According to the schematic (FIG 1) in this paper (http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.085202) the total energy of a solid with N+1 electrons is less (more negative) than the same solid (the same positions of ions) with N electrons. This was explicitly shown for the single fluorine atom (http://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.040501).(adsbygoogle = window.adsbygoogle || []).push({});

My question is that something which can be proven analytically? When I try to simulate this using DFT on a couple of semiconductors , I get the opposite, that this the N system has less energy (more negative) compared to the N+1 system. Any hints are appreciated.

EDIT: The two articles I cited above are available on arxiv as well, and these are liks:

(1) http://arxiv.org/pdf/0905.0018.pdf

(2) http://arxiv.org/pdf/cond-mat/0702283v2.pdf

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# Total energy of N+1 electron system compared to N

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