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We carried out detailed high-precision study of Ag-like Nd$^{13+}$,Sm$^{15+}$ and In-like Ce$^{9+}$, Pr$^{10+}$, Nd$^{11+}$, Sm$^{13+}$,Eu$^{14+}$ highly-charged ions. These ions were identified to be of particularinterest to the development of ultra-accurate atomic clocks, search forvariation of the fine-structure constant $\alpha$, and quantum information[Safronova et. al. Phys. Rev. Lett. 113, 030801 (2014)]. Relativisticlinearized coupled-cluster method was used for Ag-like ion calculations, and ahybrid approach that combines configuration interaction and a variant of thecoupled-cluster method was used for the In-like ion calculations. Breit and QEDcorrections were included. Energies, transition wavelengths, electric-dipole,electric-quadrupole, electric-octupole, magnetic-dipole, magnetic-quadrupole,magnetic-octupole reduced matrix elements, lifetimes, and sensitivitycoefficients to $\alpha$-variation were calculated. Detailed study of variouscontributions was carried out to evaluate uncertainties of the final results.Energies for several similar "reference" ions, where the experimental valuesare available were calculated and compared with experiment for further tests ofthe accuracy.

Study of highly-charged Ag-like and In-like ions for the development of atomic clocks and search for $\alpha$-variation