Car-Parrinello simulations with a real space method

An approach for Car-Parrinello type molecular dynamics simulations using real space discretized wave functions is presented. The implementation uses a higher order finite difference approximation for the Laplacian in the kinetic energy operator and in the Poisson equation for the evaluation of the Hartree energy. Norm conserving pseudopotentials are employed to replace the nucleus-core interactions. Both nuclei and wave functions are propagated with a second-order Verlet propagator with a timestep comparable to standard plane wave implementations. The orthonormality constraints are fulfilled via Lagrange multipliers. Both periodic and nonperiodic boundary conditions can directly be imposed within the real space approach. In order to maintain energy conservation both forces on the nuclei and the wave functions must be sufficiently accurate. It is shown that the spurious energy dependence on the nuclear positions with respect to the grid points, which is an inevitable artifact of the discretization, is mirrored in the nuclear forces, and does not affect energy conservation. In contrast to the plane wave methodology, the Hartree energy is calculated via an iterative solution of the Poisson equation. As a result, the quality of the forces on the wave function crucially depends on its convergence, as well as on the accuracy of the approximation for the boundary values in nonperiodic calculations. The influence of these factors on the energy conservation is investigated. It is shown that Car-Parrinello simulations can be performed with real space wave functions, given a proper prescription to calculate the Hartree potential is used.