Variations of the Hartree–Fock fractional-spin error for one electron

Burton, Hugh G. A.; Marut, Clotilde; Daas, Timothy J.; Gori‐Giorgi, Paola; Loos, Pierre‐François

doi:10.1063/5.0056968

Cited by 9 publications

(22 citation statements)

References 95 publications

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“…One way to illustrate the relevance of DC-DFT is to study the evolution of non-empirical functionals and their global hybrids on the total energy (or ionization energy) of the simplest possible system, a single H atom. ,, In Figure , we consider LDA (SVWN), PBE, and SCAN, and study their behavior under interpolation toward the exact functional, in this case HF, i.e., E XC DFA + α( E X HF – E XC DFA ). For α = 0, we have the original functional, but for α = 1, we have pure HF.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

et al. 2022

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Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn−Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree−Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

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Section: Theoretical Considerationsmentioning

confidence: 99%

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

et al. 2022

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“…The half-filled Hubbard dimer provides a simplified model of the hydrogen molecule in a minimal basis. It is an insightful system to understand the nature of strong correlation present in the chemical bond and there have been numerous studies of the Hubbard dimer as a benchmark for electronic correlation methods. − The exact ground state energy of the Hubbard dimer is given by , E 0 = U 2 − 1 2 U 2 + 16 t 2 To find the exact Green’s function requires the diagonalization of the single and three particle Hamiltonians as well. Using these states, it is simple to construct the exact Green’s function and polarization from their Lehmann representations.…”

Section: Results For Hubbard Modelsmentioning

confidence: 99%

A Regularized Second-Order Correlation Method from Green’s Function Theory

Coveney

Tew

2023

J. Chem. Theory Comput.

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We present a scalable single-particle framework to treat electronic correlation in molecules and materials motivated by Green's function theory. We derive a size-extensive Brillouin-Wigner perturbation theory from the single-particle Green's function by introducing the Goldstone self-energy. This new ground state correlation energy, referred to as Quasi-Particle MP2 theory (QPMP2), avoids the characteristic divergences present in both second-order Møller−Plesset perturbation theory and Coupled Cluster Singles and Doubles within the strongly correlated regime. We show that the exact ground state energy and properties of the Hubbard dimer are reproduced by QPMP2 and demonstrate the advantages of the approach for larger Hubbard models where the metal-to-insulator transition is qualitatively reproduced, contrasting with the complete failure of traditional methods. We apply this formalism to characteristic strongly correlated molecular systems and show that QPMP2 provides an efficient, size-consistent regularization of MP2.

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“…Low FC and FS errors are important because we expect them to improve various predictions even for the parent integer electron case and related systems . Here, we test this by using the DH-RSxc functionals to compute the dissociation curves of diatomic molecules, which are known to be strongly affected by FC and FS errors , and are a common and strong test case for new methods. ,,,,,,− Figure shows the obtained dissociation curves for the H 2 + , H 2 , and Li 2 molecules, calculated with the same set of functionals used in Figure (see section IX in Supporting Information for dissociation curves of the same systems, obtained with the DH-RSxc-ii functional but with a reduced fraction of exact exchange). In all calculations shown in Figure , the spin state was purposefully kept constant throughout the dissociation curve, to avoid improvements in energy owing to symmetry breaking. ,, We note that the H 2 + molecule is obviously a one-electron system; therefore, full HF exchange and zero correlation provide the exact result.…”

Section: Resultsmentioning

confidence: 99%

Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals

Prokopiou

Hartstein

Govind

et al. 2022

J. Chem. Theory Comput.

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We study the optimal tuning of the free parameters in range-separated double hybrid functionals, based on enforcing the exact conditions of piecewise linearity and spin constancy. We find that introducing the range separation in both the exchange and the correlation terms allows for the minimization of both fractional charge and fractional spin errors for singlet atoms. The optimal set of parameters is system specific, underlining the importance of the tuning procedure. We test the performance of the resulting optimally tuned functionals for the dissociation curves of diatomic molecules. We find that they recover the correct dissociation curve for the one-electron system, H 2 + , and improve the dissociation curves of many-electron molecules such as H 2 and Li 2 , but they also yield a nonphysical maximum and only converge to the correct dissociation limit at very large distances.

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Variations of the Hartree–Fock fractional-spin error for one electron

Cited by 9 publications

References 95 publications

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

A Regularized Second-Order Correlation Method from Green’s Function Theory

Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals

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