Time dependent Vibrational Electronic Coupled Cluster (VECC) theory for non-adiabatic nuclear dynamics

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photoelectron/ UV-VIS absorption spectra, as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation of the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favourable computational cost. In benchmark applications to small models and molecules the VECC method provides accurate results, compared to Multi-Configurational Time-dependent Hartree (MCTDH) calculations when predicting short-time dynamical properties (i.e. photo-elecron / UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities the VECC method is also applied successfully to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Santoro.