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 $bar{e} igamma_5 e bar{N}N$, induced by a combination of weak and electromagnetic interactions at $O(G_F^2alpha^2)$, 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.
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