AN EXTENSION OF THE `MLR' POTENTIAL FUNCTION FORM WHICH ALLOWS FOR AN ACCURATE DPF TREATMENT OF $\textrm{Li}_2(1^3\Sigma^+_g)$, WHICH COUPLES TO TWO OTHER STATES NEAR THEIR ASYMPTOTES
Loading...
Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
Ohio State University
Abstract
The only potential energy functions for the $1^3\Sigma^+_g$ state of Li$_2$ published to date were conventional RKR curves based on experimental data for the vibrational levels $\,v=1-7$,, Spectrochimica Acta {\bf 44A}, 1369 (1988);~ C.\ Linton {\em et al.}, J.\ Chem.\ Phys.\ {\bf 91}, 6036 (1989).} and they do not yield realistic predictions for the very weakly bound levels $\,v=62 - 89\,$ for $^{7,7}$Li$_2$ and $\,v=59\! -\! 79\,$ for $^{6,6}$Li$_2$, which were subsequently observed using photoassociation spectroscopy (PAS)., Phys.\ Rev.\ {\bf A 51}, R871 (1995);~ E.R.I.\ Abraham {\em et al.}\ J.\ Chem.\ Phys.\ {\bf 103}, 7773 (1995).}~ A recent analysis of data for the $1\,^3\Sigma_g^+ -a\,^3\Sigma_u^+$ and $2\,^3\Pi_g -a\,^3\Sigma_u^+$ systems of Li$_2$ was unable to incorporate these PAS data, and this was due to the lack of a potential function form with the ability to accurately describe the behaviour of the potential for a molecule which becomes coupled to two other distinct states near the dissociation asymptote., 63$^{\rm rd}$ Ohio State University Int.\ Symp.\ on Molec.\ Spec.\ (2008), paper RC11.} The current work presents and tests an extension of the `Morse/Long-Range' (MLR) potential function form, 663 (2007);~ R.J.\ Le Roy {\em et al.}, J.\ Chem.\ Phys.\ (2009, submitted).} which {\em does}\, provide an accurate description of the $1^3\Sigma^+_g$--\,state potential at {\em all}\, internuclear distances, including the long-range region where the three-state coupling occurs. The extension is based on expressions reported by Aubert-Fr{\' e}con and co-workers,, Phys,\ Rev.\ {\bf A 55}, 3458 (1997);~ M.\ Aubert-Fr{\' e}con {\em et al.}, J.\ Mol.\ Spectrosc.\ {\bf 192}, 239 (1998).} which show that the long-range tail of this potential is one of the eigenvalues of a 3x3 Hamiltonian matrix. Accordingly, this extension requires the diagonalization of this matrix at each internuclear distance $r$. Although this can be done analytically, we show that the diagonalization is in fact computed more efficiently numerically, and leads to a more accurate potential energy function.
Description
\,F.\ Martin {\em et al.\,W.I.\ McAlexander {\em et al.\,N.S. Dattani, {\em et al.\,R.J.\ Le Roy and R.D.E.\ Henderson, Mol.\, Phys.\ {\bf 105\,Martin {\em et al.
Author Institution: Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada; Universite de Lyon F-69622, Lyon, France; Universite Lyon 1; Villeurbanne; CNRS, UMR5579, LASIM; Physics Department, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada
Author Institution: Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada; Universite de Lyon F-69622, Lyon, France; Universite Lyon 1; Villeurbanne; CNRS, UMR5579, LASIM; Physics Department, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada