Energy degenerate

When electrons go into orbitals that have the same energy (degenerate orbitals), the state that has the highest number of equal spin quantum numbers will have the lowest energy. Thus electrons prefer to occupy different orbitals, if possible, since in many cases it is energetically favorable to avoid spin pairing. 

If two or more orbitals are equal in energy (degenerate), each is half-filled before any one of them is completely filled (Hund s rule). 

When there are two or more unfilled orbitals of the same energy (degenerate orbitals), the lowest-energy configuration places the electrons in different orbitals (with parallel spins) rather than paired in the same orbital, (p. 6)... 

In symmetrical cyclic conjugated systems, such as benzene, there are sets of molecular orbitals with the same energy (degenerate orbitals). (The pattern of energy levels for these aromatic systems can be determined by Frost... 

In filling orbitals of the same energy (degenerate levels), electrons in both types of orbitals tend to occupy separate orbitals and have parallel spins (Hund s rule applies). 

An atomic orbital indicates where there is a high probability of finding an electron. The closer the atomic orbital is to the nucleus, the lower is its energy. Degenerate orbitals have the same energy. Electrons are assigned to orbitals following the aufbau principle, the Pauli exclusion principle, and Hund s rule. 

In the absence of an applied magnetic field, all the spin states of a given nucleus are of equivalent energy (degenerate), and in a collection of atoms, all of the spin states should be almost equally populated, with the same number of atoms having each of the allowed spins. 

Hund s rule When we come to orbitals of equal energy (degenerate orbitals) such as the three p orbitals, we add one electron to each with their spins unpaired until each of the degenerate orbitals contains one electron. (This allows the electrons, which repel each other, to be farther apart.) Then we begin adding a second electron to each degenerate orbital so that the spins are paired. 

These two molecular orbitals are equal in energy degenerate) and are bonding orbitals. 

Fortunately, equation (10.2) is not fully borne out in practice. Many modes of vibration are often identical in energy (degenerate) and others either too weak to be observed or else entirely infrared inactive (for information on the use of character tables in the assessment of infrared and Raman activity see [1]). 

Use the cyclic HMOT rules to write the MOs for the high-energy degenerate pair of benzene. The answer should be the same as in Figure 14.13. 

Figure 10-3 The three lowest-energy degenerate MOs of methane.

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