where 𝐻 ̂ is Hamiltonian operator, E represents the total energy of the system in the atomic unit and Ψ is the many-body/electron wave function. Consider a molecular system with N electron with position {𝒓 𝒊 } and M nuclei with position {𝑹 𝑨 } as shown in the Figure . The corresponding Hamiltonian for such system can be written as;