An efficient, easily implemented method for locating singularities attributable to the failure of the defining equations in a molecular property based diabatization, termed diabolical singular points, is reported. For two state diabatizations, the singular points form a seam of dimension N^int − 2, where N^int is the number of internal degrees of freedom. The dynamical outcomes of nuclear trajectories that reach the region of this seam are flawed. The algorithm easily identifies these otherwise hard to anticipate regions of fallaciously large derivative coupling. The fact that the algorithm is easily incorporated into a two state diabatization code based on molecular properties makes it a practical tool for determining whether the existence of diabolical singularities is relevant to the problem being considered. The algorithm is illustrated using a multireference single and double excitation configuration interaction description of the 1,2¹A states of CH₃NH_2.

中文翻译：

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确定恶性奇异性是否限制了基于分子性质的非绝热表示的准确性：甲胺的1,21A状态

报道了一种有效的，易于实现的方法，该方法用于定位归因于基于分子性质的绝热作用中的定义方程式失败的奇异点，称为奇异点。对于两个状态的绝音，奇异点形成尺寸为N ^int -2的接缝，其中N ^int是内部自由度的数量。到达该煤层区域的核弹道的动力学结果是有缺陷的。该算法很容易识别出这些否则很难预测的虚假的大导数耦合区域。该算法很容易基于分子特性并入到两个状态的diabatization代码中，这一事实使它成为确定是否存在恶性奇异性与所考虑的问题相关的实用工具。使用CH ₃ NH ₂的1,2 ¹ A状态的多参考单激发和双激发配置相互作用描述来说明该算法_。