Orbital interactions metal, energies

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

Orbital interaction diagram and EHT calculations show that the 1,2 intramolecular shift of hydrogen is symmetry disfavored [10]. In presence of a transition metal fragment to which the alkyne coordinates, the activation energy is considerably lower. This has been attributed to the tendency of H to shift as a proton rather than as a hydride. 

The frontier orbital interaction between the olefin HOMO 7t(C-C) and the orbitals with c (0-0) character in the LUMO group of the metal peroxo moiety controls the activation of 0-0 bond. Electron donating alkyl substituents at the olefin double bond raise the energy of the HOMO, with the epoxidation barrier dropping concomitantly. On the other hand, a base coordinated at the metal center pushes the a (0-0) LUMO to higher energies and thus entails a higher barrier for epoxidation. 

Figure 2.38. Schematic orbital interaction diagram illustrating the interaction of the ethylene lb2u ( ) (left side) and lb3g ( ) (right side) orbitals with the metal d-band where the rf-band center of Cu lies at higher binding energy than that of Ni. From Ref. [85].

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