August 31, 2018

# Fast and accessible phonon calculations

Our recent manuscript: https://arxiv.org/abs/1808.10011 Phonon is a collective excitation in a periodic arrangement of atoms or molecules in like solid crystals and some liquids. Often designated as a quasiparticle it represents an excited state…

Our recent manuscript: https://arxiv.org/abs/1808.10011 Phonon is a collective excitation in a periodic arrangement of atoms or molecules in like solid crystals and some liquids. Often designated as a quasiparticle it represents an excited state…

#### What is a phonon?

Phonon is a collective excitation in a periodic arrangement of atoms or molecules in solid crystals and some liquids. Often designated as a quasiparticle it represents an excited state characterized by the modes of the interacting atoms. Phonons play a major role in many of the physical properties of materials, such as thermal and electrical conductivity, for example.

#### How to calculate phonons?

One of the ways to calculate phonons is to use Density Functional Perturbation Theory [2] and extract the dispersion relations that can tell how a material responds to an atomic vibration at a specific frequency and shape. This approach is well established and accurate, however, very computationally demanding. In order to calculate the phonon dispersions we need to repeat a total energy calculation for each of the perturbations of the original crystal lattice. Even when we only have 2 atoms in the unit cell, there are already 2*3 = 6 phonon modes.

In order to produce the spectra that take into account sophisticated displacements like the one pictured above, one usually needs to calculate the phonon frequencies on a grid of so called “q-points”, with even the simplest 2x2x2 grid increasing the amount of calculation 8-fold (without considering the symmetry). Thus phonons are usually two or three orders of magnitude more computationally expensive than the total energy calculations. The real limitation, however, is the wait time, as needing to spend a month before a calculation can complete .

#### How to speed up the phonon calculations?

We deploy a “map-reduce” type embarrassingly parallel workflow (as originally explained in [3]) and split the phonon calculation into many small independent tasks for each q-point and each irreducible representation.

Cloud computing is a perfect fit for this, because it allows one to provision and terminate the resources on-demand and get through all the independent tasks in parallel. This way the human time is limited by the duration of the longest individual task, which is comparable with a simple total energy calculation. Moreover, this approach also works well for large systems with many atoms in the crystal unit cell, since each individual task only has to deal with a single atomic displacement.

#### Can I see it in action?

Yes. In the video below we demonstrate the approach for a crystal of ZnO, where the calculation of the electronic structure is using a 10x10x10 k-point grid, and the phonons are computed on a 6x6x6 q-point grid. From start to finish it takes 52 min total. Readers can access the input and output data of the above run at this link and further clone and adapt the workflow to their taste and calculate phonon dispersions for other materials using platform.exabyte.io.

A screencast demonstrating an example grid-parallel phonon dispersion calculation for ZnO performed at platform.exabyte.io.