High-accuracy Rb${}_2^{+}$ interaction potentials based on coupled cluster calculations

Abstract

This work discusses a protocol for constructing highly accurate potential energy curves (PECs) for the lowest two states of Rb${}_2^{+}$, i.e. $X{}^2\Sigma {}_g^{+}$ and $(1){}^2\Sigma {}_u^{+}$, using an additivity scheme based on coupled-cluster theory. The approach exploits the findings of our previous work [J. Schnabel, L. Cheng and A. Köhn, J. Chem. Phys. 155, 124101 (2021)] to avoid the unphysical repulsive long-range barrier occurring for symmetric molecular ions when perturbative estimates of higher-order cluster operators are employed. Furthermore, care was taken to reproduce the physically correct exchange splitting of the $X{}^2\Sigma {}_g^{+}$ and $(1){}^2\Sigma {}_u^{+}$ PECs. The accuracy of our computational approach is benchmarked for ionization energies of Rb and for spectroscopic constants as well as vibrational levels of the $a{}^3\Sigma {}_u^{+}$ triplet state of Rb\textsubscript{2}. We study high-level correlation contributions, high-level relativistic effects and inner-shell correlation contributions and find very good agreement with experimental reference values for the atomic ionization potential and the binding energy of Rb${}_2$ in the $a{}^3\Sigma {}_u^{+}$ triplet state. Our final best estimate for the binding energy of the Rb${}_2^{+}$ $X{}^2\Sigma {}_g^{+}$ state including zero-point vibrational contributions is $D_0=6179{\mathrm{cm}}^{-1}$ with an estimated error bound of $\mathcal{O}(\pm 30{\mathrm{cm}}^{-1})$. This value is smaller than the experimentally inferred lower bond of $D_0\ge 6307.5{\mathrm{cm}}^{-1}$ [Bellos et al., Phys. Rev. A 87, 012508 (2013)] and will require further investigation. For the $(1){}^2\Sigma {}_u^{+}$ state a shallow potential with $D_0=78.4{\mathrm{cm}}^{-1}$ and an error bound of $\pm 9{\mathrm{cm}}^{-1}$ is computed.

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