Lattice Optimization and Phonons
********************************

DFTB Materials Science Lattice optimization Electronic band structure
Phonons Phonon band structure Thermodynamics Crystal

This tutorial will show you how to:

* Perform a geometry optimization (including lattice vectors
  optimization) for a periodic system

* Calculate and visualize the phonon dispersion curves


Set up the calculation
======================

Let us begin by starting up the AMSinput GUI module:

   1. Start **AMSjobs**
   2. Click on **SCM → New Input**. This will open **AMSinput**
   3. In **AMSinput**, select the DFTB panel: [image: ADFPanel][image] **→** [image: DFTBPanel][image]

Now we will import the silicon structure from our database:

   1. Search for **Si** in the **search box** [image: Search][image]
   2. Scroll down to the **Crystals** section and select **Crystals → Si**
 [image]

Phonons should be calculated on an optimized geometry. We therefore
first need to perform a geometry optimization:

   In the **Main panel**
   1. Select **Task → Geometry Optimization**

By default, only the internal degrees of freedom are optimized in a
geometry optimization (i.e. the atomic positions within the unit cell
are optimized, but the lattice vectors are **not** optimized). In
order to obtain a proper phonon spectrum, one **needs to optimize the
lattice vectors as well as the internal degrees of freedom**. When
optimizing the geometry for a phonon calculation, we generally
recommend using tight convergence thresholds for both the nuclear and
lattice degrees of freedom.

   1. Click on **Details → Geometry Optimization**
   2. **Tick** the **Optimize Lattice** check-box
   3. Set the **Convergence** to **Very Good**
 [image]

Finally we also need to specify that we want to calculate phonons at
the end of the optimization.

   1. Switch to the **Properties → Phonons and Elastic tensor** panel
   2. **Tick** the **Phonons** check-box

Optionally, you can tweak the settings of the phonon calculation in
the panel **Details → Phonons**. Using a larger super cell in
**Details → Phonons** will result in more accurate phonon curves, but
will also significantly increase the computation time.

[image]

We will now set a few options specific to DFTB.

   1. Go to the **Main panel**
   2. Select **Model → SCC-DFTB**
   2. Select **Parameter Directory → DFTB.org/hyb-0-2**
   3. Go to the **Details → K-Space Integration** panel
   4. Set **K-space grid type** to **Symmetric**
 [image]

We explicitly ask for the symmetric k-space integration grid for our
calculation of silicon, which is a highly symmetric system. For such a
system the symmetric grid is more accurate and faster. However, unless
your system is highly symmetric, we recommend using the default
(regular) grid.


Run the calculation
===================

We are now ready to run the calculation.

   1. Click on **File → Save** and name it "silicon_phonons"
   2. Click on **File → Run**

This will open **AMSjobs** and start the calculation. You can monitor
the progress of your calculation by opening the log file:

   In **AMSjobs**:
   1. Right-click on your job and select **Logfile** to see the log file
   2. Right-click on your job and select **Movie** to monitor the progress of the geometry optimization
   3. Click on **Properties → Lattice info → Lattice Vectors** to monitor also the lattice optimization
   3. Wait for the calculation to finish. It should only take a couple of steps.
 [image]

As you can see the high symmetry of the system is maintained: All
angles between the lattice vectors are 60 degrees and all vectors keep
the same length. However, the entire crystal has expanded ever so
slightly. (The strict nuclear gradients convergence threshold we set
earlier actually did not matter, as all the nuclear gradients
disappear due to the symmetry of the system. We were therefore
essentially only optimizing the lattice degrees of freedom.)


Visualize the Phonons
=====================

Once the calculation is completed, you can visualize the phonon
dispersion curves:

   In **AMSjobs**, right-click on your job and select **Band Structure**

This will open the AMSbandstructure visualization program:

[image]

You can visualize the motion of the atoms for certain modes (marked by
a blue dot in the dispersion curves):

   Click on one of the "Modes" dots in the phonon dispersion curves
 [image]

Thermodynamic properties derived from the phonon calculation are
printed to the output file. To open the output file:

   In **AMSjobs**, right-click on your job and select **Output**
   In **AMSoutput**, search for "Thermo"
 [image]
