Multiconfigurational gaussian wavepacket dynamics: Interpolating between accurate quantum dynamics and the quantum-classical limit

The time-dependent variational principle provides a highly efficient approach for defining an optimal time evolution of approximate wavefunctions. For complex analytic parametrizations, the variational equations of motion exhibit a symplectic structure, corresponding to a generalized Hamiltonian flow. Here, we focus on multiconfigurational wavefunctions built from Gaussian wavepackets, within the Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) approach and its variational multiconfigurational Gaussian (vMCG) variant. These methods have proven versatile tools for on-the-fly calculations as well as the explicit representation of system-bath problems. More recently, we further extended these methods such as to remedy the lack of flexibility of the Frozen Gaussian (FG) basis sets that are usually employed. To this end, novel hierarchical tensor schemes were introduced, similar to the multi-layer (ML)-MCTDH method. We show first applications of the FG-based ML-GMCTDH method to vibrational energy transport, high-dimensional nonadiabatic dynamics, and the computation of vibronic spectra for strongly anharmonic systems. Finally, we report on a novel classical-limit formulation and a new approach to adaptive basis sets based on the variational local-in-time error.