Ground- and excited-state properties of the polar and paramagnetic RbSr molecule: A comparative study

This paper deals with the electronic structure of RbSr, a molecule possessing both a magnetic dipole moment and an electric dipole moment in its own frame, allowing its manipulation with external fields. Two complementary ab initio approaches are used for the ground and lowest excited states: first, an approach relying on optimized effective core potentials with core polarization potentials based on a full configuration interaction involving three valence electrons and second, an approach using a small-size effective core potential with 19 correlated electrons in the framework of coupled-cluster theory. We have found excellent agreement between these two approaches for the ground-state properties including the permanent dipole moment. We have focused on studies of excited states correlated to the two lowest asymptotes $\mathrm{Rb}(5p{}^{2}P)$$+\mathrm{Sr}(5s^2{}^{1}S)$ and $\mathrm{Rb}(5s{}^{2}S)$$+\mathrm{Sr}(5s5p{}^{3}P)$ relevant for ongoing experiments on ultracold quantum degenerate gases. We also present approximate potential curves including spin-orbit interaction based on atomic spin-orbit constants. These potential curves are an excellent starting point for experimental studies of molecular structure of RbSr using high-resolution spectroscopy.

Figure 1

The RbSr ground-state potential energy curves obtained with the RCCSD (dotted red line), RCCSD(T) (dashed red line), and FCI–ECP+CPP methods (solid black line).

Figure 2

Permanent electric dipole moment of the RbSr ground state calculated with the finite-field method through the RCCSD(T) (dashed red line) and the FCI–ECP+CPP approach [17] (solid black line).

Figure 3

Isotropic static dipole polarizability and the corresponding anisotropy of the RbSr ground state calculated with the finite-field RCCSD(T) method.

Figure 4

Experimental excited energy levels of Rb and Sr atoms featuring the corresponding dissociation limits (adding a ground-state Sr atom on the left column and a ground-state Rb atom on the right column) of the molecular Hund's (a) case states of the RbSr molecule. The Rb ${}^2{D}_{3/2,5/2}$ energies of Rb are identical within the resolution of the plot. The origin of energies corresponds to infinitely separated ground-state Sr and Rb atoms.

Figure 5

Hund's case (a) potential energy curves of the excited RbSr molecule obtained with the EOM-CCSD method (left panel) and the FCI–ECP+CPP method (right panel). Dashed lines denote the quartet states, while the doublet states are plotted with solid lines.

Figure 6

Permanent electric dipole moments for (a) the $2{}^2{\Sigma }^{+}$ and $1{}^2\Pi$ states correlated to $\mathrm{Rb}(5p{}^{2}P)$-Sr($5s{}^{1}S)$, (b) the $3{}^2{\Sigma }^{+}$ and $2{}^2\Pi$ states correlated to $\mathrm{Rb}(5s{}^{2}S)$$+\mathrm{Sr}(5s5p{}^{3}P)$, and (c) the $1{}^4{\Sigma }^{+}$ and $1{}^4\Pi$ states correlated to $\mathrm{Rb}(5s{}^{2}S)$$+\mathrm{Sr}(5s5p{}^{3}P)$, calculated with the FCI–ECP+CPP and EOM-CCSD approaches. The solid lines denote ${}^{2,4}{\Sigma }^{+}$ symmetry and the dashed lines the ${}^{2,4}\Pi$ symmetry.

Figure 7

Transition dipole moments from the RbSr ground state $X{}^2{\Sigma }^{+}$ towards (a) the $2{}^2{\Sigma }^{+}$ state (black lines) and the $1{}^2\Pi$ (red lines) state and (b) the $3{}^2{\Sigma }^{+}$ state (black lines) and the $2{}^2\Pi$ (red lines) state, obtained with the EOM-CC (solid lines) and FCI–ECP+CPP methods (dashed lines).

Figure 8

The EOM-CCSD potential energy curves of RbSr excited states including an atomic spin-orbit interaction as explained in the text resulting from the (a) EOM-CC approach and (b) FCI–ECP+CPP approach.