Wavelets for density matrix computation in electronic structure calculation

Decay Properties of Spectral Projectors with Applications to Electronic Structure

“…Combinations of tensor product approximations and wavelets appear to be promising. We refer here to [55] for a study of the decay properties of density matrices in a wavelet basis (see also [119]), and to [16] for an early attempt to exploit near low-rank properties of spectral projectors. See also the more recent works by W. Hackbusch and collaborators [26,27,28,47,48,86].…”

Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling

“…Assume that r is actually much larger than necessary, i.e.,r << r, then the ALS algorithm costs O(dr(r 2 + rn 2 )). We refer to [77] for the discussion of wavelet methods for density matrix computation in electronic structure calculation.…”

Real‐Space and Multigrid Methods in Computational Chemistry

“…[62][63][64] The equations that result are quite similar to the FD method, but because localized basis functions are used to represent the solution, the method is variational. [73][74][75][76][77][78][79][80][81][82][83] The main feature of real-space methods is that, if we represent the Laplacian operator (Poisson equation) or Hamiltonian (eigenvalue problem) on a grid, the application of the operator to the function requires information only from a local region in space. [65][66][67] Other realspace-related methods include discrete variable representations, [68][69][70] Lagrange meshes, 71,72 and wavelets.…”

“…[123][124][125] Earlier linear-scaling developments are thoroughly summarized by Goedecker. [73][74][75][76][77][78][79][80]82,83 Electrostatics Real-space numerical solutions to problems in electrostatics have been a predominant theme in biochemistry and biophysics for some time. 206 Real-space methods have found recent application in QM/MM methods, which couple central quantum regions with more distant molecular mechanics domains.…”