Quantum molecular dynamics: Numerical methods and physical study of the structure, thermodynamics, stability and fragmentation of sodium metallic clusters.

摘要

The aim of this thesis is to study metallic sodium clusters by numerical simulation. We have developed two ab initio molecular dynamics programs within the formalism of density functional theory. The first is based on the semi- classical extended Thomas-Fermi approach. We use a real-space grid and a Car- Parrinello-like scheme. The computational cost is O(N), and we have built a pseudopotential that speeds up the calculations. By neglecting quantum shell effects, we are able to study a very large set of clusters. We show that sodium cluster energies fit well a liquid drop formula, by adjusting a few parameters. We have investigated breathing modes, surface oscillations and the net charge density. We have shown that the surface energy varies strongly with temperature, and that clusters have a lower melting point than bulk material. We have calculated fission barriers by a constraint method. The second program is based on the quantum Kohn-Sham approach. We use a real-space grid, and combine a generalized Broyden scheme for assuring self-consistency with an iterative Davidson-Lanczos algorithm for solving the Eigen-problem. The cost of the method is much higher. First of all, we have calculated some stable structures for small clusters and their energetics. We obtained very good agreement with previous works. Then, we have investigated highly charged cluster dynamics. We have identified a chaotic fission process. For high fissility systems, we observe a multi-fragmentation dynamics and we find preferential emission of monomers on a characteristic time scale less than a pico-second. This has been simulated for the first time, with the help of our adaptive grid method which follows each fragment as they move apart during the fragmentation. (author) 87 refs., 57 figs., 4 tabs.