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Singlet and triplet instability theorems.

Tomonori Yamada1, So Hirata1

  • 1Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.

The Journal of Chemical Physics
|September 24, 2015
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Summary
This summary is machine-generated.

A new definition of form-degeneracy for molecular orbitals explains instabilities in electronic structures. This research proves triplet and singlet instabilities in restricted Hartree-Fock wave functions, offering insights into chemical phenomena.

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Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Computational Chemistry

Background:

  • Restricted Hartree-Fock (RHF) theory is a fundamental method for approximating electronic wave functions.
  • Orbital degeneracy, typically defined by energy, plays a crucial role in chemical bonding and electronic properties.
  • Strongly correlated systems often exhibit complex electronic behaviors not fully captured by standard RHF theory.

Purpose of the Study:

  • To introduce and define 'form-degeneracy' as a distinct concept from energy-degeneracy for spatial orbitals.
  • To mathematically prove the existence of triplet and singlet instabilities in RHF wave functions under specific degeneracy conditions.
  • To provide theoretical explanations for observed chemical phenomena such as Hund's rule and Jahn-Teller effects.

Main Methods:

  • Introduction of a novel definition: form-degeneracy, based on the invariance of energy expectation values under two-electron excitations.
  • Mathematical proofs demonstrating triplet instability in RHF for real/complex systems when HOMO/LUMO are energy- or form-degenerate.
  • Mathematical proofs demonstrating singlet instability in RHF for real systems when HOMO/LUMO are form-degenerate (nonidentical densities) or energy-degenerate.

Main Results:

  • Established theorems link form- and energy-degeneracy to triplet instabilities in RHF wave functions.
  • Proved the existence of singlet instabilities in RHF wave functions under specific form- or energy-degeneracy conditions.
  • Extended stability theory to continuous spectra, proving oscillating spin density wave (SDW) instabilities in electron gases.

Conclusions:

  • Form-degeneracy provides a new theoretical framework for understanding electronic instabilities in quantum chemistry.
  • The theorems explain fundamental chemical rules (Hund's rule) and phenomena (Jahn-Teller, biradicaloids, bond breaking).
  • The study suggests potential for spin density wave formation in metallic solids and electron gases under specific conditions.