Light-induced spin crossover in Fe(II)-based complexes: The full photocycle unraveled by ultrafast optical and X-ray spectroscopies

The light-induced spin and structure changes upon excitation of the singlet metal-to-ligand charge transfer (¹MLCT) state of Fe(II)-polypyridine complexes are investigated in detail in the case of aqueous iron(II)-tris-bipyridine ([Fe^II(bpy)₃]²⁺) by a combination of ultrafast optical and X-ray spectroscopies. Polychromatic femtosecond fluorescence up-conversion, transient absorption studies in the 290–600 nm region and femtosecond X-ray absorption spectroscopy allow us to retrieve the entire photocycle upon excitation of the ¹MLCT state from the singlet low-spin ground state (¹GS) as the following sequence: ^1,3MLCT → ⁵T → ¹GS, which does not involve intermediate singlet and triplet ligand-field states. The population time of the HS state is found to be ～150 fs, leaving it in a vibrationally hot state that relaxes in 2–3 ps, before decaying to the ground state in 650 ps. We also determine the structure of the high-spin quintet excited state by picosecond X-ray absorption spectroscopy at the K-edge of Fe. We argue that given the many common electronic (ordering of electronic states) and structural (Fe–N bond elongation in the high-spin state, Fe–N mode frequencies, etc.) similarities between all Fe(II)-polypyridine complexes, the results on the electronic relaxation processes reported in the case of [Fe^II(bpy)₃]²⁺ are of general validity to the entire family of Fe(II)-polypyridine complexes.     

A Two-Dimensional Network Model to Simulate Permeability Decrease Under Hydrodynamic Effect of Particle Release and Capture

A model was developed to simulate permeability decrease induced by hydrodynamic effects when injecting a fluid in a reservoir with respect to particle release and capture mechanisms and the parameters of the fluid–rock system. The kinetics of particle release and capture were integrated after computing the initial permeability of the porous medium with a square lattice of a two–dimensional network model. The rate of particle release is related to the difference between a microscopic velocity of the fluid and a critical velocity. The permeability decrease shows a direct link to the reduction of pore throat radii by three mechanisms of particle capture: straining and particle accumulation through direct interception or diffusion. Comparison between the simulations and the experimental results shows that the model reproduces the physics of the permeability decrease phenomenon, although the values are overestimated. The difference between the two sets of results can be explained by the fact that the simulations are realized at constant pressure whereas the experiments are realized at constant flow rate, and that re–entrainment of the trapped particles was not taken into account in the model.     

Probing the transition from hydrophilic to hydrophobic solvation with atomic scale resolution

Picosecond and femtosecond X-ray absorption spectroscopy is used to probe the changes of the solvent shell structure upon electron abstraction of aqueous iodide using an ultrashort laser pulse. The transient L(1,3) edge EXAFS at 50 ps time delay points to the formation of an expanded water cavity around the iodine atom, in good agreement with classical and quantum mechanical/molecular mechanics (QM/MM) molecular dynamics (MD) simulations. These also show that while the hydrogen atoms pointed toward iodide, they predominantly point toward the bulk solvent in the case of iodine, suggesting a hydrophobic behavior. This is further confirmed by quantum chemical (QC) calculations of I(-)/I(0)(H(2)O)(n=1-4) clusters. The L(1) edge sub-picosecond spectra point to the existence of a transient species that is not present at 50 ps. The QC calculations and the QM/MM MD simulations identify this transient species as an I(0)(OH(2)) complex inside the cavity. The simulations show that upon electron abstraction most of the water molecules move away from iodine, while one comes closer to form the complex that lives for 3-4 ps. This time is governed by the reorganization of the main solvation shell, basically the time it takes for the water molecules to reform an H-bond network. Only then is the interaction with the solvation shell strong enough to pull the water molecule of the complex toward the bulk solvent. Overall, much of the behavior at early times is determined by the reorientational dynamics of water molecules and the formation of a complete network of hydrogen bonded molecules in the first solvation shell.     

Relativistic effects in spectroscopy and photophysics of heavy-metal complexes illustrated by spin–orbit calculations of [Re(imidazole)(CO)3(phen)]+

Spin–orbit coupling (SOC) is an essential factor in photophysics of heavy transition metal complexes. By enabling efficient population of the lowest triplet state and its strong emission, it gives rise to a very interesting photophysical behavior and underlies photonic applications such as organic light emitting diodes (OLED) or luminescent imaging agents. SOC affects excited-state characters, relaxation dynamics, radiative and nonradiative decay pathways, as well as lifetimes and reactivity. We present a new photophysical model based on mixed-spin states, illustrated by relativistic spin–orbit TDDFT and MS-CASPT2 calculations of [Re(imidazole)(CO)₃(1,10-phenanthroline)]⁺. An excited-state scheme is constructed from spin–orbit (SO) states characterized by their energies, double-group symmetries, parentages in terms of contributing spin-free singlets and triplets, and oscillator strengths of corresponding transitions from the ground state. Some of the predictions of the relativistic SO model on the number and nature of the optically populated and intermediate excited states are qualitatively different from the spin-free model. The relativistic excited-state model accounts well for electronic absorption and emission spectra of Re^I carbonyl diimines, as well as their complex photophysical behavior. Then, we discuss the SO aspects of photophysics of heavy metal complexes from a broader perspective. Qualitative SO models as well as previous relativistic excited-state calculations are briefly reviewed together with experimental manifestations of SOC in polypyridine and cyclometallated complexes of second- and third row d⁶ metals. It is shown that the relativistic SO model can provide a comprehensive and unifying photophysical picture.     

Convergence of Global and Bounded Solutions of Some Nonautonomous Second Order Evolution Equations with Nonlinear Dissipation

In this paper we study the asymptotic behavior of solutions of the following nonautonomous wave equation with nonlinear dissipation.

$\left\{\begin{array}{ll} u_{tt}+\vert u_{t}\vert^{\alpha}u_{t}-\Delta u +f(u)=g(t,x),\quad{\rm in}\,\mathbb{R}_{+}\times\Omega,\\ \qquad\qquad u(t,x)=0,\quad\, {\rm on}\,\mathbb{R}_{+}\times\partial\Omega,\end{array}\right.$

where f is an analytic function, α is a small positive real and g(t, ·) tends to 0 sufficiently fast in L ²(Ω) as t tends to ∞.

We also obtain a general convergence result and the rate of decay of solutions for a class of second order ODE containing as a special case

$\left\{\begin{array}{ll} \ddot{U}(t)+\Vert\dot{U}(t)\Vert^{\alpha}\dot{U}(t)+\nabla F(U(t))=g(t),\quad t \in \mathbb{R}_+,\\ \qquad U(0)=U_{0}\,\in \mathbb{R}^{N},\quad\dot{U}(0)=U_{1}\in \mathbb{R}^{N}. \end{array}\right.$

     

A full multiple scattering model for the analysis of time-resolved X-ray difference absorption spectra

A full multiple theoretical model (MXAN) is applied to fit picosecond difference X-ray absorption spectra at the ruthenium L(3) edge upon photoexcitation of aqueous [RuII(bpy)3]2+. We show that fitting difference spectra allows an increase in sensitivity, such that slight structural changes can be retrieved, which are not detected in fitting full spectra. The Ru-N bond distances of the excited complex in the (3)MLCT state are in good agreement with recently published values. The implementation of the present approach to L-edge spectra and its high sensitivity opens opportunities for its extension to a large class of experiments where difference X-ray absorption spectra are recorded.     

Aqueous solvation dynamics at metal oxide surfaces

Broadband transient absorption (TA) spectroscopy, three-pulse photon echo peak shift (3PEPS), and anisotropy decay measurements were used to study the solvation dynamics in bulk water and interfacial water at ZrO(2) surfaces, using Eosin Y as a probe. The 3PEPS results show a multiexponential behavior with two subpicosecond components that are similar in bulk and interfacial water, while a third component of several picoseconds is significantly lengthened at the interface. The bandwidth correlation function from TA spectra exhibits the same behavior, and the TA spectra are well reproduced using the doorway-window picture with the time constants from PEPS. Our results suggest that interfacial water is restricted to a thickness of less than 5 A. Also the high-frequency collective dynamics of water does not seem to be affected by the interface. On the other hand, the increase of the third component may point to a slowing down of diffusional motion at the interface, although other effects, may play a role, which are discussed.     

Ultrafast UV photon echo peak shift and fluorescence up conversion studies of non-polar solvation dynamics

We present photon echo peak shift and femtosecond fluorescence up-conversion studies of non-polar solvation dynamics of a simple non-polar dye p-terphenyl in ethanol and cyclohexane, using excitation in the UV range at 290 nm. The UV fluorescence up-conversion experiments were combined with a polychromatic detection and the results highlight the high sensitivity of this approach to fully characterize the excited state dynamics of the dye. We also demonstrate the feasibility of UV photon echo and transient grating and its sensitivity for the detection of non-polar solvation dynamics by measuring the frequency correlation function of the dye in the ground state. While solvation dynamics in the picosecond regime is observed in ethanol, electronic coherence dephasing occurs on timescales faster than 100 fs in ethanol as well as in the non-polar solvent cyclohexane.     

Quadratic differentials (A(z − a)(z − b)/(z − c)2) dz2 and algebraic Cauchy transform

We discuss the representability almost everywhere (a.e.) in C of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials A(z ? a)(z ? b)×(z ? c)^?2 dz². More precisely, we give a necessary and sufficient condition on the complex numbers a and b for these quadratic differentials to have finite critical trajectories. We also discuss all possible configurations of critical graphs.     

Ultrafast nonadiabatic dynamics of [Fe(II)(bpy)(3)](2+) in solution

The ultrafast relaxation of aqueous iron(II)-tris(bipyridine) upon excitation into the singlet metal-to-ligand charge-transfer band (1MLCT) has been characterized by femtosecond fluorescence up-conversion and transient absorption (TA) studies. The fluorescence experiment shows a very short-lived broad 1MLCT emission band at approximately 600 nm, which decays in < or =20 fs, and a weak emission at approximately 660 nm, which we attribute to the 3MLCT, populated by intersystem crossing (ISC) from the 1MLCT state. The TA studies show a short-lived (<150 fs) excited-state absorption (ESA) below 400 nm, and a longer-lived one above 550 nm, along with the ground-state bleach (GSB). We identify the short-lived ESA as being due to the 3MLCT state. The long-lived ESA decay and the GSB recovery occur on the time scale of the lowest excited high-spin quintet state 5T2 lifetime. A singular value decomposition and a global analysis of the TA data, based on a sequential relaxation model, reveal three characteristic time scales: 120 fs, 960 fs, and 665 ps. The first is the decay of the 3MLCT, the second is identified as the population time of the 5T2 state, while the third is its decay time to the ground state. The anomalously high ISC rate is identical in [RuII(bpy)3]2+ and is therefore independent of the spin-orbit constant of the metal atom. To reconcile these rates with the regular quasi-harmonic vibrational progression of the 1MLCT absorption, we propose a simple model of avoided crossings between singlet and triplet potential curves, induced by the strong spin-orbit interaction. The subsequent relaxation steps down to the 5T2 state dissipate approximately 2000 cm-1/100 fs. This rate is discussed, and we conclude that it nevertheless can be described by the Fermi golden rule, despite its high value.