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![The study reveals how adiabatic vibrational energy levels in KCN correlate with Planck’s constant, demonstrating the emergence of diabatic states at avoided crossings-manifested as hyperbolic curves and approximately straight lines-and further clarified through calculations detailed in equations [latex] (3) [/latex] and [latex] (4) [/latex], which differentiate between vibrational states corresponding to K-CN and K-NC linear configurations labeled by diabatic quantum numbers [latex] (n_1, n_2) [/latex].](https://arxiv.org/html/2602.06881v1/x1.png)





