### Abstract

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.

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

Pages (from-to) | 5172-5175 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 84 |

Issue number | 22 |

State | Published - May 29 2000 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*84*(22), 5172-5175.

**Degenerate Ground States and a Fractional Number of Electrons in Density and Reduced Density Matrix Functional Theory.** / Yang, Weitao; Zhang, Yingkai; Ayers, Paul W.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 84, no. 22, pp. 5172-5175.

}

TY - JOUR

T1 - Degenerate Ground States and a Fractional Number of Electrons in Density and Reduced Density Matrix Functional Theory

AU - Yang, Weitao

AU - Zhang, Yingkai

AU - Ayers, Paul W.

PY - 2000/5/29

Y1 - 2000/5/29

N2 - For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.

AB - For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.

UR - http://www.scopus.com/inward/record.url?scp=0000486590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000486590&partnerID=8YFLogxK

M3 - Article

VL - 84

SP - 5172

EP - 5175

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 22

ER -