found to be effective in bringing significant acceleration in the development and optimization of new energy storage materials . For example, in the case of rechargeable batteries, many intrinsic properties of electrode/electrolyte materials, i.e., working potential window, structural stability, metal-ion diffusivity, band structure, and electronic hopping barriers can now be computed accurately with the first-principles computation methods . Apart from the energy storage, DFT is widely used to study charge transport , material interface , biological system Therefore, this report is focused on the theoretical methodologies, e.g. Hartree-Fock (HF) theory and DFT, which were earlier developed for finding the solution of many-body Schrodinger equation. Since the solvent effect are generally included in the molecular system, therefore, the solvation models have been also discussed in the report.