The light-induced spin crossover in Fe(II) polypyridyl complexes is a phenomenon of significant interest due to its potential applications in molecular data storage and other cutting-edge technologies. Ultrafast experiments using femtosecond optical and X-ray pulses have been employed to investigate the dynamics of these complexes, revealing that irradiation with visible light promotes the system from a low-spin ground state to a high-spin quintet state within a remarkably short timeframe (less than 200 fs). However, the precise mechanism of this ultrafast transition remains a subject of debate. Two primary mechanisms have been proposed: a direct ³MLCT→⁵MC transition and a sequential ^1,3MLCT→³MC→⁵MC pathway involving a triplet metal-centered (³MC) intermediate. While transient optical absorption data has been interpreted to support the direct mechanism, X-ray emission spectroscopy (XES), highly sensitive to the metal spin state, strongly suggests the involvement of a ³MC state, indicating the sequential pathway is operative. Furthermore, a UV photoemission study has even proposed the possibility of branching between these two mechanisms. Theoretical approaches have been attempted to rationalize these experimental findings, but existing models have limitations, such as the application of Fermi's golden rule (neglecting nuclear motion) or the use of reduced-dimensionality quantum dynamics (less accurate electronic structure). These limitations have hindered a definitive resolution of the mechanistic controversy. This research aims to overcome these limitations by simulating the full singlet-triplet-quintet dynamics of the [Fe(terpy)₂]²⁺ complex using a full-dimensional spin-vibronic trajectory surface hopping method, representing a significant advancement in computational complexity.

The literature reveals a significant ongoing debate regarding the mechanism of light-induced spin crossover in Fe(II) polypyridyl complexes. Studies utilizing femtosecond transient optical absorption (TOAS), X-ray absorption spectroscopy (XAS), and X-ray emission spectroscopy (XES) have provided valuable time-resolved data, but the interpretation of these data has led to conflicting conclusions. Some studies suggest a direct transition from a triplet metal-to-ligand charge transfer (³MLCT) state to the quintet high-spin (⁵MC) state, while others propose a sequential pathway involving a triplet metal-centered (³MC) intermediate. Theoretical investigations, while providing valuable insights, have been limited by simplifying assumptions such as neglecting nuclear motion or using reduced-dimensional models. The lack of a comprehensive, high-dimensional theoretical model that accurately captures the complex dynamics of this system has contributed to the ongoing uncertainty. This paper addresses this gap in the literature by employing a computationally demanding, full-dimensional approach to unravel the intricacies of the photoswitching mechanism.

The study employs full-dimensional trajectory surface hopping (TSH) in conjunction with a linear vibronic coupling (LVC) model to simulate the singlet-triplet-quintet dynamics of the [Fe(terpy)₂]²⁺ complex. A hybrid approach combines time-dependent density functional theory (TD-DFT) potential energy surfaces (PESs) and multiconfigurational second-order perturbation theory (CASPT2) spin-orbit couplings (SOCs). The LVC potentials were obtained using B3LYP/TZVP, a functional known for its accuracy in describing excited-state energetics of Fe(II) complexes. TD-DFT calculations with the Tamm-Dancoff approximation (TDA) were used for singlet and triplet excited states, while unrestricted DFT was used for quintet states. Solvent effects were considered minimal based on calculations using a conductor-like polarisable continuum model (C-PCM) for water. The SOC matrix was calculated using CASSCF/CASPT2 with a specifically defined active space encompassing 10 electrons and 16 orbitals to accurately capture the relevant electronic states. Scalar relativistic effects were included using the Douglas-Kroll-Hess (DKH) Hamiltonian. The TSH dynamics simulations were performed using the SHARC2.1 software, employing Tully's fewest switches algorithm and a three-step propagator technique. 1000 initial conditions were sampled from a ground-state Wigner distribution, filtered based on excitation energy and oscillator strength, resulting in 716 trajectories propagated for 1.5 ps. An energy-based method was used to correct for electronic decoherence effects. The difference X-ray scattering signal was calculated using the Debye equation. The ORCA 5.0 and OpenMolcas 20.10 software packages were utilized for the quantum chemistry and TSH dynamics calculations respectively.

The full-dimensional simulations revealed a branching mechanism for the sub-picosecond conversion of [Fe(terpy)₂]²⁺ to the quintet high-spin state. This involves two sequential pathways: a dominant pathway progressing through ³MLCT→³MC(³T_2g)→³MC(³T_1g)→⁵MC and a minor pathway proceeding via ³MLCT→³MC(³T_2g)→⁵MC. The simulations demonstrate that the direct ³MLCT→⁵MC transition plays a negligible role. The quintet population rise exhibits non-exponential behavior, attributed to the dynamics through the ³MC states, which is consistent with experimental observations of ballistic dynamics. The non-exponential dynamics is driven by impulsive expansion of the Fe-N bonds, pushing the system toward regions of efficient intersystem crossing between the ³MC and ⁵MC states. The simulations show coherent oscillations in the ³MC and ⁵MC populations, with a period of ~300 fs corresponding to the breathing mode. These oscillations are a consequence of population transfer between the lower-energy ³T_1g component and the ⁵MC state, driven by the coherent nuclear dynamics along the breathing mode. The observed slight delay between structural Fe-N variations and the ¹MLCT → ³MC electronic population dynamics is explained by the necessity for ³MC state population before ballistic Fe-N expansion can occur. The coherent oscillations are consistent with experimental observations from time-resolved X-ray scattering studies, confirmed by the simulated difference X-ray scattering signal. The simulated data shows a high level of agreement with available experimental data on Fe(II) polypyridines from TOAS and XES studies.

The findings of this study resolve a long-standing debate concerning the mechanism of photoinduced spin crossover in Fe(II) polypyridyl complexes. The results decisively demonstrate the dominance of a sequential, branching mechanism involving ³MC states, contradicting previous interpretations that emphasized the role of a direct ³MLCT→⁵MC transition. The non-exponential population dynamics and coherent oscillations observed in the simulations highlight the importance of using full-dimensional dynamics frameworks to accurately capture the complex interplay between electronic and nuclear degrees of freedom in these systems. The close agreement between the simulated dynamics and the available experimental time-resolved XES data validates the accuracy and reliability of the theoretical model employed in this research. These findings significantly advance our fundamental understanding of light-induced spin crossover in transition metal complexes and have implications for the design and development of future molecular devices based on this phenomenon.

This research has successfully elucidated the branching mechanism of Fe(II) polypyridine photoswitching through full-dimensional simulation of the singlet-triplet-quintet dynamics of [Fe(terpy)₂]²⁺. The key finding is the dominance of two sequential pathways involving ³MC states, with non-exponential population dynamics and coherent oscillations. This comprehensive study resolves a long-standing mechanistic debate and underscores the power of full-dimensional theoretical methods in interpreting ultrafast experimental data. Future studies could explore the influence of different ligands or solvents on the photoswitching dynamics, investigate the effect of external stimuli (e.g., magnetic fields) on the transition process, or extend the model to include vibrational cooling effects for even greater experimental comparison.

The current model does not include vibrational cooling effects (e.g., interactions with a solvent). The absence of solvent effects could lead to discrepancies between the simulated and experimentally observed decoherence of the coherent oscillations. The accuracy of the DFT and TD-DFT methods employed are dependent on the selected functional (B3LYP) and might require further validation with other functionals for broader applicability. The high computational cost of the full-dimensional simulations limits the scope to a single complex, and extending the study to a wider range of Fe(II) polypyridyl complexes would require significant computational resources.