We report the results of our theoretical study and analysis of earlier experimental data for the g-factor tensor components of the ground $^2Pi_{1/2}$ state of free PbF radical. The values obtained both within the relativistic coupled-cluster method
combined with the generalized relativistic effective core potential approach and with our fit of the experimental data from [R.J. Mawhorter, B.S. Murphy, A.L. Baum, T.J. Sears, T. Yang, P.M. Rupasinghe, C.P. McRaven, N.E. Shafer-Ray, L.D. Alphei, J.-U. Grabow, Phys. Rev. A 84, 022508 (2011); A. Baum, B.S. thesis, Pomona College, 2011]. The obtained results agree very well with each other but contradict the previous fit performed in the cited works. Our final prediction for g-factors is $G_{parallel}= 0.081(5)$, $G_{perp}=-0.27(1)$.
It is demonstrated that the TaN molecule is the best candidate to search for T,P-violating nuclear magnetic quadrupole moment (MQM), it also looks promising to search for other T,P-odd effects. We report results of coupled-cluster calculations of T,P
-odd effects in TaN produced by the Ta nucleus MQM, electron electric dipole moment (EDM), scalar$-$pseudoscalar nucleus$-$electron interactions, also of the molecule-axis hyperfine structure constant and dipole moment. Nuclear calculations of $^{181}$Ta MQM are performed to express the T,P-odd effect in terms of the strength constants of T,P-odd nuclear forces, proton and neutron EDM, QCD parameter $theta$ and quark chromo-EDM.
