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A measurement of the magnitude of the electric dipole moment of the electron(eEDM) larger than that predicted by the Standard Model (SM) of particlephysics is expected to have a huge impact on the search for physics beyond theSM. Polar diatomic molecules containing heavy elements experience enhancedsensitivity to parity ($P$) and time-reversal ($T$)-violating phenomena, suchas the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleonsand the electrons, and are thus promising candidates for measurements. TheNL-\textit{e}EDM collaboration is preparing an experiment to measure the eEDMand 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 measurableenergy shifts is crucial for the interpretation of these measurements.  In this work we use the finite field relativistic coupled cluster approach tocalculate the $W_d$ and $W_s$ parameters in the ground state of the BaFmolecule. Special attention was paid to providing a reliable theoreticaluncertainty estimate based on investigations of the basis set, electroncorrelation, relativistic effects and geometry. Our recommended values of thetwo 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 $W_s$.

Systematic study and uncertainty evaluation of $P,T$-odd molecular enhancement factors in BaF