### Abstract

Low-order perturbation corrections to the electronic grand potential, internal energy, chemical potential, and entropy of an ideal gas of noninteracting, identical molecules at a nonzero temperature are determined numerically as the λ-derivatives of the respective quantity calculated exactly (by thermal full configuration interaction) with a perturbation-scaled Hamiltonian, Hˆ_{0}+λVˆ. The data thus obtained from the core definition of any perturbation theory serve as a benchmark against which analytical formulas can be validated. The first- and second-order corrections from finite-temperature many-body perturbation theory discussed in many textbooks disagree with these benchmark data. This is because the theory neglects the variation of chemical potential with λ, thereby failing to converge at the exact, full-interaction (λ = 1) limit, unless the exact chemical potential is known in advance. The renormalized finite-temperature perturbation theory (Hirata and He, 2013) (15) is also found to be incorrect.

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

Title of host publication | Annual Reports in Computational Chemistry |

Editors | David A. Dixon |

Publisher | Elsevier Ltd |

Pages | 3-15 |

Number of pages | 13 |

ISBN (Print) | 9780128171196 |

DOIs | |

State | Published - 2019 |

### Publication series

Name | Annual Reports in Computational Chemistry |
---|---|

Volume | 15 |

ISSN (Print) | 1574-1400 |

ISSN (Electronic) | 1875-5232 |

### Fingerprint

### Keywords

- Chemical potential
- Grand canonical ensemble
- Grand potential
- Internal energy
- Many-body perturbation theory
- Temperature
- Thermodynamics

### ASJC Scopus subject areas

- Chemistry(all)
- Computational Mathematics

### Cite this

*Annual Reports in Computational Chemistry*(pp. 3-15). (Annual Reports in Computational Chemistry; Vol. 15). Elsevier Ltd. https://doi.org/10.1016/bs.arcc.2019.08.002

**Numerical evidence invalidating finite-temperature many-body perturbation theory.** / Jha, Punit K.; Hirata, So.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Annual Reports in Computational Chemistry.*Annual Reports in Computational Chemistry, vol. 15, Elsevier Ltd, pp. 3-15. https://doi.org/10.1016/bs.arcc.2019.08.002

}

TY - CHAP

T1 - Numerical evidence invalidating finite-temperature many-body perturbation theory

AU - Jha, Punit K.

AU - Hirata, So

PY - 2019

Y1 - 2019

N2 - Low-order perturbation corrections to the electronic grand potential, internal energy, chemical potential, and entropy of an ideal gas of noninteracting, identical molecules at a nonzero temperature are determined numerically as the λ-derivatives of the respective quantity calculated exactly (by thermal full configuration interaction) with a perturbation-scaled Hamiltonian, Hˆ0+λVˆ. The data thus obtained from the core definition of any perturbation theory serve as a benchmark against which analytical formulas can be validated. The first- and second-order corrections from finite-temperature many-body perturbation theory discussed in many textbooks disagree with these benchmark data. This is because the theory neglects the variation of chemical potential with λ, thereby failing to converge at the exact, full-interaction (λ = 1) limit, unless the exact chemical potential is known in advance. The renormalized finite-temperature perturbation theory (Hirata and He, 2013) (15) is also found to be incorrect.

AB - Low-order perturbation corrections to the electronic grand potential, internal energy, chemical potential, and entropy of an ideal gas of noninteracting, identical molecules at a nonzero temperature are determined numerically as the λ-derivatives of the respective quantity calculated exactly (by thermal full configuration interaction) with a perturbation-scaled Hamiltonian, Hˆ0+λVˆ. The data thus obtained from the core definition of any perturbation theory serve as a benchmark against which analytical formulas can be validated. The first- and second-order corrections from finite-temperature many-body perturbation theory discussed in many textbooks disagree with these benchmark data. This is because the theory neglects the variation of chemical potential with λ, thereby failing to converge at the exact, full-interaction (λ = 1) limit, unless the exact chemical potential is known in advance. The renormalized finite-temperature perturbation theory (Hirata and He, 2013) (15) is also found to be incorrect.

KW - Chemical potential

KW - Grand canonical ensemble

KW - Grand potential

KW - Internal energy

KW - Many-body perturbation theory

KW - Temperature

KW - Thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=85073549068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073549068&partnerID=8YFLogxK

U2 - 10.1016/bs.arcc.2019.08.002

DO - 10.1016/bs.arcc.2019.08.002

M3 - Chapter

AN - SCOPUS:85073549068

SN - 9780128171196

T3 - Annual Reports in Computational Chemistry

SP - 3

EP - 15

BT - Annual Reports in Computational Chemistry

A2 - Dixon, David A.

PB - Elsevier Ltd

ER -