Bonding nature of open-lantern-type dinuclear Cr(II) complexes. Theoretical study with the MRMP2 method

Open-lantern-type dinuclear Cr(II) complex, [Cr(R(1)NC(R(2))NR(3))(2)](2) (R(1) = Et, R(2) = Me, and R(3) = (t)Bu), was theoretically investigated with DFT, CASSCF, and MRMP2 methods. The DFT-optimized Cr-Cr distance (1.757 A) is too short compared to the experimental value (1.960 A). The CASSCF method does not present the minimum in the range of the Cr-Cr distance from 1.75 to 2.05 A. The MRMP2 method presents the optimized Cr-Cr distance of 1.851 A, which is a little shorter than the experimental value. These results suggest that both nondynamical and dynamical correlations are considerably large in this complex. The Cr-Cr bond order is evaluated to be 2.40 with the CASSCF method, which is much smaller than the formal bond order of 4. In the Mo analogue, on the other hand, the DFT, CASSCF, and MRMP2 methods present almost the same Mo-Mo distance (2.151 A). The Mo-Mo bond order is evaluated to be 3.41, which is somewhat smaller than the formal value but much larger than the Cr-Cr bond order. These differences arise from the much larger d-d overlap integral of the Mo-Mo pair than that of the Cr-Cr pair. Though nondynamical correlation effect is very large in this dinuclear Cr(II) complex, the Cr-Cr distance of this complex was experimentally discussed to be short, based on formal shortness ratio (FSR). We wish to propose here orbital shortness ratio (OSR) based on the distance providing maximum overlap integral to discuss the M-M bond distance. According to the OSR, we understand that the Cr-Cr distance of 1.960 A is long but the Mo-Mo distance of 2.151 A is short. This understanding is consistent with much larger nondynamical correlation in the dinuclear Cr(II) complex than in the Mo(II) analogue. Interesting differences are also observed between M-M and Si-Si multiple bonds. The differences are discussed in terms of sigma- and pi-type overlap integrals and the participation of Si 3s orbital in the sigma-bonding orbital.