Few electron systems confined in Gaussian potential wells and connection to Hooke atoms

Abstract

In this work, we have computed and implemented one-body integrals concerning Gaussian confinement potentials over Gaussian basis functions. Then, we have set an equivalence between Gaussian and Hooke atoms and we have observed that, according to singlet and triplet state energies, both systems are equivalent for large confinement depth for a series of even number of electrons n = 2, 4, 6, 8 and 10.