This article addresses a fundamental problem faced by the community employing single-particle ab initio methods: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a new, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new techniques to the derivation and transcription of a few lines of algebra.

Experimental data and theoretical predictions of hydrolysis reaction kinetics of model halocarbons and phase equilibria of their associated neutralized salt reaction products are reported for a range of hydrothermal conditions. Specifically, the results of a study of hydrolysis and oxidation of methylene chloride (CH2Cl2) to produce CO2, H2O, and HCl as final mineralized products are presented.

Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allowexactrecovery of the multiresolution representation of a function from its sample values on afiniteset of points in space. We present a detailed study of the application of wavelet concepts to physical problems expressed in such bases.

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms.

Throughout the Plenary and Break-Out Sessions at the Workshop the issue was frequently brought up of linking together computational approaches which traditionally operate on distinct length scales. In response to this interest, an informal discussion was held to examine the prospects for a collaborative initiative on coupling atomistic and continuum methods.