Calculating $^{179}$HfF$^{+}$ to find the spatial parity and time invariance violation effects

The energy shifts of the sublevels of the hyperfine structure of the ground rotational state because of the interaction of the electric dipole moment of the electron (eEDM) and the magnetic quadrupole moment (MQM) of the $^{179}$Hf nucleus with the internal electromagnetic field of the cation have been calculated for the electron state $^{3}\Delta_{1}$ of the $^{179}$Hf$^{19}$F$^{+}$ ion. A special feature of the experiments on the search for $e$EDM and magnetic quadrupole moment on $^{179}$Hf$^{19}$F$^{+}$ is the use of rotating external fields, which complicates the calculations and makes them more relevant. To populate the energy levels, you need to know their structure and the knowledge of the $g$-factors of the levels will allow you to suppress a number of systematic errors in the experiment caused by incomplete control of the magnitude of the magnetic field used. Therefore, the corresponding calculations were also carried out. Our calculations can be used to plan an experiment with the $^{179}$HfF$^{+}$ cation and interpret the data obtained.