A phonon is a collective vibration of the atoms in a crystal, the periodic counterpart of a molecular normal mode.
Rowan computes harmonic phonons by the finite-displacement method, using phonopy.
The workflow requires a primitive cell, periodic in at least two dimensions. Constraints and transition-state optimizations are not supported.
The input cell is relaxed first, since the harmonic expansion is only valid at a stationary point. Residual forces leave a linear term the fit cannot represent, which biases every frequency. Rowan then builds a supercell, generates the symmetry-inequivalent displacements, and evaluates the forces on each one. Force constants are fit from those forces and symmetrized, first by the space group and then by permutation and translational invariance.
The supercell is a diagonal expansion, (2, 2, 2) by default, clamped to 1 along any non-periodic axis.
It must be large enough that force constants decay by its boundary, and since cost scales with the number of displacements, it is the main lever on runtime.
Rowan checks the acoustic sum rule, which requires the three acoustic modes to vanish at Γ. A deviation past 10 cm−1 indicates an unrelaxed cell or inconsistent forces.
Every property is derived from the same force constants. Imaginary frequencies are reported as negative.
Band-structure frequencies are sampled along the standard Setyawan–Curtarolo high-symmetry q-path at 500 points per 2π/Å, which requires the primitive cell to already be in its standard orientation. The density of states is projected per atom and sampled with the tetrahedron method on a uniform mesh of up to 30 q-points per periodic axis. Harmonic thermodynamic functions are integrated over the same mesh from 0 to 1000 K: free energy, entropy, heat capacity, and zero-point energy, per primitive cell. Thermal expansion and phonon–phonon interaction are not included.
Rowan also reports the minimum frequency over the mesh and the fraction of frequencies that are imaginary. A structure with imaginary frequencies lowers its energy along those modes and will distort into a lower-symmetry phase, though a few shallow imaginary modes at Γ are usually acoustic noise. This is a stricter stability test than the elastic tensor, which probes only homogeneous distortions of the cell.
Zone-center (Γ) modes are the ones IR and Raman spectra measure, since light carries negligible momentum on the scale of the Brillouin zone. Each is labeled with its irreducible representation of the crystal point group, its displacement pattern, and whether symmetry allows it to be IR or Raman detectable.