Ultrafast Deactivation Mechanism of the Excited Singlet in the Light‐Induced Spin Crossover of [Fe(2,2′‐bipyridine) 3 ] 2+

Femtosecond Spin-State Switching Dynamics of Fe(II) Complexes Condensed in Thin Films

The tailoring of spin-crossover films has made significant progress over the past decade, mostly motivated by the prospect in technological applications. In contrast to spin-crossover complexes in solution, the investigation of the ultrafast switching in spin-crossover films has remained scarce. Combining the progress in molecule synthesis and film growth with the opportunities at X-ray free-electron lasers, we study the photoinduced spin-state switching dynamics of a molecular film at room temperature. The subpicosecond switching from the S = 0 low-spin ground state to the S = 2 high-spin state is monitored by analyzing the transient evolution of the Fe L3 X-ray absorption edge fine structure, i.e. element-specifically at the switching center of the Fe(II) complex. Our measurements show the involvement of an intermediate state in the switching. At large excitation fluences, the fraction of high-spin molecules saturates at ≈50%, which is likely due to molecule-molecule interaction within the film.

Asymmetric conformation of the high-spin state of iron(II)-tris(2,2-bipyridine): Time-resolved x-ray absorption and ultraviolet circular dichroism

We analyze the structures of the low-spin (LS) ground state and the high-spin (HS) lowest excited state of the iron-(II)-tris bipyridine complex ([Fe(bpy)3]2+) using density functional theory PBE methods, modeling the solvent interactions with conductor-like polarizable continuum model. These calculations are globally benchmarked against a wide range of experimental observables that include ultraviolet-visible linear absorption and circular dichroism (CD) spectra and Fe K-edge x-ray absorption near edge spectra (XANES). The calculations confirm the already established D3 geometry of the LS state, as well as a departure from this geometry for the HS state, with the appearance of inequivalent Fe-N bond elongations. The simulated structures nicely reproduce the above-mentioned experimental observables. We also calculate the vibrational modes of the LS and HS states. For the former, they reproduce well the vibrational frequencies from published infrared and Raman data, while for the latter, they predict very well the low-frequency vibrational coherences, attributed to Fe-N stretch modes, which were reported in ultrafast spectroscopic experiments. We further present calculations of the high-frequency region, which agree with recent ultrafast transient infrared spectroscopy studies. This work offers a common basis to the structural information encoded in the excited state CD and the Fe K XANES of the HS state tying together different structural IR, UV-visible, and x-ray observables.

Control of Iron(II)-Tris(2,2'-Bipyridine) Light-Induced Excited-State Trapping via External Electromagnetic Fields

Light-induced excited spin-state trapping reactions in iron pyridinic complexes allow the iron's low-to-high spin transition in a sub-picosecond timescale. Employing a recently developed model for [Fe(2,2'-bipyridine)3]2+ photochemical spin-crossover reaction in conjunction with quantum wavepacket dynamics, we explore the possibility of controlling the reaction through external electromagnetic fields, aiming at stabilizing the initial metal-to-ligand charge transfer states. We show that simple Gaussian-shaped electromagnetic fields have a minor effect on the population kinetics. However, introducing vibrationally excited initial wavepacket representations allows for maintaining the population trapped in the metal-to-ligand charge transfer states. Using optimal control theory, we propose an electromagnetic field shape that increases the lifetime of metal-to-ligand charge transfer states. These results open the route for controlling the iron photochemistry through the action of external electric fields.

Ab initio multireference calculation of electronic spectra of the osmium complexes, [Os(bpy) 3 ] 2 + and [Os(phen) 3 ] 2 +

The spin-orbit coupling corrected absorption spectra of osmium complexes, [Os(bpy)   3 ]   2 + and [Os(phen)   3 ]   2 + , were calculated by using ab initio multireference perturbation method (NEVPT2) with relativistic effects taken into account throughout ZORA approximation and corresponding all-electron basis sets. For the same purpose, the time-dependent DFT techniques were used. A very good agreement between NEVPT2 and experimental spectra should be highlighted, especially for the MLCT transitions that occur in visible and near-UV regions ( 16 , 000 - 33 , 000 cm   - 1 ). Moreover, the present study offers description of excited states of titled osmium complexes and their spectra interpretation using molecular orbitals.

Time-Resolved X-ray Emission Spectroscopy and Synthetic High-Spin Model Complexes Resolve Ambiguities in Excited-State Assignments of Transition-Metal Chromophores: A Case Study of Fe-Amido Complexes

To fully harness the potential of abundant metal coordination complex photosensitizers, a detailed understanding of the molecular properties that dictate and control the electronic excited-state population dynamics initiated by light absorption is critical. In the absence of detectable luminescence, optical transient absorption (TA) spectroscopy is the most widely employed method for interpreting electron redistribution in such excited states, particularly for those with a charge-transfer character. The assignment of excited-state TA spectral features often relies on spectroelectrochemical measurements, where the transient absorption spectrum generated by a metal-to-ligand charge-transfer (MLCT) electronic excited state, for instance, can be approximated using steady-state spectra generated by electrochemical ligand reduction and metal oxidation and accounting for the loss of absorptions by the electronic ground state. However, the reliability of this approach can be clouded when multiple electronic configurations have similar optical signatures. Using a case study of Fe(II) complexes supported by benzannulated diarylamido ligands, we highlight an example of such an ambiguity and show how time-resolved X-ray emission spectroscopy (XES) measurements can reliably assign excited states from the perspective of the metal, particularly in conjunction with accurate synthetic models of ligand-field electronic excited states, leading to a reinterpretation of the long-lived excited state as a ligand-field metal-centered quintet state. A detailed analysis of the XES data on the long-lived excited state is presented, along with a discussion of the ultrafast dynamics following the photoexcitation of low-spin Fe(II)-Namido complexes using a high-spin ground-state analogue as a spectral model for the 5T2 excited state.

Controlling the Photophysical Properties of a Series of Isostructural d6 Complexes Based on Cr0, MnI, and FeII

Development of first-row transition metal complexes with similar luminescence and photoredox properties as widely used RuII polypyridines is attractive because metals from the first transition series are comparatively abundant and inexpensive. The weaker ligand field experienced by the valence d-electrons of first-row transition metals challenges the installation of the same types of metal-to-ligand charge transfer (MLCT) excited states as in precious metal complexes, due to rapid population of energetically lower-lying metal-centered (MC) states. In a family of isostructural tris(diisocyanide) complexes of the 3d6 metals Cr0, MnI, and FeII, the increasing effective nuclear charge and ligand field strength allow us to control the energetic order between the 3MLCT and 3MC states, whereas pyrene decoration of the isocyanide ligand framework provides control over intraligand (ILPyr) states. The chromium(0) complex shows red 3MLCT phosphorescence because all other excited states are higher in energy. In the manganese(I) complex, a microsecond-lived dark 3ILPyr state, reminiscent of the types of electronic states encountered in many polyaromatic hydrocarbon compounds, is the lowest and becomes photoactive. In the iron(II) complex, the lowest MLCT state has shifted to so much higher energy that 1ILPyr fluorescence occurs, in parallel to other excited-state deactivation pathways. Our combined synthetic-spectroscopic-theoretical study provides unprecedented insights into how effective nuclear charge, ligand field strength, and ligand π-conjugation affect the energetic order between MLCT and ligand-based excited states, and under what circumstances these individual states become luminescent and exploitable in photochemistry. Such insights are the key to further developments of luminescent and photoredox-active first-row transition metal complexes.

Changes in aromaticity of spin-crossover complexes: a signature for non-innocent ligands

The influence of the spin state of the metal centre in spin crossover compounds on the aromaticity of the ligands has been investigated for iron(II)tris-bipyridine (Fe(bpy)32+), and Fe(II)(formazanate)2 (as a truncated model and the full phenyl substituted compound). It was found that the aromaticity of the bipyridine ligands is unaffected by changing the spin state of the central iron atom, but that of the formazanate ligands is reduced upon transition to the high-spin state. This change in aromaticity is rationalized using the symmetry selection rules for aromaticity in terms of virtual excitations from occupied to empty orbitals. A further consequence of this loss in aromaticity is a shift to higher energy in the ring vibrations of the formazanate compounds that can be observed in either its IR or Raman spectrum; this prediction has been confirmed here. This change in aromaticity as a consequence of change in spin state can be regarded as an indication for non-innocent ligands.

Improved transition metal photosensitizers to drive advances in photocatalysis

To function effectively in a photocatalytic application, a photosensitizer's light absorption, excited-state lifetime, and redox potentials, both in the ground state and excited state, are critically important. The absorption profile is particularly relevant to applications involving solar harvesting, whereas the redox potentials and excited-state lifetimes determine the thermodynamics, kinetics, and quantum yields of photoinduced redox processes. This perspective article focuses on synthetic inorganic and organometallic approaches to optimize these three characteristics of transition-metal based photosensitizers. We include our own work in these areas, which has focused extensively on exceptionally strong cyclometalated iridium photoreductants that enable challenging reductive photoredox transformations on organic substrates, and more recent work which has led to improved solar harvesting in charge-transfer copper(i) chromophores, an emerging class of earth-abundant compounds particularly relevant to solar-energy applications. We also extensively highlight many other complementary strategies for optimizing these parameters and highlight representative examples from the recent literature. It remains a significant challenge to simultaneously optimize all three of these parameters at once, since improvements in one often come at the detriment of the others. These inherent trade-offs and approaches to obviate or circumvent them are discussed throughout.

Observation of parallel intersystem crossing and charge transfer-state dynamics in [Fe(bpy)3]2+ from ultrafast 2D electronic spectroscopy

Transition metal-based charge-transfer complexes represent a broad class of inorganic compounds with diverse photochemical applications. Charge-transfer complexes based on earth-abundant elements have been of increasing interest, particularly the canonical [Fe(bpy)3]2+. Photoexcitation into the singlet metal-ligand charge transfer (1MLCT) state is followed by relaxation first to the ligand-field manifold and then to the ground state. While these dynamics have been well-studied, processes within the MLCT manifold that facilitate and/or compete with relaxation have been more elusive. We applied ultrafast two-dimensional electronic spectroscopy (2DES) to disentangle the dynamics immediately following MLCT excitation of this compound. First, dynamics ascribed to relaxation out of the initially formed 1MLCT state was found to correlate with the inertial response time of the solvent. Second, the additional dimension of the 2D spectra revealed a peak consistent with a ∼20 fs 1MLCT → 3MLCT intersystem crossing process. These two observations indicate that the complex simultaneously undergoes intersystem crossing and direct conversion to ligand-field state(s). Resolution of these parallel pathways in this prototypical earth-abundant complex highlights the ability of 2DES to deconvolve the otherwise obscured excited-state dynamics of charge-transfer complexes.

Ultrafast Spin Crossover Photochemical Mechanism in [FeII(2,2'-bipyridine)3]2+] Revealed by Quantum Dynamics

Photoexcitation of [FeII(2,2'-bipyridine)3]2+ induces a subpicosecond spin crossover transformation from a low-spin singlet to a high-spin quintet state. The mechanism involves metal-centered (MC) and metal-ligand charge transfer (MLCT) triplet intermediates, but their individual contributions to this efficient intersystem crossing have been object of debate. Employing quantum wavepacket dynamics, we show that MC triplets are catalyzing the transfer to the high-spin state. This photochemical pathway is made possible thanks to bipyridine stretching vibrations, facilitating the conversion between the MLCT bands to such MC triplets. We show that the lifetime of the MLCT states can be increased to tens of picoseconds by breaking the conjugation between pyridine units, which increases the energetic gap between MLCT and MC states. This opens the route for the design of new chelating ligands inducing long-lived MLCT states in iron complexes.

Hydrogen-Bonding-Assisted Substituent Engineering for Modulating Magnetic Spin Couplings and Switching in m-Phenylene Nitroxide Diradicals

Rational modification of the coupler for the theoretical design of molecular magnets has attracted extensive interest. Substituent insertion is a widely used strategy for adjusting molecular properties, but its effect and modulation on magnetic spin couplings have been less investigated. In this work, we predict the magnetic properties of the design m-phenylene nitroxide (NO) diradicals regulated by introducing substituents. The calculated results for those two pairs of diradicals indicate that the signs of their magnetic coupling constants J do not change, but the magnitudes remarkably change after substituent regulation in the range from 253 to 730 cm-1. Such noticeable magnetic changes induced by introducing subsituents are mainly attributed to different electronic effects of substituents, assisted by the proximity of two NO groups, good planarity, conjugation, and an intramolecular hydrogen bond. In particular, the insertion of intramolecular H-bonds not only indicates an electronic effect but also has greatly changed the spin density distribution. Further aromaticity of the coupler ring, spin densities, and molecular orbitals and energetics was evaluated to gain a better understanding of magnetic regulation. Interestingly, further protonation of some substituents (e.g., -NO2 and -CO2) can noticeably turn the spin coupling from ferromagnetic to antiferromagnetic, showing manipulable magnetic switching. This work provides a promising strategy based on substituent engineering for magnetic spin coupling modulation, not only turning the coupling magnitude but also enabling the magnetic switching, thus providing insights into molecular magnetic manipulation for spintronics applications.

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.

Modifications of Tanabe-Sugano d6 Diagram Induced by Radical Ligand Field: Ab Initio Inspection of a Fe(II)-Verdazyl Molecular Complex

Quantum entanglement between the spin states of a metal center and radical ligands is suggested in an iron(II) [Fe(dipyvd)₂]²⁺ compound (dipyvd = 1-isopropyl-3,5-dipyridil-6-oxoverdazyl). Wave function ab initio (Difference Dedicated Configuration Interaction, DDCI) inspections were carried out to stress the versatility of local spin states. We named this phenomenon excited state spinmerism, in reference to our previous work (see Roseiro et al., ChemPhysChem 2022, e202200478) where we introduced the concept of spinmerism as an extension of mesomerism to spin degrees of freedom. The construction of localized molecular orbitals allows for a reading of the wave functions and projections onto the local spin states. The low-energy spectrum is well-depicted by a Heisenberg picture. A 60 cm^-1 ferromagnetic interaction is calculated between the radical ligands with the S_total = 0 and 1 states largely dominated by a local low-spin S_Fe = 0. In contrast, the higher-lying S_total = 2 states are superpositions of the local S_Fe = 1 (17%, 62%) and S_Fe = 2 (72%, 21%) spin states. Such mixing extends the traditional picture of a high-field d⁶ Tanabe-Sugano diagram. Even in the absence of spin-orbit coupling, the avoided crossing between different local spin states is triggered by the field generated by radical ligands. This puzzling scenario emerges from versatile local spin states in compounds which extend the traditional views in molecular magnetism.

Branching mechanism of photoswitching in an Fe(II) polypyridyl complex explained by full singlet-triplet-quintet dynamics

It has long been known that irradiation with visible light converts Fe(II) polypyridines from their low-spin (singlet) to high-spin (quintet) state, yet mechanistic interpretation of the photorelaxation remains controversial. Herein, we simulate the full singlet-triplet-quintet dynamics of the [Fe(terpy)₂]²⁺ (terpy = 2,2':6',2"-terpyridine) complex in full dimension, in order to clarify the complex photodynamics. Importantly, we report a branching mechanism involving two sequential processes: a dominant ³MLCT→³MC(³T_2g)→³MC(³T_1g)→⁵MC, and a minor ³MLCT→³MC(³T_2g)→⁵MC component. (MLCT = metal-to-ligand charge transfer, MC = metal-centered). While the direct ³MLCT→⁵MC mechanism is considered as a relevant alternative, we show that it could only be operative, and thus lead to competing pathways, in the absence of ³MC states. The quintet state is populated on the sub-picosecond timescale involving non-exponential dynamics and coherent Fe-N breathing oscillations. The results are in agreement with the available time-resolved experimental data on Fe(II) polypyridines, and fully describe the photorelaxation dynamics.

Dimerization of [FeIII(bpy)3]3+ in Aqueous Solutions: Elucidating a Mechanism Based on Historical Proposals, Electrochemical Data, and Computational Free Energy Analysis

Iron(II) tris-bipyridine, [Fe^II(bpy)₃]²⁺, is a historically significant organometallic coordination complex with attractive redox and photophysical properties. With respect to energy storage, it is a low-cost, high-redox potential complex and thus attractive for use as a catholyte in aqueous redox flow batteries. Despite these favorable characteristics, its oxidized Fe(III) form undergoes dimerization to form μ-O-[Fe^III(bpy)₂(H₂O)]₂⁴⁺, leading to a dramatic ∼0.7 V decrease during battery discharge. To date, the energetics and complete mechanism of this slow, sequential electrochemical-chemical (EC) process, which includes electron transfer, nucleophilic attack, ligand cleavage, μ-oxo bond formation, and spin state transition, have not been elucidated. Using cyclic voltammetry, redox flow battery data, and density functional theory calculations guided by previously proposed mechanisms, we modeled more than 100 complexes and performed more than 50 geometry scans to resolve the key steps dictating these complex chemical processes. Quantitative free energy surfaces are developed to model the mechanism of dimerization accounting for the spins and identities of any possible Fe(II), Fe(III), or Fe(IV) intermediates. Electrochemical reduction of the dimer regenerates [Fe^II(bpy)₃]²⁺ in an overall reversible process. Computational electrochemistry interrogates the influence of spin state, coordination environment, and molecular conformation at the electrode-electrolyte interface through a proposed stepwise dimer reduction process. Experimentally, we show that the considerable overpotential associated with this event can be catalytically mitigated with disparate materials, including platinum, copper hexacyanoferrate, and activated carbon. The findings are of fundamental and applied significance and could elevate [Fe^II(bpy)₃]²⁺ and its derivatives to play a vital role in the burgeoning renewable energy economy.

Dynamics of Spin Crossover Molecular Complexes

We review the current understanding of the time scale and mechanisms associated with the change in spin state in transition metal-based spin crossover (SCO) molecular complexes. Most time resolved experiments, performed by optical techniques, rely on the intrinsic light-induced switching properties of this class of materials. The optically driven spin state transition can be mediated by a rich interplay of complexities including intermediate states in the spin state transition process, as well as intermolecular interactions, temperature, and strain. We emphasize here that the size reduction down to the nanoscale is essential for designing SCO systems that switch quickly as well as possibly retaining the memory of the light-driven state. We argue that SCO nano-sized systems are the key to device applications where the “write” speed is an important criterion.

Trend in light-induced excited-state spin trapping in Fe(II)-based spin crossover systems

A computational study of the light-induced excited spin-state trapping (LIESST) in a number of Fe(II) spin crossover complexes, coordinated by monodentate, bidentate and multidentate ligands is carried out, with the goal to uncover the trend in the low temperature relaxation rate. A nine order of magnitude change in low temperature relaxation rate is observed among the complexes. The trend is rationalized in terms of the change in metal-ligand covalency, numerically estimated by the crystal orbital Hamiltonian population, thus influencing the back donation or delocalization of the electrons from the low-lying Fe(II)-centered molecular orbital to the empty low-lying ligand-centered π* antibonding molecular orbitals.

Nonadiabatic instanton rate theory beyond the golden-rule limit

Fermi's golden rule describes the leading-order behaviour of the reaction rate as a function of the diabatic coupling. Its asymptotic (ℏ →0) limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation and gives physical insight into reaction mechanisms. However the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the golden-rule case and, among other factors, account for the effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a golden-rule instanton calculation. It makes it possible to rigorously assess the accuracy of the golden-rule approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.

Intersystem Crossings in Late-Row Elements: A Perspective

Intersystem crossing (ISC), a vital component of the electronic and nuclear transitions that compose photophysics, has been successfully simulated in light elements and transition metal complexes. Derived from the Z-dependent spin-orbit coupling (SOC), ISC is expected to be of greater importance in heavier elements, but few attempts have been made at the simulation of ISC in lanthanides or actinides. In this work, we explore several of the challenges that will need to be overcome in order to treat ISC in late-row elements, including the loss of spin as a good quantum number, the need to include SOC variationally via two- or four-component electronic structure, and the high density of states present in late-row complexes. Density functional theory (DFT) calculations are used to illustrate several of these effects, while a model Hamiltonian is used to illustrate the importance of momentum rescaling in surface hopping simulations of strongly coupled states.

Spin–vibronic coupling in the quantum dynamics of a Fe(III) trigonal-bipyramidal complex

The presence of a high density of excited electronic states in the immediate vicinity of the optically bright state of a molecule paves the way for numerous photo-relaxation channels. In transition-metal complexes, the presence of heavy atoms results in a stronger spin–orbit coupling, which enables spin forbidden spin-crossover processes to compete with the spin-allowed internal conversion processes. However, no matter how effectively the states cross around the Franck–Condon region, the degree of vibronic coupling, of both relativistic and non-relativistic nature, drives the population distribution among these states. One such case is demonstrated in this work for the intermediate-spin Fe(III) trigonal-bipyramidal complex. A quantum dynamical investigation of the photo-deactivation mechanism in the Fe(III) system is presented using the multi-configurational time-dependent Hartree approach based on the vibronic Hamiltonian whose coupling terms are derived from the state-averaged complete active space self-consistent field/complete active space with second-order perturbation theory (CASPT2) calculations and spin–orbit coupling of the scalar-relativistic CASPT2 states. The results of this study show that the presence of a strong (non-relativistic) vibronic coupling between the optically bright intermediate-spin state and other low-lying states of the same spin-multiplicity overpowers the spin–orbit coupling between the intermediate-spin and high-spin states, thereby lowering the chances of spin-crossover while exhibiting ultrafast relaxation among the intermediate-spin states. In a special case, where the population transfer pathway via the non-relativistic vibronic coupling is blocked, the probability of the spin-crossover is found to increase. This suggests that a careful modification of the complex by incorporation of heavier atoms with stronger relativistic effects can enhance the spin-crossover potential of Fe(III) intermediate-spin complexes.

Toward Simulation of Fe(II) Low-Spin → High-Spin Photoswitching by Synergistic Spin-Vibronic Dynamics

A new theoretical approach is presented and applied for the simulation of Fe(II) low-spin (LS, singlet, t_2g⁶e_g⁰) → high-spin (HS, quintet, t_2g⁴e_g²) photoswitching dynamics of the octahedral model complex [Fe(NCH)₆]²⁺. The utilized synergistic methodology heavily exploits the strengths of complementary electronic structure and spin-vibronic dynamics methods. Specifically, we perform 3D quantum dynamics (QD) and full-dimensional trajectory surface hopping (TSH, in conjunction with a linear vibronic coupling model), with the modes for QD selected by TSH. We follow a hybrid approach which is based on the application of time-dependent density functional theory (TD-DFT) excited-state potential energy surfaces (PESs) and multiconfigurational second-order perturbation theory (CASPT2) spin–orbit couplings (SOCs). Our method delivers accurate singlet–triplet–quintet intersystem crossing (ISC) dynamics, as assessed by comparison to our recent high-level ab initio simulations and related time-resolved experimental data. Furthermore, we investigate the capability of our simulations to identify the location of ISCs. Finally, we assess the approximation of constant SOCs (calculated at the Franck–Condon geometry), whose validity has central importance for the combination of TD-DFT PESs and CASPT2 SOCs. This efficient methodology will have a key role in simulating LS → HS dynamics for more complicated cases, involving higher density of states and varying electronic character, as well as the analysis of ultrafast experiments.

Quantum dynamics simulations of the thermal and light-induced high-spin to low-spin relaxation in Fe(bpy)3 and Fe(mtz)6

TBC

Halogenation affects driving forces, reorganization energies and "rocking" motions in strained [Fe(tpy)2]2+ complexes

Controlling the energetics of spin crossover (SCO) in Fe(II)-polypyridine complexes is critical for designing new multifunctional materials or tuning the excited-state lifetimes of iron-based photosensitizers. It is well established that the Fe-N "breathing" mode is important for intersystem crossing from the singlet to the quintet state, but this does not preclude other, less obvious, structural distortions from affecting SCO. Previous work has shown that halogenation at the 6 and 6'' positions of tpy (tpy = 2,2';6',2''-terpyridine) in [Fe(tpy)₂]²⁺ dramatically increased the lifetime of the excited MLCT state and also had a large impact on the ground state spin-state energetics. To gain insight into the origins of these effects, we used density functional theory calculations to explore how halogenation impacts spin-state energetics and molecular structure in this system. Based on previous work we focused on the ligand "rocking" motion associated with SCO in [Fe(tpy)₂]²⁺ by constructing one-dimensional potential energy surfaces (PESs) along the tpy rocking angle for various spin states. It was found that halogenation has a clear and predictable impact on ligand rocking and spin-state energetics. The rocking is correlated to numerous other geometrical distortions, all of which likely affect the reorganization energies for spin-state changes. We have quantified trends in reorganization energy and also driving force for various spin-state changes and used them to interpret the experimentally measured excited-state lifetimes.

Photoinduced Low-Spin → High-Spin Mechanism of an Octahedral Fe(II) Complex Revealed by Synergistic Spin-Vibronic Dynamics

The Fe(II) low-spin (LS; ¹A_1g, t_2g⁶e_g⁰) → high-spin (HS; ⁵T_2g, t_2g⁴e_g²) light-induced excited spin state trapping (LIESST) mechanism solely involving metal-centered states is revealed by synergistic spin-vibronic dynamics simulations. For the octahedral [Fe(NCH)₆]²⁺ complex, we identify an initial ∼100 fs ¹T_1g → ³T_2g intersystem crossing, controlled by vibronic coupling to antisymmetric Fe-N stretching motion. Subsequently, population branching into ³T_1g, ⁵T_2g (HS), and ¹A_1g (LS) is observed on a subpicosecond time scale, with the dynamics dominated by coherent Fe-N breathing wavepackets. These findings are consistent with ultrafast experiments, methodologically establish a new state of the art, and will give a strong impetus for further intriguing dynamical studies on LS → HS photoswitching.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Capturing photochemical and photophysical transformations in iron complexes with ultrafast X-ray spectroscopy and scattering

Light-driven chemical transformations provide a compelling approach to understanding chemical reactivity with the potential to use this understanding to advance solar energy and catalysis applications. Capturing the non-equilibrium trajectories of electronic excited states with precision, particularly for transition metal complexes, would provide a foundation for advancing both of these objectives. Of particular importance for 3d metal compounds is characterizing the population dynamics of charge-transfer (CT) and metal-centered (MC) electronic excited states and understanding how the inner coordination sphere structural dynamics mediate the interaction between these states. Recent advances in ultrafast X-ray laser science has enabled the electronic excited state dynamics in 3d metal complexes to be followed with unprecedented detail. This review will focus on simultaneous X-ray emission spectroscopy (XES) and X-ray solution scattering (XSS) studies of iron coordination and organometallic complexes. These simultaneous XES-XSS studies have provided detailed insight into the mechanism of light-induced spin crossover in iron coordination compounds, the interaction of CT and MC excited states in iron carbene photosensitizers, and the mechanism of Fe-S bond dissociation in cytochrome c.

Theoretical modeling of the singlet-triplet spin transition in different Ni(II)-diketo-pyrphyrin-based metal-ligand octahedral complexes

The structural stability, charge transfer effects and strength of the spin-orbit couplings in different Ni(ii)-ligand complexes have been studied at the DFT (B3LYP and CAM-B3LYP) and coupled cluster (DLPNO-CCSD(T)) levels of theory. Accordingly, two different, porphyrin- and diketo-pyrphyrin-based four-coordination macrocycles as planar ligands as well as pyridine (or pyrrole) and mesylate anion molecular groups as vertical ligands were considered in order to build metal-organic complexes with octahedral coordination configurations. For each molecular system, the identification of equilibrium geometries and the intersystem crossing (the minimum energy crossing) points between the potential energy surfaces of the singlet and triplet spin states is followed by computing the spin-orbit couplings between the two spin states. Structures, based on the diketo-pyrphyrin macrocycle as the planar ligand, show stronger six-coordination metal-organic complexes due to the extra electrostatic interaction between the positively charged central metal cation and the negatively charged vertical ligands. The results also show that the magnitude of the spin-orbit coupling is influenced by the atomic positions of deprotonations of the ligands, and implicitly the direction of the charge transfer between the ligand and the central metal ion.

Ultrafast processes: coordination chemistry and quantum theory

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Behind the scenes of spin-forbidden decay pathways in transition metal complexes

The interpretation of the ultrafast photophysics of transition metal complexes following photo-absorption is quite involved as the heavy metal center leads to a complicated and entangled singlet-triplet manifold. This opens up multiple pathways for deactivation, often with competitive rates. As a result, intersystem crossing (ISC) and phosphorescence are commonly observed in transition metal complexes. A detailed understanding of such an excited-state structure and dynamics calls for state-of-the-art experimental and theoretical methodologies. In this review, we delve into the inability of non-relativistic quantum theory to describe spin-forbidden transitions, which can be overcome by taking into account spin-orbit coupling, whose importance grows with increasing atomic number. We present the quantum chemical theory of phosphorescence and ISC together with illustrative examples. Finally, a few applications are highlighted, bridging the gap between theoretical studies and experimental applications, such as photofunctional materials.

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⁺ .

Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: Application within the framework of the MCTDH method

A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear coordinates is introduced. This procedure circumvents the introduction of potential energy surfaces and non-adiabatic couplings, providing an alternative to the Born-Oppenheimer approximation. An important feature of the molecular Hamiltonian in the mixed first quantized representation for the nuclei and the SQR representation for the electrons is that all degrees of freedom, nuclear positions and electronic occupations, are distinguishable. This makes the approach compatible with various tensor decomposition Ansätze for the propagation of the nuclear-electronic wavefunction. Here, we describe the application of this formalism within the multi-configuration time-dependent Hartree framework and its multilayer generalization, corresponding to Tucker and hierarchical Tucker tensor decompositions of the wavefunction, respectively. The approach is applied to the calculation of the photodissociation cross section of the HeH⁺ molecule under extreme ultraviolet irradiation, which features non-adiabatic effects and quantum interferences between the two possible fragmentation channels, He + H⁺ and He⁺ + H. These calculations are compared with the usual description based on ab initio potential energy surfaces and non-adiabatic coupling matrix elements, which fully agree. The proof-of-principle calculations serve to illustrate the advantages and drawbacks of this formalism, which are discussed in detail, as well as possible ways to overcome them. We close with an outlook of possible application domains where the formalism might outperform the usual approach, for example, in situations that combine a strong static correlation of the electrons with non-adiabatic electronic-nuclear effects.

Spin-phonon coupling and dynamic zero-field splitting contributions to spin conversion processes in iron(II) complexes

Magnetization dynamics of transition metal complexes manifest in properties and phenomena of fundamental and applied interest [e.g., slow magnetic relaxation in single molecule magnets, quantum coherence in quantum bits (qubits), and intersystem crossing (ISC) rates in photophysics]. While spin-phonon coupling is recognized as an important determinant of these dynamics, additional fundamental studies are required to unravel the nature of the coupling and, thus, leverage it in molecular engineering approaches. To this end, we describe here a combined ligand field theory and multireference ab initio model to define spin-phonon coupling terms in S = 2 transition metal complexes and demonstrate how couplings originate from both the static and dynamic properties of ground and excited states. By extending concepts to spin conversion processes, ligand field dynamics manifest in the evolution of the excited state origins of zero-field splitting (ZFS) along specific normal mode potential energy surfaces. Dynamic ZFSs provide a powerful means to independently evaluate contributions from spin-allowed and/or spin-forbidden excited states to spin-phonon coupling terms. Furthermore, ratios between various intramolecular coupling terms for a given mode drive spin conversion processes in transition metal complexes and can be used to analyze the mechanisms of ISC. Variations in geometric structure strongly influence the relative intramolecular linear spin-phonon coupling terms and will define the overall spin state dynamics. While the findings of this study are of general importance for understanding magnetization dynamics, they also link the phenomenon of spin-phonon coupling across fields of single molecule magnetism, quantum materials/qubits, and transition metal photophysics.

Outer-sphere effects on ligand-field excited-state dynamics: solvent dependence of high-spin to low-spin conversion in [Fe(bpy)3]2

In condensed phase chemistry, the solvent can have a significant impact on everything from yield to product distribution to mechanism. With regard to photo-induced processes, solvent effects have been well-documented for charge-transfer states wherein the redistribution of charge subsequent to light absorption couples intramolecular dynamics to the local environment of the chromophore. Ligand-field excited states are expected to be largely insensitive to such perturbations given that their electronic rearrangements are localized on the metal center and are therefore insulated from so-called outer-sphere effects by the ligands themselves. In contrast to this expectation, we document herein a nearly two-fold variation in the time constant associated with the 5T2 → 1A1 high-spin to low-spin relaxation process of tris(2,2'-bipyridine)iron(ii) ([Fe(bpy)3]2+) across a range of different solvents. Likely origins for this solvent dependence, including relevant solvent properties, ion pairing, and changes in solvation energy, were considered and assessed by studying [Fe(bpy)3]2+ and related derivatives via ultrafast time-resolved absorption spectroscopy and computational analyses. It was concluded that the effect is most likely associated with the volume change of the chromophore arising from the interconfigurational nature of the 5T2 → 1A1 relaxation process, resulting in changes to the solvent-solvent and/or solvent-solute interactions of the primary solvation shell sufficient to alter the overall reorganization energy of the system and influencing the kinetics of ground-state recovery.

Direct observation of nuclear reorganization driven by ultrafast spin transitions

One of the most basic molecular photophysical processes is that of spin transitions and intersystem crossing between excited states surfaces. The change in spin states affects the spatial distribution of electron density through the spin orbit coupling interaction. The subsequent nuclear reorganization reports on the full extent of the spin induced change in electron distribution, which can be treated similarly to intramolecular charge transfer with effective reaction coordinates depicting the spin transition. Here, single-crystal [Fe^II(bpy)₃](PF₆)₂, a prototypical system for spin crossover (SCO) dynamics, is studied using ultrafast electron diffraction in the single-photon excitation regime. The photoinduced SCO dynamics are resolved, revealing two distinct processes with a (450 ± 20)-fs fast component and a (2.4 ± 0.4)-ps slow component. Using principal component analysis, we uncover the key structural modes, ultrafast Fe–N bond elongations coupled with ligand motions, that define the effective reaction coordinate to fully capture the relevant molecular reorganization.

Electron spin is a fundamental property of molecules, and changes in spin state affect both molecular structure and dynamics. Here, the authors resolve, by ultrafast electron diffraction, the nuclear reorganization stabilizing spin transitions in a [Fe^II(bpy)₃](PF₆)₂ crystal.

Photophysics and Photochemistry of Iron Carbene Complexes for Solar Energy Conversion and Photocatalysis

Earth-abundant first row transition metal complexes are important for the development of large-scale photocatalytic and solar energy conversion applications. Coordination compounds based on iron are especially interesting, as iron is the most common transition metal element in the Earth’s crust. Unfortunately, iron-polypyridyl and related traditional iron-based complexes generally suffer from poor excited state properties, including short excited-state lifetimes, that make them unsuitable for most light-driven applications. Iron carbene complexes have emerged in the last decade as a new class of coordination compounds with significantly improved photophysical and photochemical properties, that make them attractive candidates for a range of light-driven applications. Specific aspects of the photophysics and photochemistry of these iron carbenes discussed here include long-lived excited state lifetimes of charge transfer excited states, capabilities to act as photosensitizers in solar energy conversion applications like dye-sensitized solar cells, as well as recent demonstrations of promising progress towards driving photoredox and photocatalytic processes. Complementary advances towards photofunctional systems with both Fe(II) complexes featuring metal-to-ligand charge transfer excited states, and Fe(III) complexes displaying ligand-to-metal charge transfer excited states are discussed. Finally, we outline emerging opportunities to utilize the improved photochemical properties of iron carbenes and related complexes for photovoltaic, photoelectrochemical and photocatalytic applications.

Controlling the Lifetime of the Triplet MLCT State in Fe(II) Polypyridyl Complexes through Ligand Modification

A computational study is presented in which two strategies of ligand modifications have been explored to invert the relative energy of the metal-to-ligand charge transfer (MLCT) and metal-centered (MC) state in Fe(II)-polypyridyl complexes. Replacing the bipyridines by stronger σ donors increases the ligand-field strength and pushes the MC state to higher energy, while the use of ligands with a larger π conjugation leads to lower MLCT energies.

Improving the Light-Induced Spin Transition Efficiency in Ni(II)-Based Macrocyclic-Ligand Complexes

The structural stability and photoabsorption properties of Ni(II)-based metal-organic complexes with octahedral coordination having different planar ligand ring structures were investigated employing density functional theory (DFT) and its time-dependent extension (TD-DFT) considering the M06 exchange-correlation functional and the Def2-TZVP basis set. The results showed that the molecular composition of different planar cyclic ligand structures had significant influences on the structural stability and photoabsorption properties of metal-organic complexes. Only those planar ligands that contained aromatic rings met the basic criteria (thermal stability, structural reversibility, and appropriate excitation frequency domain) for light-induced excited spin state trapping, but their spin transition efficiencies were very different. While, in all three aromatic cases, the singlet electronic excitations induced charge distribution that could help in the singlet-to-triplet spin transition, and triplet excitations, which could assist in the backward (triplet-to-singlet) spin transition, was found only for one complex.

Approximating Periodic Potential Energy Surfaces with Sparse Trigonometric Interpolation

The potential energy surface (PES) describes the energy of a chemical system as a function of its geometry and is a fundamental concept in computational chemistry. A PES provides much useful information about the system, including the structures and energies of various stationary points, such as local minima, maxima, and transition states. Construction of full-dimensional PESs for molecules with more than 10 atoms is computationally expensive and often not feasible. Previous work in our group used sparse interpolation with polynomial basis functions to construct a surrogate reduced-dimensional PESs along chemically significant reaction coordinates, such as bond lengths, bond angles, and torsion angles. However, polynomial interpolation does not preserve the periodicity of the PES gradient with respect to angular components of geometry, such as torsion angles, which can lead to nonphysical phenomena. In this work, we construct a surrogate PES using trigonometric basis functions, for a system where the selected reaction coordinates all correspond to the torsion angles, resulting in a periodically repeating PES. We find that a trigonometric interpolation basis not only guarantees periodicity of the gradient but also results in slightly lower approximation error than polynomial interpolation.

Tracking the Metal-Centered Triplet in Photoinduced Spin Crossover of Fe(phen)32+ with Tabletop Femtosecond M-Edge X-ray Absorption Near-Edge Structure Spectroscopy

Fe(II) coordination complexes are promising alternatives to Ru(II) and Ir(III) chromophores for photoredox chemistry and solar energy conversion, but rapid deactivation of the initial metal-to-ligand charge transfer (MLCT) state to low-lying (d,d) states limits their performance. Relaxation to a long-lived quintet state is postulated to occur via a metal-centered triplet state, but this mechanism remains controversial. We use femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy to measure the excited-state relaxation of Fe(phen)₃²⁺ and conclusively identify a ³T intermediate that forms in 170 fs and decays to a vibrationally hot ⁵T_2g state in 39 fs. A coherent vibrational wavepacket with a period of 249 fs and damping time of 0.63 ps is observed on the ⁵T_2g surface, and the spectrum of this oscillation serves as a fingerprint for the Fe-N symmetric stretch. The results show that the shape of the M_2,3-edge X-ray absorption near-edge structure (XANES) spectrum is sensitive to the electronic structure of the metal center, and the high-spin sensitivity, fast time resolution, and tabletop convenience of XUV transient absorption make it a powerful tool for studying the complex photophysics of transition metal complexes.

Finding intersections between electronic excited state potential energy surfaces with simultaneous ultrafast X-ray scattering and spectroscopy

Combined X-ray free-electron laser techniques pinpoints loci of intersections between potential energy surfaces of a photo-excited 3d transition-metal centered molecule.

Light-driven molecular reactions are dictated by the excited state potential energy landscape, depending critically on the location of conical intersections and intersystem crossing points between potential surfaces where non-adiabatic effects govern transition probabilities between distinct electronic states. While ultrafast studies have provided significant insight into electronic excited state reaction dynamics, experimental approaches for identifying and characterizing intersections and seams between electronic states remain highly system dependent. Here we show that for 3d transition metal systems simultaneously recorded X-ray diffuse scattering and X-ray emission spectroscopy at sub-70 femtosecond time-resolution provide a solid experimental foundation for determining the mechanistic details of excited state reactions. In modeling the mechanistic information retrieved from such experiments, it becomes possible to identify the dominant trajectory followed during the excited state cascade and to determine the relevant loci of intersections between states. We illustrate our approach by explicitly mapping parts of the potential energy landscape dictating the light driven low-to-high spin-state transition (spin crossover) of [Fe(2,2′-bipyridine)₃]²⁺, where the strongly coupled nuclear and electronic dynamics have been a source of interest and controversy. We anticipate that simultaneous X-ray diffuse scattering and X-ray emission spectroscopy will provide a valuable approach for mapping the reactive trajectories of light-triggered molecular systems involving 3d transition metals.

Spin trapping and flipping in FeCO through relativistic electron dynamics

Transition metal compounds are very versatile, and their characteristics can differ profoundly depending on their electronic structure. Compounds in which a spin transition from a low-spin to a high-spin state can be achieved through means of an optical excitation are particularly intriguing, as a controlled spin-flip opens promising avenues in areas such as sensing, information technology, molecular switches and energy technology. The fundamental mechanisms in spin crossover and spin transitions remain unanswered, due to the complexity of electronic structure and interplay of relativistic effects. Presented here is a new approach that allows the first direct study of spin flip dynamics through a mapping of spin-mixed to spin-pure states. The method is applied to FeCO and addresses the spin-flip dynamics during a spin transition. Wave packets that combine different spin states are generated through optical excitation and relevant mechanisms in optically triggered spin transitions are discussed.

T. Characterizing divergent spin-orbit coupling effects on ultrafast nonradiative decay in transition-metal compounds

Two-dimensional electronic spectroscopy reveals divergent, spin-orbit coupling mediated, electronic relaxation dynamics in iridium(IV) hexa-bromide ([IrB6]2-) and the ruthenium(II)-based DSSC dye N719.