The new electron-electron interaction introduced in
chapter 
and the enhanced version of this interaction
described in section , which was designed to
remove the interaction between the periodic array of additional
electrons (holes) both have equivalent forms for dealing with
systems containing promoted electrons. The equivalent of the new
electron-electron interaction from chapter , designed
to deal with N electron systems in their ground state, can also be
written to deal with N electrons, where one is in an excited state, in
the following way;
There also exists an equivalent of the enhanced interaction introduced
in section to remove the extra electrostatic
energy introduced when an electron (hole) is added to the simulation
cell. In the case of promoting electrons rather than addition and
subtraction, this enhanced interaction (see
Eq.()) corresponds to evaluating the Hartree
interaction between the charge density due to the promoted system in
the simulation cell and the charge density due to the ground state in
all the periodic images of the simulation cell. In other words, the
enhanced form removes any additional electrostatic energy due to the
Hartree interaction between changes in charge density due to the
promotion of an electron in the simulation cell and the same changes
in the periodic images of the simulation cell
