Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques

We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent equations are solved on a heirarchy of grids of increasing resolution with a nonlinear Full Approximation Scheme, Full Multigrid algorithm. The self consistency is effected by updates of the Poisson equation and the exchange correlation potential at the end of each eigenfunction correction cycle. The algorithm leads to highly efficient solution of the equations, whereby the ground state electron distribution is obtained in only two or three self consistency iterations on the finest scale.Comment: 13 pages, 2 figure

Application of A Distributed Nucleus Approximation In Grid Based Minimization of the Kohn-Sham Energy Functional

In the distributed nucleus approximation we represent the singular nucleus as smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for theoverall electrostatic potential using a linear scaling multigrid algorithm.This work is done in the context of minimizing the Kohn-Sham energy functionaldirectly in real space with a multiscale approach. The efficacy of the approximation is illustrated bylocating the ground state density of simple one electron atoms and moleculesand more complicated multiorbital systems.Comment: Submitted to JCP (July 1, 1995 Issue), latex, 27pages, 2figure

The Quantum Mechanics of Cluster Melting

We present here prototype studies of the effects of quantum mechanics on the melting of clusters. Using equilibrium path integral methods, we examine the melting transition for small rare gas clusters. Argon and neon clusters are considered. We find the quantum-mechanical effects on melting and coexistence properties of small neon clusters to be appreciable

Locating Stationary Paths in Functional Integrals: An Optimization Method Utilizing the Stationary Phase Monte Carlo Sampling Function

A method is presented for determing stationary phase points for multidimensional path integrals employed in calculation of finite-temperature quantum time correlation functions. The method can be used to locate stationary paths at any physical time; in case that t » βħ, the stationary points are the classical paths linking two points in configuration space. Both steepest descent and simulated annealing procedures are utilized to search for extrema in the action functional. Only the first derivatives of the action functional are required. Examples are presented first of the harmonic oscillator for which the analytical solution is known, and then for anharmonic systems, where multiple stationary phase points exist. Suggestions for Monte Carlo sampling strategies utlizing the stationary points are made. The existence of many and closely spaced stationary paths as well as caustics presents no special problems. The method is applicable to a range of problems involving functional integration, where optimal paths linking two end points are desired