Electronic-structure calculations in adaptive coordinates

The plane-wave method for electronic-structure calculations is reformulated in generalized curvilinear coordinates. This introduces a new set of basis functions that depend continuously on a coordinate transformation, and can adapt themselves to represent optimally the solutions of the Schrödinger equation. As a consequence, the effective plane-wave energy cutoff is allowed to vary in the unit cell in an unbiased way. The efficiency of this method is demonstrated in the calculation of the equilibrium structures of the CO and ${\mathrm{H}}_2$O molecules using the local-density approximation of density-functional theory, and norm-conserving, nonlocal pseudopotentials. The easy evaluation of forces on all degrees of freedom makes the method suitable for ab initio molecular-dynamics applications.