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Photochemistry and Electron Transfer Kinetics in a Photocatalyst Model Assessed by Marcus Theory and Quantum Dynamics Alexander Koch,†,⊥ Daniel Kinzel,§,⊥ Fabian Dröge,‡ Stefanie Graf̈ e,‡ and Stephan Kupfer*,‡ †

Institute of Inorganic and Analytical Chemistry, Friedrich Schiller University Jena, Humboldtsraße 8, 07743 Jena, Germany Leibniz Institute of Photonic Technology Jena, Albert-Einstein-Straße 9, 07745 Jena, Germany ‡ Institute of Physical Chemistry and Abbe Center of Photonics, Friedrich Schiller University Jena, Helmholtzweg 4, 07743 Jena, Germany §

S Supporting Information *

ABSTRACT: The present computational study aims at unraveling the competitive photoinduced electron transfer (ET) kinetics in a supramolecular photocatalyst model. Detailed understanding of the fundamental processes is essential for the design of novel photocatalysts in the scope of solar energy conversion that allows unidirectional ET from a light-harvesting photosensitizer to the catalytically active site. Thus, the photophysics and the photochemistry of the bimetallic complex RuCo, [(bpy)2RuII(tpphz)CoIII(bpy)2]5+, where excitation of the ruthenium(II) moiety leads to an ET to the cobalt(III), were investigated by quantum chemical and quantum dynamical methods. Time-dependent density functional theory (TDDFT) allowed us to determine the bright singlet excitations as well as to identify the triplet states involved in the photoexcited relaxation cascades associated with chargeseparation (CS) and charge-recombination (CR) processes. Diabatic potential energy surfaces were constructed for selected pairs of donor−acceptor states leading to CS and CR along linear interpolated Cartesian coordinates to study the intramolecular ET via Marcus theory, a semiempirical expression neglecting an explicit description of the potential couplings and quantum dynamics (QD). Both Marcus theory and QD predict very similar rate constants of 1.55 × 1012 − 2.24 × 1013 s−1 and 1.21 × 1013−7.59 × 1013 s−1 for CS processes, respectively. ET rates obtained by the semiempirical expression are underestimated by several orders of magnitude; thus, an explicit consideration of electronic coupling is essential to describe intramolecular ET processes in RuCo.

1. INTRODUCTION Electron transfer (ET) processes are of outstanding importance in nature as well as in artificial applications.1−5 Biological ET chains are essential keystones in photosynthesis and cellular respiration,6,7 mediated by metalloporphyrins and derivatives.8 In artificial applications, ET phenomena are of uttermost importance, i.e., in the fields of catalysis9−13 and solar energy conversion.14 Besides the implementation of (dye-sensitized) solar cells, light-harvesting inspired by nature aims at generating high-energy compounds by utilizing an unidirectional photoinduced ET (PET) to relocate one or multiple electrons toward a catalytically active site, e.g., where reduction leads to formation of molecular hydrogen. Several theoretical models determined to describe ET processes are known.15−20 Generally, ET from a donor to an acceptor site can be understood to proceed via tunneling, overcoming large distances compared to the atomic scale. Then, Fermi’s Golden Rule provides a good estimate for the rates with which ET takes place.21 Thereby, the rate depends solely on two parameters, the (quantum mechanical) coupling element between the donor and acceptor state, V2, and the Franck−Condon (FC) density of states. V2 depends mainly on the overlap of the electronic wave functions of the two sites, © 2017 American Chemical Society

while the FC density depends on the corresponding overlap of nuclear wave functions. Assuming tunneling between the reactant and product sites, the V2 term can be approximated by an exponentially decaying function representing the electronic overlap over the distance. For the Franck−Condon overlap, the renowned Marcus theory,16,22−24 introduced by Marcus in the 1950s, can be evoked. Here, potential energy surfaces of the initial (reactant) and the final (product) state are described as parabolas with identical frequencies ℏω but different displacements (corresponding to different equilibrium internuclear distances). Thermal fluctuations of the surrounding environment introduce structural variations within the reactant that may lead in consequence to an ET between the two diabatic states in the vicinity of their crossing. The temperature-dependent ET kinetics between two states are then governed by the reaction’s driving force (ΔG, Gibbs energy or free enthalpy), the reorganization energy (λ, the energy needed to distort the initial state into the structure of the final state and vice versa), and the electronic interaction Received: March 24, 2017 Revised: June 9, 2017 Published: July 7, 2017 16066

DOI: 10.1021/acs.jpcc.7b02812 J. Phys. Chem. C 2017, 121, 16066−16078

Article

The Journal of Physical Chemistry C

1.4 × 1012 s−1 for the formation of the photoproduct 5Ru(III)Co(II)5+ (quintet) from the initial singlet 1Ru(II)Co(III)5+ species upon excitation into an 1MLCT band of the Ru(II) photosensitizer at 400 nm was determined. The back reaction occurs with a rate of 2.0 × 107 s−1. In general, moderate electronic couplings were estimated for structurally related systems.74 The crucial step to allow efficient unidirectional PET in supramolecular systems is the population of excited-state relaxation pathways leading to charge-separation (CS) competing with charge-recombination (CR) cascades.75,76 Preliminary to the investigation of any photoinduced process it is necessary to obtain insight into the nature of the electronic transitions underlying the UV−vis absorption spectrum. However, despite the interest in these systems, no theoretical investigation elucidating the involved electronic states in PET nor estimations of the rates, are available. Hence, we apply time-dependent density functional theory (TDDFT) to study the excited states in RuCo involved in the PET. Subsequently, we calculate the rate constants for the PET kinetics for CS and CR processes by means of semiclassical Marcus theory and the empirical Moser−Dutton equation and compare these results to those obtained by quantum dynamical wavepacket simulations. The paper is organized as follows: In section 2 the computational protocol is given with respect to the quantum chemical (section 2.1) and the kinetical/dynamical simulations (section 2.2). Computational results for the initial photoexcitation and the potential energy landscape of CS and CR are presented in section 3.1, while the ET kinetics obtained by Marcus theory and quantum dynamics are shown in section 3.2. Concluding remarks are given in section 4.

between both states at the crossing. The reorganization energy comprises the inner sphere effect, associated with energy changes related to structural changes of the reactant/product, and the so-called outer-sphere effect, correlated to variations of the surrounding environment, i.e., the solvent shell or the protein. Since the formulation of Marcus theory, a manifold of experimental25−27 and theoretical19,27−42 investigations have been performed, predominately in the scope of biological ET phenomena. In particular, Moser and Dutton have found for a large number of biological systems that intramolecular ET at room temperature proceeds with very similar parameters of the harmonic frequencies ω, suggesting a quasi-uniform tunneling barrier for all (biological) media.43,44 This lead to a very successful empirical expression for ET rates, the Moser−Dutton equation, independent of the coupling between the sites but solely depending on the distance between the redox sites and the energies (ΔG and λ). Several studies focused on the comparison of calculated ET rate constants obtained using semiclassical Marcus theory and molecular dynamical (MD) simulations can be found in the literature.27,29,30,33,35,45−47 However, much fewer studies based on quantum dynamical (QD) simulations36,37,39,42 especially in direct comparison to Marcus theory are reported.27,38 The present contribution aims at unraveling the competitive PET pathways in novel artificial light-harvesting devices. Many attempts have been made during recent years to realize efficient light-driven catalysis, based on either a (homogeneous or heterogeneous) multicomponent approach or a supramolecular ansatz.48−51 The initial step involves the (photo)excitation of a photosensitizer. Typically, transition metal complexes such as ruthenium(II)-polypyridyl-based dyes are utilized due to their strong stability to light, heat, and electricity as well as a pronounced visible absorption combined with redox and catalytic activities. However, also non-noble metal52−55 or even metal-free photosensitizers, e.g., those based on thiazoles,56,57 porphyrins,58−60 Eosin Y,61−63 and BODIPY dyes (boron dipyrromethene),64−66 are known in the literature. The subsequently populated inter- or intramolecular relaxation cascades may lead to energy and electron transfer toward the catalytic center. In this paper we focus exclusively on intramolecular ET phenomena in supramolecular systems, where the photosensitizer is linked to the catalytic site by a bridging ligand. Such systems feature pronounced electronic interactions, while the outer-sphere effect, i.e., the reorganization of the solvent shell, is of secondary importance for the ET kinetics. Therefore, for our investigations we have chosen a transition metal complex comprising two metal centers, ruthenium(II) as well as cobalt(III), connected by a phenazine bridging ligand. This complex, denoted as RuCo, [(bpy) 2 Ru II (tpphz)CoIII(bpy)2]5+ (bpy = 2,2′-bipyridine, tpphz = tetrapyrido (3,2-a:2′,3′-c:3″,2″-h:2‴,3‴-j) phenazine),67 can be considered a precursor for novel tpphz-bridged bimetallic complexes, where a photosensitizer, i.e., a Ru(II)-polypyridyl, is connected to a catalytic center, e.g., one based on Pd(II) or Pt(II).68−73 However, due to the absence of free coordination sites at the cobalt, no subsequent reactions, such as catalytic hydrogen formation, upon photoexcitation and successive PET from the ruthenium photosensitizer toward the cobalt are to be expected. Also, for the RuCo complex, experiments for the PET rates are accessible: The PET kinetics in RuCo were studied by Torieda et al. using transient absorption techniques.67 A rate constant of

2. COMPUTATIONAL DETAILS 2.1. Quantum Chemical Calculations. All quantum chemical calculations determining structural and electronic properties of RuCo were performed using the Gaussian 09 program.77 Fully relaxed equilibrium geometries of RuCo within the singlet and triplet ground state, respectively, were obtained at the density functional level of theory (DFT) by means of the B3LYP78,79 XC functional. The 6-31G(d) doubleζ basis set80 was employed for all main group elements, while the relativistic core potentials MWB81 and MDF82 were applied with their basis sets for the ruthenium and the cobalt atom, respectively. A subsequent vibrational analysis for the optimized ground state structures verified that minima on the potential energy surface (PES) were obtained. Excited state properties such as excitation energies, oscillator strengths, and electronic characters were calculated within the FC region, given by the equilibrium structure of the singlet ground state, for the 100 lowest singlet excited states as well as for the 100 lowest triplet states at the time-dependent DFT (TDDFT) level of theory. Thereby, the same XC functional, basis set, and core potentials were applied as for the preliminary ground state calculations. Several joint spectroscopic−theoretical studies on structurally related complexes proved that this computational protocol enables an accurate prediction of ground and excited-states properties with respect to experimental data, e.g., UV−vis absorption, resonance Raman spectra, and (spectro-)electrochemical properties.70,71,83−85 Effects of interaction with a solvent (acetonitrile: ε = 35.688, n = 1.344) were taken into account for the ground and excitedstates properties by the integral equation formalism of the polarizable continuum model.86 The nonequilibrium procedure 16067


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of the ET (Gibbs free energy), and T (295 K) corresponds to the temperature. In case of RuCo, all considered donor and acceptor states are of triplet multiplicity; see red box in Scheme 1. The donor states investigated in this study are of 3 MLCT character with one unpaired electron residing either in the d(Ru)xy or the d(Ru)xz orbital of the ruthenium and the other residing in the lowest antibonding π*-orbital localized on the phenazine moiety. These two donor states will be denoted T(BL1) and T(BL2), respectively, whereas a third MLCT donor state d(Ru)yz is not taken into account due to its higher excitation energy. Four acceptor states associated with CS were investigated, T(CS1), T(CS2), T(CS3), and T(CS5), each with semioccupied MOs (SOMOs) at the ruthenium (d(Ru)xy/ d(Ru)xz) and at the cobalt (d(Co)x2−y2/d(Co)z2). From these charge-separated triplet states, ISC may lead to the population of 5MC states (see Scheme 1); however, these quintet states were not considered in this study. Similarly, four 3MC acceptor states of CR character with an electron hole in d(Ru)xy/d(Ru)xz and an excess charge in d(Ru)x2−y2/d(Ru)z2 have been taken into account. The ET kinetics among these donor and acceptor states were described along a linear-interpolated Cartesian coordinate (LICC) connecting, at the TDDFT level of theory, fully optimized equilibrium structures of the respective states. The correlating diabatic PESs (of D and A) were constructed along the LICC, denoted RET, by means of TDDFT singlepoint calculations. As an alternative, Moser and Dutton have suggested a very successful simple semiempirical approximation to calculate intramolecular ET (IET) rates.43,44 They found, that for a wide range of systems examined, the penetration of the electronic wave function into the medium between the redox centers as well as the frequency of the harmonic oscillators approximating the donor and acceptor potentials do not differ much. Thus, eq 1 can be approximated by the semiempirical expression:43,44

of solvation was used for the calculation of the excitation energies within the FC region, which is well-adapted for processes where only the fast reorganization of the electronic distribution of the solvent is important. In contrast, the equilibrium procedure of solvation was applied to construct the Marcus parabolas based on excited-state geometry optimizations. Upon singlet excitation ultrafast population transfer to the triplet manifold is assumed to occur by intersystem crossing (ISC), followed by energy dissipation along the excited-states relaxation pathways. Several triplet states involved in such relaxation channels correlated to charge-separation (CS) and charge-recombination (CR) processes were optimized using TDDFT. Scheme 1 illustrates such photoinduced relaxation Scheme 1. States Involved in Photoinduced Relaxation Pathways in RuCo Accessible via Intersystem Crossing (ISC) and Internal Conversion (IC), Leading in Consequence to Charge-Separation (CS) or ChargeRecombination (CR)

log(kIET) = 15 − 0.6r − 3.1

(2)

where the exponential decay of kIET (given in s−1) now solely depends linearly on the distance r (in Å) between the donor and the acceptor sites and quadratically on ΔG and λ (both in eV). Here, we will compute both rates, one given by Marcus (eq 1) and the other given by the semiempirical Moser− Dutton expression (eq 2). In addition to eqs 1 and 2, we have performed onedimensional quantum dynamical (QD) simulations in the diabatic representation for each ET process, respectively. We numerically integrate the time-dependent Schrödinger equation (TDSE) on a spatial grid for the nuclear wave functions, ψi(t) in each state i (D and A). In the diabatic representation, the TDSE for the two-state model reads as

cascades typically observed for this class of tpphz-bridged ruthenium(II) complexes.67,70,83,85,87−89 Thereby a preliminary singlet metal-to-ligand charge transfer (1MLCT) from the ruthenium photosensitizer to the bridging ligand (BL) is followed by ISC, and population of 3MLCT states [T(BL)] localized on the phenanthroline or the phenazine moiety depending on the excitation energy. Subsequently, successive ET from the phenanthroline to the central phenazine moiety and eventually toward the cobalt, T(CS), associated with CS and posterior ISC to the quintet manifold [Q(CS)] competes with CR from T(BL) toward metal-centered (3MC) ruthenium states [T(CR)]. 2.2. Kinetical and Quantum Dynamical Calculations. In order to access the kinetics of such (nonadiabatic) ET processes, typically the semiclassical Marcus theory is applied, where the rate constant kET is given by16,22−24 kET =

(ΔG + λ)2 λ

iℏ

⎞ ⎛ ⎞ ⎛ ⎞⎛ ∂ ⎜ ψD(R , t )⎟ ⎜ HD(R ) HD/A(R )⎟⎜ ψD(R , t )⎟ = ∂t ⎜⎝ ψA(R , t ) ⎟⎠ ⎜⎝ HA/D(R ) HA(R ) ⎟⎠⎜⎝ ψA(R , t ) ⎟⎠

(3)

with matrix elements of the Hamiltonian given as

⎛ (ΔG + λ)2 ⎞ 2π |VD/A,max|2 (4πλkBT )−1/2 exp⎜ − ⎟ ℏ 4λkBT ⎠ ⎝

Hii = −

(1)

ℏ2 ∂ 2 + Vi (R ) 2M ∂R2

and

Hij = Vij(R ) = VD/A(R ) (4)

Here VD/A,max corresponds to the maximum potential coupling matrix element between the electron donor state D and the electron acceptor state A at the crossing point, λ corresponds to the reorganization energy, ΔG corresponds to the driving force

where M is the reduced mass and Vi(R) are the electronic diabatic PESs computed along the ET coordinate R for both the donor and acceptor states, A and D, respectively. Vij(R) = 16068


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The Journal of Physical Chemistry C VD/A(R) are the potential couplings retrieved by a unitary transformation of the adiabatic potential matrix for each R: ⎛ V ad 0 ⎞ ⎛ VD VD/A ⎞ 1 ⎟U ⎜⎜ ⎟⎟ = U†⎜ ⎜ ad ⎟ ⎝ VD/A VA ⎠ 0 V ⎝ 2 ⎠

in Figure 1, while detailed information with respect to the underlying electronic transitions and the comparison to experimental data67 is summarized in Table 1.

(5)

where U is a general rotation matrix. In order to identify the ET coordinate R, we have analyzed the most prominent geometry changes occurring for the selected donor−acceptor pairs. As stated above, these are the LICCs connecting the fully optimized equilibrium structures of the donor and acceptor sites. For the donor−acceptor pairs T(BL1)−T(CS1) and T(BL2)−T(CS3), the most dominant geometry changes occur along the cobalt−nitrogen bond, r6 (see Table S1), which is defined to be the 1D-reaction coordinate, R. This defines the reduced mass to be M = 188.7 amu, according to the relative motion of the Co(bpy)2 fragment with respect to the bridging ligand moiety. In the same way, the axial nitrogen−nitrogen distance in the cobalt moiety, r4+r4′ (see Table S1), is used as the ET coordinate for the state pairs T(BL1)−T(CS2) and T(BL2)−T(CS5) with a reduced mass of M = 78.0 amu, according to the vibration of the two bpy ligands toward each other. For the quantum dynamics, donor and acceptor potential energy curves along the LICC have been fitted to a quadratic polynomial to best represent the region around the crossing, while simultaneously considering the correct behavior at the minimum structures (see Table S2). The total spatial grid is then composed of 1024 points along r6 between 1.5 and 2.7 Å for T(BL1)−T(CS1) and T(BL2)−T(CS3), and along r4+r4′ between 2.9 and 5.5 Å for T(BL1)−T(CS2) and T(BL2)− T(CS5). The potential coupling, determined by eq 5, has been assumed to be a Gaussian function centered at the diabatic crossing and has been fitted accordingly (for more details see Figure S1). The diabatic TDSE (eq 3) is solved with the help of the splitoperator method90,91 for the first 5 ps with a time discretization of Δt = 0.01 fs. The initial Gaussian-shaped wavepacket is placed on the donor state with an energy determined by the energy difference between S0 and the corresponding donor triplet state; recall T(BL) in Scheme 1 within the S 0 equilibrium. The population transfer from donor to acceptor state is assumed to be a first-order reaction, and as such, we determined the rate constant of the transfer, kQD, by fitting the time-dependent population in the acceptor state to an exponential function: |ψA(t )|2 = 1 − e−kQD(t − t0)

Figure 1. Simulated UV−vis absorption spectrum of RuCo. Calculated oscillator strengths of the singlet excited states are represented by black bars; Lorentzian functions with a full width at half-maximum of 0.15 eV are employed to broaden the transitions. Excitation energies of (excited) triplet states involved in the subsequent excited states ET processes within the Franck−Condon region are displayed by colored bars: T(BL) states (3MLCT states toward the bridging ligand) are given in red, charge-separated states, T(CS) are in green and chargerecombination states, T(CR) are in blue.

In agreement with the experimental data, the broad absorption feature at 2.79 eV (445 nm) is correlated to several 1 MLCT excitations, namely, into the states S27, S31, and S32, while a further state, S2, can be associated with the red-sided shoulder at approximately 2.48 eV (500 nm) in the experimental spectrum. The S2 state, at 2.35 eV (528 nm), and partially the S27 and S31 states, at 2.88 and 2.96 eV (431 and 419 nm), respectively, are of MLCT character toward the tpphz bridging ligand, while S27 and S31 populate the lowest antibonding MOs of the phenanthroline and the bipyridine in close vicinity of the ruthenium (π*(Ru)bpy). Excitation into S2 transfers the charge directly to the central phenazine moiety of the tpphz ligand; see involved MOs in Table S3. A further MLCT state, S32, is predicted by TDDFT at 3.01 eV (412 nm). This state transfers the charge from the ruthenium toward π*(Ru)bpy-orbitals and thus does not contribute (directly) to the PET processes between the two metal centers. The UV region of the absorption spectrum mainly involves ligandcentered (LC) states, such as the states S37 and S44 with excitation energies of 3.52 and 3.58 eV (352 and 346 nm), respectively. Both states are of mixed electronic character and show contributions of local π−π* transitions of the bridging ligand as well as of ligand-to-ligand charge transfer (LLCT) from the bipyridine sphere (at the ruthenium side) toward the bridging ligand and are assigned to the double band structure in the experimental spectrum at 3.26 and 3.44 eV (380 and 360 nm). Thus, the computational results on the UV−vis absorption spectrum of RuCo are in good agreement with the experimental data, while in general the calculated excitation energies are overestimated by approximately 0.10−0.25 eV. Very similar results have been obtained by TDDFT methods for structurally related bimetallic complexes and their precursors.71,83,84 Photoexcitation into the bright 1MLCT band of RuCo, i.e., as carried out by Torieda et al. using an excitation wavelength

(6)

3. RESULTS AND DISCUSSION 3.1. UV−Vis Absorption and Initial Photoactivation. The UV−vis absorption spectrum of RuCo is associated with a manifold of different excitations; the experimental spectrum features a broad 1MLCT band in the visible region centered at approximately 2.79 eV (445 nm) and in the UV a structured IL band of the tpphz ligand at 3.26 and 3.44 eV (380 and 360 nm). Further contributions to the UV absorption (4.00 and 4.28 eV/310 and 290 nm) arise from the bpy ligand spheres coordinating the ruthenium as well as the cobalt.67 The calculated singlet absorption spectrum of RuCo, obtained at the TDDFT level of theory using the B3LYP XC functional and the 6-31G(d) basis set as well as a PCM (acetonitrile), is depicted 16069


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Table 1. Calculated Vertical Excitation Energies (Ee), Wavelengths (λe), Oscillator Strengths ( f), Experimental Wavelengths (λexp), and Singly-Excited Configurations of the Main Excited Singlet and Triplet States Involved in the Subsequent Excited States ET Processes (Labeled: BL, CS, and CR) within the Franck−Condon Region state S2 S27

S31

S32 S37 S44 T4(BL1) T8(BL2) T9(BL3) T10(BL) T11(CS1) T12(CS2) T13(BL) T16(CS3) T17(BL) T19(CS4) T20(CS5) T22(CS6) T26(BL) T27(BL)

T29(BL) T43(CR1) T44(CR2) T50(CR3) T54(CR4) T56(CR5) T64(CR6) a

transition

weight (%)

singlet−singlet excitations, S0 geometry d(Ru)xy(276) → π*BL(280) (MLCT) 85 d(Ru)xy(276) → π*BL(285) (MLCT) 54 d(Ru)xy(276) → π(Ru)*bpy(286) (MLCT) 30 d(Ru)yz(275) → π(Ru)*bpy(287) (MLCT) 34 d(Ru)xy(276) → π(Ru)*bpy(286) (MLCT) 28 d(Ru)xy(276) → π*BL(285) (MLCT) 22 d(Ru)xy(276) → π*BL(283) (MLCT) 10 d(Ru)yz(275) → π(Ru)*bpy(286) (MLCT) 52 d(Ru)xy(276) → π(Ru)*bpy(287) (MLCT) 42 π(Ru)bpy(274) → π*BL(280) (LLCT) 56 πBL(271) → π*BL(280) (LC) 20 πBL(271) → π*BL(280) (LC) 56 π(Ru)bpy(274) → π*BL(280) (LLCT) 19 singlet−triplet excitations, S0 geometry d(Ru)xz(277) → π*BL(280) (MLCT) 79 d(Ru)xy(276) → π*BL(280) (MLCT) 79 58 d(Ru)yz(275) → π*BL(280) (MLCT) d(Ru)xz(277) → π*BL(285) (MLCT) 10 30 d(Ru)xz(277) → π*BL(285) (MLCT) d(Ru)yz(275) → π*BL(280) (MLCT) 22 d(Ru)xz(277) → d(Co)x2+ y2(278) (MMCT) 18 76 d(Ru)xz(277) → d(Co)x2+ y2(278) (MMCT) d(Ru)xz(277) → π*BL(280) (MLCT) 8 d(Ru)xz(277) → d(Co)z2(279) (MMCT) 99 38 d(Ru)xy(276) → π*BL(285) (MLCT) d(Ru)xy(276) → π*(Ru)bpy(286) (MLCT) 19 d(Ru)xz(277) → π*BL(284) (MLCT) 18 d(Ru)xy(276) → d(Co)x2+ y2(278) (MMCT) 95 d(Ru)xz(277) → π*BL(281) (MLCT) 84 d(Ru)yz(275) → d(Co)x2+ y2(278) (MMCT) 95 d(Ru)xy(276) → d(Co)z2(279) (MMCT) 96 d(Ru)yz(275) → d(Co)z2(279) (MMCT) 100 d(Ru)xy(276) → π*BL(281) (MLCT) 74 31 d(Ru)yz(275) → π*BL(285) (MLCT) d(Ru)yz(275) → π*BL(281) (MLCT) 24 d(Ru)xy(276) → π*(Ru)bpy(287) (MLCT) 15 d(Ru)yz(275) → π*(Ru)bpy(286) (MLCT) 13 61 d(Ru)yz(275) → π*BL(281) (MLCT) d(Ru)yz(275) → π*BL(285) (MLCT) 24 d(Ru)xz(277) → d(Ru)x2+ y2(304) (MC) 62 36 d(Ru)xz(277) → d(Ru)z2(305) (MC) π(Ru)bpy(274) → π*(Ru)bpy(286) (LC) 17 π(Ru)bpy(273) → π*(Ru)bpy(287) (LC) 17 56 d(Ru)yz(275) → d(Ru)x2+ y2(304) (MC) d(Ru)xy(276) → d(Ru)z2(305) (MC) 25 48 d(Ru)xy(276) → d(Ru)z2(305) (MC) d(Ru)yz(275) → d(Ru)x2+ y2(304) (MC) 26 d(Ru)xy(276) → π*(Ru)bpy+d(Ru)z2(306 (MLCT)) 8 37 d(Ru)yz(275) → π*BL(289) (MLCT) d(Ru)xy(276) → d(Ru)x2+ y2(304) (MC) 33 49 d(Ru)yz(275) → d(Ru)z2(305) (MC) d(Ru)xy(276) → d(Ru)x2+ y2(304) (MC) 29 d(Ru)yz(275) → π*(Ru)bpy+d(Ru)z2(306) (MLCT) 9

Ee (eV)

λe (nm)

f

λexp (nm)a

2.35

528

0.046

500

2.88

431

0.096

445

2.96

419

0.171

445

3.01

412

0.127

445

3.52

352

0.217

380

3.58

346

0.207

360

2.16 2.29

574 542

0.000 0.000

2.35

527

0.000

2.38

521

0.000

2.38

521

0.000

2.41

515

0.000

2.44

509

0.000

2.54 2.54 2.56 2.56 2.58 2.69

489 488 485 485 481 461

0.000 0.000 0.000 0.000 0.000 0.000

2.71

457

0.000

2.73

455

0.000

3.17

391

0.000

3.19

389

0.000

3.41

363

0.000

3.53

351

0.000

3.53

351

0.000

3.60

345

0.000

Experimental wavelengths were obtained from ref.67

of λexc = 400 nm,67 may lead to an ultrafast population transfer to the triplet manifold upon ISC. As can be seen in Figure 1

and Table 1, displaying a preselection of (i) nine 3MLCT states from the three occupied d-orbitals of the ruthenium, 16070


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Figure 2. Relative energies of states involved in PET cascades leading to either CS or CR, namely S0, S2, and S27 (in black), T(BL1)−T(BL3) (in red), T(CS1)−T(CS6) (in green), T(CR1)−T(CR6) (in blue), within the optimized singlet states S0 and S2 and the triplet states T(BL1), T(BL2), T(CS1), T(CS2), T(CS3), T(CS5), T(CR1), and T(CR2). The SOMOs of the leading transitions of each state are given below using the same color code as mentioned above.

in the FC region. The six charge-separated states, namely, T11(CS1), T12(CS2), T16(CS3), T19(CS4), T20(CS5), and T22(CS6), are calculated at 2.38, 2.41, 2.54, 2.56, 2.56, and 2.58 eV, respectively, while the six CR states T43(CR1), T44(CR2), T50(CR3), T54(CR4), T56(CR5), and T64(CR6) are found at 3.17, 3.19, 3.41, 3.53, 3.53, and 3.60 eV. Detailed information regarding the leading electronic transitions involved in these states is summarized in Table 1, while all participating frontier orbitals are depicted in Table S3. To reduce the number of triplet states involved in the PET (dashed red box in Scheme 1), we neglect contributions of excited triplet states featuring an electron hole at the orbital d(Ru)yz(275). This is justified since the initial photoexcitation into S2 occurs from d(Ru)xy(276), while the lowest triplet state in the FC region features an electron hole at d(Ru)xz(277). Therefore, the number of electron donor states involved in the PET is decreased from three to two, T4(BL1) and T8(BL2). Simultaneously, the number of acceptor states associated with CS and CR is reduced from six to four [CS: T11(CS1), T12(CS2), T16(CS3) and T20(CS5) and CR: T43(CR1), T44(CR2), T54(CR4), and T56(CR5)], respectively. In order to obtain an overview of the energy landscape of the singlet, S0,

d(Ru)xy(276), d(Ru)xz(277), and d(Ru)yz(275), into the lowest-lying antibonding orbitals of the phenacetin, π* BL (280), and the phenanthroline, π* BL (285) and π*BL(281), in vicinity to ruthenium and cobalt moieties, respectively, denoted T(BL), and (ii) six charge-separated triplet states, T(CS), where the electron hole is localized at the ruthenium [d(Ru)xy(276), d(Ru)xz(277), or d(Ru)yz(275)] and the transferred electron is localized either in d(Co)x2−y2(278) or d(Co)z2(279) of the cobalt. The six possible CR states, where one unpaired electron resides either in d(Ru)xy(276), d(Ru)xz(277) or d(Ru)yz(275) and the other unpaired electron is localized in d(Ru)x2−y2(304) or d(Ru)z2(305), are found at considerably higher energies. Thus, merely the T(BL) and the T(CS) states are directly accessible upon excitation into the 1 MLCT band (S2, S27, S31, and S32). In the following, we restrict our investigation exclusively to an initial photoexcitation into S2, which populates the lowest antibonding orbital of the phenacetin [π*BL(280)]. Therefore, and in accordance with Scheme 1, no further ET from the phenanthroline toward the phenacetin moiety is considered. The three respective 3MLCT states, T4(BL1), T8(BL2), and T9(BL3), feature excitation energies of 2.16, 2.29, and 2.35 eV 16071


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Figure 3. Calculated diabatic PESs of preselected pairs of donor (black circles) and acceptor states (gray circles) obtained at the TDDFT level of theory along a LICC (RET); a quadratic polynomial (E(RET) = a(R − R0,a)2 + b(R − R0,b) + c) was fitted to the respective data sets (see Table S2). Driving forces (ΔG), reorganization energies (λD and λA), and potential couplings (VD/A,max) are given for the respective pairs of states leading to CS (a−d) and CR (e and f). LICCs are illustrated by displacement vectors within T(BL1)/T(BL2) for all six pairs of states; hydrogen atoms were omitted for simplicity.

lying T(BL) states, no pronounced alterations are observed in the relative energies of all involved singlet and triplet states upon relaxation in T(BL1) and T(BL2), respectively. In the T(BL1) equilibrium, the three T(BL) states are found between 2.02 and 2.33 eV, the CS states between 2.45 and 2.77 eV and the CR states between 3.28 and 3.79 eV; similar values are obtained for the T(BL2) structure (Figure 2 and Table S4). A pronounced reordering of states is observed upon relaxation in the four CS states. In the T(CS1) and T(CS2) structures, the optimized CS state is considerably lowered to 1.70 and 1.73 eV, respectively. For the equilibrium of T(CS3), a degeneracy of T(CS2) and T(CS3) is found at slightly higher energy (1.84 and 1.85 eV). Likewise, a degeneracy between T(CS2) and T(CS5) was observed in the optimized T(CS5) structure at 1.87−1.88 eV. Interestingly, all optimized T(CS) structures feature three substantially stabilized T(CS) states, which are all lower in energy than the lowest T(BL) state in its optimized geometry; thus, an ET from the T(BL) to the CS states is energetically favored. However, all three T(BL) states and six CR states are increased in energy within the optimized T(CS) states and are localized at 2.84−3.17 eV and 3.85−4.38 eV, respectively. Competing with the PET from the T(BL) donor states to the T(CS) acceptor states, intramolecular ET can also occur toward the ruthenium centered 3MC CR states. As mentioned above, convergence was only achieved for the two CR states, T(CR1) and T(CR2),

S2, and S27, as well as the four CS and four CR triplet states involved in the PET, optimizations at the (TD)DFT level of theory and subsequent TDDFT single-point calculations were performed for all aforementioned states. However, for the CR states, equilibrium geometries for merely two of the four states, namely, T43(CR1), T44(CR2), could be generated. For simplicity, we refrain from indicating the state number for the respective TDDFT calculation in the nomenclature of the triplet states and label these states as T(BL1−3), T(CS1−6), and T(CR1−6) for non-FC points. Figure 2 depicts the resulting energies of the singlet and triplet states of interest in their respective fully optimized equilibrium structure with respect to the S0 energy in its optimized equilibrium; all energies are summarized in Table S4. As can be seen from Figure 2, relaxation within S2 does not alter the order of the T(BL) states, while T(BL2) is slightly stabilized from 2.29 to 2.16 eV. In contrast, almost no influence on the energies of T(BL1) and T(BL3) was obtained, which in consequence leads to a degeneracy of T(BL1) and T(BL2). This finding can be easily rationalized by means of the donor MO involved in the leading transition of S2: d(Ru)xy(276). Accordingly, all CS and CR states are destabilized upon relaxation in S2 up to 0.20 eV, whereas the CS and CR states featuring a partially occupied d(Ru)xy(276) orbital, T(CS3) and T(CS5) as well as T(CR4) and T(CR5), show with 0.02−0.06 eV the lowest destabilizations. Due to the similar electronic character of S2 and the low16072


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Table 2. Driving Forces (ΔG), Reorganization Energies (λD and λA), Potential Couplings (VD/A,max), Distance between Donor and Acceptor (r) and Rate Constants (k) for Respective Pairs of States Leading to CS and CRa Marcus theory donor−acceptor

ΔG (eV)

λi (eV)

T(BL1)−T(CS1)

−0.33

T(BL1)−T(CS2)

−0.29

T(BL2)−T(CS3)

−0.31

T(BL2)−T(CS5)

−0.27

T(BL1)−T(CR1)

−0.46

T(BL1)−T(CR2)

−0.38

0.84 0.75 0.82 0.75 0.84 0.75 0.81 0.74 2.18 1.72 2.27 1.67

VD/A,max (eV)

r (Å)

0.09

6.396

0.12

6.325

0.12

6.395

0.05

6.325 6.816 6.506

ki,ET (s−1) 6.56 1.50 9.45 1.78 1.01 2.24 1.55 3.13

× × × × × × × ×

1012 1013 1012 1013 1013 1013 1012 1012

QD

ki,IET (s−1) 1.50 2.61 1.49 2.28 1.30 2.22 1.26 2.02 5.42 1.14 1.68 1.06

× × × × × × × × × × × ×

1010 1010 1010 1010 1010 1010 1010 1010 106 108 106 108

kQD (s−1) 1.78 × 1013 7.59 × 1013 2.78 × 1013 1.21 × 1013

a Rate constants are calculated via semi-classical Marcus theory (eq 1, kET), the semi-empirical expression for intra-molecular ET (eq 2, kIET), and QD simulations based on the population transfer within the first 5 ps (kQD), see eq 6.

(CR2)] leading to CR. For each pair of states, additional TDDFT calculations were performed along a LICC RET (ET coordinate) in order to construct the diabatic PESs for the respective donor and acceptor state pair, as described above. The resulting PESs for the four processes involved in CS and the two processes leading to CR are depicted in Figures 3a,d and 3e,f, respectively, along with the calculated driving forces (ΔG), reorganization energies (λ), and maximum potential coupling matrix elements (VD/A,max). Figure 3 shows that all ET processes are within the normal regime of ET (−λ < ΔG < 0).23 The diabatic potential couplings along RET of all four pairs of states leading to CS, obtained by means of eq 5 (see the “Computational Details” section), as well as the PESs in diabatic and adiabatic representation are illustrated in Figure S1. For the CS processes in Figure 3a−d, all calculated PESs (along RET) are parabolic, which is rationalized by the reduced χ2 values for the fitted quadratic functions collected in Table S2. However, the curvature for each donor−acceptor pair (see aD and aA in Table S2) are not identical; thus, two values for the reorganization energy were obtained, λD and λA. For T(BL1)− T(CS1), illustrated in Figure 3a), a driving force of −0.33 eV is calculated, and reorganization energies of 0.84 and 0.75 eV in the donor and acceptor state, respectively. A unitary transformation performed around the point of degeneracy between the potentials yielded a maximum potential coupling matrix element of 0.09 eV (recall eq 5). Similar values of ΔG (−0.29 eV) and λ (0.82 and 0.75 eV) are obtained for T(BL1)− T(CS2), where ET leads to the population of d(Co)z2. The coupling between these two states is with VD/A,max = 0.12 eV slightly stronger than for the previous T(BL1)−T(CS1) states. Figure 3c,d depict the ET between the donor state T(BL2) and the CS states T(CS3) and T(CS5). The respective values for ΔG (−0.31 and −0.27 eV) as well as for λD (0.84 and 0.81 eV) and λA (0.75 and 0.74 eV) are again very similar; however, the calculated potential coupling is for T(BL2)−T(CS3) with 0.12 eV considerably stronger than for T(BL2)−T(CS3) with merely 0.05 eV. The rate constants for the CS processes have been calculated for all four pairs of donor−acceptor states by means of the semiclassical Marcus theory (eq 1) and by virtue of the semiempirical Moser−Dutton expression for intramolecular ET processes in eq 2. Furthermore, QD simulations on the diabatic PESs have been performed. The calculated rate constants are

where d(Ru)xz(277) and d(Ru)x2−y2(304) or d(Ru)xz(277) and d(Ru)z2(305) are partially occupied. In these two structures, the energy landscape of the electronic states is even more distorted. T(CR1) and T(CR2) are stabilized to 1.56 and 1.64 eV in their respective equilibrium and are thus lower in energy than the T(CS) states in their optimized structures. Furthermore, all T(BL) states are found at substantially higher energies (4.20− 4.66 eV). Similarly, the energies of the six CS states are increased to 4.37−4.93 eV. Remarkable is the fact that the energy of the singlet ground state increases to 1.96 and 2.04 eV in the CR equilibria, which is above the energy of the lowest T(CR) state. This finding can be related to the distinct distortion of the T(CR) equilibrium structures with respect to structures of S0 and S2 as well as all optimized T(BL) and T(CS) states; see Table S1. Because all T(CS) and T(CR) states feature antibonding character between the metal, either cobalt or ruthenium, and the nitrogen atoms of the respective ligand sphere, an elongation of the corresponding bonds is evident. The cobalt−nitrogen bonds are stretched by up to 0.29 Å (from approximately 1.96 to 2.23 Å) with respect to the FC region, which is in agreement with the experimentally observed variation of the cobalt−nitrogen bonds from 1.93 to 2.13 Å,67,92,93 whereas the ruthenium−nitrogen bond lengths are increased by up to 0.63 Å (within the optimized T(CR) states) with respect to the S0 equilibrium structure. Since DFT is unable to describe bonding situations far from the equilibrium, the energies of the S0 closed-shell wave function are most likely overestimated in the optimized TDDFT structures of the CR states. In addition, this elongation is accompanied by a substantial twist of the bipyridine ligands (see dihedral angles δ1, δ1′, δ2, and δ2′ in Table S1), while more pronounced nonplanar distortions are predicted for the bipyridine sphere attached to the ruthenium (up to 23°) in the CR states than for the cobalt bipyridine ligands in the CS states (merely up to 11°). 3.2. Excited-States Electron Transfer Channels. On the basis of Scheme 1, the competitive PET processes leading either to CS or CR are examined by virtue of Marcus theory and QD simulations. Therefore, excited-state relaxation cascades were investigated for four pairs of donor−acceptor states [T(BL1)−T(CS1), T(BL1)−T(CS2), T(BL2)−T(CS3), and T(BL2)−T(CS5)] describing CS and for two pairs of donor−acceptor states [T(BL1)−T(CR1) and T(BL1)−T16073


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The Journal of Physical Chemistry C summarized in Table 2. Semiclassical Marcus theory predicts rate constants ranging between 1.55 × 1012 and 2.24 × 1013 s−1 at T = 295 K. The ET rates calculated for one respective pair of donor−acceptor states vary up to 56% for λA and λD. The fastest ET processes are predicted for T(BL1)−T(CS2) and T(BL2)−T(CS3) with 9.45 × 1012 and 1.78 × 1013 s−1 as well as 1.01 × 1013 and 2.24 × 1013 s−1, respectively. These pairs of states feature the strongest potential couplings of 0.12 eV, while slightly lower rates (6.56 × 1012 and 1.50 × 1013 s−1) were obtained for T(BL1)−T(CS1) with a coupling of 0.09 eV. The lowest rates (1.55 × 1012 and 3.13 × 1012 s−1) were calculated for T(BL2)−T(CS5) which also holds the smallest VD/A,max of merely 0.05 eV. Thus, the PET among the investigated states of interest are mostly governed by the potential couplings, while the driving forces and reorganization energies are similar for all donor−acceptor states. The rate constants obtained by virtue of wavepacket propagation along the diabatic potentials, ranging between 1.21 × 1013 and 7.59 × 1014 s−1, are in good agreement with semiclassical Marcus theory. The evolution of the wavepacket, and thus the real-time ET dynamics, from a donor state to an acceptor state is exemplarily illustrated for T(BL1)−T(CS1) by means of snapshots at t = 0, 70, 100, 200, and 260 fs of propagation time in Figure 4a−e. Again, not surprisingly, the highest rate constants of 2.78 × 1013 and 7.59 × 1013 s−1 are determined for T(BL1)−T(CS2) and T(BL2)−T(CS3), respectively, featuring the strongest couplings (VD/A,max = 0.12 eV). The difference between these two rates is mainly reasoned by the differences in the initial energies of the wavepackets of 2.16 and 2.29 eV for T(BL1) and T(BL2), respectively. Likewise, as in semiclassical Marcus theory, T(BL1)−T(CS1) features with 1.78 × 1013 s−1 a slightly lower ET rate constant, while the lowest kQD, with a value of 1.21 × 1013 s−1, is predicted for the weakly coupled donor−acceptor states T(BL2)−T(CS5). The time-dependent population for the respective acceptor states over the first 5 ps and the fitted exponential function (recall eq 6) yielding kQD are shown in Figure S2. The PESs for the preselected pairs of CR states along the LICC in Figure 3e,f are not harmonic, which can be easily seen based on the fitted quadratic function as well as on the reduced χ2 ranging between 0.05 and 0.26 in Table S2. This is reasoned by a pronounced mixing of both T(CR1) and T(CR2) along the ET coordinate. Furthermore, as mentioned above, the structural variations found in T(CR1) and T(CR2), namely, the considerable elongation of the ruthenium−nitrogen bonds as well as the torsion of the coordinating bipyridine ligands, are more distinct than for the CS states. Therefore, it can be concluded that the one-dimensional LICC is not an appropriate coordinate to describe CR processes in RuCo, and hence, no potential coupling matrix elements and rate constants based on eqs 1 and 6, kET and kQD, have been calculated for these processes. In addition to the rate constants obtained by semiclassical Marcus theory and QD simulations, semiempirical rate constants (eq 2, kIET) are calculated for all four pairs of CS and both pairs of CR states. Here, no explicit potential couplings are given; however, the coupling between the states is correlated to the distance (r) between the redox (donor and acceptor) centers. For the processes leading to CS, values of r ranging from 6.325 to 6.396 Å are extracted, while slightly longer distances are estimated for the CR states (6.506 and 6.816 Å). Because all pairs of CS states feature very similar

Figure 4. Wavepacket propagation on the diabatic PESs of T(BL1)− T(CS1) along the coordinate r6 (see Table S1) upon (a) 0 fs, (b) 70 fs, (c) 100 fs, (d) 200 fs, and (e) 260 fs. Diabatic potentials curves and probability densities of donor [T(BL1)] and acceptor state [T(CS1)] are shown in black and gray, respectively. (f) Population of acceptor state CS1 (|ψCS1|2 in gray) and rate constant kQD (in black) obtained according to eq 6 for T(BL1)−T(CS1), kQD was fitted for 70 fs ≤ t ≤ 5000 fs.

driving forces, reorganization energies, and distances, all kIET rates are very similar and range merely from 1.26 × 1010 to 2.61 × 1010 s−1. These rate constants are 3−4 orders of magnitude lower than the rates obtained by means of semiclassical Marcus theory and the wavepacket propagations. Interestingly, the rates, kIET, for the processes leading to CR are accessible based on the semiempirical expression in eq 2, yielding even lower values of 5.42 × 106 and 1.14 × 108 s−1 for T(BL1)−T(CR1) and 1.68 × 106 and 1.06 × 108 s−1 for T(BL1)−T(CR2). This finding is reasoned by the slightly increased driving forces of −0.46 and −0.38 eV as well as by the substantially increased reorganization energies of λD = 2.18 and 2.27 eV as well as λA = 1.72 and 1.67 eV for T(BL1)−T(CR1) and T(BL1)−T(CR2), respectively. Thus, the investigated CR processes are 16074


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species by population of d(Ru)x2−y2 and d(Ru)z2 from the photoreduced 3tpphz ligand. ET rates for these four CS and two CR processes were elucidated based on semiclassical Marcus theory and by a semiempirical expression, neglecting an explicit description of the potential couplings between the donor and the acceptor states, as well as to the best of our knowledge for the first time by means of QD simulations along LICCs between the respective states. The performed quantum chemical calculation revealed very similar driving forces, in the range of −0.27 to −0.33 eV, and reorganization energies, ranging from 0.74 to 0.84 eV, for all six donor−acceptor states leading to CS. However, distinct variations of the potential coupling matrix elements (0.05− 0.12 eV) consequently lead to rate constants for the CS processes from 1.55 × 1012 s−1 for loosely coupled states to 2.24 × 1013 s−1 for strongly coupled states, as obtained by semiclassical Marcus theory. Quantum dynamical simulations on the diabatic PESs result in very similar rate constants ranging from 1.21 × 1013−7.59 × 1013 s−1. However, rate constants for the CS states as obtained by means of the semiempirical expression neglecting a direct coupling between the states are with 1.26 × 1010−2.61 × 1010 s−1, approximately 3 or 4 orders of magnitude smaller. Thus, it is concluded that an interaction between the states merely described based on the distance between the redox centers is insufficient to reproduce the PET kinetics in the present system. Experimentally, a rate constant of kET = 1.4 × 1012 s−1 is obtained; however, this value results from an initial population of higher (and brighter) 1 MLCT states and further includes ISC processes. Thus, the calculated rates (semiclassical Marcus theory and QD simulations), which are 1−2 orders of magnitude higher, are in good agreement with the experiment. Unfortunately, due to the nonquadratic shape of the respective potentials, the rate constants for CR could only be computed by the semiempirical expression of Marcus theory yielding values from 1.68 × 106 to 1.14 × 108 s−1. These are in good agreement with the experimental value of 2.1 × 107 s−1, which is however assigned to the regeneration of the initial singlet species 1Ru(II)Co(III) from the charge-separated quintet 5Ru(III)Co(II) species. We conclude that both calculations based on semiclassical Marcus theory as well as on QD simulations on the TDDFT potential energy landscape allow a quantitative description of the PET phenomena in RuCo. On the basis of this encouraging finding, future computational studies on stepwise multi-PET phenomena in supramolecular photocatalysts are envisioned. Furthermore, we aim to extend the applied PET scheme by additional excited-state relaxation channels involved in CS and CR processes.

approximately 2−4 orders of magnitude slower than those leading to CS, which suggests, in consequence that the primary ET cascades in RuCo photoexcitation are of ℏν

Ru(II)Co(III) → Ru(III)Co(II) character. However, the fact that all kIET values are substantially lower than the respective rates obtained by semiclassical Marcus theory and quantum dynamics leads to the assumption that the explicit consideration of potential couplings is of substantial importance for a quantitative description of PET dynamics in RuCo. The computational results obtained by semiclassical Marcus theory and QD simulations as well as by the semiempirical expression are generally in close agreement with the experimental observations. Torieda et al. provide in ref 67 ET rates of 1.4 × 1012 s−1 for the formation of the charge-separated photoproduct and 2.1 × 107 s−1 for the recovery processes yielding the initial singlet ground state species based on transient absorption spectroscopic techniques. The first rate constant (1.4 × 1012 s−1) obtained upon photoexcitation of the initial singlet species at λexc = 400 nm and at T = 295 K includes vibrational cooling, ISC processes, and excited state, as well as solvent relaxation processes, whereas at 400 nm an initial population of the MLCT states S27, S31, and S32 is taking place, as in Figure 1 and Table 1. The charge-separated photoproduct is of quintet character as indicated in Scheme 1. The ET phenomena investigated in the present contribution stem from an initial excitation of the S2 MLCT state and do not include excited-state relaxation from higher excited (singlet and triplet) states; furthermore, no rate constants for ISC processes (singlet−triplet states and triplet−quintet states) were computed. Therefore, it is evident that the calculated ET rates associated with CS are approximately 1−2 orders of magnitude higher than the experimental value. In the same manner, the CR process yielding the initial singlet species from the charge-separated 5Ru(III)Co(II) species with a rate constant of 2.1 × 107 s−1 cannot be directly compared to the calculated kIET values ranging between 1.68 × 106−1.42 × 108 s−1. In addition, further electronic states not included in Scheme 1 might contribute to CR and the formation of the initial species as suggested in ref 67.

4. CONCLUSIONS The present contribution aims at investigating the photophysics and subsequent kinetic processes of RuCo following photoexcitation. This bimetallic complex can be considered a precursor for supramolecular photocatalysts in the field of light-driven hydrogen generation, where light-harvesting proceeds at the ruthenium(II) photosensitizer linked intramolecularly to a catalytic center by a bridging ligand. A comprehensive understanding of photoinduced processes in such supramolecular photocatalysts is of uttermost importance for future theory−spectroscopy-guided design strategies in the field of solar energy conversion. Therefore, (TD)DFT was used to study the initial photoexcitation within the FC region, 1 Ru(II)Co(III). Starting from a low-lying 1MLCT state (S2), exhibiting a charge transfer from the ruthenium(II) toward the tpphz bridging ligand, preselected pairs of electron donor and acceptor states of triplet multiplicity were optimized at the TDDFT level of theory. Four processes leading to the chargeseparated 3Ru(III)Co(II), where ET takes place from the photoreduced bridging ligand into the d(Co)x2−y2 and d(Co)z2 orbitals of the cobalt, were studied, as well as two processes leading to the regeneration of the photoexcited ruthenium(II)

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b02812. Fitted quadratic polynomials, structural data, potential coupling elements and PESs within adiabatic and diabatic representation along the ET coordinate, MOs involved in the initial photoexcitation, relative energies of the involved singlet and triplet states in the PET, and timedependent population transfer (PDF) 16075


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Stefanie Gräfe: 0000-0002-1747-5809 Stephan Kupfer: 0000-0002-6428-7528 Author Contributions ⊥

A.K. and D.K. contributed equally to the creation of this article. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support by the COST Action CM1202 Perspect-H2O is gratefully acknowledged. A.K. thanks the Fonds der Chemischen Industrie im Verband der Chemischen Industrie e.V. for a generous Ph.D. stipend. D.K. and S.G. thank the Thuringian State Government for financial support within the ACP Explore project. We thank Piet Sielck for providing an inspiring working climate. All calculations have been performed at the Universitätsrechenzentrum of the Friedrich Schiller University.

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