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Quantum-Classical Modeling of Chemical Phenomena

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Transitions caused by avoided crossings of electron energy levels

George Hagedorn

Virginia Tech


Abstract:   We describe the classification of generic avoided crossings. We then review mathematical results about the propagation of molecular wave packets through them. In a Born-Oppenheimer limit in which the avoided crossing gap is appropriately shrunk as the nuclear masses are increased, we discuss the precise behavior of the non-adiabatic transitions produced by the avoided crossing. If time permits, we shall also describe a simple situation with a fixed, but small gap that can be analyzed rigorously, but demonstrates somewhat surprising results.

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