Running the calculation

A k-path taken from the Brillouin-zone viewer, a calculator, and the run returns E(k) with the projected density of states beside it. Orbital and site projections draw as fatbands. The irreducible-representation labels at each high-symmetry point are computed from the wavefunctions rather than looked up from the space group, so they stay correct when a defect or a strain lowers the symmetry. Supercell calculations unfold onto the primitive zone, which is what makes an alloy or defect band structure legible at all.

Finite displacements in a supercell, reduced by spglib to the irreducible set, give the force constants and from them the dispersion, the phonon DOS and the thermodynamic functions. Born effective charges supply the LO–TO splitting for polar materials. Imaginary branches are reported rather than hidden. They are the signature of a structure that is not at a minimum, and the most useful thing the calculation can tell you.

The dielectric function ε(ω) from the independent-particle or RPA response, with the intraband Drude term added for metals, and from it the absorption coefficient, reflectivity and refractive index. Non-centrosymmetric structures also give second-harmonic generation and the shift current. Monolayers use a 2D formulation, because the bulk expression depends on a vacuum spacing that is a convergence parameter, not a property.

Maximally localized Wannier functions from the converged Bloch states, with the spread minimization reported per iteration so a failed disentanglement is visible instead of silent. The resulting tight-binding model interpolates bands onto a dense k-mesh for almost nothing, which is what puts Fermi surfaces, Berry curvature and topological invariants within reach.