Ordering of energy levels

In a hydrogen atom, the orbital energy is determined exclusively by the principal quantum number n—all the different values of / and mi are degenerate. In a multielectron atom, however, this degeneracy is partially broken the energy increases as / increases for the same value of n. 

We can illustrate this by comparing the energies of the Is, 2s and 2 p orbitals for a helium atom, which has two electrons. The first electron goes into the Is orbital. Thus the atom He+ has an electronic probability distribution which is given by putting Z = 2 into Equation 6.24 above  

FIGURE 6.5 Left effective charge in He+ (nuclear charge minus the shielding from the one electron) as a function of distance from the nucleus. Right probability of finding an electron at different positions for the Is, 2s, and 2p orbitals of He+. 

In hydrogen the 2s and 2p orbitals have the same energy. We can see qualitatively why this might be true the 2s orbital has a small lobe very close to the nucleus, but the main lobe is farther from the nucleus than the bulk of the 2 p orbital, and these effects exactly offset one another. 

Even in a helium atom, however, the situation is different. The electron in the Is orbital makes the effective charge greater for r ao, as shown in the left figure. This will have a more favorable effect on a 2s orbital than it will on alp orbital, because the 2s orbital is larger in that region. Hence the 2s orbital is lower in energy. 

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Problem 11-6. The following rules are a generally reliable guide to relative order of energy levels ... 

Two groups have studied the bonding in pentadienyl-metal-tricar-bonyl complexes (119, 238) and are agreed that effective overlap between the pentadienyl nonbonding orbital and an orbital of suitable symmetry on the metal (Fig. 17) makes a major contribution to the stability of these complexes. However, the two types of molecular orbital calculation [one an extended Hiickel (119) and the other a parameter-free approximate Hartree-Fock calculation (255)] disagree about the precise ordering of energy levels in this type of complex. 

Such solvent perturbations are largely responsible for the variation of photochemical behaviour of a molecule in different solvents, because the order of energy levels may change with change of solvent. Many such examples will be presented in appropriate places. 

Energy-level diagram Drawing used to arrange atomic orbitals in order of energy levels. 

Lower-energy orbitals fill before higher-energy orbitals. (The ordering of energy levels for orbitals is shown in Figure 5.9.)... 

The photoelectron spectra of O2 (Figure 5-11) and of CO (Figure 5-14) show the expected order of energy levels. The vibrational fine strucmre indicates that all the orbitals are important to bonding in the molecules. 

The relative energies of all four of these orbitals depend on the nature of the specific ligands and metal involved in some cases, as shown in Figure 10-15, the ability of ligands to tt donate can cause the order of energy levels to be different than shown in Figure 13-11. 

As with many planar complexes of other metals, there has been some dispute about the exact ordering of energy levels. One of the main subjects of this article is to try to clarify these questions for Co(II) complexes with Schiff bases and related compounds as ligands. We shall exclude from our discussion compounds of high symmetry, e.g. porphyrins, on which review articles have been written (52) and also complexes with tripod ligands (17). In general we shall restrict our discussion to complexes with a distinct deviation from axial symmetry as is the case for complexes formed by coordination of Schiff bases. 

The maximum number of electrons in each subshell (2, 6, 10, or 14) determines the number of elements in each block, and the order of energy levels for subshells creates the pattern of blocks. These blocks also usually correspond to the value of / for the outermost electron of the atom. This has important consequences for the physical and chemical properties of the elements. The outermost shell or valence shell principle quantum number (for example, 4 for Se) is also the period number for the element in the table. 

Cu2+ and Ni2+ derivatives of STPPS results in metal centered reduction suggesting that the metal dx2 y2 orbital in both the metals are infact lower in energy than the eg(n ) orbitals of the porphyrin ring. The reverse is true for metal derivatives of normal porphyrins. The structures of CuSTPPCl and NiSTPPCl have revealed that the porphyrin plane is nonplanar and the thiophene ring is sharply bent out of the plane of the porphyrin. On the other hand, both CuTPP and NiTPP have a planar porphyrin core. Thus, this difference in the structures of the porphyrin core around the metal ion is probably responsible for the reversal of order of energy levels. 

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