Exploring Ground and Excited States Via Single Reference Coupled-Cluster Theory and Algebraic Geometry.

The exploration of the root structure of coupled cluster (CC) equations holds both foundational and practical significance for computational quantum chemistry. This study provides insight into the intricate root structures of these nonlinear equations at both the CCD and CCSD level of theory. We utilize computational techniques from algebraic geometry, specifically the monodromy and parametric homotopy continuation methods, to calculate the full solution set.