  We show that in transition metal compounds containing structural metal dimers
there may exist in the presence of different orbitals a special state with
partial formation of singlets by electrons on one orbital, while others are
effectively decoupled and may give e.g. long-range magnetic order or stay
paramagnetic. Similar situation can be realized in dimers spontaneously formed
at structural phase transitions, which can be called orbital-selective Peierls
transition. This can occur in case of strongly nonuniform hopping integrals for
different orbitals and small intra-atomic Hund's rule coupling JH. Yet another
consequence of this picture is that for odd number of electrons per dimer there
exist competition between double exchange mechanism of ferromagnetism, and the
formation of singlet dimer by electron on one orbital, with remaining electrons
giving a net spin of a dimer. The first case is realized for strong Hund's rule
coupling, typical for 3d compounds, whereas the second is more plausible for
4d-5d compounds. We discuss some implications of these phenomena, and consider
examples of real systems, in which orbital-selective phase seems to be
realized.
