Multiresolution quantum chemistry: Basic theory and initial applications

Abstract

Articles you may be interested inNorbornane: An investigation into its valence electronic structure using electron momentum spectroscopy, and density functional and Green's function theories J. Chem. Phys. 121, 10525 (2004) We describe a multiresolution solver for the all-electron local density approximation Kohn-Sham equations for general polyatomic molecules. The resulting solutions are obtained to a user-specified precision and the computational cost of applying all operators scales linearly with the number of parameters. The construction and use of separated forms for operators ͑here, the Green's functions for the Poisson and bound-state Helmholtz equations͒ enable practical computation in three and higher dimensions. Initial applications include the alkali-earth atoms down to strontium and the water and benzene molecules.

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

“…[13] Although HF and (pure and hybrid) DFT calculations using multiresolution grids have been reported in the literature [29][30][31] and the approach holds great promise, it is still in its infancy and has larger computational requirements than basis set calculations performed at moderate accuracy.…”

Exploiting Locality in Quantum Computation for Quantum Chemistry

“…We find that this is sufficient for the systems we consider, but note that there have been a number of advances in orthogonal basis sets that are local in both the occupied and virtual spaces and may find utility in quantum computation [39]. Moreover, there has been recent work in the use of multiresolution wavelet basis sets that have natural sparsity and orthogonality while providing provable error bounds on the choice of basis [40]. Such a basis also allows one to avoid costly integral transformations related to orthogonality, which are known to scale as O(M 5 ) when performed exactly.…”

Low-rank quadrature-based tensor approximation of the Galerkin projected Newton/Yukawa kernels

“…In the recent years, the idea of tensor approximation of operators and functions has lead to powerful numerical algorithms in large-scale problems of computational physics, in particular, in electronic structure calculations based on the Hartree-Fock or DFT models [6,10,8]. In these applications one deals with numerical computations of integral transforms which include Green's kernels in R d [5,7,9].…”

“…Hence, these terms represent the most complicated part in the numerical treatment of the Hartree-Fock equation, see, e.g., [7,9,10,12]. Another popular modification of the Hartree-Fock and Schrödinger equations is based on the so-called Lippmann-Schwinger integral formulation, which contains also the convolution transform with the Yukawa potential e −λ x x (λ ∈ R + ) [6,8]. Traditionally, the Hartree-Fock equation is solved by meshless methods based on the usage of the so-called Gaussian type orbitals which allow analytical evaluation of the basic convolution transforms.…”

“…Traditionally, the Hartree-Fock equation is solved by meshless methods based on the usage of the so-called Gaussian type orbitals which allow analytical evaluation of the basic convolution transforms. Application of the finite element and wavelet methods [13,6] might be of the particular interest if the volume integral transforms can be evaluated efficiently [13,6,12]. In particular, due to the recent development of tensor numerical methods, the combination of the finite element with nonlocal problem dependent basis sets leads to the linear scaling methods O(n) [12].…”