Force constant extraction with hiphive

Erik Fransson and Fredrik Eriksson

Link to tutorial

Link to user guide

Learning objectives

Force constants (FCs) are the primary tool for analyzing thermal properties of crystaline solids such as

  • phonon dispersion relations and density of states
  • vibrational free energies
  • thermal conductivity

In this tutorial you will learn how to use the hiphive package for efficiently extracting both second and higher order FCs from atomistic calculations.


The tutorial comprises three parts that cover respectively the extraction and analysis of second, third, and fourth-order FCs. These parts are provided in the form of jupyter notebooks along with supporting data.

Basic introduction and second-order FCs

  • preparation of reference data
  • force constant potential construction
  • thermal properties in the harmonic approximation

Third-order FCs

  • extraction of third-order FCs
  • calculation of the thermal conductivity using phono3py

Fourth-order FCs

  • construction of a fourth-order FC model for FCC-Ni
  • molecular dynamics simulations using this model
  • prediction of the mean square displacement

Additional material

When the above parts have been completed as well as users with prior experience with hiphive, some shorter notebooks are available that cover

  • convergence study for a provided Si dataset
  • extraction of harmonic force constants for a system with a defect
  • construction of a fourth-order model for a Ni surface


You need a laptop with a working Python3 environment with ASE 3.18.0 or newer and hiphive 0.5 or newer. To install hiphive run

pip3 install --user hiphive


Further information