Finite size scaling for critical parameters of simple diatomic molecules

Qicun Shi, Sabre Kais

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

We use the finite size scaling method to study the critical points, points of non-analyticity, of the ground state energy as a function of the coupling parameters in the Hamiltonian. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given molecular Hamiltonian. To illustrate this approach, we give detailed calculations for systems of one electron and two nuclear centres. Z+e-Z+. Within the Born-Oppenheimer approximation, there is no critical point, but without the approximation the system exhibits a critical point at Z = Zc = 1.228 279 when the nuclear charge, Z, varies. We show also that the dissociation occurs in a first-order phase transition and calculate the various related critical exponents. The possibility of generalizing this approach to larger molecular systems using Gaussian basis sets is discussed.

Original languageEnglish
Pages (from-to)1485-1493
Number of pages9
JournalMolecular Physics
Volume98
Issue number19
DOIs
Publication statusPublished - 10 Oct 2000
Externally publishedYes

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Hamiltonians
Phase Transition
diatomic molecules
critical point
Electrons
Born approximation
scaling
Molecules
Eigenvalues and eigenfunctions
Ground state
Born-Oppenheimer approximation
Phase transitions
eigenvectors
exponents
dissociation
ground state
approximation
electrons
energy

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Finite size scaling for critical parameters of simple diatomic molecules. / Shi, Qicun; Kais, Sabre.

In: Molecular Physics, Vol. 98, No. 19, 10.10.2000, p. 1485-1493.

Research output: Contribution to journalArticle

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