Methods exhibiting linear scaling with respect to the size of the system, the so-called O (N)
methods, are an essential tool for the calculation of the electronic structure of large systems …

One of the most dangerous technical failures of materials is intergranular brittle fracture
(temper embrittlement) as it proceeds very quickly and its appearance is often hardly …

Linear-scaling methods, or methods, have computational and memory requirements which
scale linearly with the number of atoms in the system, N, in contrast to standard approaches …

The tight-binding method of modelling materials lies between the very accurate, very
expensive, ab initio methods and the fast but limited empirical methods. When compared …

Owing to their non-planar cores, 1/2〈 111〉 screw dislocations govern the plastic
deformation of body-centered cubic (bcc) metals. Atomistic studies of the glide of these …

Two methods are suggested for performing ground-state electronic-structure calculations
within the independent-electron approximation. Both methods involve the purification of a …

Publisher Summary This chapter discusses basic modeling. The chapter illustrates that
quantum chemistry aims at understanding the properties of matter through the modeling of …

A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and
Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires …

We describe recent progress in developing linear scaling ab initio electronic structure
methods, referring in particular to our highly parallel code CONQUEST. After reviewing the …

We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in
which the electron density is determined from an average of correlated stochastic densities …