Existence of Diabatic Potentials and the Quantization of the Nonadiabatic Matrix

In this work are considered nonadiabatic matrices which were not derived from first principles. For this type of nonadiabatic matrices we derived the conditions for such an N × N matrix to yield an N × N diabatic potential matrix which is continuous throughout configuration space. It is shown that these conditions are very close to being quantization type conditions which select from all possible matrices only a certain group. The final theoretical results are supported by examples (a) for the N = 2 case and (b) for the N = 3 case.