Charge compensation in charged system

Dear Users,

It is known , that in order to perform calculations on a periodic cell with non-zero net charge, a compensating background (jellium) is requied.

How in particular is that done in Elk?
What is the effect of the background on total energy?
Is it physically meaningful to compare total energies of two systems with different net charges?

Thank you.
Andrew

mfechner - 2019-03-18

Dear Andrew,

I used this feature several times and I assumed the implementation is done similiar to other codes, where to compensate the violation of the charge neutraltiy some background for the ewald summation is added. But I guess you find the detail in the code.

Adding the charge will indeed change the energy particular the band energy as you have now more or less electrons. However, as the particle number changes it is not really possible to compare total energies of computations with differnet number of electrons. What you could do is to compare energy differences. So you can check for example how this ''pseudo doping'' affects the energy difference between an antiferromagnetic and ferromagnetic states.

hope this helps

best regards
Michael

Dear Michael,

Thank you for your comments.

I was asking in regard of the so called Delta-SCF approaches used to locate defect levels in band gap. I tried it and got a defect in conduction band (i.e. relating to expermental value of the gap), while it must be well below conduction band. I was looking for a source of error. The pairs of calculations used to calculate Deltas had different number of electrons and were both charged, hence the question.

Also, I've noticed something else. I did a calculation of an undoped solid, charge zero, then a calculation with charge -1 (add 1 electron) on the same geometry. The energy of the second structure was higher almost exactly by the band gap value (determined from Kohn-Sham, KS levels). Noteworthy, KS gas was almost the same in both cases. So, does the charge background affect KS levels? Or, can we thus say that the effect of the background on KS levels is small? Is it also small for total energy?

And another thing: Delta-SCF people say that KS gap makes no physical sence, while the Delta-SCF one does (with warnings about charge background, in small text). In the mentioned test case, the two are equal. Does that mean that Delta-SCF aproach is not so good, or, at least, is as bad as the respective KS levels?

Best regards.
Andrii

https://sourceforge.net/p/elk/discussion/897820/thread/4b5c85edc4/