Plane-wave electronic-structure calculations on a parallel supercomputer

We present a detailed description of the implementation on a parallel supercomputer (hypercube) of the first-order equation-of-motion solution to Schr\"odinger's equation, using plane-wave basis functions and ab initio separable pseudopotentials. By distributing the plane waves across the processors of the hypercube many of the computations can be performed in parallel, resulting in decreases in the overall computation time relative to conventional vector supercomputers. This partitioning also provides ample memory for large fast-Fourier-transform (FFT) meshes and the storage of plane-wave coefficients for many hundreds of energy bands. The usefulness of the parallel techniques is demonstrated by benchmark timings for both the FFT's and iterations of the self-consistent solution of Schr\"odinger's equation for different sized Si unit cells of up to 512 atoms.