Orbital interactions zero electron

When the second capping ligand is introduced, it interacts with the remaining non-bonding orbitals of e symmetry. Therefore a frans-bicapped octahedral complex is unfavourable because the remaining available non-bonding orbitals have zero electron density along the z axis. 

Fig. XVIII-16. A four-electron two-orbital interaction that a) has no net bonding in the free molecule but can be bonding to a metal surface if (b) the Fermi level is below the antibonding level. In the lower part of the figure, a zero-electron two-orbital situation (c) has no bonding but there can be bonding to a metal surface as in (d) if the Fermi level is above the bonding level. (From Ref. 160.)...

In all three frontier orbital combinations shown above, the upper orbital components are the same sign, and their overlap is positive. In the two cases on the left, the lower orbital components also lead to positive overlap. Thus, the upper and lower interactions reinforce, and the total frontier orbital interaction is non-zero. Electron movement (chemical reaction) can occur. The right-most case is different. Here the lower orbital components lead to negative overlap (the orbitals have opposite signs at the interacting sites), and the total overlap is zero. No electron movement and no chemical reaction can occur in this case. 

D is the zero-field splitting tensor, a traceless, rank-two tensorial quantity. The ZFS tensor is a property of a molecule or a paramagnetic complex, with its origin in the mixing of the electrostatic and spin-orbit interactions (80). In addition, the dipole dipole interaction between individual electron spins can contribute to the ZFS (81), but this contribution is believed to be unimportant... 

Figure 3.11. Zero-electron, two-orbital interaction The system is more Lewis acidic, and some Lewis acidity is transferred to A.

If each of the six n electrons in benzene occupied a single atomic n orbital and there were no interaction, each would have an energy of a. The total energy would then be 6a, which is zero if we assume, as above, that a is the zero of our energy scale. However, when the atomic orbitals interact to produce the MOs, the six electrons will now occupy these MOs according to Hund s rule and the Pauli exclusion principle. The first two will enter the A orbital, and the remaining four occupy the E orbitals. The total energy of the system is then... 

From these examples it can be seen that CT characters of electronic states vary from 0 to 1, depending on the interaction of the localized orbitals. A CT character of 1 (100%) would correspond to the transfer of a whole electronic charge, and this could exist only if the donor and acceptor orbitals were totally separated in space. Such an electronic transition would be forbidden because the spatial overlap of the orbitals is zero. We shall see however that total charge separation can take place in some rather special cases, though not through a direct transition. Before discussing these twisted intramolecular CT ( TICT ) states, a few words about donor-aromatic-acceptor (DArA) molecules are appropriate. 

The other mechanism is called the Fermi contact interaction and it produces the isotropic splittings observed in solution-phase EPR spectra. Electrons in spherically symmetric atomic orbitals (s orbitals) have finite probability in the nucleus. (Mossbauer spectroscopy is another technique that depends on this fact.) Of course, the strength of interaction will depend on the particular s orbital involved. Orbitals of lower-than-spherical symmetry, such as p or d orbitals, have zero probability at the nucleus. But an unpaired electron in such an orbital can acquire a fractional quantity of s character through hybridization or by polarization of adjacent orbitals (configuration interaction). Some simple cases are described later. 

Interaction of the momenta is contained in a non-spherical part of the Coulomb interaction and in the spin-orbit interaction. The value of the energy of the interaction of two momenta depends on the angle between them, therefore, in such a case the definite inter-orientation of all one-electronic momenta is settled. Differently oriented states have different energy, i.e. the zero-order level splits into sublevels and its degeneracy disappears. 

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