Nuclear clock based on the Th V ion

We propose that a nuclear clock based on the Th V ion can surpass the accuracy of clocks built with other thorium ions. The Th$^{4+}$ ion has a rigid closed-shell core with zero total electron angular momentum, suppressing frequency shifts from black-body radiation and stray external fields that act mainly on electrons. We calculate the energy shift of the nuclear clock transition frequency in $^{229}$Th due to the Coulomb field of atomic electrons and find a relative frequency difference of $2.8 \times 10^{-7}$ between Th IV and Th V - twelve orders of magnitude larger than the projected $10^{-19}$ fractional uncertainty of a nuclear clock. We also perform calculations for Th V energy levels, ionization potential, static polarizability, and the black-body radiation shift of the nuclear line. Additionally, we determine the nuclear transition frequencies in two thorium ions and neutral atom: $\omega_N=2,020,406.964(70)$ GHz in Th III, $\omega_N=2,020,408.264(100)$ GHz in Th II, and $\omega_N=2,020,408.364(100)$ GHz in Th I.