dft-phonons

DFT Phonon Calculations

Description

This skill covers lattice dynamics from first principles: computing phonon dispersion curves, phonon density of states (PDOS), and thermal properties using the finite-displacement method (Phonopy + VASP/QE) and density functional perturbation theory (DFPT via Quantum ESPRESSO ph.x or VASP IBRION=7/8). It covers the full workflow from supercell construction and displaced-supercell DFT calculations through force constant extraction, acoustic sum rule enforcement, non-analytical corrections for polar materials, and phonon band structure post-processing. Invoke this skill when computing harmonic phonon properties, diagnosing dynamical instabilities, validating ML interatomic potentials against DFT phonons, or generating phonon reference data for materials databases.

Domain Context

Phonons are the quantum of lattice vibration. They are essential for predicting thermodynamic stability, heat capacity, thermal conductivity, electron-phonon coupling, and phase transitions. Two formally equivalent but practically distinct methods are used in DFT practice:

Finite-displacement (supercell) method: Construct symmetry-inequivalent displaced supercells → run DFT single-point calculations → extract forces → build real-space force constants → Fourier transform to get the dynamical matrix D(q) at arbitrary q-points → diagonalize to get phonon frequencies ω(q). Implemented by Phonopy, which is DFT-code-agnostic.

DFPT (Density Functional Perturbation Theory): Compute the response of the charge density to an atomic displacement as a perturbation at a given wavevector q directly, without supercells. Gives the dynamical matrix at specified q-points directly from a single calculation. Native to Quantum ESPRESSO (ph.x) and also available in VASP (IBRION=7/8). More expensive per q-point than finite displacement for a single structure but avoids the supercell approximation entirely.

Dynamical matrix: D_αβ(q) = (1/√(m_α m_β)) Σ_R Φ_αβ(0,R) e^{iq·R}, where Φ_αβ are the interatomic force constants (second derivatives of the total energy). Eigenvalues of D(q) give ω²(q,s) for each phonon branch s. Negative eigenvalues (imaginary frequencies) signal dynamical instability at that q-point.