Planar polyaromatic molecules eta5-coordinated to transition metal complexes are well-studied and applied in organometallic chemistry. Much less attention is paid to curved polyaromatic systems, so-called buckybowls or fullerene fragments. Here we present results of theoretical investigation of eta5-adducts of corannulene as representative model for buckybowls with VIIIB group transition metals (Co, Rh, Ir and Fe, Ru, Os). Natural bonding orbital (NBO) analysis revealed that corannulene acts as a pi-donor whereas transition metal center behaves as an acceptor, using its empty d xy orbital. Additionally, relatively weak back-donation from transition metals to corannulene was also observed. Energetics of the bonding was further explored with help of Energy Decomposition Analysis (EDA), which includes repulsive Pauli and attractive electrostatic (ionic) and orbital (covalent) components. Combined with EDA, NOCV (Natural Orbitals for Chemical Valence) analysis of donor-acceptor pairs associated with shape of charge flow and quantification of its magnitude in terms of energy confirmed the aforementioned nature of the orbital interactions. For comparison, eta6-coordination mode of corannulene was also analyzed.