Exchange Forces in Transition-Metal Bonding

Citation

Goodgame, Marvin Mark (1984) Exchange Forces in Transition-Metal Bonding. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xs72-nm31. https://resolver.caltech.edu/CaltechTHESIS:10232009-150307132

Abstract

We have examined multiple bonds (σ, π, and δ) to transition metals and find that intra-atomic exchange forces on these metals are crucial for correct prediction of ground states and that a proper description of these terms is required for a quantitative understanding of bond energies.

Our calculations on models for bridged Fe porphyrin dimers show that intra-atomic exchange forces on the Fe's are critical to the explanation for the dramatic differences in the Fe-Fe coupling for µ-oxo and µ-nitrido bridged Fe porphyrin dimers. The qualitative bonding concepts obtained are used to predict properties of the µ-carbido bridged Fe porphyrin dimer.

In most cases, the interactions responsible for bonding lead to antifer'romagnetic coupling between the d orbitals localized on adjacent centers, resulting in overall low-spin couplings. However, some extended metal systems (eg. metallic Ni) lead to net ferromagnetic interactions between d orbitals localized on different centers. In order to elucidate these effects, we have examined the direct and indirect d-d couplings in the Ni₄ cluster as a function of bond distance. We find that ferromagnetic coupling dominates in a region of bond distance around the bulk Ni value of 2.5 Å with antiferromagnetic coupling dominating for short R (by 2.0 Å) and for long R (by 3.5 Å). The dominant interactions responsible for ferromagnetic coupling involve spin polarization of the conduction band (s-like), supporting a model for ferromagnetism in bulk metallic systems very similar to the Ruderman-Kittel model for magnetic impurities.

The dimers Cr₂ and Mo₂ provide the most dramatic illustration of the importance of exchange forces in bonding. With six unpaired electrons on each atom, there is the potential for up to six covalent bonds. However, formation of d-d covalent bonds requires a concomitant loss in intra-atomic d-d exchange energy. The net result is a double well where the long-R minimum (3 Å is dominated by s-s pairing (no loss of intra-atomic d-d terms) while the short-R minimum (1.7 to 1.9 Å) involves a strong quintuple bond of d orbitals plus an antibonding s-s interaction. To properly handle the intra-atomic exchange terms during this transition from long R with local high-spin coupling to small R with dominant singlet pairing within bonding pairs presents a formidable challenge to ab initio computation. To carry out such studies, we have extended the GVB and related approaches of ab initio calculations and have also developed a simple approximate method of including the electron correlation missing in GVB wavefunctions that provides a quantitatively accurate description of these systems.

The effects studied here should be of comparable importance for multiple bonds involving transition metals, lanthanides, and actinides bonding to each other and to such ligands as CR₂, CR, O, N, and NR. Correlation terms beyond GVB are most important for the least electronegative ligands. Thus, the proper treatment of intra-atomic exchange and of interatomic d-d coupling should be of considerable importance in studies of heterogeneous and homogeneous catalytic systems.

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