Molecular dynamics with quantum forces: Vibrational spectra of localized systems

We present molecular-dynamics simulations with quantum forces for localized systems using a real-space method. We illustrate calculations for the vibrational modes of small molecules and clusters. Unlike other real-space methods using adaptive grids, this procedure does not require any Pulay corrections for the forces, nor does it suffer from the complication of redefining a grid after each time step of the molecular-dynamics simulation. Our method is based on combining higher order finite difference methods with ab initio pseudopotentials. We also introduce an iterative diagonalization scheme based on preconditioned Krylov techniques. Compared to plane-wave-supercell methods, this method is more efficient and simpler to implement. Examples are presented for the CO2 molecule and a silicon cluster, Si-4.