Ultrafast solvent migration in an iron complex revealed by nonadiabatic dynamics simulations

Abstract

The response of a solvation shell to molecular solute photoexcitation is an ubiquitous phenomenon of great relevance in chemistry. This response can occur within just few tens of femtoseconds, making it very challenging to resolve experimentally. Thus, the details of the (an)isotropy of the solvent response around a solute, the presence of coherent solvent fluctuations, hydrogen bond reorganization mechanisms, and the intricate interplay between electronic, spin, nuclear, and solvent dynamics remain elusive. Here, we report large-scale nonadiabatic molecular dynamics simulations of [Fe(CN)₄(bipy)]^2- (bipy=2,2'-bipyridine) in water, where the electronic evolution from singlet metal-to-ligand charge transfer (MLCT) states to triplet MLCT and metal-centered (MC) states overlaps temporally with the molecule's nuclear motion and a strong solvent shell response. We leverage vibronic coupling model potentials combined with electrostatic embedding, within our so-called vibronic coupling/molecular mechanics (VC/MM) method, to be able to compute several thousand nonadiabatic excited-state trajectories, including all relevant singlet and triplet states as well as several thousand explicit water molecules. This superior statistics affords an unprecedented view on the three-dimensional solvent distribution dynamics at few-fs and sub-Å resolution. The results reveal a direct solvent migration mechanism, where excitation to the MLCT states leads to the breaking of hydrogen bonds to the cyanide ligands within less than 100 fs, followed by the formation of hydrogen bonds with the negatively charged bipyridyl ligand by the same water molecules. Furthermore, the MLCT and MC states show very distinct solvent responses, which are overlapping in time, as governed by the electronic dynamics. More broadly, this work demonstrates how VC/MM nonadiabatic dynamics simulations can resolve anisotropic solvent dynamics around a photoexcited solute with unprecedented detail, offering a new perspective that could stimulate the development of time-resolved experimental techniques capable of probing such solvent behaviour.

Fig. 1. Time-resolved electronic population dynamics. (a) Stacked-area plot showing the contributions from each adiabatic excited state with the singlet ground state (black, top), excited singlet states (dark blue to light blue), and excited triplet states (dark red to light orange). (b) Total singlet and triplet populations (thin lines) and corresponding mono-exponential fits (thick semitransparent lines). (c) Time-dependent diabatic populations (thin lines) for the ground state (GS, black), the ¹MLCT states that was excited into (blue), the ³MC states (orange), and the ³MLCT states comprising all other triplet states (majorly MLCT character, red). The thick lines indicate the global fitting results from the shown kinetic model.

Fig. 2. Symmetry-adapted three-dimensional spatial distribution functions (3D-SDFs) of water oxygen and hydrogen atoms at t = 0 fs and time-dependent difference 3D-SDFs thereafter. In all panels at t = 0 fs, spatial regions with an occurrence higher than 2.5 times the average are colored green for oxygen atoms and light green for hydrogen atoms. For the Δ3D-SDFs at t > 0 fs, the iso value is set to 0.5 and 0.3 times the average with solid and shaded colors respectively; positive deviations are colored with red colors and negative deviations, with blue colors with oxygens in the darker and hydrogens in the lighter shade. Panels (a–c) show different orientations of the system.

Fig. 3. Average Δ3D-SDFs for a subset of trajectories with dominant ³MLCT (a–c, 2657 trajectories) and ³MC (d–f, 1353 trajectories) character at t = 5000 fs (differences relative to the ground-state equilibrium). The used subset of trajectories had a stable population in the respective states of at least 76% for the last 1000 fs. In all panels, the iso value was set to 0.5 times the average; positive deviations are colored with red and negative ones with blue, with oxygens in the darker and hydrogens in the lighter shade.

Fig. 4. Schematic representation of the initial hydrogen bonding state of [Fe(CN)₄(bipy)]²⁻ in the ground state (a)—with three to four hydrogen bonds per cyanide—and the rearrangement (b and c) and final hydrogen bonding state (d) in the ³MLCT states. The upper right (b) pathway shows a hypothetical bulk exchange mechanism, whereas the lower left (c) pathway illustrates the direct migration pathway found for [Fe(CN)₄(bipy)]²⁻, as discussed in the text.

Fig. 5. (a–d) Simulated total time-resolved difference scattering signals and its Cartesian components, computed from all solute–solvent RDFs. Details are provided in Section S2.8. Note that X is orthogonal to the bipyridine plane, Y is along the bipyridine long axis, Z is along the molecule's axis of symmetry. The sum of the X, Y, and Z components is identical to the total signal, although in the figure the total signal was multiplied by 1/3 to enable the usage of the same color scale.