Crystalline solids are often characterized by a collective vibrations of atoms. In solid state physics, these collective vibrations are described by “phonons,” defined as the discrete quanta of collective atomic vibrations. Since atomic motions are present for all temperatures, so are phonons. Understanding phonon behavior is, therefore, crucial for exploring the properties of crystals. One way to do this is using computer simulations. In fact, due to the exponential increase in computing power in the last few decades, phonon simulations using first principles has become a practical approach in several fields of science and engineering.

In this review article, researcher Atsushi Togo from National Institute for Materials Science and Kyoto University in Japan takes stock of the current state-of-the-art first principles phonon calculation techniques, with a focus on the finite displacement supercell approach.

The review first looks at phonon calculations under the harmonic approximation, showing how, using the finite displacement supercell approach and phonon coordinates, harmonic phonon properties like thermal properties at constant volume and atomic displacements are calculated.

The review then considers phonon properties including quasi-harmonic approximations. These include descriptions of thermal expansion and structural phase transitions.

Next, phonon-phonon interactions are discussed as anharmonic phonon calculations and how they can be used for calculating the lattice thermal conductivity.

Finally, the article describes a computational workflow for typical phonon calculations with an eye on automation for more efficient use of computing power.

Overall, the present capabilities can help describe material properties better and more reliably, leading to advances in computing, development of wearable devices, and automobile fuel efficiency, among others.