Department of Chemistry and Institute of Theoretical Science, University of Oregon Eugene, Oregon 97403, USA.
J Phys Chem A. 2010 Sep 16;114(36):9825-31. doi: 10.1021/jp102957u.
Critical points and bifurcations are considered for the acetylene effective Hamiltonian in the polyad space of total bend and vibrational angular momentum quantum numbers [N(b), [Formula: see text]]. A "phase diagram" is constructed for the surface of minimum energy critical points. The phases denote vibrational modes of different character, including new types of anharmonic modes born in bifurcations from the ordinary normal modes. A tetracritical point is the outstanding feature of the diagram. Patterns in the energy levels are considered. We start with a search for "defects" in the lattice of energy levels, similar to what is found with quantum monodromy in integrable systems. No such pattern is found. Instead, patterns are predicted in the first and second derivatives of the energy with respect to the quantum numbers, by close analogy to the theory of phase transitions. The tetracritical point finds striking manifestation in these patterns. This may be amenable to experimental test. Moreover, the minimum energy path, analogous to the reaction path, has derivative patterns that can already be compared with experiment. Agreement of theory and experiment is found within experimental error.
对于乙炔有效哈密顿量在总弯曲和振动角动量量子数 [N(b), [Formula: see text]] 的多体空间中，考虑临界点和分歧。为最小能量临界点的表面构建了“相图”。这些相表示具有不同特征的振动模式，包括从普通简正模分歧产生的新类型的非谐模式。四临界点是该图的突出特征。考虑了能级中的图案。我们从搜索能级晶格中的“缺陷”开始，类似于在可积系统中的量子幺正中发现的情况。没有发现这样的模式。相反，通过与相变理论的紧密类比，预测了能量对量子数的一阶和二阶导数中的图案。四临界点在这些图案中找到了惊人的表现。这可能适合实验测试。此外，类似于反应路径的最小能量路径具有可以与实验进行比较的导数图案。在实验误差范围内发现了理论与实验的一致性。
