  We report the results of theoretical investigation of electronic structure of
ThF$^+$ cation which is one of the most interesting systems to search for the
electron electric dipole moment (eEDM) [H. Loh, K.C. Cossel, M.C. Grau, K.-K.
Ni, E.R. Meyer, J.L. Bohn, J. Ye, E.A. Cornell, Science {\bf 342}, 1220 (2013)]
and other effects of violation of time reversal (T) and spacial parity (P)
symmetries in fundamental interactions. For the working $^3\Delta_1$ state we
have found a quite high value of the effective electric field acting on
unpaired electrons (37.3 GV/cm). The field will be required to interpret the
experiment planed on ThF$^+$ in terms of eEDM. Within the concept of atoms in
compounds [A.V. Titov, Y.V. Lomachuk, and L.V. Skripnikov, Phys. Rev. A {\bf
90}, 052522 (2014)] we have compared the ThF$^+$ electronic structure with that
of ThO. Also we have calculated other parameters of T,P-odd interactions:
$W_{T,P}$, which is needed for interpretation of the experiment in terms of the
dimensionless constant $k_{T,P}$ characterizing the strength of the T,P-odd
pseudoscalar$-$scalar electron$-$nucleus neutral current interaction (50 kHz);
$W_M$, which is required to search for the Th nuclear magnetic quadrupole
moment in $^{229}$ThF$^+$ (0.88 $\frac{10^{33}\mathrm{Hz}}{e {\rm cm}^2}$). A
number of properties which can be measured are also calculated: hyperfine
structure constant, the molecule-frame dipole moment, and g-factor.
