  The first-principle prediction of nanocluster stable structure is often
hampered by the existence of many isomer configurations with energies close to
the ground state. This fact attaches additional importance to many-electron
effects going beyond density functional theory (DFT), because their
contributions may change a subtle energy order of competitive structures. To
analyze this problem, we consider, as an example, the energetics of silicon
nanoclusters passivated by hydrogen Si$_{10}$H$_{2n}$ with $0\le n\le 11$, the
structure of which varies with passivation from compact to loose-packed,
similar to branching polymers. Our calculations performed by the DFT, hybrid
functionals and Hartree-Fock (H-F) methods, as well as by the GW approximation
(GWA), confirm a considerable sensitivity of structure prediction and isomer
energy ordering to many-electron effects and show some results which may be
obtained with the methods less computationally demanding than the GWA.
