In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree theory. We establish existence results and qualitative information about the solutions of these equations that also sheds light on the numerically observed behavior. In particular, we compute the topological index of the zeros of the single-reference Coupled-Cluster mapping. For the truncated Coupled-Cluster method, we derive an energy error bound for approximate eigenstates of the Schrodinger equation.

翻译：在本系列的两篇论文中，我们为耦合簇类型方法建立了一个全面的数学框架。第二部分采用拓扑度理论，分析了单参考耦合簇方法的非线性方程。我们获得了这些方程解的存在性结果与定性信息，揭示了数值观测现象的本质。特别地，我们计算了单参考耦合簇映射零点的拓扑指数。对于截断耦合簇方法，我们推导了薛定谔方程近似本征态的能量误差界。