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Hyper-sparsity of the density matrix in a wavelet representation
S. Goedecker, O. V. Ivanov
O(N) methods are based on the decay properties of the density matrix in real space, an effect sometimes refered to as near-sightedness. We show, that in addition to this near-sight…
Electronic Structure Methods Exhibiting Linear Scaling of the Computational Effort with Respect to the Size of the System
Stefan Goedecker
Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large sys…
The Decay Properties of the Finite Temperature Density Matrix in Metals
S. Goedecker
Using ordinary Fourier analysis, the asymptotic decay behavior of the density matrix F(r,r') is derived for the case of a metal at a finite electronic temperature. An oscillatory b…
Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn
C. Hartwigsen, S. Goedecker, J. Hutter
We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole periodi…
The solution of multi-scale partial differential equations using wavelets
Stefan Goedecker, Oleg Ivanov
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show…