### Abstract

Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, these corrections give rise to orbital-density-dependent functionals and potentials. We show that the simplest implementations of Koopmans' compliance provide accurate estimates for the quasiparticle excitations and leave the total energy functional almost or exactly intact, i.e., they describe correctly electron removals or additions, but do not necessarily alter the electronic charge density distribution within the system. Additional Koopmans-compliant functionals can be constructed that modify the potential energy surface, starting, e.g., from Perdew-Zunger corrections. These functionals become exactly one-electron self-interaction free and, as all Koopmans-compliant functionals, are approximately many-electron self-interaction free. We discuss in detail these different formulations, and provide extensive benchmarks for the 55 molecules in the reference G2-1 set, using Koopmans-compliant functionals constructed from local-density or generalized-gradient approximations. In all cases, we find excellent performance in the electronic properties, comparable or improved with respect to that of many-body perturbation theories, such as G0W0 and self-consistent GW, at a fraction of the cost and in a variational framework that also delivers energy derivatives. Structural properties and atomization energies preserve or slightly improve the accuracy of the underlying density-functional approximations.

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

Article number | 075135 |

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

Volume | 90 |

Issue number | 7 |

DOIs | |

State | Published - Aug 20 2014 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

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

*90*(7), [075135]. https://doi.org/10.1103/PhysRevB.90.075135

}

*Physical Review B - Condensed Matter and Materials Physics*, vol. 90, no. 7, 075135. https://doi.org/10.1103/PhysRevB.90.075135

**Koopmans-compliant functionals and their performance against reference molecular data.** / Borghi, Giovanni; Ferretti, Andrea; Nguyen, Ngoc Linh; Dabo, Ismaila; Marzari, Nicola.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Koopmans-compliant functionals and their performance against reference molecular data

AU - Borghi, Giovanni

AU - Ferretti, Andrea

AU - Nguyen, Ngoc Linh

AU - Dabo, Ismaila

AU - Marzari, Nicola

PY - 2014/8/20

Y1 - 2014/8/20

N2 - Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, these corrections give rise to orbital-density-dependent functionals and potentials. We show that the simplest implementations of Koopmans' compliance provide accurate estimates for the quasiparticle excitations and leave the total energy functional almost or exactly intact, i.e., they describe correctly electron removals or additions, but do not necessarily alter the electronic charge density distribution within the system. Additional Koopmans-compliant functionals can be constructed that modify the potential energy surface, starting, e.g., from Perdew-Zunger corrections. These functionals become exactly one-electron self-interaction free and, as all Koopmans-compliant functionals, are approximately many-electron self-interaction free. We discuss in detail these different formulations, and provide extensive benchmarks for the 55 molecules in the reference G2-1 set, using Koopmans-compliant functionals constructed from local-density or generalized-gradient approximations. In all cases, we find excellent performance in the electronic properties, comparable or improved with respect to that of many-body perturbation theories, such as G0W0 and self-consistent GW, at a fraction of the cost and in a variational framework that also delivers energy derivatives. Structural properties and atomization energies preserve or slightly improve the accuracy of the underlying density-functional approximations.

AB - Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate density-functional theory, these corrections give rise to orbital-density-dependent functionals and potentials. We show that the simplest implementations of Koopmans' compliance provide accurate estimates for the quasiparticle excitations and leave the total energy functional almost or exactly intact, i.e., they describe correctly electron removals or additions, but do not necessarily alter the electronic charge density distribution within the system. Additional Koopmans-compliant functionals can be constructed that modify the potential energy surface, starting, e.g., from Perdew-Zunger corrections. These functionals become exactly one-electron self-interaction free and, as all Koopmans-compliant functionals, are approximately many-electron self-interaction free. We discuss in detail these different formulations, and provide extensive benchmarks for the 55 molecules in the reference G2-1 set, using Koopmans-compliant functionals constructed from local-density or generalized-gradient approximations. In all cases, we find excellent performance in the electronic properties, comparable or improved with respect to that of many-body perturbation theories, such as G0W0 and self-consistent GW, at a fraction of the cost and in a variational framework that also delivers energy derivatives. Structural properties and atomization energies preserve or slightly improve the accuracy of the underlying density-functional approximations.

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U2 - 10.1103/PhysRevB.90.075135

DO - 10.1103/PhysRevB.90.075135

M3 - Article

AN - SCOPUS:84927609604

VL - 90

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 7

M1 - 075135

ER -