Knowledge Bank

The only potential energy functions for the $13\Sigma g+$ 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 $\mathrm{<mrow\; data-mjx-texclass="ORD">7,7</mrow>}$Li$2$ and $v=59-79$ for $\mathrm{<mrow\; data-mjx-texclass="ORD">6,6</mrow>}$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 $13\Sigma g+-a3\Sigma u+$ and $23\Pi g-a3\Sigma u+$ 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 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 $13\Sigma g+$--,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.