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Inverted-sandwich-type and open-lantern-type dinuclear transition metal complexes: theoretical study of chemical bonds by electronic stress tensor

We study the electronic structure of two types of transition metal complexes, the inverted-sandwich-type and open-lantern-type, by the electronic stress tensor. In particular, the bond order b_e measured by the energy density which is defined from the electronic stress tensor is studied and compared with the conventional MO based bond order. We also examine the patterns found in the largest eigenvalue of the stress tensor and corresponding eigenvector field, the "spindle structure" and "pseudo-spindle structure". As for the inverted-sandwich-type complex, our bond order b_e calculation shows that relative strength of the metal-benzene bond among V, Cr and Mn complexes is V > Cr > Mn which is consistent with the MO based bond order. As for the open-lantern-type complex, we find that our energy density based bond order can properly describe the relative strength of Cr--Cr and Mo--Mo bonds by the surface integration of the energy density over the "Lagrange surface" which can take into account the spatial extent of the orbitals.