BSE@GW-Based Protocol for Spin-Vibronic Quantum Dynamics Using the Linear Vibronic Coupling Model. Formulation and Application to an Fe(II) Compound

A protocol for generating potential energy surfaces and performing photoinduced nonadiabatic multidimensional wave packet propagation is presented. The workflow starts with the parameterization of a linear vibronic coupling (LVC) Hamiltonian using the BSE@GW approach. In a second step, the LVC model is used as input for multi-layer multi-configurational time-dependent Hartree (ML-MCTDH) wave packet propagation. To facilitate automated ML tree generation, a spectral clustering algorithm is applied based on a correlation matrix obtained from nuclear coordinate expectation values of a full-dimensional Time-dependent Hartree (TDH) simulation. The performance of the protocol is tested on the photoinduced spin-vibronic dynamics of a transition metal complex, [Fe(cpmp)]$^{+2}$. For this example, it is shown that BSE@GW provides a more robust description of the character of the transitions contributing to the absorption spectrum compared to TD-DFT. Furthermore, the LVC parameterization is tested against explicit calculations of potential energy curves to find the validity of the linear approximation over a wide range of normal mode elongation. Finally, the flexibility of spectral clustering is used to generate different ML trees, resulting in very different numerical efficiencies for ML-MCTDH propagation. In terms of electronic structure and dimensionality, [Fe(cpmp)]$^{+2}$ is a challenging example, suggesting that the new protocol should be applicable to a wide range of systems.