On Wed, 10 Jan 2007, Oleksandr Voznyy wrote: | Hi, | till recently I though that checking the convergence of total energy vs k-grid | cutoff is enough. | However, now I've found that while total energy can be very well converged, | Fermi level position is not, and requires at least twice denser k-grid (and ~4 | times more time). | | Here is my example for bulk GaAs:
Dear Alexander, the problem you describe stems from the fact that k-space summation, done by sampling, is not accurate enough. However, this is technically no problem for systems with large enough band gap and/or molecules. On the contrary, for metallic systems, or those where the Fermi level crosses states in the gap, the convergency of results with k-points in indeed disappointingly slow (as compared with codes using tetrahedron integration). The Fermi level is normally calculated by setting the cumulative occupation number of all bands to the number of valence electrons. As I understand the situation in Siesta, this cumulative occupation is obtained by integrating the Fermi function smeared with ElectronicTemperature, and summed up over k-points with their respective weights. That's why increasing ElectronicTemperature usually suppresses the fluctuations and helps the convergency, but somehow deteriorates the resulting energy values. Considering your example, for pure GaAs (or any semiconductor) you probably won't care much about the exact value of E-Fermi because you get the valence and conduction bands right, and total energy is stable. Etot is more stable because it is "integral" property while the calculated E-Fermi is "differential" one which shifts back and forth with every single k-point added. Correspondingly, the DOS is a sum of smeared delta-peaks, it also wildly changes with adding k-points, and converges extremely slowly to the DOS found from other band structure code with tetrahedron integration. In a metal system, metal Etot won't be so stable against k-mesh as in semiconductor, and would normally require much much more dense k-mesh. It would be such a good investment to add a tetrahedron integration in Siesta... And a not very difficult one... Best regards, Andrei Postnikov +-- Dr. Andrei Postnikov ---- Tel. +33-387315873 ----- mobile +33-666784053 ---+ | Paul Verlaine University - Institute de Physique Electronique et Chimie, | | Laboratoire de Physique des Milieux Denses, 1 Bd Arago, F-57078 Metz, France | +-- [EMAIL PROTECTED] ------------ http://www.home.uni-osnabrueck.de/apostnik/ --+ On Wed, 10 Jan 2007, Oleksandr Voznyy wrote: | Hi, | till recently I though that checking the convergence of total energy vs k-grid | cutoff is enough. | However, now I've found that while total energy can be very well converged, | Fermi level position is not, and requires at least twice denser k-grid (and ~4 | times more time). | | Here is my example for bulk GaAs: | kgrid Ef, eV k-pnts SCFtime forces Etot | cutoff | 8 -5,3105 32 1 0,00509 -789,50149 | 10 -4,9698 -- -- 2,19E-4 -789,44567 | 12,2 -4,1639 108 -- 0,0052 -789,50521 | 16,287 -4,1839 256 1,37 0,0028 -789,50544 | 20,359 -4,7579 500 -- 1E-3 -- | 26,467 -5,1201 1183 3,139 2E-4 -789,5052 | 30,5 -4,9783 1800 -- 4E-5 -789,5054 | 32,575 -4,7802 2048 4,73 6E-6 -789,50545 | 40,7 -4,7676 4000 -- 1,28E-4 50 -5,1057 16 | 2,07E-4 | | As you can see, Fermi level varies in the range of 0.6 eV!!! (all the bands | don't shift). The middle of the gap is at -4,75 | | My questions are: | | 1. How Fermi level is calculated? | Is it just filling the available bands with a given amount of electrons (based | on calculated DOS on a given k-grid) after all calculations are done? What | smoothing of DOS is used then??? | | Ef doesn't converge actually. | If 1. is true then I can understand it - DOS shape changes quite significantly | and real convergence would be only when one gets all possible k-points. | | 2. Since the total energy is calculated on the same k-grid, why it doesn't | show the same behavior? i.e why it is less sensitive than Ef? | Should one bother at all about Ef during geometry relaxation? | | 3. Does the filling of the bands affect the forces on atoms, and thus | explicitly affects total energy? | Imagine such a situation: | a molecule adsorbs to a dangling bond on a surface only if it is empty or only | partially filled, | if I set the Ef 0.5eV higher, I make the dangling bond completely filled and | moleculed would not adsorb at all, | i.e. we end up in a completely different geometry and total energy. | | I will appreciate very much any comments or suggestions. | | Sincerely, | Alexander. | |
