We present an extension of the Hamiltonian of the two dimensional limit of the vibron model to encompass all possible interactions up to four-body operators. We apply this Hamiltonian to the modeling of the bending spectrum of four molecules: HNC, H${}_2$S, Si${}_2$C, and NCNCS. The selected molecular species include linear, bent, and nonrigid equilibrium structures, proving the versatility of the algebraic approach which allows for the consideration of utterly different physical cases within a single Hamiltonian and a general formalism. For each case we compute predicted bending energies and wave functions, that we use to depict the associated quantum monodromy diagram, Birge-Sponer plot, and participation ratio. In nonrigid cases, we also show the bending energy functional obtained using the coherent –or intrinsic– state formalism.

我们提出了振动子模型的二维极限的哈密顿量的扩展，以涵盖所有可能的相互作用，直到四体算子。我们将此哈密顿量应用于四个分子的弯曲光谱的建模：HNC，H${}_2$硅${}_2$C和NCNCS。选定的分子种类包括线性，弯曲和非刚性的平衡结构，证明了代数方法的多功能性，从而可以考虑单个哈密顿量和一般形式论中的完全不同的物理情况。对于每种情况，我们都计算预测的弯曲能和波函数，用它们来描述相关的量子单峰图，Birge-Sponer图和参与率。在非刚性情况下，我们还展示了使用相干或本征态形式主义获得的弯曲能函数。