Extensivity of energy and electronic and vibrational structure methods for crystals

So Hirata, Murat Keçeli, Yu Ya Ohnishi, Olaseni Sode, Kiyoshi Yagi

Research output: Contribution to journalReview articlepeer-review


A pedagogical proof is presented for the extensivity of energies of metallic and nonmetallic crystals that proceeds by elucidating the asymptotic distance dependence of the effective chemical interactions: kinetic, Coulomb, exchange, and correlation. On this basis, a guideline for the size-consistent design of electronic and vibrational methods is proposed. This guideline underscores the significance of the distinct use of the intermediate and standard normalization of wave functions for extensive and intensive quantities, includes the extensive and intensive diagram theorems as the unambiguous criteria for determining size consistency of a method for extensive and intensive quantities, and introduces the extensive-intensive consistency theorem, which stipulates the precise balance between the determinant spaces reached by extensive and intensive operators. Electronic and vibrational methods for crystals are reviewed that are inspired by these formal analyses or developed in accordance with the guideline. ©

Original languageEnglish (US)
Pages (from-to)131-153
Number of pages23
JournalAnnual Review of Physical Chemistry
StatePublished - May 2012


  • Diagrams
  • Extensive quantities
  • Intensive quantities
  • Lattice sums
  • Size consistency
  • Thermodynamic limit

ASJC Scopus subject areas

  • General Medicine


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