Abstract
An algebraic derivation of the Jahn-Teller theorem is presented within the framework of the adiabatic approximation. It is shown that two electronic states with nonzero energies cannot be both degenerate and exhibit vanishing forces for the same set of nuclear coordinates. This, in essence, is the general Jahn-Teller theorem. The adiabatic approximation is shown to fail completely in regions where electronic states are degenerate, if at least one of the states possesses nonvanishing forces. The significance of this result is that it demonstrates that there are regions in the nuclear configuration space which cannot be traversed adiabatically.
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