First-order dyson coordinates and geometry

Matthew R. Hermes, So Hirata

Research output: Contribution to journalArticlepeer-review


The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.

Original languageEnglish (US)
Pages (from-to)7179-7189
Number of pages11
JournalJournal of Physical Chemistry A
Issue number32
StatePublished - Aug 15 2013

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry


Dive into the research topics of 'First-order dyson coordinates and geometry'. Together they form a unique fingerprint.

Cite this