The ’’noncrossing’’ rule for electronic potential energy surfaces: The role of time-reversal invariance

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Abstract
Two new proofs are presented for the well‐known noncrossing rule. It is believed that these proofs are not subject to the objections recently raised against other proofs in the literature. In both proofs, we calculate the number of independent conditions that must be satisfied for an arbitrary number n of potential energy surfaces to intersect. The answer is shown to depend on the behavior of the system under the operation of time reversal. One must distinguish three cases: In case (T+), the system is invariant under time reversal, and the overall spin is an integer. In case (T−), there is time‐reversal invariance, but the total spin is half‐odd integer, and the relevant question concerns the intersection of n Kramers doublets. Finally, in case (NT), there is no time‐reversal invariance.

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