Energies of the ground and excited states of confined two-electron atom in finite potential well

For the ground and excited configurations, we have carried out the energy eigenvalues and corresponding wavefunctions of two-electron atom enclosed by finite confining potential by using Quantum Genetic Algorithm (QGA) procedure and Hartree-Fock Roothaan (HFR) method. Besides, we have analysed in detail orbital energies and probabilities of finding electron for the configurations 1S (1s2), 3S (1s2s), 3P (1s2p), 3D (1s3d) and 3F (1s4f). The results reveal that the potential barrier height plays a significant role on average energies, state energies, orbital energies and probabilities of finding electrons in orbitals. As dot size is extremely small and extremely large, the energies for 1snl configurations are getting close to each other, but between these two extreme situations they are separating from each other. While going to higher excited states, singlet and triplet states are almost the same due to the weakening of the exchange energy.