Here we apply the orbital and variational approach to study the Li+ ion, which is isoelectronic with Helium. 1. Apply the methods taught in class to compute the approximate energy of Li+ using a 1s2 trial wavefunction for the 2 electrons, each described by the effective nuclear charge (ENC) = Z.
Follow these steps for He ground state:
(a) Write the exact Hamiltonian for Li+, putting in the form discussed in class depending on Z.
(b) Compute the ground-state energy for Li+ ignoring electronic repulsion; should depend on Z. To do this, you will need to compute the difference between the real electron-nucleus attraction (with Z=3) and that for variable Z, as shown in class.
(c) Recall the known 2-electron repulsion integral for 1s electrons with ENC = Z, shown in class.
(d) Compute total energy by adding up all terms; then minimize with respect to Z to find optimal ENC. +
(e) Plug optimal ENC into energy to get best estimate of Li 2. Use this result to compute the ionization energy of the Li+ ion using exact results for hydrogenic species.