Converging finite-temperature many-body perturbation theory in the grand canonical ensemble that conserves the average number of electrons

So Hirata, Punit K. Jha

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A finite-temperature perturbation theory for the grand canonical ensemble is introduced that expands the chemical potential in a perturbation series and conserves the average number of electrons, ensuring charge neutrality of the system at each perturbation order. Two (sum-over-state and reduced) classes of analytical formulas are obtained in a straightforward, algebraic, time-independent derivation for the first-order corrections to the chemical potential, grand potential, and internal energy, with the aid of several identities of the Boltzmann sums also introduced in this study. These formulas are numerically verified against benchmark data from thermal full configuration interaction. For a nondegenerate ground state, the finite-temperature perturbation theory reduces analytically to and is consistent with the Møller–Plesset perturbation theory as temperature (T) tends to zero. For a degenerate ground state, it should instead reduce to the Hirschfelder–Certain degenerate perturbation theory as T → 0.

Original languageEnglish (US)
Title of host publicationAnnual Reports in Computational Chemistry
EditorsDavid A. Dixon
PublisherElsevier Ltd
Pages17-37
Number of pages21
ISBN (Print)9780128171196
DOIs
StatePublished - 2019

Publication series

NameAnnual Reports in Computational Chemistry
Volume15
ISSN (Print)1574-1400
ISSN (Electronic)1875-5232

Keywords

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

ASJC Scopus subject areas

  • Chemistry(all)
  • Computational Mathematics

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  • Cite this

    Hirata, S., & Jha, P. K. (2019). Converging finite-temperature many-body perturbation theory in the grand canonical ensemble that conserves the average number of electrons. In D. A. Dixon (Ed.), Annual Reports in Computational Chemistry (pp. 17-37). (Annual Reports in Computational Chemistry; Vol. 15). Elsevier Ltd. https://doi.org/10.1016/bs.arcc.2019.08.003