3 research outputs found
Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer
The SCAN (strongly constrained and appropriately normed) meta-generalized
gradient approximation (meta-GGA), which satisfies all 17 exact constraints
that a meta-GGA can satisfy, accurately describes equilibrium bonds that are
normally correlated. With symmetry breaking, it also accurately describes some
sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds
are nearly always normally correlated, the C2 singlet ground state is known to
be a rare case of strong correlation in an sp equilibrium bond. Earlier work
that calculated atomization energies of the molecular sequence B2, C2, O2, and
F2 in the local spin density approximation (LSDA), the Perdew-Burke-Ernzerhof
(PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule,
found that only SCAN was accurate enough to reveal an anomalous under-binding
for C2. This work shows that spin symmetry breaking in singlet C2, the
appearance of net up- and down-spin densities on opposite sides (not ends) of
the bond, corrects that under-binding, with a small SCAN atomization-energy
error more like that of the other three molecules, suggesting that
symmetry-breaking with an advanced density functional might reliably describe
strong correlation. This article also discusses some general aspects of
symmetry breaking, and the insights into strong correlation that
symmetry-breaking can bring.Comment: 10 pages, 3 figures, 1 Tabl
Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory
Exact density functionals for the exchange and correlation energies are
approximated in practical calculations for the ground-state electronic
structure of a many-electron system. An important exact constraint for the
construction of approximations is to recover the correct non-relativistic
large- expansions for the corresponding energies of neutral atoms with
atomic number and electron number , which are correct to leading order
( and respectively) even in the lowest-rung or
local density approximation. We find that hydrogenic densities lead to
(as known before only for )
and . These asymptotic estimates are most correct
for atomic ions with large and , but we find that they are
qualitatively and semi-quantitatively correct even for small and for . The large- asymptotic behavior of the energy is pre-figured in
small- atoms and atomic ions, supporting the argument that widely-predictive
approximate density functionals should be designed to recover the correct
asymptotics. It is shown that the exact Kohn-Sham correlation energy, when
calculated from the pure ground-state wavefunction, should have no contribution
proportional to in the limit for any fixed .Comment: This work has been accepted for publication at the Journal of
Chemical Physics. Revisions: new Appendix A (former Appendix A is now
Appendix B) discussing exact Kohn-Sham perturbation series for Ec. Added
material discussing the Becke 1988 functional. More discussion of
non-empirical functionals' recovery of the asymptotic series, and their
accuracy in predicting atomic/molecular energie
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Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory.
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to the leading order (-0.221Z5/3 and -0.021Z ln Z, respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to Ex(N, Z) β -0.354N2/3Z (as known before only for Z β« N β« 1) and Ec β -0.02N ln N. These asymptotic estimates are most correct for atomic ions with large N and Z β« N, but we find that they are qualitatively and semi-quantitatively correct even for small N and N β Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely predictive approximate density functionals should be designed to recover the correct asymptotics. It is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z β β limit for any fixed N