Zero-Electron, Two-Orbital Interaction

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

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. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

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... 

When the number of electrons is more than one, there are more than one possibilities for such interactions. In a completed shell or a subshell the contributions of individual electrons cancel each other and the total angular momentum is zero. For two electrons in an unfilled shell where the orbital angular momenta are denoted by /, and 4 and spin angular momenta by sx and ss, the possible interactions are ... 

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... 

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. 

The p orbitals are dumbbell-shaped rather than spherical, with their electron distribution concentrated in identical lobes on either side of the nucleus and separated by a planar node cutting through the nucleus. As a result, the probability of finding a p electron near the nucleus is zero. The two lobes of a p orbital have different phases, as indicated in Figure 5.12 by different shading. We ll see in Chapter 7 that these phases are crucial for bonding because only lobes of the same phase can interact in forming covalent chemical bonds. 

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