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<p>Valley-ridge inflection (VRI) points play an important role in organic chemistry, especially in post-TS bifurcations. We explain a new discovery of a special structure of the region with another, weaker type of a valley bifurcation (VB) without a ridge in between. We apply the theory of Newton trajectories (NTs) and gradient extremals (GEs) to cases of two-dimensional potential energy surfaces. We define an indicator of the valley bifurcation where the gradient of the potential energy surface is the eigenvector of the Hessian matrix at eigenvalue zero. The new type of bifurcation point is connected with a ‘dead’ valley of the PES. The example is a nice demonstration that the index theorem for NTs holds, nevertheless. NTs and GEs are important tools to explore the region of the bifurcation point.</p>

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Exploring of a potential energy surface around a valley bifurcation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月16日

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  • Wolfgang Quapp,
  • Grace Hsiao-Han Chuang,
  • Josep Maria Bofill

摘要

Valley-ridge inflection (VRI) points play an important role in organic chemistry, especially in post-TS bifurcations. We explain a new discovery of a special structure of the region with another, weaker type of a valley bifurcation (VB) without a ridge in between. We apply the theory of Newton trajectories (NTs) and gradient extremals (GEs) to cases of two-dimensional potential energy surfaces. We define an indicator of the valley bifurcation where the gradient of the potential energy surface is the eigenvector of the Hessian matrix at eigenvalue zero. The new type of bifurcation point is connected with a ‘dead’ valley of the PES. The example is a nice demonstration that the index theorem for NTs holds, nevertheless. NTs and GEs are important tools to explore the region of the bifurcation point.