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Real space pseudopotentials have a number of advantages in solving for the electronic structure of materials. These advantages include ease of implementation, implementation on highly parallel systems, and great flexibility for describing partially periodic systems. One limitation of this approach, shared by other electronic structure methods, is the slow convergence of interatomic forces when compared to total energies. For real space methods, this requires a fine grid to converge a solution of the Kohn-Sham problem, which is accompanied by concurrent increase in memory and additional matrix-vector multiplications. Here we introduce a method to expedite the computation of interatomic forces by employing a high order integration technique. We demonstrate the usefulness of this technique by calculating accurate bond lengths and vibrational frequencies for molecules and nanocrystals without using fine real space grids.

A method for performing ab initio molecular dynamics simulations using a real-space pseudopotential density-functional approach is presented in this work. The Kohn-Sham equation is represented on a real-space grid and solved using higher-order finite differencing. A crucial ingredient of our method is the replacement of "standard" diagonalizations at each self-consistent-field iteration by a Chebyshev subspace filtering step, resulting in a speed up of an order of magnitude or more. This increase in computational efficiency allows molecular dynamics simulations to be carried out for large systems. As an illustration, we apply this method to the study of liquid Al.

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