Internal conversion and the crossing of molecular potential energy surfaces

A re-examination is made of the Landau-Zener formula relating to the probability of an electronic jump near the crossing-point of two potential energy curves (or surfaces). Three cases are distinguished: discrete-discrete, discrete-continuum and continuum-continuum transitions. Different formulae are obtained for each of these cases. These formulae involve certain matrix elements of the interaction between the energy curves. A careful analysis is made of the order of magnitude of the terms that appear, and some corrections are made of previous work. It appears that the limits within which the original Landau-Zener formula is valid are seldom found in actual practice. A new formula (50) of greater validity is presented.