Density functional theory of small quantum systems

We propose to extend and systematically apply our coordinate-space algorithm for solving the Kohn-Sham equation to various problems in the area of quantum dots and metallic clusters. Our algorithm is formulated entirely in configuration space and profits from the familiar advantages of coordinate space methods. It consists of several newly developed components, (a) a fourth order diffusion algorithm for solving eigenvalue problems, (b) a subspace orthogonalization that speeds up the convergence of the eigenvalue solver and (c) a method for updating the electron density that is based on a collective formulation of linear response theory. We have now versions of the code for two- and three-dimensional geometries which have been thoroughly tested during the last funding period and are ready for large scale spplications. We want to try a few minor technical improvements of the three- dimensional code, but the main emphasis of the proposed work will (a) to apply the methods to physically relevant questions, and (b) to address new questions like electrons and quantum dots in strong magnetic fields and time- dependent problems.

We propose to extend and systematically apply our coordinate-space algorithm for solving the Kohn-Sham equation to various problems in the area of quantum dots and metallic clusters. Our algorithm is formulated entirely in configuration space and profits from the familiar advantages of coordinate space methods. It consists of several newly developed components, (a) a fourth order diffusion algorithm for solving eigenvalue problems, (b) a subspace orthogonalization that speeds up the convergence of the eigenvalue solver and (c) a method for updating the electron density that is based on a collective formulation of linear response theory. We have now versions of the code for two- and three-dimensional geometries which have been thoroughly tested during the last funding period and are ready for large scale spplications. We want to try a few minor technical improvements of the three- dimensional code, but the main emphasis of the proposed work will (a) to apply the methods to physically relevant questions, and (b) to address new questions like electrons and quantum dots in strong magnetic fields and time- dependent problems.