The recent experimental results for the upper limit for the electron EDM in heavy diatomic molecules with open electron shells YbF, ThO as well as proposals for the similar measurements in other heavy heteronuclear diatomic molecules are analyzed. It is argued that the enhancement factor for the electron EDM in a molecule, presented as an "effective" electric field epsilon(eff) is limited by the value epsilon(eff),max approximate to 100. 10(9) V/cm for the molecular states with any value of Omega in diatomic molecules. (C) 2014 Elsevier B.V. All rights reserved.