Analysing the chromium–chromium multiple bonds using multiconfigurational quantum chemistry

Abstract

a b s t r a c tThis Letter discusses the nature of the chemical bond between two chromium atoms in different di-chromium complexes with the metal atoms in different oxidation states. Starting with the Cr diatom, with its formally sextuple bond and oxidation number zero, we proceed to analyse the bonding in some Cr(I)-Cr(I) XCrCrX complexes with X varying from F, to Phenyl, and Aryl. The bond distance in these complexes varies over a large range: 1.65-1.83 Å and we suggest explanations for these variations. A number of dichromium complexes with bond distances around or shorter than 1.80 Å have recently been synthesized and we study one of these complexes, Cr 2 (diazadiene) 2 and show how the Cr-Cr bond order is related to the oxidation number and the ligand bonding, factors that are all involved in the determination of the short Cr-Cr bond length: 1.80 Å. The discussion is based on the use of multiconfigurational wave functions, which give a qualitatively correct description of the electronic structure in these multiply bonded systems.

Assessing Metal–Metal Multiple Bonds in CrCr, MoMo, and WW Compounds and a Hypothetical UU Compound: A Quantum Chemical Study Comparing DFT and Multireference Methods

“…In the [Ph-MMPh] calculations the geometries of the systems were constrained to C 2h symmetry, while in the [Ar-MM-Ar] calculations they were constrained to C 2 symmetry. For all species under investigation we have computed the effective bond order (EBO) [14,39] which quantifies the formation of a chemical bond from CASSCF wavefunctions. For a single bond the EBO is given by Equation (1), in which h b and h ab are the sums of the occupation numbers of the bonding and anti-bonding molecular orbital pair derived from the CASSCF wavefunction.…”

“…A closer inspection of EBO values and weights of the dominating electronic configurations indicates that the magnitude of the M À M bond order goes as: Cr < Mo % W, in agreement with the trend found for the simpler [Ph-MMPh] models and for the diatomic molecules. [14,39] The relative bond order is maintained along the series as Ph is replaced by Ar: the Mo À Mo and W À W bond orders are about one unit larger than the Cr À Cr bond order.…”

Second-order perturbation theory with complete and restricted active space reference functions applied to oligomeric unsaturated hydrocarbons

“…When supplemented by multireference second-order perturbation theory, CASSCF/CASPT2, 16 so as to account for dynamical electron correlation effects not already included at the CASSCF level, accuracies on the order of 0.2 eV have been documented for state-energy splittings in molecules containing elements throughout the periodic table. [17][18][19][20][21][22][23][24][25] The major drawback of the CASSCF formalism is that the number of configuration state functions (CSFs) required for the multiconfigurational expansion increases factorially with the number of active electrons and active orbitals. Memory and disk storage limit the size of the active space in modern software packages to about 15 electrons in 15 orbitals, which is on the order of 1 Â 10 6 to 16 Â 10 6 CSFs depending on spin and spatial symmetry.…”

Orienting spins in dually doped monolayer MoS2: from one-sided to double-sided doping

“…Generally, magnetism in the doubly Cr-doped systems is very different from the antiferromagnetism in the ground state of the Cr2 dimer. 34,35 All Cr homo-doped systems, with the exception of the totally geometrically symmetric Cr(0)-MoS2-Cr(1), are FM in their ground states. Their total magnetic moments are 8 µB, which is equal to twice the 4 µB of the single substitutional Cr dopant atom.…”