  A measurement of the magnitude of the electric dipole moment of the electron
(eEDM) larger than that predicted by the Standard Model (SM) of particle
physics is expected to have a huge impact on the search for physics beyond the
SM. Polar diatomic molecules containing heavy elements experience enhanced
sensitivity to parity ($P$) and time-reversal ($T$)-violating phenomena, such
as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons
and the electrons, and are thus promising candidates for measurements. The
NL-\textit{e}EDM collaboration is preparing an experiment to measure the eEDM
and S-PS interaction in a slow beam of cold BaF molecules [Eur. Phys. J. D, 72,
197 (2018)]. Accurate knowledge of the electronic structure parameters, $W_d$
and $W_s$, connecting the eEDM and the S-PS interaction to the measurable
energy shifts is crucial for the interpretation of these measurements.
  In this work we use the finite field relativistic coupled cluster approach to
calculate the $W_d$ and $W_s$ parameters in the ground state of the BaF
molecule. Special attention was paid to providing a reliable theoretical
uncertainty estimate based on investigations of the basis set, electron
correlation, relativistic effects and geometry. Our recommended values of the
two parameters, including conservative uncertainty estimates, are 3.13 $\pm$
$0.12 \times 10^{24}\frac{\text{Hz}}{e\cdot \text{cm}}$ for $W_d$ and 8.29
$\pm$ 0.12 kHz for $W_s$.
