Efficient and accurate calculation of exact exchange and RPA correlation energies in the Adiabatic-Connection Fluctuation-Dissipation theory

Recently there has been a renewed interest in the calculation of exact-exchange and RPA correlation energies for realistic systems. These quantities are main ingredients of the so-called EXX/RPA+ scheme which has been shown to be a promising alternative approach to the standard LDA/GGA DFT for weakly bound systems where LDA and GGA perform poorly. In this paper, we present an efficient approach to compute the RPA correlation energy in the framework of the Adiabatic-Connection Fluctuation-Dissipation formalism. The method is based on the calculation of a relatively small number of eigenmodes of RPA dielectric matrix, efficiently computed by iterative density response calculations in the framework of Density Functional Perturbation Theory. We will also discuss a careful treatment of the integrable divergence in the exact-exchange energy calculation which alleviates the problem of its slow convergence with respect to Brillouin zone sampling. As an illustration of the method, we show the results of applications to bulk Si, Be dimer and atomic systems.Comment: 12 pages, 6 figures. To appear in Phys. Rev.

A BEM-BDF scheme for curvature driven moving Stokes flows

A backward differences formulae (BDF) scheme, is proposed to simulate the deformation of a viscous incompressible Newtonian fluid domain in time, which is driven solely by the boundary curvature. The boundary velocity field of the fluid domain is obtained by writing the governing Stokes equations in terms of an integral formulation that is solved by a boundary element method. The motion of the boundary is modelled by considering the boundary curve as material points. The trajectories of those points are followed by applying the Lagrangian representation for the velocity. Substituting this representation into the discretized version of the integral equation yields a system of non-linear ODEs. Here the numerical integration of this system of ODEs is outlined. It is shown that, depending on the geometrical shape, the system can be stiff. Hence, a BDF-scheme is applied to solve those equations. Some important features with respect to the numerical implementation of this method are high-lighted, like the approximation of the Jacobian matrix and the continuation of integration after a mesh redistribution. The usefulness of the method for both two-dimensional and axisymmetric problems is demonstrated