PHYSICAL REVIEW A 99, 012507 (2019) Ab initio and analytical studies of the spin-orbit coupling in heteronuclear alkali-metal dimers AB (A, B = Li, Na, K, Rb) at long ranges E. A. Bormotova, S. V. Kozlov, E. A.Pazyuk, and A. V. Stolyarov * Department of Chemistry, Lomonosov Moscow State University, 119991 Moscow, Leninskie gory 1/3, Russia W. Skomorowski Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA I. Majewska and R. Moszynski † Quantum Chemistry Laboratory, Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland (Received 10 November 2018; published 11 January 2019) 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: ξ SO if (R ) = α + β [k] if /R k , where (1) k = 6 and α = ξ SO n 2 P is the SO splitting of the atom A(n 2 P) for the states of the AB molecule converging to the same A(n A 2 P) + B(n B 2 S) dissociation limit, and (2) k = 3 and α = 0 for the molecular i and f states converging to the A(n A 2 P) + B(n B 2 S) and A(n A 2 S) + B(n B 2 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. DOI: 10.1103/PhysRevA.99.012507 I. INTRODUCTION The spin-orbit (SO) coupling effect is the main source of intramolecular perturbations due to the flexible selection rules for the corresponding SO operator [1]. Typically, the strength of the SO interaction decreases as electronic excitation in- creases. However, the impact of this interaction on the nona- diabatic mixing of excited states does not diminish, instead remaining significant, because the density of interacting states grows rapidly when looking at more highly excited states. The SO functions themselves, expectedly, are strongly depen- dent on internuclear distance, R, and their long-range tails are responsible for the complex dynamics of states near the dissociation threshold. Therefore, a rigorous coupled-channel (CC) deperturbation treatment [2] of the excited diatomic states with spectroscopic (experimental) accuracy indispens- ably includes detailed potential energy curves (PECs) and SO functions over a wide range of internuclear distances. This requirement is furthermore complicated by the fact that the optical pathways most frequently applied in * avstol@phys.chem.msu.ru † rmoszyns@tiger.chem.uw.edu.pl photoassociation [3], magnetoassociation [4], and stimulated Raman adiabatic passage [5] (STIRAP) processes of ultra- cold atom assembly [6,7] include bound and quasi-bound rovibronic levels located in the vicinity of the dissociation threshold. Therefore, it is necessary that both PEC and SO functions be physically correct over the entire range of R, so the relevant Feshbach resonances can be predicted with the required spectroscopic accuracy. The SO coupling effect is especially dominant in the complex electronic structure of open-shell diatomic systems (in particular, those containing a transition metal) which are important in the astrophysics of “cool” stars, brown dwarfs, and, most recently, extrasolar planets [8]. In addi- tion, the SO interaction dramatically changes the radiative, magnetic, and electric properties of the excited molecular states. The pronounced SO coupling makes intercombination (spin-forbidden) transitions, autoionization, and dissociative recombination possible and plays a crucial role in the correct description of the collisions of slow atoms in cold plasma. The adiabatic interatomic potentials for the ground and low-lying excited electronic states of homonuclear and het- eronuclear [9] alkali dimers were comprehensively studied (both experimentally and theoretically) during the past three decades [10]. The corresponding quasirelativistic and fully relativistic PECs of K-, Rb-, and Cs-containing molecules 2469-9926/2019/99(1)/012507(14) 012507-1 ©2019 American Physical Society