New benchmarks for the second‐order correlation energies of Ne and Ar through the finite element MP2 method

Flores, Jesús R.

doi:10.1002/qua.21742

Cited by 19 publications

(11 citation statements)

References 36 publications

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“…Numerical estimates of the MP2 limit (Δ E ∞ MP2 ) are not as common as for the HF limit . Fortunately, Ranasinghe et al have collated accurate literature values of the MP2 core–core and core–valence contributions from finite element calculations of atoms, − explicitly correlated calculations of molecules, and proposed a simple linear extrapolation method to obtain near-reference results from [3,4,5]-ζ calculations (eq ). …”

Section: Resultsmentioning

confidence: 99%

Basis Set Extrapolations for Density Functional Theory

Kraus

2020

J. Chem. Theory Comput.

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Basis set extrapolation is a common technique in wavefunction theory, used to squeeze better performance out of the highest affordable level of theory by combining it with lower quality calculations. In this work, I present analogous techniques for basis set extrapolation in density functional theory, focusing on [2,3]-ζ calculations, and including double hybrid and dispersion corrected functionals. My recommendations are based on basis set limit data from finite element calculations, estimates of basis set limits for double hybrid corrections, and they are validated using the GMTKN55 and NCDT datasets. A short review of extrapolation methods for Hartree-Fock calculations based on modern finite element data is carried out to inform this work. Extrapolation of [2,3]-ζ calculations in cc-pvXz-pp and def2-Xvpd basis sets with the proposed recipes routinely matches and sometimes outperforms 4-ζ calculations at a fraction of the cost. The methods are implemented in Psi4, allowing for an automated and intuitive application.

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Section: Resultsmentioning

confidence: 99%

Basis Set Extrapolations for Density Functional Theory

Kraus

2020

J. Chem. Theory Comput.

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“…In fact, the problem appears already for two‐electron systems, for example, in CI calculations on the 1 s 2 state of He as discovered in the late 1970s in seminal work by Silverstone and coworkers . Because of this, even atomic fully numerical calculations have to rely on extrapolation approaches . Although extrapolation techniques are commonly used even for SCF energies in the context of LCAO calculations, as the SCF energy affords exponential convergence, such approaches are usually not necessary except for highly accurate benchmark studies.…”

Section: Discussionmentioning

confidence: 99%

“…In addition to enabling variational calculations—approaching the converged value strictly from above—and making sure orbital orthonormality is always honored, the use of an explicit radial basis set instead of the implicit basis set of the finite‐difference method also enables the straightforward use of post‐HF methods . For instance, Flores et al have calculated correlation energies with Møller‐Plesset perturbation theory truncated at the second order, while Sundholm and coworkers have relied on highly accurate multiconfigurational self‐consistent field (MCSCF) methods to study the ground state of the beryllium atom, electron affinities, excitation energies and ionization potentials, hyperfine structure, nuclear quadrupole moments, the extended Koopmans' theorem, and the Hiller–Sucher–Feinberg identity . Braun and Engel and coworkers have in turn reported finite‐element calculations of atoms in strong magnetic fields.…”

Section: Applicationsmentioning

confidence: 99%

“…In addition to enabling variational calculations -approaching the converged value strictly from above -and making sure orbital orthonormality is always honored, the use of an explicit radial basis set instead of the implicit basis set of the finite-difference method also enables the straightforward use of post-HF methods. 451 For instance, Flores et al have calculated correlation energies with Møller-Plesset perturbation theory 58 truncated at the second order, [452][453][454][455][456][457][458][459][460][461][462][463][464] while Sundholm and coworkers have relied on highly accurate multiconfigurational SCF methods 465 to study the ground state of the beryllium atom, 466 electron affinities, [467][468][469][470][471] excitation energies and ionization potentials, [472][473][474] hyperfine structure, [475][476][477] nuclear quadrupole moments, [477][478][479][480][481][482][483][484][485][486][487][488][489][490][491][492] the extended Koopmans' theorem, …”

Section: Atomsmentioning

confidence: 99%

“…432,433 Because of this, even atomic fully numerical calculations have to rely on extrapolation approaches. 461,463,464 Although extrapolation techniques are commonly used even for SCF energies in the context of LCAO calculations, as the SCF energy affords exponential convergence such approaches are usually not necessary except for highly accurate benchmark calculations. Regardless of the used basis set, the key to obtaining accurate post-HF energetics, however, is the extrapolation to the CBS limit, which has been studied extensively in the literature using a wealth of extrapolation formulas.…”

Section: Post-hf Approachesmentioning

confidence: 99%

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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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Computing accurate molecular properties in real space using multiresolution analysis

Bischoff

2019

State of the Art of Molecular Electronic Structure Computations: Correlation Methods, Basis Sets and More

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New benchmarks for the second‐order correlation energies of Ne and Ar through the finite element MP2 method

Cited by 19 publications

References 36 publications

Basis Set Extrapolations for Density Functional Theory

Basis Set Extrapolations for Density Functional Theory

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

Computing accurate molecular properties in real space using multiresolution analysis

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