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The energetics and atomic structure associated with the localized hole formed near an Al-atom dopant in α-quartz are calculated using a variational, self-consistent implementation of the Perdew–Zunger self-interaction correction with complex optimal orbitals. This system has become an important test problem for theoretical methodology since generalized gradient approximation energy functionals, as well as commonly used hybrid functionals, fail to produce a sufficiently localized hole due to the self-interaction error inherent in practical implementations of Kohn–Sham density functional theory. The self-interaction corrected calculations are found to give accurate results for the energy of the defect state with respect to both valence and conduction band edges as well as the experimentally determined atomic structure where only a single Al–O bond is lengthened by 11%. The HSE hybrid functional, as well as the PW91 generalized gradient approximation functional, however, gives too small an energy gap between the defect state and the valence band edge, overly delocalized spin density and lengthening of more than one Al–O bond.

We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew– Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a densitydriven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/H₂O from about 42 meV/H₂O for SCAN. By decomposing the total binding energy into manybody components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

Here, we gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/ H 2 O from about 42 meV/ H 2 O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These findings suggest that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

The paper addresses the problem of the self-interaction correction (SIC) in static calculations of atoms and molecules. Key observable is the electron removal energy, the energy required to remove one electron from the given system and to leave it in a definite hole state whereby we discuss hole states not only in the Highest Occupied Molecular Orbital (HOMO), but also deeper lying holes. To that end, we employ a newly developed technique to compute a stationary state for a configuration with a definite hole in a chosen single-particle state. We also compare two different definitions of removal energies, first, the genuine one taking the difference of the total energy of the original system and the energy of final system sustaining the hole, and second, simply the single-particle energy in the original system. According to Koopman’s theorem, both should be close to each other. Four different systems are considered, one atom and three molecules with different bond types, covalent, metallic, and dipolar. The general result is that any SIC brings considerable improvement as compared to the initial Local-Density Approximation (LDA), the better the closer the hole stays to the HOMO. There are variations between different SIC approximations whereby systems with strong binding (atom and covalent molecule) show least variations. Here, the quality of Koopman’s theorem is very satisfying for the HOMO and degrades slightly toward deeper binding. Systems with metallic or dipolar binding are more reactive and show stronger changes with approximation and hole level.

During the last decades, density functional theory (DFT) has advanced under a wide range of possibilities: from the local-density approximations and gradient corrections to the modern orbital functionals. Size-consistency has emerged as a usual ingredient to be considered, since it has to do, for example, with the capability of accurately describing subsystems which are made far apart from each other. We here revisit N-dependent self-interaction corrections (SICs), that is, which depend explicitly upon the number of electrons N and are usually classified as not consistent in size. This history has begun long before what is today called DFT, with the Fermi–Amaldi SIC applied to the Thomas–Fermi formalism. In this context, we here propose an investigation of a modified Fermi–Amaldi approach, with the inclusion of exponents which can lead to great accuracy. We also introduce the idea of exponents written as density functionals, in order to treat, for example, ionization and dissociation processes.

The computational implementation of orbital functionals has become one of the great modern challenges for density-functional theory (DFT). In static cases, the exact procedure of implementing orbital functionals is the so-called optimized effective potential method (OEP). In situations involving temporal variations, in the context of the time-dependent density-functional theory (TDDFT), TDOEP becomes the correct approach. However, both OEP and TDOEP are known by their severe computational costs, and for this reason they are used in a very restricted set of situations. Therefore, the development of approximations is important. In this work, using one-dimensional model systems, we investigate strategies for the implementation of time-dependent orbital functionals, in order to circumvent or avoid the use of TDOEP. We have found that a local scaling approximation to the TDOEP yields encouraging results aiming the numerical implementation of orbital functionals within the TDDFT context.

Without self-interaction corrections or the use of hybrid functionals, approximations to the density-functional theory (DFT) often favor intermediate spin systems over high-spin systems. In this paper, we apply the recently proposed Fermi–Löwdin-orbital self-interaction corrected density functional formalism to a simple tetra-coordinated Fe(II)-porphyrin molecule and show that the energetic orderings of the S = 1 and S = 2 spin states are changed qualitatively relative to the results of Generalized Gradient Approximation (developed by Perdew, Burke, and Ernzerhof, PBE-GGA) and Local Density Approximation (developed by Perdew and Wang, PW92-LDA). Because the energetics, associated with changes in total spin, are small, we have also calculated the second-order spin–orbit energies and the zero-point vibrational energies to determine whether such corrections could be important in metal-substituted porphins. Our results find that the size of the spin–orbit and vibrational corrections to the energy orderings are small compared to the changes due to the self-interaction correction. Spin dependencies in the Infrared (IR)/Raman spectra and the zero-field splittings are provided as a possible means for identifying the spin in porphyrins containing Fe(II).

The energetics and atomic structure associated with the localized hole formed near an Al-atom dopant in -quartz are calculated using a variational, self-consistent implementation of the Perdew-Zunger self-interaction correction with complex optimal orbitals. This system has become an important test problem for theoretical methodology since generalized gradient approximation energy functionals, as well as commonly used hybrid functionals, fail to produce a sufficiently localized hole due to the self-interaction error inherent in practical implementations of Kohn-Sham density functional theory. The self-interaction corrected calculations are found to give accurate results for the energy of the defect state with respect to both valence and conduction band edges as well as the experimentally determined atomic structure where only a single Al-O bond is lengthened by 11%. The HSE hybrid functional, as well as the PW91 generalized gradient approximation functional, however, gives too small an energy gap between the defect state and the valence band edge, overly delocalized spin density and lengthening of more than one Al-O bond.

Density function theory study on novel lithium battery cathode material, Li2FeVO4, has been analyzed using full potential linearized augmented plane wave approach. Calculations are based on two types of ground states; (1) self-interaction correction applied to Fe atom only and (2) self-interaction correction applied to both Fe and V atoms. Calculations on geometrical structure (volume optimization/force minimization), electronic structure, and Li de-intercalation voltage suggest changes in the geometric/electronic structure of the Li+ de-intercalated component, (i.e., LiFeVO4/FeVO4) and end products in comparison to their pristine counterpart (i.e. Li2FeVO4). Calculated density of states indicate that Li2FeVO4 would either be metallic (for self-interaction correction (SIC) to Fe only) or have narrow band gap (∼0.8 eV for SIC to both Fe/V). Calculation on de-intercalation voltage suggests two step de-lithiation process in Li2FeVO4 favoring high theoretical capacity (∼290 mAh/g) and acceptable potential window vs. Li making it suitable as a novel cathode for lithium battery applications. However, it requires experimental validation.

We use the self-interaction corrected local spin-density approximation to investigate the ground state valency configuration of transition metal (TM = Mn, Co) impurities in n- and p-type ZnO. We find that in pure Zn^sub 1-x^TM^sub x^O, the localized TM^sup 2+^ configuration is energetically favored over the itinerant d-electron configuration of the local spin density (LSD) picture. Our calculations indicate furthermore that the (+/0) donor level is situated in the ZnO gap. Consequently, for n-type conditions, with the Fermi energy ε^sub F^ close to the conduction band minimum, TM remains in the 2+ charge state, while for p-type conditions, with ε^sub F^ close to the valence band maximum, the 3+ charge state is energetically preferred. In the latter scenario, modeled here by co-doping with N, the additional delocalized d-electron charge transfers into the entire states at the top of the valence band, and hole carriers will only exist, if the N concentration exceeds the TM impurity concentration. [PUBLICATION ABSTRACT]