Configuration average, state, orbital, Coulomb and exchange energies of confined beryllium atom

We have analysed the electronic structure for the ground and excited configurations of the confined beryllium atom under impenetrable spherical walls by using Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) methods. The wavefunction is built up from the one-electron wavefunctions which constitute the Slater-type basis sets. When the dot radius increases, all energies approach the corresponding values of free beryllium atom. In addition, in large dot radii, the ratio of the average potential energy to the total kinetic energy for each configuration approaches to the virial coefficients for free atoms (-2). It is found that the Coulomb interaction energy between the electrons occupying the 1s orbital is the biggest. For the 1s22s2p configuration, in small dot radii, while the 2s orbital energy is larger than the 2p orbital energy, the 2s orbital energy is smaller than that of 2p in large dot radii.