Modeling 2D electronic spectroscopy of coupled excited states in the condensed phase using tensor network approaches.

Two-dimensional electronic spectroscopy (2DES) provides one of the most detailed probes of a system's nonlinear response function, offering insights into time-resolved energy-transfer and relaxation pathways. In systems with strongly coupled excited states, these pathways are heavily influenced by nonadiabatic couplings arising from nuclear motion. Simultaneously accounting for nonadiabatic, finite temperature, and environmental effects in complex, condensed-phase systems is challenging and prone to the curse of dimensionality; however, the recently-developed tensor network-based thermalized time-evolving density matrix with orthogonal polynomials algorithm (T-TEDOPA) has been shown to be a particularly effective approach in the context of linear spectroscopy. Here, we extend the methodology to first-principles modeling of 2DES signals and apply it to solvated pyrazine and 4-(N,N-dimethylamino)benzonitrile (DMABN), two systems with notable nonadiabatic excited-state character. Efficient calculation of the full nonlinear response function of the system is enabled by utilizing graphics processing units (GPUs), both for parameterizing an effective system Hamiltonian from molecular dynamics simulations and for carrying out the explicit quantum dynamics with T-TEDOPA. The specific applications underscore how nonadiabatic excited-state dynamics give rise to nonlinear spectral features otherwise absent in adiabatic treatments, and reveal a complex interplay between nonradiative energy transfer between excited states and solvent-driven relaxation dynamics.