Finite size scaling for critical parameters of simple diatomic molecules

Qicun Shi, Sabre Kais

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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
Issue number19
Publication statusPublished - 10 Oct 2000
Externally publishedYes


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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