Efficient multiscale simulation of simple metallic systems

The steady increase in computational resources and numerical sophistication has brought about a new approach in physical simulation. The methods that comprise this approach are known as multiscale methods, and have the defining characteristic of combining several simulation methods together, rendering tractable physical problems that no single simulation method can resolve. We have developed an approach for coupling quantum-mechanical and classical methods for the efficient simulation of multiscale problems in simple metals.; The present multiscale method employs orbital-free density functional theory, in which fictitious orbitals are never introduced. We review the theory, and describe the state-of-the-art functionals associated with it. We have developed an efficient simulation code for performing orbital-free density functional theory calculations, and we describe the methods developed to treat the functional minimization problem.; One of the biggest barriers hindering the widespread use of orbital-free methods is that only local pseudopotentials can be used, and hence the powerful machinery of norm-conserving pseudopotentials is inapplicable. We develop a similar machinery for local pseudopotentials, and we report on the application of these methods.; We solve several problems associated with the efficient use of orbital-free density functional methods. Certain orbital-free methods are formulated in reciprocal space and are applicable to periodic systems. Incorporation of these methods in a multiscale setting requires that the effects of periodicity be absent. A direct translation of the methods to real space is extremely inefficient. Motivated by these considerations, we have developed an efficient method for applying orbital-free methods to non-periodic systems.; We also overcome an algorithmic problem with the calculation of ionic forces in grid-based electronic structure methods in general. We develop and test an efficient method for computing ionic forces that scales quasi-linearly (O(N log N)) with the system size.; We develop and examine a multiscale method for the simulation of simple metallic systems. Part of the system is treated quantum-mechanically, and part classically, with consideration made to the coupling of the two. We apply this method to several physical systems.