Implementation of ultrasoft pseudopotentials in large-scale grid-based electronic structure calculations

An implementation of Vanderbilt ultrasoft pseudopotentials in real-space grid-based electronic structure calculations is presented. Efficient utilization of these pseudopotentials requires the use of different grids for (i) wave functions, (ii) charge density, and (iii) sharply peaked operators within the atomic core radii. High-order interpolation between the various grids is important for accuracy, as is high-order discretization for the differential operators. However, efficiency is also of paramount importance, especially when parallelizing over hundreds or thousands of processors. We describe algorithms and procedures used to achieve an effective implementation in the real-space multigrid code, and provide test results for first-row diatomics, bulk transition metals, and energy-conserving quantum molecular dynamics of water. The code parallelizes efficiently over several thousands of processors on modern parallel supercomputers, such as the Cray XT3 and XT4.