Temperature Dependent Effective Potentials (TDEP)

Briefly summarized, the package provides all the tools you need to build accurate model Hamiltonians for finite temperature lattice dynamics from first principles. TDEP includes several programs for different tasks:

• generate_structure: Generate supercells of target size, with options to make them as cubic as possible to maximize the real-space cutoff for the force constants.

• canonical_configuration: Create supercells with thermal displacements from an initial guess or existing force constants, using Monte Carlo sampling from a classical or quantum canonical distribution.

• extract_forceconstants: Obtain (effective) harmonic force constants from a set of supercell snapshots with displaced positions and forces. Optionally fit higher-order force constants.

• phonon_dispersion_relations: Calculate phonon dispersion relations and related harmonic thermodynamic properties from the second-order force constants.

• thermal_conductivity: Compute thermal transport by solving the phonon Boltzmann transport equation with perturbative treatment of third-order anharmonicity.

• lineshape: Compute phonon spectral functions including lifetime broadening and shifts for single q-points, q-point meshes, or q-point paths in the Brillouin zone. The grid mode computes spectral thermal transport properties as well.

More details, examples, and theoretical background can be found in the online documentation. See below which references should be cited for which program.

Tutorials

You can find a range of tutorials for realistic research workflow using TDEP in a dedicated repository.

Installation

Please find installation instructions in the TDEP repository.

Report bugs and issues

Please use our github issue tracker to report any problems. Please make sure to include input/output and log files so that we can reproduce and investigate the question.

Contribute

Please find instructions in the repository.

Other things to look at

• tdeptools a package to facilitate working with TDEP and perform additional postprocessing can be found here: https://github.com/flokno/tools.tdep

How to cite

This software is distributed under the MIT license. If you use it, please consider citing

F. Knoop et al., J. Open Source Softw 9(94), 6150 (2024)

and the respective publications for the algorithms that were used:

canonical_configuration

• Classical statistics: D. West and S. K. Estreicher, Phys Rev Lett 96, 115504 (2006)
• Quantum statistics: N. Shulumba, O. Hellman, and A. J. Minnich, Phys. Rev. Lett. 119, 185901 (2017)

extract_forceconstants

• Second order: O. Hellman et al., Phys Rev B 87, 104111 (2013)

• Third order: O. Hellman and I. A. Abrikosov, Phys Rev B 88, 144301 (2013)

• Fourth order: A. H. Romero et al., Phys Rev B 91, 214310 (2015)

thermal_conductivity

• Method: D. A. Broido et al., Appl Phys Lett 91, 231922 (2007)

• Implementation: O. Hellman and D.A. Broido, Phys. Rev. B 90, 134309 (2014)

• Fourth-order contributions: J. Klarbring et al., Phys Rev Lett 125, 045701 (2020)

• Off-diagonal contributions:

  • Simoncelli, M. & Marzari, N. & Mauri, F. (2019), Nat. Phys. 15 803-819
  • Isaeva, L & Barbalinardo, G. & Donadio, D. & Baroni, S., Nat. Comm. 10 3853 (2019)
  • Fiorentino, A. & Baroni, S, Phys. Rev. B, 107, 054311 (2023)

lineshape

• A. H. Romero et al., Phys Rev B 91, 214310 (2015)
• N. Shulumba, O. Hellman, and A. J. Minnich, Phys. Rev. Lett. 119, 185901 (2017)
• Grid mode for spectral transport: Đ. Dangić et al., Npj Comput Mater 7, 57 (2021)

Troubleshooting

Some common issues:

Symmetry errors

TDEP is very strict about crystal symmetries. In phonopy world, the symmetry precision is about 1e-10. If you see an error like

ERROR
exit code 4: symmetry error

chances are high that your structure input files are not perfectly symmetric and consistent. Precise input structures are a prerequisite for using TDEP successfully.