### Abstract

Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schlüter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.

Original language | English (US) |
---|---|

Article number | 195134 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 89 |

Issue number | 19 |

DOIs | |

State | Published - May 27 2014 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*89*(19), [195134]. https://doi.org/10.1103/PhysRevB.89.195134

}

*Physical Review B - Condensed Matter and Materials Physics*, vol. 89, no. 19, 195134. https://doi.org/10.1103/PhysRevB.89.195134

**Bridging density-functional and many-body perturbation theory : Orbital-density dependence in electronic-structure functionals.** / Ferretti, Andrea; Dabo, Ismaila; Cococcioni, Matteo; Marzari, Nicola.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bridging density-functional and many-body perturbation theory

T2 - Orbital-density dependence in electronic-structure functionals

AU - Ferretti, Andrea

AU - Dabo, Ismaila

AU - Cococcioni, Matteo

AU - Marzari, Nicola

PY - 2014/5/27

Y1 - 2014/5/27

N2 - Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schlüter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.

AB - Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schlüter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.

UR - http://www.scopus.com/inward/record.url?scp=84902151929&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902151929&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.89.195134

DO - 10.1103/PhysRevB.89.195134

M3 - Article

VL - 89

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 19

M1 - 195134

ER -