  All current experiments searching for an electron EDM d_e are performed with
atoms and diatomic molecules. Motivated by significant recent progress in
searches for an EDM-type signal in diatomic molecules with an uncompensated
electron spin, we provide an estimate for the expected signal in the Standard
Model due to the CKM phase. We find that the main contribution originates from
the effective electron-nucleon operator $\bar{e} i\gamma_5 e \bar{N}N$, induced
by a combination of weak and electromagnetic interactions at
$O(G_F^2\alpha^2)$, and not by the CKM-induced electron EDM itself. When the
resulting atomic P,T-odd mixing is interpreted as an {\it equivalent} electron
EDM, this estimate leads to the benchmark $d_e^{equiv}(CKM) \sim 10^{-38}$ ecm.
