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Register a new userFull self-consistency in Fermi-orbital self-interaction correction
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The Perdew-Zunger self-interaction correction cures many common problems associated with semilocal density functionals, but suffers from a size-extensivity problem when Kohn-Sham orbitals are used in the correction. Fermi-L{o}wdin-orbital self-interaction correction (FLOSIC) solves the size-extensivity problem, allowing its use in periodic systems and resulting in better accuracy in finite systems. Although the previously published FLOSIC algorithm [J. Chem. Phys. 140, 121103 (2014)] appears to work well in many cases, it is not fully self-consistent. This would be particularly problematic for systems where the occupied manifold is strongly changed by the correction. In this paper we demonstrate a new algorithm for FLOSIC to achieve full self-consistency with only marginal increase of computational cost. The resulting total energies are found to be lower than previously reported non-self-consistent results.
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(Semi)-local density functional approximations (DFAs) suffer from self-interaction error (SIE). When the first ionization energy (IE) is computed as the negative of the highest-occupied orbital (HO) eigenvalue, DFAs notoriously underestimate them compared to quasi-particle calculations. The inaccuracy for the HO is attributed to SIE inherent in DFAs. We assessed the IE based on Perdew-Zunger self-interaction corrections on 14 small to moderate-sized organic molecules relevant in organic electronics and polymer donor materials. Though self-interaction corrected DFAs were found to significantly improve the IE relative to the uncorrected DFAs, they overestimate. However, when the self-interaction correction is interiorly scaled using a function of the iso-orbital indicator z{sigma}, only the regions where SIE is significant get a correction. We discuss these approaches and show how these methods significantly improve the description of the HO eigenvalue for the organic molecules.
Semi-local approximations to the density functional for the exchange-correlation 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 one-electron 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 one-electron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, 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.
We study the importance of self-interaction errors in density functional approximations for various water-ion clusters. We have employed the Fermi-Lowdin orbital self-interaction correction (FLOSIC) method in conjunction with LSDA, PBE, and SCAN to describe binding energies of hydrogen-bonded water-ion clusters, textit{i.e.}, water-hydronium, water-hydroxide, water-halide, as well as non-hydrogen-bonded water-alkali clusters. In the hydrogen-bonded water-ion clusters, the building blocks are linked by hydrogen atoms, although the links are much stronger and longer-ranged than the normal hydrogen bonds between water molecules, because the monopole on the ion interacts with both permanent and induced dipoles on the water molecules. We find that self-interaction errors overbind the hydrogen-bonded water-ion clusters and that FLOSIC reduces the error and brings the binding energies into closer agreement with higher-level calculations. The non-hydrogen-bonded water-alkali clusters are not significantly affected by self-interaction errors. Self-interaction corrected PBE predicts the lowest mean unsigned error in binding energies ($leq$ 50 meV/ce{H2O}) for hydrogen-bonded water-ion clusters. Self-interaction errors are also largely dependent on the cluster size, and FLOSIC does not accurately capture the subtle variation in all clusters, indicating the need for further refinement.
The Perdew-Zunger self-interaction correction(PZ-SIC) improves the performance of density functional approximations(DFAs) for the properties that involve significant self-interaction error(SIE), as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by LSIC, local scaling of the PZ-SIC to the local spin density approximation(LSDA). Here we propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of atomic number Z in the asymptotic expansion of the exchange-correlation(xc) energy for atoms. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator z{sigma}, which distinguishes one-electron regions from many-electron regions. LSIC+ applied to LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof(PBE) generalized gradient approximation(GGA), and almost as well as the strongly constrained and appropriately normed(SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, both fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bond, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. To make a locally scaled-down SIC to functionals beyond LSDA requires a gauge transformation of the functionals energy density. The resulting SCAN-sdSIC, evaluated on SCAN-SIC total and localized orbital densities, leads to an acceptable description of many equilibrium properties including the dissociation energies of weak bonds.
Perdew-Zunger self-interaction correction (PZ-SIC) offers a route to remove self-interaction errors on an orbital-by-orbital basis. A recent formulation of PZ-SIC by Pederson, Ruzsinszky and Perdew proposes restricting the unitary transformation to localized orbitals called Fermi-Lowdin orbitals. This formulation, called the FLOSIC method, simplifies PZ-SIC calculations and was implemented self-consistently using a Jacobi-like (FLOSIC-Jacobi) iteration scheme. In this work we implement the FLOSIC approach using the Krieger-Li-Iafrate (KLI) approximation to the optimized effective potential (OEP). We compare the results of present FLOSIC-KLI approach with FLOSIC-Jacobi scheme for atomic energies, atomization energies, ionization energies, barrier heights, polarizability of chains of hydrogen molecules etc. to validate the FLOSIC-KLI approach. The FLOSIC-KLI approach, which is within the realm of Kohn-Sham theory, predicts smaller energy gaps between frontier orbitals due to the lowering of eigenvalues of the lowest unoccupied orbitals. Results show that atomic energies, atomization energies, ionization energy as an absolute of highest occupied orbital eigenvalue, and polarizability of chains of hydrogen molecules between the two methods agree within 2%. Finally the FLOSIC-KLI approach is used to determine the vertical ionization energies of water clusters.
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