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6.1 Finite-displacement phonons with Phonopy

These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.

6.1.1 Model, units and provenance

Use eV for energy, Å for length and eV/Å for force; 1 kbar = 0.1 GPa. State normalization per atom, molecule, primitive cell or simulation cell. Record PAW identifiers, release, ZVAL, ENMAX and permitted hashes; never redistribute POTCAR. SCF convergence addresses the chosen electronic problem; convergence of the target property requires separate tests.

Finite-displacement phonons with Phonopy — original conceptual schematic

Original schematic. Curves explain concepts; blank data areas await verified learner results. No calculation is claimed.

\[ \Phi_{i\alpha,j\beta}=-\frac{\partial F_{i\alpha}}{\partial u_{j\beta}},\qquad D(\mathbf q)\mathbf e=\omega^2\mathbf e \]

6.1.2 Worked case: procedure, interpretation and checks

Why displaced atoms tell us about vibrations

At equilibrium every force is nearly zero, but that does not tell us how strongly atoms resist motion. Move one atom slightly and measure the force response on all atoms. Repeating symmetry-independent displacements reconstructs the harmonic spring network. With displacement u and force F, Φiα,jβ = −∂Fiα/∂ujβ. Central differences use the force difference from ±u. Mass-weight the force constants and Fourier-transform them to form D(q); eigenvalues are ω². A negative eigenvalue gives an imaginary frequency, conventionally plotted below zero. That is not a negative physical oscillation frequency.

VASP supplies first-principles forces. Phonopy, an external program, generates displacements, constructs/interpolates force constants, and performs the reciprocal-space analysis. It is not an INCAR tag and is not bundled implicitly into a standard VASP run.

Reproducible sequence

Use a well-relaxed, dynamically plausible crystal. Begin with a nonpolar cubic example to separate short-range force convergence from LO–TO splitting. Preserve the relaxed cell, atom order, and chosen primitive-cell transformation.

  1. Select a supercell matrix. A 2×2×2 repeat is an initial size experiment, not a universal convergence guarantee; anisotropic cells often need anisotropic repeats.
  2. Generate displacements. Current v4-style external CLI example: phonopy-init -d --dim 2 2 2 -c POSCAR-unitcell. Older versions may use the monolithic phonopy command; check installed help and record the version.
  3. Give each generated displaced POSCAR its own directory with identical material settings. Reduce electronic k-point counts according to the larger supercell, while testing equivalent reciprocal-space density.
  4. Run a static force calculation, never relax a displaced structure. The displacement is the measurement probe; relaxing removes the probe.
  5. Collect complete vasprun.xml files in the exact displacement order with phonopy-init -f disp-001/vasprun.xml .... The ellipsis means an explicit verified file list, not literal shell input. Retain the matching displacement YAML.
  6. Inspect force constants and compute a band path defined for the actual primitive reciprocal lattice. Separately use a three-dimensional q mesh for the DOS and thermal integrations. An electronic k mesh and a phonon q mesh are not interchangeable.

Convergence and diagnosis

Test displacement amplitudes, for example 0.01 and 0.02 Å. Very small displacements amplify force noise; large displacements include anharmonic terms. Compare supercell sizes, electronic meshes, and the acoustic region rather than judging only a high optical branch. The three acoustic modes should approach zero at Γ for a freely translating bulk crystal. Acoustic sum-rule enforcement can remove small translational noise; it cannot repair grossly unconverged forces or a wrong structure.

Plot and animate any imaginary eigenvector. Tiny near-Γ artifacts may shrink with tighter force accuracy or larger cells. A robust imaginary branch across a finite region may indicate a genuine structural instability. Do not silently delete it to obtain a smooth thermal curve. For polar insulators, long-range dipole interactions need Born effective charges and the high-frequency electronic dielectric tensor, mapped consistently into a Phonopy BORN file. The total static dielectric tensor is not the appropriate substitute for this nonanalytic phonon correction.

Exercise

6.1.3 Unexecuted inputs and analysis scaffolds

These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.

6.1.3.1 Input block 1

# VASP force job for each externally displaced structure
IBRION = -1
NSW    = 0
PREC   = Accurate
EDIFF  = 1E-8
LREAL  = .FALSE.
LWAVE  = .FALSE.
LCHARG = .FALSE.
# Use tested ENCUT and material-appropriate occupations.

6.1.5 Technical sources