How to Excite Nuclear Wavepackets into Electronically Degenerate States in Spin-Vibronic Quantum Dynamics Simulations

The excited-state dynamics of two functional Fe-carbene complexes, [Fe(bmip)₂]²⁺ (bmip = 2,6-bis(3-methyl-imidazole-1-ylidene)-pyridine) and [Fe(btbip)₂]²⁺ (btbip = 2,6-bis(3-tert-butyl-imidazole-1-ylidene)pyridine), are studied using the spin-vibronic model. In contrast to the usual projection of the ground state nuclear wavefunction onto an excited state surface, the dynamics are initiated by an explicit interaction term between the external time-dependent electric field (laser pulse) and the transition dipole moment of the molecule. The results show that the spin-vibronic model, as constructed directly from electronic structure calculations, exhibits erroneous, polarization-dependent relaxation dynamics stemming from artificial interference of coupled relaxation pathways. This is due to the lack of rotational invariance in the description of excitation into degenerate states. We introduce and discuss a correction using the spherical basis and complex transition dipole moments. This modification in the Hamiltonian leads to rotationally invariant excitation and produces polarization-independent population dynamics.