Ab initioand analytical studies of the spin-orbit coupling in heteronuclear alkali-metal dimersAB(A, B= Li, Na, K, Rb) at long ranges

Abstract

The spin-orbit (SO) coupling matrix elements between the excited states of the lightest heteronuclear alkali metal dimers AB(A, B = Li, Na, K, Rb) converging to the first three dissociation limits were evaluated by employing the quasirelativistic electronic wave functions in a wide range of interatomic distances, $R$. The inner-shell electrons of alkali atoms were described using nonempirical shape-consistent effective core potentials. To take the core-valence correlation effects into account, core polarization potentials for each atom were implemented. Dynamical correlation was introduced through the multireference configuration interaction method, which was applied to two valence electrons keeping all subvalence electrons frozen. The reliability of the derived SO functions is accessed through comparison, wherever possible, with their preceding theoretical and experimental counterparts. The ab initio SO matrix elements were approximated beyond the LeRoy radius using the formula: ${\ensuremath{\xi}}_{if}^{\text{SO}}(R)=\ensuremath{\alpha}+{\ensuremath{\beta}}_{if}^{[k]}/{R}^{k}$, where (1) $k=6$ and $\ensuremath{\alpha}={\ensuremath{\xi}}_{n^{2}\mathrm{P}}^{\text{SO}}$ is the SO splitting of the atom $\mathrm{A}(n^{2}\mathrm{P}$) for the states of the AB molecule converging to the same $\mathrm{A}({n}_{\mathrm{A}}^{2}\mathrm{P}$) + $\mathrm{B}({n}_{\mathrm{B}}^{2}\mathrm{S}$) dissociation limit, and (2) $k=3$ and $\ensuremath{\alpha}=0$ for the molecular $i$ and $f$ states converging to the $\mathrm{A}({n}_{\mathrm{A}}^{2}\mathrm{P})+\mathrm{B}({n}_{\mathrm{B}}^{2}\mathrm{S})$ and $\mathrm{A}({n}_{\mathrm{A}}^{2}\mathrm{S})+\mathrm{B}({n}_{\mathrm{B}}^{2}\mathrm{P}$) atomic thresholds, respectively. A theoretical justification of these formulas was derived from the multipole expansion of the molecular SO operator in terms of the inverse powers of the internuclear distance and of products of operators acting on the electronic coordinates of the atoms A and B.