The 'noncrossing' rule for electronic potential energy surfaces: The role of time-reversal invariance
The 'noncrossing' rule for electronic potential energy surfaces: The role of time-reversal invariance
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电子势能面的“不交叉”规则：时间反转不变性的作用
DOI：
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发表时间：
1979
期刊：
影响因子：
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通讯作者：
C. Mead
中科院分区：
文献类型：
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作者：
C. Mead
对著名的不相交规则给出了两个新的证明。据信，这些证据是不受反对最近提出的其他证据在文献中。在这两个证明中，我们计算了任意数量n个势能面相交所必须满足的独立条件的数量。答案是依赖于操作下的时间反转系统的行为。我们必须区分三种情况：在情况（T+）下，系统在时间反演下是不变的，并且整体自旋是整数。在情形（T−）中，存在时间反演不变性，但总自旋是半奇整数，相关的问题涉及n个克拉默斯双峰的相交。最后，在情况（NT）中，没有时间反演不变性。
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.