Hydrogenic degeneration

For the case of a central field, the energy of an atom does not depend on magnetic quantum number m/. This means that the energy level, characterized by quantum numbers n and /, is degenerated 2/+1 times. For a pure Coulomb field there exists additional (hydrogenic) degeneration the energy of such an atom does not depend on /. Wave function (1.14) may... 

Asimple example is the formation of the hydrogen molecule from two hydrogen atoms. Here the original atomic energy levels are degenerate (they have equal energy), but as the two atoms approach each other, they interact to form two non degenerate molecular orbitals, the lowest of which is doubly occupied. 

The 2p and 2py AOs on A cannot combine with either l +l or l —on the hydrogen atoms because their symmetry does not allow it. They remain as doubly degenerate AOs on A classified as 1ti in D f. ... 

The number of electrons in an atom affects the properties of the atom. The hydrogen atom, with one electron, has no electron-electron repulsions therefore, all the orbitals of a given shell in the hydrogen atom are degenerate. For instance, the 2s-orbital and all three 2p-orbitaIs have the same energy. In many-electron atoms, however, the results of spectroscopic experiments and calculations show... 

The explanation of these facts is not difficult but is subtle. We recall that the energies of all hydrogen orbitals belonging to the same principal quantum shell (n) are equal the >d, 3p and 35 hydrogen orbitals are degenerate. These orbital subsets... 

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