Script for calculating the voltage drop.

[nori]

I offer some calculation examples of voltage drop.
All calculations were done with the algorithm "ElectrodeConstraints.DensityMatrix".

As Nordland mentioned above, "ElectrodeConstraints.DensityMatrix" instead of "ElectrodeConstraints.Off" should be used when you calculate the voltage drop.
But in some cases such as "Au-DTB-Au", you might get less convergence of SCF with "ElectrodeConstraints.DensityMatrix" (More correctly, the electronic structure that seems to be strange is obtained).
Then, you had better use "ElectrodeConstraints.RealSpaceDensity" instead of "ElectrodeConstraints.DensityMatrix".

[M.Albert]

Thank you ,Nordland.
But I have some questions.As we know ,the length of central scattering region
is 17.136A in Z axial in lih2li two probe system.You plot voltage drop from 0 to 140 Bohr(0 to 74.2 A)in the picture.What is the origin,the first Li atom in the central scattering region from the left?
Do you consider the voltage drop in the electrode in the picture?

[Nordland]

Yes, as the potential calculated by ATK includes a padded layer of the electrode, the voltage drop includes the voltage drop into the first layer of the electrode. The origin is the left side of this paddede electrode layer in the left side.

[M.Albert]

Sorry I don't know what's the mean about " a padded layer of the electrode".
The whole length of the lih2li system is 40.34A.Why you plot 140 Bohr,that is 74.2A?
Secondly, there are 4 Li atoms in the left electrode(also the right),then next is the first Li atom in the center scattering region which I call "Li(1)".
The origin is "Li(1)" I mentioned above. Is that right.
Lastly,why your picture is not symmetric?I think lih2li is a symmetric system.

[Nordland]

I will try to illustrate it with a drawning done in ASCII

Left        |     Scattering region   |   Right
Li Li Li Li | Li Li Li Li H H Li Li Li Li | Li Li Li Li

So the scattering region is the number of elements you have entered as the scattering position in the TwoProbe configuration. Once the calculation starts, ATK includes the first layer of the electrode on each side, also called padding layers, and when the potential/voltage drop is calculated, the potential extends into these padding layers, therefore the value Z=0 bohr is the potential at the left side of the padded electrode layer. And the Z=140 bohr is the at the right side of the right padded layer.
Therefore the atoms you have specifed for the scattering region, is in the middle of the plot.

Yes, the Li-H2-Li is symmetric, and so should the voltage drop be, but it is a matter of convergence, if the tolerance is low!

[Anders Blom]

The word "padding" should probably be avoided; the voltage drop (and all 3D grid quantities such as the electron denstiy etc) is simply computed over the left electrode + central cell + right electrode. This can easily be seen when plotting them in VNL together with the two-probe geometry.

Second, 70 Angstrom corresponds to over 24 "lattice constants"; the Li-Li distance is 2.88 Angstrom in these scripts, so probably the calculation behind the plot from 0 to 140 Bohr was for a larger system, with more atoms in the electrode and central region?

[Nordland]

The Li-H2-Li system has 6 atoms in each electrode, and 6 Li atoms on each side of the H2, making it a total of 26 atoms.

[nori]

Yes, the Li-H2-Li is symmetric, and so should the voltage drop be, but it is a matter of convergence, if the tolerance is low!

It seems there is no need for this system to have the symmetric voltage drop under finite bias.
Because the non-equilibrium part of the electron density exists.

I'll give you the example with attached, which is the voltage drop of au111_vacuum_au111 system.
The structure has symmetry but the voltage drop does not.
You can understand that It's reasonable with the following reasons:

# As regards left electrode part, any incident electron can't be transmitted from right to left due to vacuum region, so that the electric structure does not change compared with equilibrium and the potential gets flat-shift.
# As regards right electrode part, all incident electrons are perfectly reflected , so that the electric structure changes compared with equilibrium and the potential gets more complex.

That's why the voltage drop Norland offered has no matter.

[Anders Blom]

If you are interested in computing the voltage drop, you might find my new post on extracting the effective potential from a VNL file useful!

See http://quantumwise.com/forum/index.php?topic=3.msg3210;topicseen#msg3210

[zdhlover]

I offer some calculation examples of voltage drop.
All calculations were done with the algorithm "ElectrodeConstraints.DensityMatrix".

As Nordland mentioned above, "ElectrodeConstraints.DensityMatrix" instead of "ElectrodeConstraints.Off" should be used when you calculate the voltage drop.
But in some cases such as "Au-DTB-Au", you might get less convergence of SCF with "ElectrodeConstraints.DensityMatrix" (More correctly, the electronic structure that seems to be strange is obtained).
Then, you had better use "ElectrodeConstraints.RealSpaceDensity" instead of "ElectrodeConstraints.DensityMatrix".

I have been build all the two-probe system as you post, but I could't get none of the beautiful pictures of voltage drop as your examples,where is my problem?
I have been notice the use of "ElectrodeConstraints.DensityMatrix" instead of "ElectrodeConstraints.Off" when I calculate the voltage drop.

The append files is my au(111) scripts and outputs,all computation performed in VNL 2008.10.

  I have been modify the scripts  that upload before because the wrong monkhorst_pack_parameters,but also the same results. And upload the modified scripts and results.

I also  test the FFT methods,but also the same results,and I can't get nori's beautiful  image!Why?

[nori]

I regard your voltage drop as qualitatively the same as mine.
Perhaps the quantitative difference comes from k-point sampling.
I couldn't find out the script used for the calculation in my hard disc, so that I'm not sure precise k-point sampling in my calculation.
However, it would probably not be (10,10,10) but like (6,6,100).
  

[zdhlover]

I regard your voltage drop as qualitatively the same as mine.
Perhaps the quantitative difference comes from k-point sampling.
I couldn't find out the script used for the calculation in my hard disc, so that I'm not sure precise k-point sampling in my calculation.
However, it would probably not be (10,10,10) but like (6,6,100).
 

I also test the k-point sampling  like (6,6,100)and even better ,but he same results happen? And I am very interesting to know how can I get the very beautiful voltage-drop image as you.

[zdhlover]

Thanks nori and Anders Blom，the last voltage-drop I get is same as nori's.
After my  handling, I get the beautiful image as below!

Thanks again!
Wish good luck!

[ipsecog]

@zdhlover: Your two last images are identical, I think, and not exactly the same as Nori's. Can you check, and perhaps also post the final script that made it all work out, for the benefit of others?

[zdhlover]

I offer some calculation examples of voltage drop.
All calculations were done with the algorithm "ElectrodeConstraints.DensityMatrix".

As Nordland mentioned above, "ElectrodeConstraints.DensityMatrix" instead of "ElectrodeConstraints.Off" should be used when you calculate the voltage drop.
But in some cases such as "Au-DTB-Au", you might get less convergence of SCF with "ElectrodeConstraints.DensityMatrix" (More correctly, the electronic structure that seems to be strange is obtained).
Then, you had better use "ElectrodeConstraints.RealSpaceDensity" instead of "ElectrodeConstraints.DensityMatrix".

I have been build all the two-probe system as you post, but I could't get none of the beautiful pictures of voltage drop as your examples,where is my problem?
I have been notice the use of "ElectrodeConstraints.DensityMatrix" instead of "ElectrodeConstraints.Off" when I calculate the voltage drop.

The append files is my au(111) scripts and outputs,all computation performed in VNL 2008.10.

  I have been modify the scripts  that upload before because the wrong monkhorst_pack_parameters,but also the same results. And upload the modified scripts and results.

I also  test the FFT methods,but also the same results,and I can't get nori's beautiful  image!Why?

Please notice the difference of unit between me and nori's image.
and the the final scripts that made it all work out as same that I have been send it above ,but only modify the k-point sampling  to (6,6,100).as nori said.