Energy of atomic orbitals

LO Name and explain the relation of each of the four quantum numbers to the properties and relative energies of atomic orbitals (Sections 1.8—1.1 1). 

Quantitative information about energies of atomic orbitals is obtained using photoelectron spectroscopy, which applies the principles of the photoelectric effect to gaseous atoms. Our Box (on the next page) explores this powerful spectroscopic technique. 

Figure 2.3 Relative energies of atomic orbitals (not to scale)...

So far the discussion has concerned only the shapes and energies of atomic orbitals (AOs). Organic chemists really need to look at the orbitals for whole molecules. One way to construct such molecular orbitals (MOs) is to combine the atomic orbitals of the atoms that make up the molecule. This approach is known as the Linear Combination of Atomic Orbitals (LCAO). 

The energies of atomic orbitals in a hydrogen atom are given by the formula... 

Fig. 1.26 The relative energies of atomic orbitals of X and Y will dictate whether an interaction (formally allowed by symmetry) will lead to efficient overlap or not. Here, an interaction occurs but the contribution made by 4 y to V mo is greater than that made by ipx> while ipx contributes more than ->pY to the antibonding MO. The diagrams on the right give pictorial representations of the bonding and antibonding MOs.

Using equation 1.16, determine the energies of atomic orbitals of hydrogen with = 1, 2, 3, 4 and 5. What can you say about the relative spacings of the energy levels ... 

Fig. 19-1. The variation of the energies of atomic orbitals with increasing atomic number in neutral atoms (energies not strictly to scale).

F recent perspective on electron configurations, energies of atomic orbitals, the periodic system, and related topics, see S-G. Wang and W. H. E. Schwarz, Angew. Chem. Int. Ed., 2009,48, 3404. 

Before continuing the discussion of bonding theory, it is necessary to review briefly the electronic structure of the atom. Note that electrons in atoms are described as occupying orbitals which in turn constitute subshells and shells. Each orbital can hold no more than two electrons and electrons occupy the lowest energy orbitals of the atom. Figure 2.1 illustrates relative energies of atomic orbitals, where small circles represent orbitals. Note there is one s orbital in each shell, and three p orbitals, five d orbitals, and seven / orbitals in each shell. 

The relative energies of atomic orbitals in the first and second principal shells are as follows ... 

Several points need to be made about these principles.The first principle does not, in fact, refer to the ordering of energies of atomic orbitals. What it really refers to is the order offilhng of the various orbitals. These are related but separate issues. But there is more involved in the occupation of orbitals than their individual energies, as discussed further below. The n + /rule has not yet been derived from the principles of quantum mechanics. This failure has been described as one of the outstanding problems in quantum mechanics by the leading quantum chemist Per-Olav Lowdin. ... 

Electrons do not occupy fixed positions within an atom, nor do they follow orbits in the shells. Electrons occupy volumes or regions of space called orbitals (Figure 2.55). The four types of orbitals, s, p, d and f, all have different shapes. (The shapes and energies of atomic orbitals are obtained by solving the Schrodinger wave equation.)... 

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