Symmetric Electron Transfer Coordinates are Intrinsic to Bridged Systems: An ab Initio Treatment of the Creutz-Taube Ion.

A long-standing question in electron transfer research concerns the number and identity of collective nuclear motions that drive electron transfer or localisation. It is well established that these nuclear motions are commonly gathered into a so-called electron transfer coordinate. In this theoretical study, we demonstrate that both anti-symmetric and symmetric vibrational motions are intrinsic to bridged systems, and that both are required to explain the characteristic shape of their intervalence charge transfer bands. Using the properties of a two-state Marcus-Hush model, we identify and quantify these two coordinates as linear combinations of normal modes from ab initio calculations. This quantification gives access to the potential coupling, reorganization energy and curvature of the potential energy surfaces involved in electron transfer, independent of any prior assumptions about the system of interest. We showcase these claims with the Creutz-Taube ion, a prototypical Class III mixed valence complex. We find that the symmetric dimension is responsible for the asymmetric band shape, and trace this back to the offset of the ground and excited state potentials in this dimension. The significance of the symmetric dimension originates from geometry dependent coupling, which in turn is a natural consequence of the well-established superexchange mechanism. The conceptual connection between the symmetric and anti-symmetric motions and the superexchange mechanism appears as a general result for bridged systems.

Vibrational Coherences of the Photoinduced Mixed-Valent Creutz-Taube Ion Revealed by Excited State Dynamics.

A recent study of photoinduced mixed-valency in the one-electron reduced form (µ-pz)[RuII(NH3)5]24+ of the Creutz-Taube ion used transient absorption spectroscopy with vis-NIR broadband detection to uncover a mixed-valent excited state with a typical intervalence charge transfer band and a nanosecond lifetime [Pieslinger et al. Angew. Chem., Int. Ed. 2022, 61, e202211747]. Herein, we use excited state dynamics simulations with implicit solvation to elucidate the electronic and vibrational evolution in the first 10 ps after the optical excitation. A manifold of excited states with weak interaction between the metal centers is populated already at time zero due to the breakdown of the Condon approximation and dominates the population of electronic states at short time scales (<0.5 ps). A long-lived vibrational wave packet mostly confined to oscillations of the metal center-bridge distances is observed. The oscillations are traced to the electronic structure properties of states with weak metal-metal coupling. The long-lived mixed-valent excited state of the Creutz-Taube ion analogue is formed vibrationally cold and has a more compact geometry. While experimentally, intersystem crossing and vibrational relaxation were deduced to be completed within 1 ps, our analysis indicates that both processes might persist at longer times.

The Marcus dimension: identifying the nuclear coordinate for electron transfer from ab initio calculations.

The Marcus model forms the foundation for all modern discussion of electron transfer (ET). In this model, ET results in a change in diabatic potential energy surfaces, separated along an ET nuclear coordinate. This coordinate accounts for all nuclear motion that promotes electron transfer. It is usually assumed to be dominated by a collective asymmetric vibrational motion of the redox sites involved in the ET. However, this coordinate is rarely quantitatively specified. Instead, it remains a nebulous concept, rather than a tool for gaining true insight into the ET pathway. Herein, we describe an ab initio approach for quantifying the ET coordinate and demonstrate it for a series of dinitroradical anions. Using sampling methods at finite temperature combined with density functional theory calculations, we find that the electron transfer can be followed using the energy separation between potential energy surfaces and the extent of electron localization. The precise nuclear motion that leads to electron transfer is then obtained as a linear combination of normal modes. Once the coordinate is identified, we find that evolution along it results in a change in diabatic state and optical excitation energy, as predicted by the Marcus model. Thus, we conclude that a single dimension of the electron transfer described in Marcus-Hush theory can be described as a well-defined nuclear motion. Importantly, our approach allows the separation of the intrinsic electron transfer coordinate from other structural relaxations and environmental influences. Furthermore, the barrier separating the adiabatic minima was found to be sufficiently thin to enable heavy-atom tunneling in the ET process.

Nonadiabatic excited-state dynamics of ReCl(CO)3(bpy) in two different solvents.

We present a study of excited-states relaxation of the complex ReCl(CO)3(bpy) (bpy = 2,2-bipyridine) using a nonadiabatic TD-DFT dynamics on spin-mixed potential energy surfaces in explicit acetonitrile (ACN) and dimethylsulfoxide (DMSO) solutions up to 800 fs. ReCl(CO)3(bpy) belongs to a group of important photosensitizers which show ultrafast biexponential subpicosecond fluorescence decay kinetics. The choice of solvents was motivated by the different excited-state relaxation dynamics observed in subpicosecond time-resolved IR (TRIR) experiments. Simulations of intersystem crossing (ISC) showed the development of spin-mixed states in both solvents. Transformation of time-dependent populations of spin-mixed states enabled to monitor the temporal evolution of individual singlet and triplet states, fitting of bi-exponential decay kinetics, and simulating the time-resolved fluorescence spectra that show only minor differences between the two solvents. Analysis of structural relaxation and solvent reorganization employing time-resolved proximal distribution functions pointed to the factors influencing the fluorescence decay time constants. Nonadiabatic dynamics simulations of time-evolution of electronic, molecular, and solvent structures emerge as a powerful technique to interpret time-resolved spectroscopic data and ultrafast photochemical reactivity.