# PDOS calculation with Quantum Espresso (need help for further analysis)

I have two silicon in an unit cell, for a test calculation. Each silicon as 12 electrons in the pseudopotential (1s is frozen). I have done the partial density of states (PDOS) calculation using DFT with QUANTUM ESPRESSO. What I need to know is, I have been suggested to do the following two tasks (which instructs like):

1. Take your PDOS summed over the different atomic orbitals (2s, 2p, 3s, 3p, 3d), and summed over energies up to the Fermi level (i.e. all the occupied states)
2. Then subtract this from the total number of electrons in the unit cell. It will find the number of electrons that are not in those atomic orbitals (this is the ultimate goal of the task).

Could you please suggest me how to solve these two to get the number of electrons that are not in those atomic orbitals (any process or modification of input files or steps or resource links would be greatly appreciated)?

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Note (optional, in case it gives more insight): I got the Fermi energy value as 21.653 eV from the DOS calculation. My DOS input code:

&DOS
prefix='silicon'
outdir='.',
DeltaE=0.2,
Emin=-119.233,
Emax=109.567,
fildos='si.dos',
/


And my PDOS input was

&projwfc
prefix='silicon'
outdir='./'
degauss=0.2
DeltaE=0.2
filpdos='si.pdos.dat'
/


From DOS calculation, the output data obtained is like this (shown portion to get idea):

#  E (eV)   dos(E)     Int dos(E) EFermi =   21.653 eV
-119.233  0.1148E-84  0.2295E-85
-119.033  0.1148E-84  0.4591E-85
-118.833  0.1148E-84  0.6886E-85


And from the PDOS calculation, the output data files from one atom are (shown portions to get ideas):

For 2s:

# E (eV)   ldos(E)   pdos(E)
-119.233  0.379E-04  0.379E-04
-119.033  0.589E-04  0.589E-04
-118.833  0.907E-04  0.907E-04


For 2p:

# E (eV)   ldos(E)   pdos(E)    pdos(E)    pdos(E)
-119.233  0.174E-08  0.580E-09  0.580E-09  0.580E-09
-119.033  0.271E-08  0.902E-09  0.902E-09  0.902E-09
-118.833  0.416E-08  0.139E-08  0.139E-08  0.139E-08


For 3s:

# E (eV)   ldos(E)   pdos(E)
-119.233  0.327E-06  0.327E-06
-119.033  0.511E-06  0.511E-06
-118.833  0.788E-06  0.788E-06


and for 3p:

# E (eV)   ldos(E)   pdos(E)    pdos(E)    pdos(E)
-119.233  0.149E-05  0.498E-06  0.498E-06  0.498E-06
-119.033  0.232E-05  0.773E-06  0.773E-06  0.773E-06
-118.833  0.356E-05  0.119E-05  0.119E-05  0.119E-05


The PDOS image for this case is:

• For item (1) I think that you need to do an integral instead a sum, as you got a "continuous" curve. Using a graphical software like ORIGIN, for example, you can integrate those curves numerically. Be aware that building those curves you used a smearing value (as the DOS is build as a sum of Gaussian or Lorentzian functions). For item (2), I think that there is something wrong as the electrons have to be distributed in all those orbitals.
– Camps
Oct 28, 2022 at 22:30
• Thanks @Camps for your suggestions. Regarding (1), I would then try to see ORIGIN. Or even I can use python too, using any numerical approximation method using the data of the files. Just could you elaborate, what I need to do actually (I mean a pseudocode or flow-chart)? For (2), actually there is minor charges in empty spaces - these are called electrides. That's why need to estimate the charge outside of these orbitals. Could you please suggest any for (2)?
– Sak
Oct 29, 2022 at 15:56
• How the charges are in "empty space" out of they orbitals calculated from the Schrodinger equation? Aren't all the possible states calculated from Schrodinger equation?
– Camps
Oct 31, 2022 at 15:29
• Hi Sak, would it be easy for you to answer the questions by Camps? Nov 12, 2022 at 0:40
• Hi @Camps, I am not sure. But recent papers show that charges can remain out of orbitals (interstitial space) forming electride materials.
– Sak
Nov 12, 2022 at 18:07