Effects of Electrons on Nuclear Clock Transition Frequency in ²²⁹Th Ions

We perform calculations of the energy shift of the nuclear clock transition frequency Th-229 as a function of the number of electrons in Th ion. We demonstrate that the dependence of the nuclear frequency on electron configuration is significant, for example, removing one electron from the atom leads to relative shift of the nuclear frequency similar to 10(-7), which is 12 orders of magnitude larger than the expected relative uncertainty of the nuclear clock transition frequency (similar to 10(-19)). This leads to the difference of the nuclear clock frequencies in Th IV, Th III, Th II, and Th I. The relative change of the nuclear frequency between neutral Th and its bare nucleus is 1%. We also calculate the field shift constants for isotopic and isomeric shifts of atomic electron transitions in Th ions.