DFT + Hubbard U, PDOS

This tutorial will show you how to perform a single point calculation with the DFT+U formalism using the BAND engine.

Step 1: amsinput

1. Start AMSinput
2. Switch to BAND: ADFPanel → BANDPanel
/scm-uploads/doc.2023/Tutorials/_images/amsinput_BAND_Main.png

Step 2: Setup the system - NiO

You can copy-paste the following information into the AMSinput directly.

2

Ni    0.000  0.000  0.000
O     2.085  2.085  2.085
VEC1  0.000  2.085  2.085
VEC2  2.085  0.000  2.085
VEC3  2.085  2.085  0.000

By default, only the central unit cell is shown. To see a few unit-cell repetitions:

1. Click on View → Periodic → Periodic View Type → Repeat Unit Cell
2. Use the mouse to rotate (right mouse button) and translate (left mouse button) the crystal to your favorite orientation.

Note

If needed. To repeat the unit cell in each direction, choose the range [-1,1]. Click on View → Periodic → Unit Cell Range…. In the first cell of the pop-up window, enter 1. The other cells will automatically update with the proper range.

/scm-uploads/doc.2023/Tutorials/_images/geom.png

Step 3: BP86 without Hubbard

Change the calculation setup (Unrestricted, XC functional, basis set) as follows:

1. Check the Unrestricted box.
2. Set XC functional to GGA:BP86.
3. Set Basis Set to TZP
4. Tick the checkbox PDOS
/scm-uploads/doc.2023/Tutorials/_images/Hubbard_2.png

Step 3a: Run the calculation

Now you can save and run the calculation.

File → Save, give it a name and press Save.
File → Run

Note

AMSjobs should come to the foreground, and your job should be visible at the top. On the right side you can see that the job is running (this is indicated by the gear-icon). When running, in the AMSjobs window the progress of your simulation is showing (from the logfile).

Step 3b: Checking the results

After the calculation finished, you can check the Output for the ‘Band Gap Info’.

SCM → Output
Properties → Band Gap Info

One can see that there is no band gap at all. This contradicts experimental studies, which predict values between 3.7 to 4.3 eV.

/scm-uploads/doc.2023/Tutorials/_images/BP_Output_BandGapInfo.png

Plotting and examining the partial density of states (pDOS) for this calculation reveals that the d-orbital contributions of Ni are crossing the Fermi level.

SCM → DOS
In the system viewer on the left, select a Ni atom
Choose Partial → Ni(1) → d-DOS
Make a double click on the Energy axis and change its minimum and maximum values.
X Axis → Minimum value: -15
X Axis → Maximum value: -2 then OK.
/scm-uploads/doc.2023/Tutorials/_images/Ni_D_DOS_BP.png

Step 4: Run the calculation - BP86+U

Go back to the Main menu of amsinput, change to HubbardU menu, and apply an U value of 0.6 a.u. to the d-orbitals of the Ni atom.

Go to Model → HubbardU.
Set for Ni the l-value to d and the U value to 0.6.
/scm-uploads/doc.2023/Tutorials/_images/Hubbard_4.png

This will influence the Hamiltonian and results in a state which tries to omit partial occupation or degeneracy with reference to the d-orbitals.

Step 4a: Run the calculation

Now you can save and run the calculation.

File → Save As…, give it a name and press Save.
File → Run

Step 4b: Checking the results

After the calculation finished, you can check the Output for the ‘Band Gap Info’.

SCM → Output
Properties → Band Gap Info

One can see that there is now a band gap of around 2 eV. This is still less than the experimental values. That can be traced back to the neglection of the correct magnetic behavior of NiO.

/scm-uploads/doc.2023/Tutorials/_images/BP+U_Output_BandGapInfo.png

Plotting and examining the partial density of states (pDOS) for this calculation reveals that the d-orbital contributions of Ni are no longer crossing the Fermi level.

SCM → DOS
Select the Ni atom.
Choose Partial → Ni(1) → d-DOS
Make a double click on the Energy axis and change its minimum and maximum values.
X Axis → Minimum value: -25
X Axis → Maximum value: 5 then OK.
You can move the legend with the mouse by drag and drop it to the desired location.
/scm-uploads/doc.2023/Tutorials/_images/Ni_D_DOS_BP+U.png

You can also shift the Fermi energy to 0, if you prefer:

Graph → Shift Fermi Energy To Zero
/scm-uploads/doc.2023/Tutorials/_images/shifted_fermi.png