Semianalytical wavefunctions and Kohn–Sham exchange-correlation potentials for two-electron atomic systems in two-dimensions

We propose accurate semianalytical wavefunctions for two-electron atomic systems in two-dimensions. These wavefunctions take into account the cusp conditions arising due to the Coulombic nature of external potential and electron–electron interaction, and the screening effects. The first wavefunction is motivated by the Le Sech wavefunction for two-electron atoms and ions in three-dimensions while the second one is constructed to give more variational freedom to the Le Sech wavefunction and is obtained by solving a Schrödinger like equation self-consistently. The results for energies, densities and other quantities are highly accurate and therefore may play an essential role in developing and testing density functional methods for two-dimensional systems. (paper)