Two avenues to self-interaction correction within Kohn—Sham theory: unitary invariance is the shortcut

Kümmel, Stephan; Perdew, John P.

doi:10.1080/0026897031000094506

Cited by 49 publications

(26 citation statements)

References 49 publications

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“…An expression for the gradient of the SIC functional, which also constrains the orbitals to be orthogonal, has been derived 33 and applied to atoms and molecules with a mixture of successes and bad failures. [34][35][36] The second strategy uses the canonical orbitals and seeks the minimization of the SIC energy by varying both the orbitals and the unitary transformation M. The corresponding set of equations is…”

Section: Review Of Existing Methodsmentioning

confidence: 99%

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids

et al. 2007

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We present an atomic-orbital-based approximate scheme for self-interaction correction ͑SIC͒ to the localdensity approximation ͑LDA͒ of density-functional theory. The method, based on the idea of Filippetti and Spaldin ͓Phys. Rev. B 67, 125109 ͑2003͔͒, is implemented in a code using localized numerical atomic-orbital basis sets and is now suitable for both molecules and extended solids. After deriving the fundamental equations as a nonvariational approximation of the self-consistent SIC theory, we present results for a wide range of molecules and insulators. In particular, we investigate the effect of re-scaling the self-interaction correction and we establish a link with the existing atomiclike corrective scheme LDA+ U. We find that when no re-scaling is applied, i.e., when we consider the entire atomic correction, the Kohn-Sham highest occupied molecular orbital ͑HOMO͒ eigenvalue is a rather good approximation to the experimental ionization potential for molecules. Similarly the HOMO eigenvalues of negatively charged molecules reproduce closely the molecular affinities. In contrast a re-scaling of about 50% is necessary to reproduce insulator band gaps in solids, which otherwise are largely overestimated. The method therefore represents a Kohn-Sham based single-particle theory and offers good prospects for applications where the actual position of the Kohn-Sham eigenvalues is important, such as quantum transport.

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Section: Review Of Existing Methodsmentioning

confidence: 99%

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids

et al. 2007

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“…It is worth noting that improvement for all pairs of atoms can be expected from recent development of hyper-GGA functionals 25 and modern hybrids 26 -28 applied in the framework of the optimized effective potential method. [29][30][31] To better understand the critical value r t we refer to Fig. 3.…”

Section: The Water Moleculementioning

confidence: 99%

Water molecule by the self-consistent atomic deformation method

et al. 2003

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We present a density functional method which expresses the charge density of a system of atoms as a sum over localized atomiclike densities derived from potentials defined variationally from the total energy expression, which includes contributions from overlapping densities. An approach for systematically increasing the variational freedom of the atomiclike densities is introduced and tested for the water molecule. For the water molecule our method results in complete charge transfer for sufficiently small bond lengths and reverses the charge transfer at large bond lengths. In case of complete charge transfer the overlap contributions are zero, allowing a direct comparison with the traditional Kohn-Sham approach.

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“…Since a response quantity like the polarizability determines how a system reacts to a field that induces a density shift, calculating the polarizability also probes the ability to correctly describe charge transfer. As a second, positive side effect, investigating hydrogen chains also allows us to address the question of size-consistency of the OEP-SIC functional [13,26,27].…”

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confidence: 99%

Electrical Response of Molecular Systems: The Power of Self-Interaction Corrected Kohn-Sham Theory

2008

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The accurate prediction of electronic response properties of extended molecular systems has been a challenge for conventional, explicit density functionals. We demonstrate that a self-interaction correction implemented rigorously within Kohn-Sham theory via the Optimized Effective Potential (OEP) yields polarizabilities close to the ones from highly accurate wavefunction-based calculations and exceeding the quality of exact-exchange-OEP. The orbital structure obtained with the OEP-SIC functional and approximations to it are discussed.PACS numbers: 31.15. Ew,71.15.Mb,72.80.Le Gaining microscopic insight into the quantummechanical electronic effects that govern energy-and charge transfer in processes like light-harvesting, chargeseparation in organic solar cells, or the response of molecular opto-electronic devices would be extremely beneficial to the understanding of these phenomena. But the computational complexity of solving the manyelectron Schrödinger equation leaves little hope that wave-function based approaches can address these problems any time soon. The formulation of quantum mechanics without wavefunction, i.e., density functional theory (DFT) in the Kohn-Sham framework, is computationally much more efficient and allows to handle systems with up to several hundreds of electrons. Therefore, it appears as the ideal tool for investigating the above mentioned problems. However, the predictive power of DFT calculations depends crucially on the approximations made in the description of the exchange-correlation effects. Structural, ground-state molecular properties are obtained with reasonable to excellent accuracy using standard, explicit density functionals like the Local Spin Density Approximation (LSDA) or Generalized Gradient Approximations (GGAs). But these functionals notoriously fail in the description of charge transfer processes [1, 2] and associated problems like predicting the response [3] or transport [4] properties of extended molecular systems. There is, thus, a serious need for exchange-correlation approximations that allow to calculate response properties like polarizabilities of extended systems reliably on a quantitative scale and with bearable computational costs.It has been demonstrated that improvements in the density-functional description of the response of conjugated polymers can be achieved based on current density functional theory [5] and related ideas [6], or by incorporating full [3,7,8] or partial [9] exact exchange. It has also been argued that correlation effects play a non-negligible role in the proper description of response properties [10]. However, evaluating the Fock integrals in exact exchange approaches increases numerical costs substantially, and the computational complexity of approaches using exact exchange with "compatible" correlation is significant [11].In this manuscript we demonstrate that these problems can be overcome with a self-interaction correction (SIC) employed rigorously within Kohn-Sham theory. In the SIC-scheme, only direct, i.e., self-exchange int...

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Two avenues to self-interaction correction within Kohn—Sham theory: unitary invariance is the shortcut

Cited by 49 publications

References 49 publications

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids

Water molecule by the self-consistent atomic deformation method

Electrical Response of Molecular Systems: The Power of Self-Interaction Corrected Kohn-Sham Theory

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