Trends in the Bond Multiplicity of Cr₂, Cr₃, and Cr₂M (M = Zn, Ni, Fe, Mn) Complexes Extracted from Multiconfigurational Wave Functions

Abstract

Extended metal atom chains constitute an interesting class of molecules from both theoretical and applied points of view. In the chromium-based series Cr 2 M(dpa) 4 X 2 (with M = Zn, Ni, Fe, Mn, Cr), the direct metal−metal interactions span a wide range of possibilities and so do their associated properties. The multiplicity and symmetry components of the metal−metal bond are herein analyzed via the effective bond order (EBO) concept using complete active space self-consistent field wave functions and compared with similar bimetallic Cr 2 L 4 X 2 systems. The bond multiplicity follows a trend dominated by the Cr−Cr distance which, in turn, depends on the nature of the axial ligand (X). Cr 2 M compounds present asymmetric structures with virtually no interaction between the Cr 2 unit and M, whereas fully symmetric structures with delocalized bonding among the three metals are also possible in Cr 3 complexes. In such cases, a strategy that involves localization of the molecular orbitals into each Cr−Cr pair is applied to quantify the contribution of each pair to the overall metal−metal bond multiplicity.

Paramagnetic Metal–Metal Bonded Heterometallic Complexes

“…210 To capture the multiconfigurational nature of Cr 2 M(dpa) 4 X 2 complexes, CASSCF and CASPT2 approaches have been employed by Loṕez and co-workers to correlate trends in effective bond order (EBO, see section 2.3.2) in the series of Cr 2 M HEMACs, as well as the homometallic Cr 3 (dpa) 4 Cl 2 . 211 The CASSCF wave functions for Cr 2 M compounds show a set of bonding and antibonding orbitals localized on the Cr 2 unit that were used to calculate EBO values. These values may be compared to the EBO of 2.14 for the isolated Cr 2 (dpa) 4 molecule to assess how the M atom affects the Cr≣Cr bond.…”

Extending the ASS1ST Active Space Selection Scheme to Large Molecules and Excited States

“…Finally, the performance of ASS1ST was tested for the notorious case of Cr 2 , which has been the subject of numerous studies with multireference electronic structure methods on account of its complicated bonding pattern. ,− Experimentally, detailed information about the potential energy surface was obtained from RKR (Rydberg–Klein–Rees) inversion of high-resolution photoelectron spectra (see Figure ). At a bond distance of 1.678 Å, which is at the minimum of the experimental potential energy surface, ASS1ST suggests an active space of 12 electrons in 14 orbitals when thresholds of 0.02 and 1.98 are applied (see the SI).…”

Computational Spectroscopy of the Cr–Cr Bond in Coordination Complexes

“…The concept of an effective bond order (EBO), which accounts for the partial occupation of low-lying antibonding orbitals, has been used to quantify the nature of the overall Cr–Cr bond that is composed of multiple partial bonds. , Furthermore, these computations highlight that the multiconfigurational electronic structure of Cr 2 bonds is more nuanced compared to Mo 2 and W 2 analogues . As a result, the Cr–Cr bond order often does not correlate with bond distance. − Note that for some particularly short Cr–Cr distances, density functional theory (DFT) has been used successfully since the electronic structure can be represented by fully occupied bonding orbitals …”

“…For example, DFT geometry optimizations can be performed keeping the Cr–Cr bond distance fixed at the experimental value with subsequent analysis of the electronic structure with CASPT2 . Alternatively, a series of constrained DFT optimizations can be performed to determine the Cr–Cr bond distance point wise with CASPT2 yielding good agreement with the experiment. − These hybrid approaches, however, are not applicable to the computation of the vibrational spectra. Moreover, full CASPT2 geometry optimization for complexes with transition metals had only been performed on small molecules, and even then, not routinely. − …”