# [CP2K-user] [CP2K:17074] Re: Density of states with k-points in CP2K

Marcella Iannuzzi marci.akira at gmail.com
Fri Jun 3 09:38:05 UTC 2022

```
Hi,

The Fermi energy is not well defined for electronic structures with an
energy gap.
Using the Fermi-Dirac distribution, CP2K sets the Fermi energy somewhere in
the middle of the gap.

The histogram calculated by activating PRINT%DOS is just counting the
number of eigenvalues falling into each histogram bit.
The partitioning of the histogram in bits is determined from the DELTA_E
keyword, the default of this is 0.001.
The final value of the density (sum of states per bit) is then normalised
by the number of NMO.
The column occupation reports the sum of the occupation numbers of the
eigenstates with energy falling into the corresponding bit.
For small DELTA_E, there are bits with zero density and zero occupation
number.
Setting DELTA_E to zero, the histogram is replaced by simply the list of
eigenvalues.

When using k-point sampling the procedure is more or less the same, but
each contribution to the density as well as each contribution to the
occupation are multiplied by the weight of the corresponding k-point.

Regards
Marcella

On Thursday, June 2, 2022 at 10:05:09 PM UTC+2 nwi... at berkeley.edu wrote:

> It is a static calculation, so iteration = 0. I redid the calculation with
> cell optimization. Didn't seem much of change. Here at the plots using the
> occupation first and the density second. I set fermi level to be 0, and it
> doesn't put it anywhere near the VBM like we expect. In the second case it
> looks like there is a gap, but its too big.
>
> Any knowledge maybe about the definition of fermi level? Maybe that's
> where I'm tripping up.
> [image: Screen Shot 2022-06-02 at 1.00.02 PM.png]
> Do you know anything about the fermi level definition?
> [image: Screen Shot 2022-06-02 at 12.59.51 PM.png]
> On Thursday, June 2, 2022 at 9:04:42 AM UTC-7 wave... at gmail.com wrote:
>
>> Hi
>>
>> It's not clear to me why you are looking at the first step. Did it
>> converge in just one step?
>>
>> At any rate, you'll notice a difference between &DOS and &PDOS. PDOS
>> returns values per orbital (s, p, d, f). If I understand it correctly, the
>> density is the DOS as a solid state physicist would understand it, and
>> occupation gives you a fractional filling at that energy. Not quite the
>> same thing.
>>
>> Regards
>> Sam
>>
>> On Wednesday, June 1, 2022 at 7:39:20 PM UTC+2 nwi... at berkeley.edu wrote:
>>
>>> Hi everyone,
>>>
>>> I know that DOS and points aren't what people first think of when using
>>> cp2k, but the functionality does seem to be there in some limited way...
>>>
>>> Anyway, I'm wondering how to properly use it, because my test case
>>> doesn't look right. I'm running a point calculation on GaAs with a 16x16x16
>>> Monkhorst-Pack pack grid and then printing the total DOS. I then take the
>>> columns from the DOS file (head attached) and plot energy (column 1)
>>> against occupation (column 3) using the reported Fermi energy from the
>>> output file of ~0.14 Ha. This results in a DOS where the Fermi energy does
>>> not line up with the VBM. What's more, if I visually inspect this DOS, the
>>> band gap of GaAs is >1eV. While that is closer to the experimental value,
>>> the reported band gap using GGA PBE is closer to 0.3eV.
>>>
>>> Questions:
>>> (1) What is the distinction between columns 2 and 3 in the DOS file?
>>> They give similar, but not equivalent looking dos plots.
>>> (2) Is the Fermi energy printed in the output file the same as the Fermi
>>> energy of the DOS, or is it defined different?
>>>
>>> I've attached my input file for reference. Thanks in advance.
>>>
>>>  # DOS at iteration step i = 0
>>>
>>>     Energy[a.u.]       Density     Occupation
>>>
>>>     -0.40682067         0.0009         0.0957
>>>
>>>     -0.40582067         0.0015         0.1543
>>>
>>>     -0.40482067         0.0000         0.0000
>>>
>>>     -0.40382067         0.0000         0.0000
>>>
>>>     -0.40282067         0.0034         0.3516
>>>
>>>     -0.40182067         0.0026         0.2656
>>>
>>>     -0.40082067         0.0038         0.3828
>>>
>>>     -0.39982067         0.0000         0.0000
>>>
>>> [image: Screen Shot 2022-06-01 at 10.32.10 AM.png]
>>>
>>

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