A Subsystem Perspective on Vibrational Coupled Cluster Response Theory

Based on a theoretical analysis of systems composed of subsystems described using a coupled cluster parametrization, we developed a vibrational coupled cluster embedding theory specifically tailored for the computation of response properties. This work identifies several strategies for calculating excitation energies, transition probabilities, and other response functions in large systems of interacting subsystems. A particularly effective embedding approach was formulated around a Lagrangian with multilinear interaction terms, yielding a structure that is nonlinear in both coupled cluster amplitudes and multipliers. Within this framework, we derived the corresponding response functions and associated eigenvalue equations. We also explored partitioning strategies for these equations, resulting in approximate exciton-like models that combine computational efficiency with conceptual clarity. This exciton-inspired methodology establishes a unified framework for computing excitation energies and transition properties in both electronic and vibrational coupled cluster response theories, applicable in both vacuum and embedded contexts. It provides a theoretical foundation for the future development of efficient methods for simulating vibrational spectra in extended systems.