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Electron-Electron Interaction for Promoted States

The new electron-electron interaction introduced in chapter gif and the enhanced version of this interaction described in section gif, 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 gif, 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 gif 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.(gif)) 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


Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996