Tyng Vivian, Kellman Michael E
Department of Chemistry and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA.
J Chem Phys. 2009 Apr 14;130(14):144311. doi: 10.1063/1.3046547.
A catastrophe map analysis is presented of the birth of new modes in bifurcations of the normal modes of the acetylene pure bending system using a spectroscopic fitting Hamiltonian that is nonseparable with multiple resonances. The map splits into two independent maps for subspaces defined by the resonance frequency conditions. Nonetheless, both resonance couplings act on each of the resonance subspaces, since the system is nonseparable. With this generalized notion of independent resonances, the map accounts for partial resemblances to single resonance models but maintains the full complexity inherent in the nonseparable Hamiltonian. This suggests a way to extend both the generalized Fermi resonance and the catastrophe map analysis to systems with higher degrees of freedom.
利用具有多个共振且不可分离的光谱拟合哈密顿量，对乙炔纯弯曲系统正常模式分叉中新模式的诞生进行了灾变图分析。根据共振频率条件定义的子空间，该图分为两个独立的图。然而，由于系统是不可分离的，两种共振耦合都作用于每个共振子空间。基于这种独立共振的广义概念，该图解释了与单共振模型的部分相似性，但保留了不可分离哈密顿量固有的全部复杂性。这为将广义费米共振和灾变图分析扩展到具有更高自由度的系统提供了一种方法。
