Efficient Simulation of Higher-Order Transitions in Resonance Raman Spectroscopy and Its Chiral Extension

We present an automated path-integral generator for resonance Raman (RR) calculations supporting Herzberg-Teller effects and Duschinsky rotation, and able to treat any type of vibrational transition, including overtones, combination bands, as well as hot bands. The method constructs the required tensor invariants directly from low-rank intermediates, avoiding both transition-specific manual derivations and the explicit construction of high-order correlation functions. The generated expressions are canonicalized symbolically and evaluated through optimized contraction paths. Compared to formulations based on explicit high-rank correlation tensors, this substantially lowers the asymptotic cost for several higher-order transition classes while providing a unified workflow for automatic expression generation. We validate the approach for multiple transition families, examine the influence of finite-temperature effects through hot-band contributions, and show how it can be straightforwardly extended to resonance Raman optical activity (RROA).