Electron Density...

[Dipankar Saha]

Hello,
I wanted to know,
what  actually these peaks and valleys  are referring to? / Isn't it the ground state carrier density... obtained self-consistently??

Regards_
Dipankar

[Jess Wellendorff]

It is the average of the electron density, projected along an axis. It says nothing about which part(s) of the electron distribution are carriers.

[Dipankar Saha]

Thank you Jess for your reply..../ But, I didn't get what actually you meant by saying.....

"It says nothing about which part(s) of the electron distribution are carriers" .... Did you mean Neutral Atom Electron Density?  /


Moreover, does such a variation mean the directional  in-homogeneity in distribution?

[Jess Wellendorff]

The plot shows that average electron density (in units of 1/Angstrom^3) projected along the C axis. Yes, the plot does not show a straight line, so the electron density is (of course) inhomogeneous when you "walk around" in the unit cell. A particular electron may or may not be regarded a "carrier", depends on whether it is far below the valence band or not in a band structure calculation...

[Anders Blom]

Exactly, it's really easy (and seriously, how is that not obvious?): peak = high electron density,  valley = low density! And what would it have to do with selfconsistency? I don't understand the question, Dipankar...

[Dipankar Saha]

Dr. A . Blom,

Thank u for the reply...  / By saying  "self-consistency" ..... I just wanted to mean..... from the initial guess, how  DFT calculation obtains the final ground state value..!!! Tell, me  if it's not so....

Now, as the output of the mixing algorithm... ultimately whatever that we will get must be a number  .....!!

But, if I think in real scenario....it should not be... and you are correct.....there must be variations...../ But my point is.... how that variation can be so continually repeating .... Rather I find that the cut-plane gives it properly (color bar showing the variation in density across the diff. atoms, bonds and vacuum )..... / That's why I was a getting confused ...that whether this variation in the 1D plot is actually showing any in-homogeneity...or, interpreting something else?

[Anders Blom]

Thank u for the reply...  / By saying  "self-consistency" ..... I just wanted to mean..... from the initial guess, how  DFT calculation obtains the final ground state value..!!! Tell, me  if it's not so....

Of course, DFT is always self-consistent, that's a basic thing.

Now, as the output of the mixing algorithm... ultimately whatever that we will get must be a number  .....!!

A number? For what? The electron density is a 3D function in space, rho(x,y,z). Not "a number".

But, if I think in real scenario....it should not be... and you are correct.....there must be variations...../ But my point is.... how that variation can be so continually repeating .... Rather I find that the cut-plane gives it properly (color bar showing the variation in density across the diff. atoms, bonds and vacuum )..... / That's why I was a getting confused ...that whether this variation in the 1D plot is actually showing any in-homogeneity...or, interpreting something else?

Well, that depends on what the system is, which I have no way of knowing since you didn't include any information about that. But generally there is of course a lot of inhomogeneity in the cell, the atoms are discrete and are connected with bonds which actually represent electron density.

[Dipankar Saha]

Dr. A . Blom,

Thanks a lot......!!! 

rho(r) ....is the charge density which is a three dimensional object....  and can be equated with the square of the wave-function i.e., |psi(r)| ^2    ....../ On the other hand, what  I find ......the electron density of the system  [n(r) ] provides the information regarding the occupied eigenstates ..... Thus, there is always a concept of Fermi function...../ Is this the correct way to differentiate  or,   correlate  b/w rho(r) and n(r) ?? Besides,  when it says avg. (for any of the directions)....what avg. it actually projects?

Regards_
Dipankar

[Anders Blom]

rho(r) ....is the charge density which is a three dimensional object....  and can be equated with the square of the wave-function i.e., |psi(r)| ^2

That is not correct. Maybe for a single particle in vacuum, but not in DFT. You can write the density as the sum of the wave function amplitudes of all occupied states though.

The "average" in the plugin means that you can specify to plot the density or any other 3D grid as function of Z, averaged over X and Y, for instance.

[Dipankar Saha]

That is not correct. Maybe for a single particle in vacuum, but not in DFT. You can write the density as the sum of the wave function amplitudes of all occupied states though.

May be you wanted to mean...that how those wave functions are expanded in a set of basis functions...to fit the 1 elec.  K-S_Hamiltonian into a many body problem (with,  the Hamiltonian matrix H_ij ) ..... and the n(r) is calculated conveniently using the Density matrix, D_ij ....

But, my emphasis was on the terms charge and electron densities (way these are  used in ATK) ...../ If I consider only the Real parts of Density Matrix...then the charge density and the electron density are synonymous...??!!  Is it correct?

The "average" in the plugin means that you can specify to plot the density or any other 3D grid as function of Z, averaged over X and Y, for instance.

Okayyyy...!!! Thanks.....once again ...

[Dipankar Saha]

Considering MO theory....if the charge balance within a  particular system (not an interfaced struct. , so no charge redistribution here...) ends up forming a neutral one ......with some depletion and accumulation regions (as per the vacuum region and the various atoms  within the system)......then how can I dope such a system in to a 'p' type one??  Rather, my question is..... looking at what criteria..... I should say...that the charge neutral sample is now converted into the 'p' type  sample?

[Dipankar Saha]

I find the electron-diff density is varying from some "-Ve" value (say, -0.36  Ang^-3) to a "+Ve" one ( say, 0.45  Ang^-3) .....

What does a "-Ve" value of electron-diff density interpret ?

[Jess Wellendorff]

The electron difference density is the difference between the self-consistent valence electron density and the superposition of atomic valence electron densities. This will show you if charge transfer has occurred when the device was assembled from free atoms (in practice impossible, but illustrative from a theoretical point of view). Negative electron difference density indicates charge depletion. Obviously, depletion in one region implies accumulation in another region (positive electron difference density).

[Dipankar Saha]

Thank you Jess for your reply...
______________________________

Negative electron difference density indicates charge depletion. Obviously, depletion in one region implies accumulation in another region (positive electron difference density).

If the negative value of electron difference density  relates to charge depletion....then what is meant by the zero??!!   In this context, I want to mention that....instead of electron difference density, if I look at the electron density ... then I find.....it varies from zero(obviuosly the vacuum region...) to some  '+Ve'  value....!!!

[Jess Wellendorff]

OK, let me explain it like this:

1) the electron density is the selfconsistent density of valence electrons in the Kohn-Sham system - it can be either zero or positive. The integral of the electron density over all space in the unit cell is equal to the total number of valence electrons in the calculation.

2) the electron difference density illustrates how the selfconsistent valence electron density is different from what it would have been if the electrons from neighboring atoms did not interact at all. When bringing atoms together to form e.g. a device, the ground state valence electron density around each atom is redistributed because of electron-electron and electron-nucleus interactions. The electron difference density is a representation of this redistribution.

See also http://quantumwise.com/forum/index.php?topic=2283.0 and  http://www.quantumwise.com/documents/manuals/ATK-13.8/ReferenceManual/ref.electrondifferencedensity.html.