Locally Refined Multigrid Solution of the All-Electron Kohn–Sham Equation

Cohen, O.; Kronik, Leeor; Brandt, Achi

doi:10.1021/ct400479u

Cited by 16 publications

(7 citation statements)

References 64 publications

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“…A number of FEM implementations for all-electron HF or DFT calculations on molecules or solids with arbitrary geometries have been reported in the literature. [343][344][345][346][347][348][349][350][351][352][353][354][355][356][357][358][359][360][361] Another solution is to use grids with hierarchical precision 362,363 or adaptive multiresolution multiwavelet approaches 198,249,324,[364][365][366][367][368] that are under active development and which have recently achieved microhartree-accuracy in molecular calculations, even at the post-HF level of theory. [369][370][371][372] Regularization of the nuclear cusp [373][374][375] and approaches employing adaptive coordinate systems 376 also have been suggested.…”

Section: Overview On General Approaches For Arbitrary Moleculesmentioning

confidence: 99%

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

102

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The need for accurate calculations on atoms and diatomic molecules is motivated by the opportunities and challenges of such studies. The most commonly used approach for all-electron electronic structure calculations in general-the linear combination of atomic orbitals (LCAO) method-is discussed in combination with Gaussian, Slater a.k.a. exponential, and numerical radial functions. Even though LCAO calculations have major benefits, their shortcomings motivate the need for fully numerical approaches based on, for example, finite differences, finite elements, or the discrete variable representation, which are also briefly introduced. Applications of fully numerical approaches for general molecules are briefly reviewed, and their challenges are discussed. It is pointed out that the high level of symmetry present in atoms and diatomic molecules can be exploited to fashion more efficient fully numerical approaches for these special cases, after which it is possible to routinely perform allelectron Hartree-Fock and density functional calculations directly at the basis set limit on such systems. Applications of fully numerical approaches to calculations on atoms as well as diatomic molecules are reviewed. Finally, a summary and outlook is given.atomic calculations, density functional theory, diatomic calculations, fully numerical electronic structure theory, Hartree-Fock | INTRODUCTIONThanks to decades of development in approximate density functionals and numerical algorithms, density functional theory [1,2] (DFT) is now one of the cornerstones of computational chemistry and solid-state physics. [3][4][5] Since atoms are the basic building block of molecules, a number of popular density functionals [6][7][8][9][10] have been parametrized using ab initio data on noble gas atoms; these functionals have been used in turn as the starting point for the development of other functionals. A comparison of the results of density-functional calculations to accurate ab initio data on atoms has, however, recently sparked controversy on the accuracy of a number of recently published, commonly used density functionals. [11][12][13][14][15][16][17][18][19][20][21] This underlines that there is still room for improvement in DFT even for the relatively simple case of atomic studies.The development and characterization of new density functionals require the ability to perform accurate atomic calculations. Because atoms are the simplest chemical systems, atomic calculations may seem simple; however, they are in fact sometimes surprisingly challenging. For instance, a long-standing discrepancy between the theoretical and experimental electron affinity and ionization potential of gold has been resolved only very recently with high-level ab initio calculations. [22] Atomic calculations can also be used to formulate efficient starting guesses for molecular electronic structure calculations via either the atomic density [23,24] or the atomic potential as discussed in Ref. [25].

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Section: Overview On General Approaches For Arbitrary Moleculesmentioning

confidence: 99%

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Lehtola

2019

Int J of Quantum Chemistry

102

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“…In the simulation, the mesh density is adjusted dynamically according to the numerical results with the mesh adaptive methods, and computational resource can be potentially saved. Although there have been a lot of works on developing mesh adaptive methods for ground-state calculations [10,35,8], rare of them is related to the RT-TDKS simulations.…”

Section: Introductionmentioning

confidence: 99%

Real-time adaptive finite element solution of time-dependent Kohn–Sham equation

Bao

Liu

2015

Journal of Computational Physics

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“…5 In recent years it has been recognized that real-space methods hold several advantages over plane-wave approaches. [7][8][9][10][11][12][13][14][15] These advantages include nearlocality in iterative updates, adaptivity, and the possibility of linear-scaling algorithms 16 due to the spatial decay of the density matrix coupled with multiscale solvers for the Poisson and electronic energy minimization problems.…”

Section: Introductionmentioning

confidence: 99%

“…13 Efficient multiscale eigenvalue solvers, even though they can process much of the global information on coarse scales, still require solution of matrix equations that scale faster than linear with system size. 11,15 In light of these issues, in ref. 11 we suggested a potential alternative new direction for DFT modeling based on a stochastic hybrid of DFT and Quantum Monte Carlo (QMC) approaches.…”

Section: Introductionmentioning

confidence: 99%

A real-space stochastic density matrix approach for density functional electronic structure

Beck

2015

Phys. Chem. Chem. Phys.

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The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

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Locally Refined Multigrid Solution of the All-Electron Kohn–Sham Equation

Cited by 16 publications

References 64 publications

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

A review on non‐relativistic, fully numerical electronic structure calculations on atoms and diatomic molecules

Real-time adaptive finite element solution of time-dependent Kohn–Sham equation

A real-space stochastic density matrix approach for density functional electronic structure

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