[CP2K-user] Fermi energy too high?
Matt W
mattwa... at gmail.com
Mon Mar 1 14:25:25 UTC 2021
You need to look at the values on the cell edges of the non-periodic
direction. If you get an planar avereraged potential from cube cruncher
you should see it plateus either side of system (depending on charge /
dipole etc in your cell).
On Wednesday, February 24, 2021 at 4:42:37 PM UTC Harsha wrote:
> Hi Matt or Phill,
>
> I have a question based on your conversion above. How do I extract vacuum
> level?
>
> I printed &V_HARTREE_CUBE file used cubecruncher to extract the averaged Y
> profile.
>
> But how do I know the vacuum level? Is it printed somewhere like the Fermi
> level which is printed in the output file or is that something that we have
> to get from the plot?
>
> Best regards
>
> Harsha
>
> On Monday, April 15, 2019 at 11:55:12 AM UTC Phil G. wrote:
>
>> Dear Matt,
>>
>> The Fermi smearing was turned on during the calculations, so probably the
>> Fermi level will be the electronic level of 50% occupation probability of
>> electrons (lies in the band gap between the band edges).
>>
>> The slab used in the calculation has to mimic the ferroelectric single
>> crystal with the two polar surfaces exposed to vacuum. The both polar
>> surfaces have the opposite surface charges due to the spontaneous
>> polarization of the bulk crystal (in the middle region of the slab), so for
>> example the top surface (in the calculation using wavelet poisson solver it
>> is the positively y-directed surface) is positively polarized and the
>> bottom surface (negatively y-directed surface in this calculation) is
>> negatively polarized. The polarization is aligned along the polar axis of
>> the crystal. The value of the surface charge depends on the magnitude of
>> the spontaneous polarization in the bulk region (so: sigma = P_s *
>> normalvector ). The slab system has to fulfill the 2D periodic boundary
>> (surface problem, in this calculation x-z periodicity).
>>
>> I would like to calculate the electronic (structure) properties of the
>> single crystal surface exposed to vacuum (air) and later to water in order
>> to get the Fermi level, work function, electron affinity, ionization energy
>> of both the polar surfaces.
>>
>> Kind regards,
>>
>> Phil
>>
>> Am Freitag, 5. April 2019 17:39:23 UTC+2 schrieb Matt W:
>>>
>>> Hi Phil,
>>>
>>> a lot of questions / good points here, mainly physics rather than CP2K,
>>> I guess. Quick reply, I'll try and do a bit better later (if I remember).
>>>
>>> The fermi level depends on the algorithm. If there is no smearing, the
>>> reported fermi level is the HOMO of the system. If smearing, it is really
>>> the fermi level at the given electronic temperature.
>>>
>>> Maybe try looking at papers by Jacek Goniakowski (metal insulator
>>> systems) or Emilio Artacho (2d metals) that discuss some issues with
>>> semi-infinite slab models / dipoles / electostatics etc.
>>>
>>> If you can clearly define the boundary conditions that you actually want
>>> then we can probably suggest how to get them in CP2K.
>>>
>>> Matt
>>>
>>>
>>>
>>>
>>> On Friday, April 5, 2019 at 1:28:56 PM UTC+1, Phil G. wrote:
>>>>
>>>> Dear Matt (or someone in the CP2K group),
>>>>
>>>> after I get the 'reliable' Fermi level and the 'vacuum levels' which
>>>> are the same as Matt got them (-4.61 eV and +- 0.75 eV, see message on this
>>>> topic on 16th January). But I am bit confusing, why the vacuum levels are
>>>> of the same value (but with opposite signs) on both surfaces of the slab.
>>>> Should they do depend on the electronic properties of the surface? What is
>>>> the vacuum level exactly mean? (I mean that their values are not zero and
>>>> what correlates to the zero level?) I want to plot the PDOS against the
>>>> certain energy level scale as defined in the electrochemistry, e.g. NHE
>>>> (normal hydrgen electrode), SHE (standard hydrogen electrode). Is the zero
>>>> level in the potential plot defined as the vacuum level at infinity
>>>> distance and the both vacuum levels (+- 0.75 eV) the local vacuum levels?
>>>>
>>>> Important question: How was the Fermi level or the Fermi energy of a
>>>> slab (with two surfaces) in the CP2K calculated? Is it the same as the
>>>> energy where the valence band maximum is (globally?) or is it defined as
>>>> the value where the probability for an electron to occupy between
>>>> conductance and valence band edges is exactly 0.5 (according to the
>>>> Fermi-Dirac distribution function)?
>>>> If I get the pdos file of the slab, I get only a value of the Fermi
>>>> energy. Is that the average value for the Fermi energies throughout the
>>>> whole slab or is that rather the bulk property? (Because I would like to
>>>> plot PDOS as a function of atom layer coordinates (I have inset integer
>>>> indices to the atom types referring to the atom layers along the axis
>>>> perpendicular to their surfaces), and you can see that the energy positions
>>>> of the band edges change with the atom layer coordinate. It seems to be
>>>> like a graphical plot of band bending on both surface sites, but the energy
>>>> position change is overall linear throughout the slab (see attached image,
>>>> the Fermi level was shifted to zero in the energy scale). In my opinion,
>>>> this is not the realistic/reproducible band bending diagram as we know it
>>>> from the semiconductor heterostructures (junction between semiconductor and
>>>> a medium (solid, electrolyte or something)). Is it rather the result of
>>>> constant potential difference between the slab surfaces (at position z = 0
>>>> and z = - 54 Angstrom), and it seems to be the same irrespective of the
>>>> slab lengths (26 Angstroms). The potential difference is conceived to be
>>>> determined by the polarization of the slab material. How can I change the
>>>> constant potential model to the constant (surface) charge model and how to
>>>> implement it into the CP2K code?
>>>>
>>>> Kind regards,
>>>>
>>>> Phil
>>>>
>>>>
>>>> Am Montag, 21. Januar 2019 12:25:54 UTC+1 schrieb Phil G.:
>>>>>
>>>>> Dear Matt,
>>>>>
>>>>> thank you very much for the suggestions and after some tests it also
>>>>> worked ! :-)
>>>>> To check the effect of dipole correction on the calculation, I started
>>>>> different slab systems and used cell length in y-direction at 50 Angstrom
>>>>> (much more than this value will lead to error (index to radix array not
>>>>> found)):
>>>>> The slab systems are defined as in the first message above (9th
>>>>> January)
>>>>>
>>>>> a) without dipole correction: E_F = -3.31475 eV
>>>>> with dipole correction: E_F = -3.2983 eV
>>>>>
>>>>> b) without dipole correction: E_F = -4.642 eV
>>>>> with dipole correction: E_F = -4.72 eV
>>>>>
>>>>> It seems that the dipole correction leads to a marginal reduction of
>>>>> the Fermi energy.
>>>>> Now I want to check, if the vacuum level has another value that the
>>>>> Fermi energy as you showed (+/- 0.75 eV) by plotting pdos as a function of
>>>>> atom coordinates, i.e. in slab y-direction.
>>>>>
>>>>> Thanks again for your helpful suggestions! :-)
>>>>>
>>>>> Kind regards,
>>>>>
>>>>> Phil
>>>>>
>>>>>
>>>>> Am Mittwoch, 16. Januar 2019 14:20:18 UTC+1 schrieb Matt W:
>>>>>>
>>>>>> I added
>>>>>>
>>>>>> &CENTER_COORDS
>>>>>> &END
>>>>>>
>>>>>> in the topology section. I get the 'fermi level' reported at -4.61
>>>>>> eV. And the vacuum levels at +- 0.75 eV
>>>>>>
>>>>>> So the work functions of the two faces are ~5.4 and 3.8 eV
>>>>>> respectively. I got the profile of the potential by adding &V_HARTREE_CUBE
>>>>>> and using the cubecruncher utility (bundled in the tools directory) to
>>>>>> extract the averaged y profile to find the vacuum levels.
>>>>>>
>>>>>> Matt
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Wednesday, January 16, 2019 at 9:26:32 AM UTC, Matt W wrote:
>>>>>>>
>>>>>>> Hi,
>>>>>>>
>>>>>>> the xyz file you sent doesn't have the y coords centred in the cell.
>>>>>>> The cell goes from 0 to L. You centre as if it goes from -L/2 to L/2.
>>>>>>>
>>>>>>> If you print V_HARTREE_CUBE you can work out the potential profile
>>>>>>> across the slab.
>>>>>>>
>>>>>>> BTW your slab is too small in X and Z for reliable results without
>>>>>>> k-point sampling...
>>>>>>>
>>>>>>> Matt
>>>>>>>
>>>>>>> On Wednesday, January 16, 2019 at 8:54:56 AM UTC, Phil G. wrote:
>>>>>>>>
>>>>>>>> yes, the slab was centered in y-direction (xyz file attached here),
>>>>>>>> but in x- and z- direction from 0 to the corresponding lengths of the slab.
>>>>>>>> Maybe I should extend the size of vacuum space or turn on the
>>>>>>>> dipole correction?
>>>>>>>> For searching for reason, the input file is also attached here.
>>>>>>>>
>>>>>>>> Phil
>>>>>>>>
>>>>>>>> Am Dienstag, 15. Januar 2019 16:07:55 UTC+1 schrieb Matt W:
>>>>>>>>>
>>>>>>>>> Is your slab in the centre of the cell (Y direction)? - the cell
>>>>>>>>> runs from 0 to L, so the slab must be centred at L/2.
>>>>>>>>>
>>>>>>>>> Matt
>>>>>>>>>
>>>>>>>>> On Tuesday, January 15, 2019 at 2:21:26 PM UTC, Phil G. wrote:
>>>>>>>>>>
>>>>>>>>>> Dear Matt,
>>>>>>>>>>
>>>>>>>>>> thank you for the suggestions and after centering the slab in
>>>>>>>>>> y-direction and turning off the surface dipole correction, the program
>>>>>>>>>> finally runs and I get the result, but there are some error messages such
>>>>>>>>>> as:
>>>>>>>>>>
>>>>>>>>>> *** WARNING in pw/ps_wavelet_methods.F:236 :: Density non-zero
>>>>>>>>>> on the ***
>>>>>>>>>> *** edges of the unit cell: wrong results in WAVELET
>>>>>>>>>> solver ***
>>>>>>>>>>
>>>>>>>>>> 89 Broy./Diag. 0.10E+00 2.3 0.00000880
>>>>>>>>>> -3020.8753805067 4.85E-05
>>>>>>>>>>
>>>>>>>>>> *** SCF run converged in 89 steps ***
>>>>>>>>>>
>>>>>>>>>> I have chosen the cell length of 40 angstroms in Y direction
>>>>>>>>>> (slab length in y-direction is about 27.6 angstroms).
>>>>>>>>>> For the LiNbO3 slab consisting of 14 trilayers as stated in the
>>>>>>>>>> message of 9th January, I obtain the result of the Fermi energy:
>>>>>>>>>>
>>>>>>>>>> E_F = 11.174 eV (in comparison to the -0.8516 eV in case b) )
>>>>>>>>>>
>>>>>>>>>> This is unrealistic...should I have to enlarge the cell length in
>>>>>>>>>> y-direction or should I turn on the dipole correction?
>>>>>>>>>>
>>>>>>>>>> Phil
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Am Dienstag, 15. Januar 2019 12:31:22 UTC+1 schrieb Matt W:
>>>>>>>>>>>
>>>>>>>>>>> Ah, OK. The extended FFT lengths only works with FFTW not with
>>>>>>>>>>> the wavelet FFT.
>>>>>>>>>>>
>>>>>>>>>>> You do not need such a large vacuum with the wavelet solver as
>>>>>>>>>>> it is genuinely non-periodic. Place the slab in the center and 5A of vacuum
>>>>>>>>>>> either side should be sufficient - allow 10 A either side to get a clear
>>>>>>>>>>> decay to vacuum level(s). You will get two vacuum levels if you have a
>>>>>>>>>>> dipole. I don't know if wavelet will work with the dipole correction, I'd
>>>>>>>>>>> turn it off to start with.
>>>>>>>>>>>
>>>>>>>>>>> Matt
>>>>>>>>>>>
>>>>>>>>>>> On Tuesday, January 15, 2019 at 8:52:35 AM UTC, Phil G. wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> Hello again,
>>>>>>>>>>>>
>>>>>>>>>>>> have tried some attempts to start calculation with WAVELET
>>>>>>>>>>>> poisson solver, but all attempts have failed due to following error
>>>>>>>>>>>> messages:
>>>>>>>>>>>>
>>>>>>>>>>>> 1) the FFT in the x direction is not allowed
>>>>>>>>>>>> n01 dimension 154
>>>>>>>>>>>> (pw/ps_wavelet_util.F:358)
>>>>>>>>>>>>
>>>>>>>>>>>> ===== Routine Calling Stack =====
>>>>>>>>>>>>
>>>>>>>>>>>> 13 S_FFT_dimensions
>>>>>>>>>>>> 12 RS_z_slice_distribution
>>>>>>>>>>>> 11 ps_wavelet_create
>>>>>>>>>>>> the FFT in the x direction is not allowed
>>>>>>>>>>>> n01 dimension 154
>>>>>>>>>>>> 10 pw_poisson_rebuild
>>>>>>>>>>>> 9 pw_poisson_solve
>>>>>>>>>>>> 8 qs_ks_build_kohn_sham_matrix
>>>>>>>>>>>> 7 rebuild_ks_matrix
>>>>>>>>>>>> the FFT in the x direction is not allowed
>>>>>>>>>>>> n01 dimension 154
>>>>>>>>>>>> the FFT in the x direction is not allowed
>>>>>>>>>>>> n01 dimension 154
>>>>>>>>>>>> the FFT in the x direction is not allowed
>>>>>>>>>>>> n01 dimension 154
>>>>>>>>>>>> the FFT in the x direction is not allowed
>>>>>>>>>>>> n01 dimension 154
>>>>>>>>>>>> 6 qs_ks_update_qs_env
>>>>>>>>>>>> 5 scf_env_do_scf_inner_loop
>>>>>>>>>>>> 4 scf_env_do_scf
>>>>>>>>>>>> 3 qs_energies
>>>>>>>>>>>> 2 qs_forces
>>>>>>>>>>>> 1 CP2K
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> 2) after that I turn off the command EXTENDED_FFT_LENGTHS,
>>>>>>>>>>>> then:
>>>>>>>>>>>>
>>>>>>>>>>>> Index to radix array not found.
>>>>>>>>>>>> (pw/fft_tools.F:293)
>>>>>>>>>>>>
>>>>>>>>>>>> ===== Routine Calling Stack =====
>>>>>>>>>>>>
>>>>>>>>>>>> 6 pw_grid_setup
>>>>>>>>>>>> 5 pw_env_rebuild
>>>>>>>>>>>> 4 qs_env_rebuild_pw_env
>>>>>>>>>>>> 3 qs_env_setup
>>>>>>>>>>>> 2 qs_init_subsys
>>>>>>>>>>>> 1 CP2K
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> That's strange and I don't know what to do.
>>>>>>>>>>>> In my input file there are some info about commands:
>>>>>>>>>>>>
>>>>>>>>>>>> [...]
>>>>>>>>>>>> SURFACE_DIPOLE_CORRECTION .TRUE.
>>>>>>>>>>>> SURF_DIP_DIR Y
>>>>>>>>>>>> [...]
>>>>>>>>>>>> &MGRID
>>>>>>>>>>>> CUTOFF 600
>>>>>>>>>>>> NGRIDS 5
>>>>>>>>>>>> REL_CUTOFF 50
>>>>>>>>>>>> &END MGRID
>>>>>>>>>>>> [...]
>>>>>>>>>>>> &POISSON
>>>>>>>>>>>> POISSON_SOLVER WAVELET
>>>>>>>>>>>> PERIODIC XZ
>>>>>>>>>>>> &END POISSON
>>>>>>>>>>>> [...]
>>>>>>>>>>>>
>>>>>>>>>>>> [...]
>>>>>>>>>>>> &CELL
>>>>>>>>>>>> A 5.148 0.0 0.0
>>>>>>>>>>>> B 0.000 100.0 0.0
>>>>>>>>>>>> C 0.0 0.0 8.9166
>>>>>>>>>>>> PERIODIC XZ
>>>>>>>>>>>> &END CELL
>>>>>>>>>>>> [...]
>>>>>>>>>>>>
>>>>>>>>>>>> Phil
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Am Donnerstag, 10. Januar 2019 10:56:24 UTC+1 schrieb Phil G.:
>>>>>>>>>>>>>
>>>>>>>>>>>>> Dear Matt,
>>>>>>>>>>>>>
>>>>>>>>>>>>> how can find the potential in the vacuum (which type of
>>>>>>>>>>>>> potential? potential energy or electric/electrostatic potential?) ?
>>>>>>>>>>>>> For the case of electric/electrostatic potential, there is a
>>>>>>>>>>>>> flat curve with a step near the vacuum center as a consequence of dipole
>>>>>>>>>>>>> correction in Z direction, while in the bulk slab there is a periodic
>>>>>>>>>>>>> curve.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I will try to use the wavelet solver with PERIODIC XY.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Phil
>>>>>>>>>>>>>
>>>>>>>>>>>>> Am Mittwoch, 9. Januar 2019 14:05:04 UTC+1 schrieb Matt W:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hello again,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> did you find the potential in the vacuum and align to that?
>>>>>>>>>>>>>> You need to set a reference to get absolute values.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You could also try using the wavelet solver
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> &POISSON
>>>>>>>>>>>>>> PSOLVER WAVELET
>>>>>>>>>>>>>> PERIODIC XZ
>>>>>>>>>>>>>> &END
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> and PERIODIC XZ in the &CELL section. The Y direction must
>>>>>>>>>>>>>> be the non-periodic one. That gives an absolute reference (if there is no
>>>>>>>>>>>>>> dipole in the cell otherwise you need the dipole correction switched on).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> On Wednesday, January 9, 2019 at 8:18:58 AM UTC, Phil G.
>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Dear Matt,
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> thank you for your reply and good suggestions. Now I have
>>>>>>>>>>>>>>> let different LiNbO3 slab systems to be calculated:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> a) 14 trilayer system as from Sanna et al., *Appl. Surf.
>>>>>>>>>>>>>>> Sci.* *301* (2014), 70-78 with Nb-O3-Li2 surface
>>>>>>>>>>>>>>> termination on the one side of the slab and Li-O surface termination on the
>>>>>>>>>>>>>>> other side. Vacuum space of at least 40 Angstroms was included. The bulk
>>>>>>>>>>>>>>> region was already geometry-optimized and bulk atoms were fixed in the
>>>>>>>>>>>>>>> inner 6 trilayers. Geometry optimization on the whole slab system was
>>>>>>>>>>>>>>> performed and then the pdos of the system was calculated and plotted for
>>>>>>>>>>>>>>> every atom layers.
>>>>>>>>>>>>>>> Result: E_F = 0.1552 eV (fermi energy is overall constant,
>>>>>>>>>>>>>>> in every atom layers)
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> b) the same as a), but the bulk region was not already
>>>>>>>>>>>>>>> geometry-optimized before. Geometry optimization was performed and
>>>>>>>>>>>>>>> calculation of pdos.
>>>>>>>>>>>>>>> Result: E_F = - 0.8516 eV
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> c) the same as b), but 26 trilayers instead of 14 trilayers.
>>>>>>>>>>>>>>> Geometry optimization and calculation of pdos were performed.
>>>>>>>>>>>>>>> Result: E_F = 2.3372 eV
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So, I am wondering why these values differ so much. Should I
>>>>>>>>>>>>>>> need band structure calculation of the bulk LiNbO3 in order to find the
>>>>>>>>>>>>>>> global valence band edge maximum (with KPOINT calculation)?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Kind regards,
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Phil
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Am Freitag, 14. Dezember 2018 17:41:03 UTC+1 schrieb Matt W:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> In a periodic system the zero of the one electron levels is
>>>>>>>>>>>>>>>> arbitrary. If you need a reference you need to run a slab calculation with
>>>>>>>>>>>>>>>> vacuum or try to align semi-core states to something.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Matt
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On Friday, December 14, 2018 at 4:33:13 PM UTC, Phil G.
>>>>>>>>>>>>>>>> wrote:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Dear people and experts of CP2K,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> after the geometry optimization of the lithium niobate
>>>>>>>>>>>>>>>>> (LiNbO3) unit cell I would like to obtain pdos in order to determine the
>>>>>>>>>>>>>>>>> band gap and Fermi energy of the bulk system.
>>>>>>>>>>>>>>>>> After the calculation with ENERGY_FORCE I got pdos files
>>>>>>>>>>>>>>>>> of the three atoms (indexing depends on the z-position of the atoms) and
>>>>>>>>>>>>>>>>> I'm wondering about the value of Fermi energy: E_F = 0.300174 a.u. which is
>>>>>>>>>>>>>>>>> 8.168 eV. Is that not too high? And which energy has the value 0 and what
>>>>>>>>>>>>>>>>> is the reference? What is the Fermi energy defined in the language of CP2K?
>>>>>>>>>>>>>>>>> The energy band gap (HOMO-LUMO gap) of 3.62 eV agrees well
>>>>>>>>>>>>>>>>> with experimental values of 3.7 to 3.9 eV. But I cannot imagine that Fermi
>>>>>>>>>>>>>>>>> level has too high energy values.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Has anyone an idea what is the reason for such high Fermi
>>>>>>>>>>>>>>>>> energy values?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Here the input and output files are attached here.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Kind regards,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Phil
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
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