  Relativistic ab initio calculations have been performed to assess the
suitability of RaF for experimental search of P- and T,P-violating
interactions. The parameters of P- and T,P-odd terms of the spin-rotational
Hamiltonian have been calculated for the ${^2}\Sigma$ electronic ground state
of RaF molecule. They include the parameter $W_a$, which is critical in
experimental search for nuclear anapole moment and the parameters $W_d$ and
$W_{\rm SP}$ required to obtain restrictions on the electric dipole moment of
the electron and T,P-odd scalar-pseudoscalar interactions, respectively. The
parameter $X$ corresponding to the "volume effect" in the T,P$-$odd interaction
of the $^{223}$Ra nuclear Schiff moment with electronic shells of RaF has also
been computed. Spectroscopic and hyperfine structure constants for $^{223}$RaF
and $^{223}$Ra$^+$ have been computed as well, demonstrating the accuracy of
the methods employed.
