### Abstract

Density-functional theory is an extremely powerful and widely used tool for quantum simulations. It reformulates the electronic-structure problem into a functional minimization with respect to the charge density of interacting electrons in an external potential. While exact in principle, it is approximate in practice, and even in its exact form it is meant to reproduce correctly only the total energy and its derivatives, such as forces, phonons, or dielectric properties. Quasiparticle levels are outside the scope of the theory, with the exception of the highest occupied state, since this is given by the derivative of the energy with respect to the number of electrons. A fundamental property of the exact energy functional is that of piecewise linearity at fractional occupations in between integer fillings, but common approximations do not follow such piecewise behavior, leading to a discrepancy between total and partial electron removal energies. Since the former are typically well described, and the latter provide, via Janak’s theorem, orbital energies, this discrepancy leads to a poor comparison between predicted and measured spectroscopic properties. We illustrate here the powerful consequences that arise from.

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

Pages (from-to) | 193-234 |

Number of pages | 42 |

Journal | Topics in Current Chemistry |

Volume | 347 |

DOIs | |

State | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Chemistry(all)

### Cite this

*Topics in Current Chemistry*,

*347*, 193-234. https://doi.org/10.1007/128_2013_504

}

*Topics in Current Chemistry*, vol. 347, pp. 193-234. https://doi.org/10.1007/128_2013_504

**Piecewise linearity and spectroscopic properties from koopmans-compliant functionals.** / Dabo, Ismaila; Ferretti, Andrea; Marzari, Nicola.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Piecewise linearity and spectroscopic properties from koopmans-compliant functionals

AU - Dabo, Ismaila

AU - Ferretti, Andrea

AU - Marzari, Nicola

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Density-functional theory is an extremely powerful and widely used tool for quantum simulations. It reformulates the electronic-structure problem into a functional minimization with respect to the charge density of interacting electrons in an external potential. While exact in principle, it is approximate in practice, and even in its exact form it is meant to reproduce correctly only the total energy and its derivatives, such as forces, phonons, or dielectric properties. Quasiparticle levels are outside the scope of the theory, with the exception of the highest occupied state, since this is given by the derivative of the energy with respect to the number of electrons. A fundamental property of the exact energy functional is that of piecewise linearity at fractional occupations in between integer fillings, but common approximations do not follow such piecewise behavior, leading to a discrepancy between total and partial electron removal energies. Since the former are typically well described, and the latter provide, via Janak’s theorem, orbital energies, this discrepancy leads to a poor comparison between predicted and measured spectroscopic properties. We illustrate here the powerful consequences that arise from.

AB - Density-functional theory is an extremely powerful and widely used tool for quantum simulations. It reformulates the electronic-structure problem into a functional minimization with respect to the charge density of interacting electrons in an external potential. While exact in principle, it is approximate in practice, and even in its exact form it is meant to reproduce correctly only the total energy and its derivatives, such as forces, phonons, or dielectric properties. Quasiparticle levels are outside the scope of the theory, with the exception of the highest occupied state, since this is given by the derivative of the energy with respect to the number of electrons. A fundamental property of the exact energy functional is that of piecewise linearity at fractional occupations in between integer fillings, but common approximations do not follow such piecewise behavior, leading to a discrepancy between total and partial electron removal energies. Since the former are typically well described, and the latter provide, via Janak’s theorem, orbital energies, this discrepancy leads to a poor comparison between predicted and measured spectroscopic properties. We illustrate here the powerful consequences that arise from.

UR - http://www.scopus.com/inward/record.url?scp=84921730266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84921730266&partnerID=8YFLogxK

U2 - 10.1007/128_2013_504

DO - 10.1007/128_2013_504

M3 - Article

AN - SCOPUS:84921730266

VL - 347

SP - 193

EP - 234

JO - Topics in Current Chemistry

JF - Topics in Current Chemistry

SN - 0340-1022

ER -