Real-space adaptive-coordinate electronic-structure calculations

We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive-coordinate method. The discretized Kohn-Sham equations are written in generalized curvilinear coordinates and solved self-consistently by means of an iterative approach. The Poisson equation is solved in real space using the multigrid algorithm. We implemented the method on a massively parallel computer, and applied it to the calculation of the equilibrium geometry and harmonic vibrational frequencies of the ${\mathrm{CO}}_2$, CO, ${\mathrm{N}}_2$, and ${\mathrm{F}}_2$ molecules, yielding excellent agreement with the results of accurate quantum-chemistry and local-density-functional calculations.