Wavepacket and reduced-density approaches for high-dimensional quantum dynamics: Application to the nonlinear...

Excitation-energy transfer (EET) and relaxation in an optically excited building block of poly(phenylene ethynylene) (PPE) dendrimers are simulated using wavepackets with the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method and reduced-density matrices with the hierarchical equations of motion (HEOM) approach. The dynamics of the ultrafast electronic funneling between the first two excited electronic states in the asymmetrically meta-substituted PPE oligomer with two rings on one branch and three rings on the other side, with a shared ring in between, is treated with 93-dimensional ab initio vibronic-coupling Hamiltonian (VCH) models, either linear or with bilinear and quadratic terms. The linear VCH model is also used to calibrate an open quantum system that falls in a computationally demanding non-perturbative non-Markovian regime. The linear-response absorption and emission spectra are simulated with both the ML-MCTDH and HEOM methods. The latter is further used to explore the nonlinear regime toward two-dimensional spectroscopy. We illustrate how a minimal VCH model with the two main active bright states and the impulsive-pulse limit in third-order response theory may provide at lower cost polarization-sensitive time-resolved signals that monitor the early EET dynamics. We also confirm the essential role played by the high-frequency acetylenic and quinoidal vibrational modes.