All-electron calculations

This tutorial ontains some exercises to illustrate some general issues involved in computing the electronic structure of the atom. Run the examples by typing, for example:


These exercises are not essential to follow the examples of pseudopotential generation, but they might help to broaden your understanding.

Guide to all-electron calculation examples:


The ground state and the Si+3 ion (unpolarized calculations). Note the insensitivity of the core electrons to the ionization of three valence electrons. The file contains a series of jobs to study several excited states of the atom.


We know that Hund’s rule should be obeyed for orbitals not completely full. Use the file to test whether that is so. In the first calculation the effect of the spin is neglected. The second deals with spin polarization effects, but the occupation of the 2p level is “wrong”: there are 2 electrons “down” and one “up”. The third calculation should correspond to the true ground state, with all the 2p electrons with their spins aligned.


Here is another example of the importance of spin effects in certain cases. Iron has 6 electrons in the 3d orbital. The proper spin polarization lowers the energy.


Lead is a heavy atom, and most of the electrons have velocities which are a significant fraction of the speed of light. A relativistic calculation should then be essential. The Dirac equation is solved, and spin effects appear naturally through the j quantum number.


Its core is quite large, and it is customary to consider the 5s and 5p as “semicore states”, putting them in the valence complex.