Tensor decompositions for the bubbles and cube numerical framework

Solala, Eelis; Parkkinen, P.; Sundholm, Dage

doi:10.1016/j.cpc.2018.05.016

Cited by 3 publications

(8 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Vice versa, real‐space methods tend to struggle with core orbitals, but are well adapted to the description of diffuse character. This has lead to approaches that hybridize aspects of LCAO and real‐space calculations . By representing the core electrons using an atom‐centric radial description, a significantly smaller real‐space basis set may suffice, making the approaches scalable to large systems while still maintaining a very high level of accuracy.…”

Section: Applicationsmentioning

confidence: 99%

“…This has lead to approaches that hybridize aspects of LCAO and real-space calculations. 191,193,[328][329][330][331][332][333][334][335][336][337][338][339][340] By representing the core electrons using an atom-centric radial description, a significantly smaller real-space basis set may suffice, making the approaches scalable to large systems while still maintaining a very high level of accuracy. In a somewhat similar spirit, the multi-domain finite element muffin-tin and full-potential linearized augmented plane-wave + local-orbital approaches have also been recently shown to afford high-accuracy all-electron calculations for molecules.…”

Section: Overview On General Approaches For Arbitrary Moleculesmentioning

confidence: 99%

See 1 more Smart Citation

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

Lehtola

2019

Int J of Quantum Chemistry

102

View full text Add to dashboard Cite

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].

show abstract

Section: Applicationsmentioning

confidence: 99%

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

View full text Add to dashboard Cite

show abstract

“…To mitigate the increase in memory usage and computational costs due to the large dimension, tensor decomposition techniques can be applied to real-space methods. 6 − 9 …”

Section: Introductionmentioning

confidence: 99%

“…Solala et al applied tensor decomposition to density functional calculations to minimize memory load. 6 Their results show that the Tucker decomposition method can successfully compress the orbitals represented on a cubic grid from the results of bubbles and the cube numerical framework, which is a variation of real-space methods. Tensor decomposition can be used to compress orbitals on a three-dimensional (3D) grid and build a basis for a self-consistent field (SCF) procedure.…”

Section: Introductionmentioning

confidence: 99%

System-Specific Separable Basis Based on Tucker Decomposition: Application to Density Functional Calculations

Woo

Kim

Choi

2022

J. Chem. Theory Comput.

View full text Add to dashboard Cite

For fast density functional calculations, a suitable basis that can accurately represent the orbitals within a reasonable number of dimensions is essential. Here, we propose a new type of basis constructed from Tucker decomposition of a finite-difference (FD) Hamiltonian matrix, which is intended to reflect the system information implied in the Hamiltonian matrix and satisfies orthonormality and separability conditions. By introducing the system-specific separable basis, the computation time for FD density functional calculations for seven two- and three-dimensional periodic systems was reduced by a factor of 2–71 times, while the errors in both the atomization energy per atom and the band gap were limited to less than 0.1 eV. The accuracy and speed of the density functional calculations with the proposed basis can be systematically controlled by adjusting the rank size of Tucker decomposition.

show abstract

“…20 Tensor decomposition approaches are used for reducing memory requirements. 21,22 The aim of this work is to implement the KS-DFT method into the above framework. The implementation of the XC functional in the double basis (bubbles and cube) involves novel challenges because of the nonlinear nature of the XC term.…”

Section: Introductionmentioning

confidence: 99%

Density Functional Theory under the Bubbles and Cube Numerical Framework

Parkkinen

Solala

et al. 2018

J. Chem. Theory Comput.

Self Cite

View full text Add to dashboard Cite

Density functional theory within the Kohn–Sham density functional theory (KS-DFT) ansatz has been implemented into our bubbles and cube real-space molecular electronic structure framework, where functions containing steep cusps in the vicinity of the nuclei are expanded in atom-centered one-dimensional (1D) numerical grids multiplied with spherical harmonics (bubbles). The remainder, i.e., the cube, which is the cusp-free and smooth difference between the atomic one-center contributions and the exact molecular function, is represented on a three-dimensional (3D) equidistant grid by using a tractable number of grid points. The implementation of the methods is demonstrated by performing 3D numerical KS-DFT calculations on light atoms and small molecules. The accuracy is assessed by comparing the obtained energies with the best available reference energies.

show abstract

Tensor decompositions for the bubbles and cube numerical framework

Cited by 3 publications

References 42 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

System-Specific Separable Basis Based on Tucker Decomposition: Application to Density Functional Calculations

Density Functional Theory under the Bubbles and Cube Numerical Framework

Contact Info

Product

Resources

About