Effective numerical method for theoretical studies of small atomic clusters

We present an effective numerical method to study the electronic and ionic dynamics of small atomic systems, like alkali-metal clusters. Our approach is based on the density functional theory (DFT) combined with molecular dynamics (MD). The time-dependent Kohn-Sham (KS) equations describing the electronic subsystem are solved self-consistently in the coordinate space. Their numerical solution is performed using the time-splitting method on a three-dimensional coordinate grid by means of the generalized pseudospectral method (GPS). The KS orbitals are expanded over a spherical harmonics basis, and their radial part are represented on a non-uniform radial grid. We employ an optimal radial mapping of the collocation points consistent with the GPS method, which allows achieving a higher density of radial points inside the cluster where electronic density is larger and the potential varies rapidly. This method allows evaluating both the Coulomb potential and the kinetic energy operator with high accuracy. Unlike FFT based methods, the GPS method with non-uniform radial mapping, allows to use large grids at lower cost and thus to study efficiently negatively charged cluster. As an example, we present the number of emitted electrons of a negatively charged sodium cluster Na7-, irradiated by a femtosecond laser pulse, as a function of the grid size. We show that the value of the electron emission converges only for large grids.