[Pw_forum] fermi level (XQ Wang)

Eyvaz Isaev eyvaz_isaev at yahoo.com
Fri Aug 15 15:30:33 CEST 2008

Dear Wang,

Now I am confused with the questions you post.

--- On Fri, 8/15/08, wangxinquan <wangxinquan at tju.edu.cn> wrote:

> Do you mean that the occupations of electrons were
> constrained during iterations? 


> To my limited experiences, the occupations should be 
> changed by setting the "starting_ns_eigenvalue" parameters > (lda+u calculation) and the occupation matrix will be 
> tuned through the iterations process. 

I am not so experienced in the LDA+U calculations, but the idea that an occupation number should be defined self-consistently, is correct. 

> I'm sorry for that I confused "electron density" with > "occupation". In my opinion, both  concepts describe 
> the probabilty of electrons locating at lattic site. 

This is a WRONG conception, electrons are delocalized in the unit cell and you (and anybody) can not locate an electron on a lattice site. 

Besides, electron density is a square of a wavefunction \Psi(r), but occupation number is a consequence of quantum statistics. 

> The "electron density" which is derived from 
> wavefunctions belongs to quantum
> mechanics field, while "occupation" 
> belongs to condensed matter physics field with respect to
> band structure.The electron density 
> should be changed but the occupation of bands should be
> fixed in scf calculation. right?

No, this is not true for metals. Only for semiconductors (insulators) valence bands are kept fully occupied, i.e. 2 electrons per band according to Pauli principle. 
> The electron states(eigenvalue of the density matrix) which
> construct the band structures will not
> be occupated entirely. 

Probably I missed something, but eigenvalues are solutions of (T+V_H+V_XC+V_ext)\Psi=E\Psi
The second part of your suggestion is misleading completely. In this case where you put electrons?

> For insulator, the valence band is full while the conduct band is empty. 


> In the output file of scf I have no idea what the
> "fermi energy" results are. Does it not mean the 
> "real" fermi energy? 

By definition: the Fermi energy is an energy which separates the valence (occupied) electrons from the conductivity (unoccupied) electrons.

In our DFT calculations there is no "real" Fermi energy (E_F), only the one for which \int_{E_min}^{E_F)N(E)dE = N is fulfilled (N(E) is the DOS, N is total number of valence electrons).  
> E.J.Yoffa and D.Adler (Phy. Rev. B, 12, 2260) have 
> talked about the calculation of fermi energy for 
> Mott insulator. I'm afraid the definition of fermi 
> energy were misunderstood.

At least, from Abstract of the paper it is clear that what they did does not contradict to what we discussed before.

> My brain doesn't work. 

It should work. Please read again Kittel's or Ashcroft-Mermin's or Ricahrd Martin's o Harrison's or Zyman's, etc. etc etc texbooks.  


>Any help to remove my
> understanding to fermi energy will be deeply appreciated.
> Best regards,
> XQ Wang
> =====================================
> X.Q. Wang
> wangxinquan at tju.edu.cn
> School of Chemical Engineeringand and Technology
> Tianjin University
> 92 Weijin Road, Tianjin, P. R. China
> tel:86-22-27890268, fax: 86-22-27892301
> =====================================

Prof. Eyvaz Isaev, 
Theoretical Physics Department, Moscow State Institute of Steel & Alloys, Russia, 
Department of Physics, Chemistry, and Biology (IFM), Linkoping University, Sweden 
Condensed Matter Theory Group, Uppsala University, Sweden 
Eyvaz.Isaev at fysik.uu.se, isaev at ifm.liu.se, eyvaz_isaev at yahoo.com


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