An improved model electronic Hamiltonian for potential energy surfaces and spin−orbit couplings of low-lying d−d states of [Fe(bpy)3]2+

Ultrafast Electronic Relaxation in Aqueous [Fe(bpy)3]2+: A Surface Hopping Study

Trajectory surface hopping simulations are performed to better understand the electronic relaxation dynamics of [Fe(bpy)₃]²⁺ in aqueous solution. Specifically, the ultrafast relaxation from the photoexcited singlet metal-to-ligand charge-transfer (MLCT) to the metastable quintet metal-centered (MC) states is simulated through the surface hopping method, where the MLCT and MC states of [Fe(bpy)₃]²⁺ in aqueous solution are computed by using a model electronic Hamiltonian developed previously. As a result, most of the trajectories are interpreted to show the sequential relaxation pathways via the triplet MC states, though some are the direct pathway from MLCT to the quintet MC states. Even though the triplet MC states are involved in the relaxation, the population transfer to the singlet MC ground state is very small, and the population of the quintet MC states reaches more than ∼96%, reasonably consistent with the unity quantum efficiency discussed experimentally.

A quantum chemical model for a series of self-assembled nanocages: the origin of stability behind the coordination-driven formation of transition metal complexes up to [M12L24]24

Herein, we present a systematic computational model to study the electronic states and free energies of a self-assembled multi-metal complex series. By combining the previously developed model Hamiltonian approach for transition-metal complexes and the generalized Born model, the thermodynamics, optimized geometries, and electronic states of the [Pd12L24]24+ nanocage are revealed, together with [PdnLm]2n+ complex series. The effective model Hamiltonian is a theoretical method to obtain the d-electron wavefunction and potential energy including interaction energy between the transition-metal and ligands. In the present improvement, the electronic state on each transition-metal center is focused as a building unit and solved under the whole electronic field of the assembling system. We realize a reliable and systematic treatment of multi-transition-metal complexes with different sizes and charges. Consequently, our model could reproduce binding energies of the [PdnLm]2n+ complex series quantitatively as compared to density functional theory (DFT). Regarding free energy, we revealed that the assembling solute becomes unstable due to the electrostatic interaction, and effects of the solvent and counter anions mainly compensated it. Optimized geometries were also analysed. The local square-planar coordination structures around the palladium centres were characterized in the complex series. The relationships between the entire symmetrical geometries and the local coordination structures are also discussed. Finally, electronic structures of the [Pd12L24]24+ nanocage were well characterized as a single-determinant, where only dx2-y2 is unoccupied due to the ligand-field effect. We also found that the solvent polarized the electronic states of the Pd ions, whereas the counter anion suppressed the polarization. The present method realizes size-independent reliable and rapid computations, and therefore can be expected to further application studies on self-assembly dynamics.

A model electronic Hamiltonian to describe low-lying d-d and metal-to-ligand charge-transfer excited states of [Fe(bpy)3 ]2

A simple practical method to compute both d-d and metal-to-ligand charge-transfer (MLCT) excited states of iron(II) polypyridyl complexes is proposed for use in simulation studies. Specifically, a model electronic Hamiltonian developed previously for d-d excited states of [Fe(bpy)₃ ]²⁺ is extended to deal with low-lying MLCT excited states simultaneously by including the MLCT electronic configurations into the basis functions of the model Hamiltonian. As a first attempt, parameters in the model Hamiltonian matrix elements are determined by using density functional theory (DFT) and time-dependent (TD-)DFT calculation results as benchmarks. To examine the performance of the model Hamiltonian, the potential energy curves along the interpolation between the lowest singlet and quintet state structures are compared to those from the (TD-)DFT calculations and to those from CASPT2 calculations in literature. The electronic absorption spectrum computed through molecular dynamics simulation is compared to the experimental spectrum. The spin-orbit couplings at the ground state structure are also compared to those from wavefunction-based ab initio electronic structure calculations. The results indicate that the constructed model Hamiltonian provides reasonable information on both the low-lying d-d and MLCT excited states of [Fe(bpy)₃ ]²⁺ .

Spin-inversion mechanisms in O2 binding to a model heme complex revisited by density function theory calculations

Spin-inversion mechanisms in O₂ binding to a model heme complex, consisting of Fe(II)-porphyrin and imidazole, were investigated using density-functional theory calculations. First, we applied the recently proposed mixed-spin Hamiltonian method to locate spin-inversion structures between different total spin multiplicities. Nine spin-inversion structures were successfully optimized for the singlet-triplet, singlet-quintet, triplet-quintet, and quintet-septet spin-inversion processes. We found that the singlet-triplet spin-inversion points are located around the potential energy surface region at short Fe-O distances, whereas the singlet-quintet and quintet-septet spin-inversion points are located at longer Fe-O distances. This suggests that both narrow and broad crossing models play roles in O₂ binding to the Fe-porphyrin complex. To further understand spin-inversion mechanisms, we performed on-the-fly Born-Oppenheimer molecular dynamics calculations. The reaction coordinates, which are correlated to the spin-inversion dynamics between different spin multiplicities, are also discussed.

Monitoring Ultrafast Spin Crossover Intermediates in an Iron(II) Complex by Broad Band Stimulated X-ray Raman Spectroscopy

The photoinduced spin crossover dynamics of transition metal complexes is of fundamental scientific importance and is used for sensor device applications and solar energy harvesting. Current X-ray and optical spectroscopy experiments for [Fe^II(bpy)₃], an archetypal earth-abundant metal complex, show conflicting spin dynamics. We have simulated the broad band transient X-ray absorption and hybrid (broad + narrow band) X-ray stimulated Raman signals at the N and Fe K-edges of the key excited state intermediates involved in the spin crossover process of this complex. We find that these signals are much more sensitive to electron and spin populations than transition absorption and may be useful in the design of photovoltaic and artificial photosynthetic systems.

Effect of Second-Order Spin-Orbit Coupling on the Interaction between Spin States in Spin-Crossover Systems

The second-order spin-orbit coupling is evaluated in two transition-metal complexes to establish the effect on the deactivation mechanism of the excited low-spin state in systems that undergo spin transitions under the influence of light. We compare the standard perturbational approach to calculate the second-order interaction with a variational strategy based on the effective Hamiltonian theory and show that the former one can only be applied in some special cases and even then gives results that largely overestimate the interaction. The combined effect of geometry distortions and second-order spin-orbit coupling leads to sizeable interactions for states that are nearly uncoupled in the symmetric (average) structure of the complex. This opens the possibility of a direct deactivation from the singlet and triplet states of the metal-to-ligand charge-transfer manifold to the final high-spin state as suggested from the interpretation of experimental data but so far not supported by theoretical descriptions of the light-induced spin crossover.

A model electronic Hamiltonian for the self-assembly of an octahedron-shaped coordination capsule

A model electronic Hamiltonian to describe ligand exchange reactions of palladium(ii) complexes with pyridine (Py) and tridentate (L) ligands was developed. It was shown that the model Hamiltonian can adequately reproduce the structures and potential energies of the reactant/product, intermediate, and transition state of the ligand exchange reaction of [PdPy₄]²⁺ with free Py. The model Hamiltonian was extended to describe reactions of multi-metal complexes and was adequately applied to describe various clusters, [Pd_aL_bPy_c]^2a+, in the self-assembly of an octahedron-shaped coordination capsule, [Pd₆L₈]¹²⁺. The heterogeneity in the energetics of intermediate species [Pd_aL_bPy_c]^2a+ was strongly suggested by the calculations, and the underlying microscopic interactions were clarified with the geometrical motif. The present framework provides a way to examine the reaction mechanisms of complex metal ligand self-assembly, which can be complementary microscopic information to the recently investigated novel experimental results for the real time evolutions.

Ultrafast intersystem crossings in Fe-Co Prussian blue analogues

Ultrafast spincrossover is studied in Fe-Co Prussian blue analogues using a dissipative quantum-mechanical model of a cobalt ion coupled to a breathing mode. All electronic interactions are treated on an equal footing. It is theoretically demonstrated that the divalent cobalt ion reaches 90% of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S{\boldsymbol{=}}\frac{{\bf{3}}}{{\bf{2}}}$$\end{document}S=32 value within 20 fs after photoexciting a low-spin Co³⁺ ion by an iron-to-cobalt charge transfer. The doublet-to-quartet spin crossover is significantly faster than the oscillation period of the breathing mode. The system relaxes to the lowest manifold of divalent cobalt (⁴T₁) in 150–200 fs. Strong oscillations in spin-orbit coupling and the involvement of higher-lying quartets are found.

TD-DFT study of the light-induced spin crossover of Fe(iii) complexes

Two light-induced spin-crossover Fe(iii) compounds have been studied with time-dependent density functional theory (TD-DFT) to investigate the deactivation mechanism and the role of the ligand-field states as intermediates in this process.

Insight into the light-induced spin crossover of [Fe(bpy)3]2+ in aqueous solution from molecular dynamics simulation of d–d excited states

Lifetimes of triplet d–d states were evaluated through molecular dynamics simulations to gain insight into relaxation dynamics of aqueous [Fe(bpy)₃]²⁺.