Theoretical Studies of Multiple Metal–Metal Bonds between Divalent Molybdenum Ions in Dimers, Tetramers, and Clusters

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Abstract
The multiple metal–metal bonds between divalent molybdenum (Mo(II)) ions in dimers and tetramers were investigated theoretically. The orbital energy gaps, occupation numbers of natural orbitals (NO) and effective bond orders for the naked Mo(II)2 dimer (1) were calculated by ab initio UHF MO and density functional (DFT) methods. The effective exchange integrals (Jab) of 1 were calculated by approximately spin-projected UHF and DFT methods, and the complete active space (CAS) CI by the use of UHF NO. The calculated Jab values were discussed in relation to the temperature-dependent paramagnetism observed for the edge-sharing and face-sharing bioctahedral molybdenum complexes. The CAS CI calculations showed that the Heisenberg model is not appropriate for 1 under the condition that the Mo–Mo distance is shorter than 2.5 Å. The UHF and DFT MO calculations were also performed for the linear naked Mo(II)4 tetramer (2) to elucidate possible electronic structures of the d–d conjugated systems. The continuous changes from closed-shell (diamagnetic) electronic structures to antiferromagnetic states were investigated by elongating the Mo–Mo distances. Similarities and differences between Mo(II)2 (1) and naked Cr(II)2 (3) or between Mo(II)4 (2) and Cr(II)4 (4) were examined and compared, since the nature of direct exchange couplings between divalent chromium ions in 3 and 4 was already studied extensively in relation to the electron correlation effect. The metal-insulator transitions induced by elongation of the Mo(II)–Mo(II) distance in Mo(II) clusters were discussed from the viewpoint of electron correlation and size effects in mesoscopic systems.

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