Computational Spectroscopy of the Cr–Cr Bond in Coordination Complexes

Abstract

We report the accurate computational vibrational analysis of the Cr–Cr bond in dichromium complexes using second-order multireference complete active space methods (CASPT2), allowing direct comparison with experimental spectroscopic data both to facilitate interpreting the low-energy region of the spectra and to provide insights into the nature of the bonds themselves. Recent technological development by the authors has realized such computation for the first time. Accurate simulation of the vibrational structure of these compounds has been hampered by their notorious multiconfigurational electronic structure that yields bond distances that do not correlate with bond order. Some measured Cr–Cr vibrational stretching modes, ν­(Cr2), have suggested weaker bonding, even for so-called ultrashort Cr–Cr bonds, while others are in line with the bond distance. Here, we optimize geometries and compute ν­(Cr2) with CASPT2 for three well-characterized complexes, Cr2(O2CCH3)4(H2O)2, Cr2(mhp)4, and Cr2(dmp)4. We obtain CASPT2 harmonic ν­(Cr2) modes in good agreement with experiment at 282 cm–1 for Cr2(mhp)4 and 353 cm–1 for Cr2(dmp)4, compute 50Cr and 54Cr isotope shifts, and demonstrate that the use of the so-called IPEA shift leads to improved Cr–Cr distances. Additionally, normal mode sampling was used to estimate anharmonicity along ν­(Cr2), leading to an anharmonic mode of 272 cm–1 for Cr2(mhp)4 and 333 cm–1 for Cr2(dmp)4.

Importance of Dispersion in the Molecular Geometries of Mn(III) Spin-Crossover Complexes

“…This would require 342 gradient calculations for 1 and 390 for 2 . Since our interest is focused on the geometric parameters within the first coordination sphere, partial Hessian vibrational analysis (PHVA) was performed including seven atoms (Mn and the first coordination sphere) for the high-spin and intermediate-spin states of both complexes . This reduced the number of gradient calculations to 42.…”

“…Although not a spin-crossover complex, a very serious example of this can be seen in the metal–metal bonding in dichromium complexes. These complexes have very small energy differences between the bonding and antibonding orbitals, leading to significant populations in the antibonding orbitals that, in turn, means that a DFT calculation, assuming that all bonding orbitals are doubly occupied, cannot predict a reliable geometry. , This failure of DFT is due to its use of a single determinant and is well known to occur. In addition to these challenging examples, efforts have been made to improve DFT-computed geometries in spin-crossover complexes by “point-wise” CASPT2 calculations. , However, for low-symmetry or asymmetric complexes, this approach becomes tedious since the metal–ligand bond distances can no longer be stretched isotropically.…”

“…These complexes have very small energy differences between the bonding and antibonding orbitals, leading to significant populations in the antibonding orbitals that, in turn, means that a DFT calculation, assuming that all bonding orbitals are doubly occupied, cannot predict a reliable geometry. 41,42 This failure of DFT is due to its use of a single determinant and is well known to occur. In addition to these challenging examples, efforts have been made to improve DFT-computed geometries in spin-crossover complexes by "point-wise" CASPT2 calculations.…”

Molecular Geometry and Electronic Structure of Copper Corroles

“…To confirm that XMS-CASPT2-optimized geometries are minima, full harmonic vibrational analyses (FHVA) were performed by means of a gradient finite difference for the S 0 , S 1 , and T 0 states of the bare copper corrole. Due to the large size of the triphenyl copper corrole, partial Hessian vibrational analysis (PHVA) 79 was performed for the S 0 and T 0 states. The three phenyl groups were not included in the vibrational analysis.…”

Analytic First-Order Derivatives of CASPT2 with IPEA shift

“…39 Some studies in the literature have statistically proved that vertical excitation energies are indeed improved with IPEA shift. 40,41 It has also been reported that geometrical parameters 42,43 and molecular properties 44,45 may be improved. In spite of its potential utility, no analytic derivatives using IPEA shift have yet been developed; this may be partially due to the requirement for introducing an empirical parameter into "ab initio" methodology rather than technical difficulties.…”