\label{eq:errd}$$ where $\delta a_i^{\text{PC}}$ is the error associated to the chiral expansion of the PC potential and $\delta a_i^{\text{TRV}}$ the error associated with the chiral expansion of the TRV potential. Both the contributions were evaluated following the prescriptions of Epelbaum [*et al.*]{} [@EE15] where as reference momentum in the calculation of the errors we used the mass of the pion. It is straightforward to understand that the errors are dominated by the TRV part because we are using the N2LO potential for it and the N4LO potential for the PC part.

The coefficients for the deuteron, evaluated with the N4LO PC potential and the N2LO TRV potential and the associated errors for the three different choices of the cutoff parameters, are given in Table \[tab:2hdpc\]. The coefficients $a_p$ and $a_n$ multiplying the intrinsic neutron and proton EDM, as already pointed out first in Ref. [@NY15] and then in Ref. [@JB151], are given by, $$a_n=a_p=\left(1-\frac{3}{2}P_D\right)\, ,$$ where $P_D$ is the percentage of D-wave present in the deuteron wave function. The values of $a_n$ and $a_p$ obtained using the Entem and Machleidt at N4LO for three different choices of the cut off are reported in Table \[tab:2hdpc\]. The operator ${\hat{\boldsymbol{D}}}_{\rm PC}$ for 