Density Functional Theory under the Bubbles and Cube Numerical Framework

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

doi:10.1021/acs.jctc.8b00456

Cited by 5 publications

(6 citation statements)

References 47 publications

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“…We note that multiresolution methods are alternative approaches capable of very high accuracy and alleviate the user from selecting a proper basis set for the problem at hand, but these methods are in a development phase. 15,16 ■ METHODOLOGY Core-level spectroscopy was advocated by Siegbahn et al 17,18 in the 1960s, and considerable effort has been put into reproducing experimental core ionization and excitation energies using quantum chemical methods at varying levels of theory. The core−electron binding energy (CEBE) can be defined as the difference between the energy of the ground state E 0 and the hole state E + .…”

Section: ■ Introductionmentioning

confidence: 99%

“…All of these properties can be considered as energy differences, and do not directly involve perturbing electric or magnetic fields, but the fact that they involve ionization of core orbitals implies that standard basis sets will not be optimum. We note that multiresolution methods are alternative approaches capable of very high accuracy and alleviate the user from selecting a proper basis set for the problem at hand, but these methods are in a development phase. , …”

Section: Introductionmentioning

confidence: 99%

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Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Δ Self-Consistent-Field Approach

Ambroise

Jensen

2018

J. Chem. Theory Comput.

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We investigate the basis set requirements for calculating properties corresponding to removing core electrons by the Δ self-consistent-field approach using Hartree–Fock and density functional theory. Standard contracted basis sets are shown to produce large errors and the improved performance of core-augmented basis sets is traced to the fact that the core-augmenting functions effectively create an auxiliary set of uncontracted functions in the core region. We propose two specific basis sets of double and triple-ζ quality based on exponent interpolation of the polarization consistent basis sets, denoted pcX-1 and pcX-2, that display significantly lower basis set errors compared to other alternatives. These are suitable for both nonrelativistic and relativistic calculations of the Douglas–Kroll–Hess type, with typical basis set errors of 0.1 and 0.01 eV, respectively, and they can be used in a mixed basis set approach with only a minor degradation in performance. The versions augmented with diffuse functions (aug-pcX-1 and aug-pcX-2) are shown to perform better than other alternatives for X-ray absorption spectroscopy. When used in connection with range-separated hybrid density functional methods and relativistic corrections, the pcX-n basis sets can in favorable cases reproduce experimental results to within a few tenths of an eV.

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Section: ■ Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Δ Self-Consistent-Field Approach

Ambroise

Jensen

2018

J. Chem. Theory Comput.

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“…Exponential functions are used in at least one widely used program, [29] and alternative functions, such as sinc [30] and ramp [31] have also been proposed. The use of delta functions leads to methods usually denoted as grid-based or finite element, [32] and such real-space methods have been used for providing results very close to the CBS limit. [33] While these alternatives each have advantages over Gaussian or plane wave basis functions, they have yet to find their way into widely used program packages and demonstrate that they are computational superior to existing methods for providing an answer of a given accuracy for a similar or lower computational effort.…”

Section: The Boring Details Basis Set Essentialsmentioning

confidence: 99%

Computational Chemistry: The Exciting Opportunities and the Boring Details

Jensen

2021

Israel Journal of Chemistry

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Computational chemistry has emerged as a subfield in science over the last five decades, not at least due to the amazing increase in computational resources. Equally important, however, is the continuing developments of theoretical methods and in software technology. The refinement of theoretical models moves forward at a steady pace, but at times takes a radical turn in new directions. Computational chemistry methods are now integrated elements in many research fields and are routine tools for non-experts. The plethora of different models, however, forms a bewildering jungle of choices, often resulting in practitioners defaulting to the tried and true. The present contribution contains some personal reflections on the development of computational chemistry methods over the last four decades, with special focus on the development of basis sets and density functional methods.

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“…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%

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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Density Functional Theory under the Bubbles and Cube Numerical Framework

Cited by 5 publications

References 47 publications

Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Δ Self-Consistent-Field Approach

Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Δ Self-Consistent-Field Approach

Computational Chemistry: The Exciting Opportunities and the Boring Details

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

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