Energies of Orbitals

Figure 5. Niels Bohr came up with the idea that the energy of orbiting electrons would be in discrete amounts, or quanta. This enabled him to successfully describe the hydrogen atom, with its single electron, In developing the remainder of his first table of electron configurations, however, Bohr clearly relied on chemical properties, rather than quantum theory, to assign electrons to shells. In this segment of his configuration table, one can see that Bohr adjusted the number of electrons in nitrogen s inner shell in order to make the outer shell, or the reactive shell, reflect the element s known trivalency.

In a many-electron atom, because of the effects of penetration and shielding, the order of energies of orbitals in a given shell is s < p < d < f. 

The energies of orbitals are calculated today by solving the Schrodinger equation with computer software. The commercial software available is now so sophisticated that this approach can be as easy as typing in the name of the molecule or drawing it on screen. But these values are theoretical. How do we determine orbital energies experimentally ... 

Fig. 6. Energies of orbitals and states of a single-bonded A2 molecule as a function of the bond length...

FIGURE 17.9 Energies of orbitals in a square planar field produced by four ligands. 

Over half of this article has been devoted to the interpretation of d-d spectra this is a fair reflection on the dominance of this area in applications of the AOM. However, we hope that readers who may have associated the AOM exclusively with electronic spectra will appreciate its value in other directions. Indeed, the AOM is applicable to all problems which depend on the relative energies of orbitals. 

Here Cia is the partial kinetic energy of orbital-spin ia, it is given by... 

The operator T in this equation is called the Fock operator, and E,- is the energy of orbital / . According to Koopmans theorem, —e, is approximately equal to the energy required to ionize a molecule by removing an electron from / . 

What should be correlated In an orbital correlation diagram, the shapes and energies of orbitals are examined to see if the electronic structure of the reactants could be smoothly converted into the electronic structure of the products, each defined by the structures and occupancies of their respective orbitals. The nodal characteristics of orbitals are very resistant even to rather large perturbations and will tend to be conserved in chemical reactions. If an element of symmetry, for example, a mirror plane, is maintained during the course of the reaction, the nodal characteristics separate the orbitals into two sets, the members of one set being symmetric with respect to reflection... 

Figure 3 Qualitative order of energies of orbitals formed by metal d-d overlaps...

The numerical evaluation of the energies of orbitals and states is fundamentally a matter of making quantum mechanical computations. As indicated in Chapter 1, quantum mechanics per se is not the subject of this book, and indeed we have tried in general to avoid any detailed treatment of methods for solving the wave equation, emphasis being placed on the properties that the wave functions must have purely for reasons of symmetry and irrespective of their explicit analytical form. However, this discussion of the symmetry aspects of ligand field theory would be artificial and unsatisfying without some... 

Fig. 5.1 Energies of orbitals available to the outer electron in sodium. Orbitals with different / values are shown in separate columns, in the atomic ground state, the 3s orbital Is occupied. Lines with arrows indicate some of the transitions observed in the absorption and emission spectra of sodium.

Fig. 5.8 The relative energies of orbitals appropriate to the point in the pericxSc table at which they are first occupied. [He], [Ne], etc. on the right-hand side show the noble gases which have their electron shells filled to the level indicated.

The energies of orbitals also get altered, especially for electrons close to highly charged nuclei. Inner shells are most affected but they are not of much importance in chemistry. 

Usually we refer to the energy of orbitals while what is really meant is the energy of an electron in that orbital. It was mentioned earlier that only the principal quantum number n influences the orbital energy in the hydrogen atom. This means that while Is and 2s orbitals have different energies, the Is and all three 2p orbitals have the same... 

The statement a chemical reaction is symmetry allowed or symmetry forbidden, should not be taken literally. When a reaction is symmetry allowed, it means that it has a low activation energy. This makes it possible for the given reaction to occur, though it does not mean that it always will. There are other factors which can impose a substantial activation barrier. Such factors may be steric repulsions, difficulties in approach, and unfavorable relative energies of orbitals. Similarly, symmetry forbidden means that the reaction, as a concerted one, would have a high activation barrier. However, various factors may make the reaction still possible for example, it may happen as a stepwise reaction through intermediates. In this case, of course, it is no longer a concerted reaction. 

---