Hybrid Kernel/Bath Quantum Dynamics Reveal Conical Intersection Signatures in X-ray Raman Spectroscopy

Quantum dynamical (QD) descriptions of the coupled electronic and nuclear dynamics can deliver full information on photochemical reactions providing a firm basis for the simulation of their time-resolved spectroscopic signatures. Yet, treating all vibrational degrees of freedom explicitly rapidly becomes computationally intractable. Here, we introduce a hybrid reactive-kernel/bath (RK/B) partitioning of the vibronic Hamiltonian into an anharmonic reactive kernel and a parametrically coupled harmonic bath. Using the cis–trans photoisomerization of a minimal retinal chromophore model PSB3, we perform nonadiabatic QD simulations on a hierarchy of models of increasing dimensionality and simulate two representative N K-edge X-ray Raman signals, resonant inelastic X-ray scattering (RIXS) and TRUECARS, to assess how the vibrational bath shapes them. We observe that RIXS, which is sensitive to the electronic populations, is governed almost entirely by the reactive coordinates and is already reproduced by the bare reactive kernel. Conversely, TRUECARS, which is sensitive to the electronic coherence, is shaped by the coupling modes, whose explicit inclusion is indispensable and is accurately captured by a quadratic bath treatment. These results suggest that RIXS and TRUECARS provide complementary, mode-selective views of photochemical dynamics, and establish the RK/B strategy as a computationally affordable route to investigate multimode effects on the quantum dynamics and nonlinear X-ray signals of complex photoactive systems.