phq: A Fortran code to compute phonon quasiparticle properties and dispersions

Z. Zhang, D. B. Zhang, T. Sun, R. M. Wentzcovitch

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We here introduce a Fortran code that computes anharmonic free energy of solids from first-principles based on our phonon quasiparticle approach. In this code, phonon quasiparticle properties, i.e., renormalized phonon frequencies and lifetimes, are extracted from mode-projected velocity auto-correlation functions (VAF) of modes sampled by molecular dynamics (MD) trajectories. Using renormalized frequencies as input, the code next constructs an effective harmonic force constant matrix to calculate anharmonic phonon dispersions over the whole Brillouin zone and thus the anharmonic free energy in the thermodynamic limit (N→∞). A detailed description of all the input parameters and the subroutines is provided as well. We illustrate the use of this code to compute ab initio temperature-dependent anharmonic phonons of Si in the diamond structure. Program summary: Program Title: phq Program Files doi: Licensing provisions: GPLv3 Programming language: Fortran 90 Nature of problem: Accurate free energy calculations deliver predictive thermodynamic properties of solids. Although the quasi-harmonic approximation (QHA) has been widely used for various materials, its validity at very high temperatures is not guaranteed because of intrinsic anharmonic effects. The QHA cannot be used even at low temperatures for strongly anharmonic systems, e.g., those that are stabilized by anharmonic fluctuations. When anharmonicity is non-negligible, phonon frequencies display a pronounced dependence on temperature, which impacts thermodynamic properties. Therefore, the calculation of anharmonic phonon dispersions is critical for an accurate estimation of the free energy. Solution method: We calculate phonon quasiparticle properties, i.e., renormalized phonon frequencies and lifetimes, by combining molecular dynamics (MD) trajectories and harmonic normal modes (HNM). MD velocities are projected into HNMs and the mode-projected velocity auto-correlation functions (VAF) are then calculated. Quasiparticle properties are then obtained by analyzing the VAFs, if they are well defined. Using the renormalized phonon frequencies and HNMs we build an effective (temperature-dependent) harmonic force constant matrix from which the anharmonic phonon dispersions can be obtained.

Original languageEnglish (US)
Pages (from-to)110-120
Number of pages11
JournalComputer Physics Communications
StatePublished - Jan 1 2019
Externally publishedYes


  • Anharmonic phonon dispersion
  • First-principles molecular dynamics
  • Lattice dynamics
  • Phonon quasiparticle
  • Velocity auto-correlation function


Dive into the research topics of 'phq: A Fortran code to compute phonon quasiparticle properties and dispersions'. Together they form a unique fingerprint.

Cite this