Hylleraas-like functions with the correct cusp conditions: K-shell electrons for the neutral atoms

Abstract

We present simple correlated wavefunctions for the two K-shell electrons of neutral atoms. A variational method was chosen to calculate the mean energy of the ground state, in which the electrons are subject to a local Hartree potential representing the presence of the outer shell electrons. The functions are constructed in terms of exponential and power series, where special care has been taken in order to fulfill the exact behavior at the electron–electron and electron–nucleus coalescence points (Kato cusp conditions). Global properties, such as the energies and virial coefficients, as well as local properties, such as spatial mean values, are also analyzed.