Semi-local approximations to the density functional for the exchangecorrelation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all oneelectron ground-or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for oneelectron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGA's) and meta-GGA's, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.
Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree–Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H*, covalently bound to the donor oxygen atom) from the acceptor (OA) and donor (OD) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.
The physical origin of the dark energy that causes the accelerated expansion rate of the universe is one of the major open questions of cosmology. One set of theories postulates the existence of a self-interacting scalar field for dark energy coupling to matter. In the chameleon dark energy theory, this coupling induces a screening mechanism such that the field amplitude is nonzero in empty space but is greatly suppressed in regions of terrestrial matter density. However measurements performed under appropriate vacuum conditions can enable the chameleon field to appear in the apparatus, where it can be subjected to laboratory experiments. Here we report the most stringent upper bound on the free neutron-chameleon coupling in the strongly-coupled limit of the chameleon theory using neutron interferometric techniques. Our experiment sought the chameleon field through the relative phase shift it would induce along one of the neutron paths inside a perfect crystal neutron interferometer. The amplitude of the chameleon field was actively modulated by varying the millibar pressures inside a dual-chamber aluminum cell. We report a 95 % confidence level upper bound on the neutron-chameleon coupling β ranging from β < 4.7 × 10 6 for a Ratra-Peebles index of n = 1 in the nonlinear scalar field potential to β < 2.4 × 10 7 for n = 6, one order of magnitude more sensitive than the most recent free neutron limit for intermediate n. Similar experiments can explore the full parameter range for chameleon dark energy in the foreseeable future.
The Perdew-Zunger(PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional. Unfortunately, it spoils the slowly-varying-in-space limits of the uncorrected approximate functionals, where those functionals are right by construction. The right limits can be restored by locally scaling down the energy density of the PZ SIC in many-electron regions, but then a spurious correction to the exact functional would be found unless the self-Hartree and exact self-xc terms of the PZ SIC energy density were expressed in the same gauge. Only the local density approximation satisfies the same-gauge condition for the energy density, which explains why the recent local-scaling SIC (LSIC) is found here to work excellently for atoms and molecules only with this basic approximation, and not with the more advanced generalized gradient approximations (GGAs) and meta-GGAs, which lose the Hartree gauge via simplifying integrations by parts. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can also be applied to approximate functionals. Doing so leads to a simple scaled-down self-interaction (sdSIC) correction that is typically much more accurate than PZ SIC in tests for many molecular properties (including equilibrium bond lengths). The present work shows unambiguously that the largest errors of PZ SIC applied to standard functionals at three levels of approximation can be removed by restoring their correct slowlyvarying-density limits. It also confirms the relevance of these limits to atoms and molecules.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.