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The binding-energy differences for $^{163}\mathrm{Ho}^{q+}$ and$^{163}\mathrm{Dy}^{q+}$ ions with ionization degrees $q = 38$, $39$, and $40$are calculated. The calculations are performed using the large-scalerelativistic configuration-interaction and relativistic coupled-clustersmethods. The contributions from quantum-electrodynamics, nuclear-recoil, andfrequency-dependent Breit-interaction effects are taken into account. The finaluncertainty does not exceed $1$ eV. Combining the obtained results with thebinding-energy difference for neutral atoms calculated in [Savelyev et al.,Phys. Rev. A 105, 012806 (2022)], we get the secondary differences of theion-atom binding energies. These values can be used to evaluate the amount ofenergy released in the electron capture process in $^{163}\mathrm{Ho}$ atom(the $Q$ value), provided mass differences of highly charged ions$^{163}\mathrm{Ho}^{q+}$ and $^{163}\mathrm{Dy}^{q+}$ is known from experiment.The $Q$ value is required by experiments on the determination of the absolutescale of the electron neutrino mass by studying the beta-decay process.

Calculations of the binding-energy differences for highly-charged Ho and Dy ions