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The theory of the magnetic coupling between the localized spins, mediated by the mobile excess electron, is generalized to the case of a trigonal, six-center, four-electron molecule with partial valence delocalization. The combination of the electron transfer occurring within the valence-delocalized subsystem and the interatomic exchange producing coupling of the spin of the mobile electron of valence-delocalized fragment with the three localized spins forming the valence-localized subsystem leads to the appearance of a special kind of double exchange (DE), termed the "external core double exchange" (ECDE), in order to distinguish such DE from the conventional "internal core double exchange" for which the mobile electron is coupled with the spin-cores on the same center via the intra-atomic exchange. The effect of the ECDE on the ground spin state of the considered trigonal molecule is compared with earlier reported effect produced by DE in the four-electron, mixed-valence (MV) trimer. A high diversity of the ground spin states is revealed, depending on the relative magnitudes and signs of the electron transfer and interatomic exchange parameters, with part of these states not appearing to be the ground states in a trigonal trimer exhibiting DE. We briefly discuss some examples of trigonal MV systems from the point of view of the possibility to have different combinations of signs of the transfer and exchange parameters and, accordingly, different ground spin states. The tentative role of the considered systems in molecular electronics and spintronics is also noticed. [ABSTRACT FROM AUTHOR]