Re: [SIESTA-L] Fermi level and k-grid
On Wed, 10 Jan 2007, Oleksandr Voznyy wrote: | The Fermi level is normally calculated by setting the cumulative occupation | number of all bands to the number of valence electrons. | | As I understand this means that Ef in semiconductor would always be | at the VBM and not in the middle of the gap? Alexander - sorry, it seems that I was wrong. I just checked my old calculation for a wide-gap dielectric and see that Fermi energy = -6.866874 eV while the energies bordeing the gap -8.08 and -4.66. One should look into details of implementation... Yes in other band structure codes I know the Fermi energy is fixed by the last occupied band, i.e. it is set at the valence band top. Then if it technically lies higher, this must be due to the energy broadening introduced. But apparently in Siesta it is done differently. | By the way, how the bandstructure is calculated using only several k-points? The band structure as such (continuous bands) is not calculated, each k-point enters independently of others and contributes a (smeared) peak in the density of states. This summary DOS is (roughly speaking) integrated, and as the number of electrons is achieved, the Fermi level is set. (The details of implementation might be different). Best regards, Andrei +-- 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/ --+
Re: [SIESTA-L] Fermi level and k-grid
The Fermi level is normally calculated by setting the cumulative occupation number of all bands to the number of valence electrons. As I understand this means that Ef in semiconductor would always be at the VBM and not in the middle of the gap? How it could happen that Ef appeared somewhere in the middle of the gap in my calculations (see my previous post)? There are no states in the gap independently on the amount of k-points. By the way, how the bandstructure is calculated using only several k-points? 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. Well in my case of partially filled dangling bonds on the surface I end up as a metallic system. Would Methfessel-Paxton smearing help in my case? Again, does population of the bands affect the band structure and total energy or population is a secondary property? - see my example of molecule adsorption to dangling bond in previous post. It would be such a good investment to add a tetrahedron integration in Siesta... And a not very difficult one... From my experience one needs about 10*10*10 mesh nodes along each direction in BZ to get convergence with tetrahedrons. Does one need that much points for metals? I don't see the problem of SCF convergence in my bulk GaAs. I see that Ef(k-points) doesn't converge (up to 50A). I think that 4000 k-points is more than enough for convergence even for metals. But I don't see convergence at all even for more k-points. Thanks, Alexander
Re: [SIESTA-L] Fermi level and k-grid
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: | kgridEf, 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 1,370,0028 -789,50544 | 20,359-4,7579 500 -- 1E-3-- | 26,467-5,1201 11833,139 2E-4-789,5052 | 30,5 -4,9783 1800-- 4E-5-789,5054 | 32,575-4,7802 20484,736E-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. | |
[SIESTA-L] Fermi level and k-grid
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: kgridEf, 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 1,370,0028 -789,50544 20,359 -4,7579 500 -- 1E-3-- 26,467 -5,1201 11833,139 2E-4-789,5052 30,5-4,9783 1800-- 4E-5-789,5054 32,575 -4,7802 20484,736E-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.