How to understand very weak Cr-Cr double bonds and negative spin populations in trinuclear Cr complexes: theoretical insight.

Trinuclear Cr(ii) complex [Cr-3(dpa)(4)Cl-2] 1 (Hdpa = dipyridylamine) has two Cr-Cr double bonds linked with each other. DMRG-CASPT2 calculations reproduced its symmetrical structure. The Cr-Cr effective bond order (EBO) was evaluated to be only 0.59 based on the density matrix based on localized orbitals from DMRG-CASSCF orbitals. The CASCI calculations showed a significantly large alpha-spin population on the terminal Cr atoms as expected but a significantly large beta-spin population on the central Cr atom against expectations. The very small EBO and the presence of a large beta-spin population are not consistent with the simple understanding that 1 has two Cr-Cr double bonds and a quintet ground state, which requests correct understanding of 1 from the viewpoint of chemical bond theory. Comparison of 1 with the allene molecule and allyl radical disclosed that the linked Cr-Cr bonds of 1 resembled the C-C bond of the allyl radical but completely differed from the linked C-C double bonds of allene despite the similar molecular structure. Its N-3 analogue [Cr-3(dpa)(4)(N-3)(2)] 2 has non-symmetrical structure with shorter Cr-1-Cr-2 and longer Cr-2-Cr-3 bonds unlike 1, indicating that 2 is a valence tautomer of 1. DMRG-CASPT2 could reproduce its non-symmetrical structure but DFT/B3PW91 could not. In 2, the EBO is 0.95 for the shorter Cr-1-Cr-2 bond and 0.47 for the longer Cr-2-Cr-3 one. The terminal Cr-3 has a very large alpha spin population, and the other terminal Cr-1 has a somewhat large alpha spin population, but the central Cr-2 has a considerably large beta spin population. These results indicate that the Cr-1-Cr-2 bond conjugates with the Cr-2-Cr-3 bond, which is inconsistent with the simple understanding that 2 has a quadruple bond between Cr-1 and Cr-2 and no bond between Cr-2 and Cr-3. The symmetrical structure has a stronger Cr-X coordinate bond (X = Cl or N-3) but less stable Cr-3 core than does the non-symmetrical one. The relative stabilities of the symmetrical and the non-symmetrical structures are determined by the balance between stabilization energies from the Cr-3 core and the Cr-X coordinate bond. All these findings show that electronic structures and Cr-Cr bonds of 1 and 2 are interesting from the viewpoint of molecular science.