  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. K\"ohn, 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.
