The three kingdoms—Photoinduced electron transfer cascades controlled by electronic couplings Open Access

Solar energy conversion is among the most promising approaches to transform our energy sector toward sustainability.^1–10 In this context, supramolecular photocatalysis allows the conversion of sunlight into chemical energy, such as molecular hydrogen as well as the conversion of, e.g., carbon dioxide into commodity chemicals such as formaldehyde or methanol.^11–17 In such photocatalytic processes, molecular excited states are the key species, with the critical parameters, such as excitation energy, accessibility, and lifetime, governing their potential applications. The character of the excited state also plays a prominent role, with charge-separated excited states being of particular relevance to photocatalytic applications. In order to meet these criteria, 4d and 5d transition metal complexes are most often used as photosensitizers due to their favorable photophysical and electrochemical properties, alongside thermal, light, and pH stability.^18–21 Although considerable progress has been made in the application of earth abundant 3d metal-based photocenters, these systems still suffer from rather short excited state lifetimes due to the presence of ultrafast deactivation pathways. Therefore, in molecular transition metal-based photosensitizers, there is a design tension between the creation of long-lived excited (triplet) states and the population of such states. Long-lived triplet states have low spin–orbit coupling (SOC) and hence their population, either by direct photoexcitation or via subsequent excited state relaxation is low. Thus, a long-lived triplet state can be populated but inefficiently. If the SOC is increased, the triplet state population efficiency is improved—however, this is accompanied by a decrease in the excited state lifetime.^22,23 In this regard, the efficiency of intersystem crossing (ISC) and in consequence the population of charge-separated triplet states in transition metal complexes is highly beneficial. In particular, metal-to-ligand charge transfer (¹MLCT) excitations involved in the light-harvesting processes typically provide pronounced SOCs and allow efficient population transfer to potentially long-lived charge-separated states, e.g., of ³MLCT character. However, at the same time, the SOCs between (emissive) ³MLCT states and the singlet ground state foster radiative deactivation processes, while even stronger SOCs among low-lying ³MC (metal-centered) states and the singlet ground state may yield rapid deactivation of the charge-separated state, particularly in the case of 3d metal-based compounds.^24–28 An alternative to transition metal complexes in the frame of light-harvesting molecules are organic chromophores. However, long-lived charge-separated triplet states in organic dyes are often inaccessible or populated inefficiently due to small SOCs.

One promising molecular approach to enable panchromatic absorption in the visible spectral region as well as efficient population of long-lived charge-separated states is to combine organic and inorganic chromophores into one structure. This strategy allows light-harvesting by both chromophores, efficient ISC along a ^1/3MLCT gateway and subsequently isolating the triplet excited state away from the metal—onto the organic chromophore, e.g., by means of intra-ligand or ligand-to-ligand charge transfer (³ILCT and ³LLCT) states, see Fig. 1(a), or by virtue of energy transfer channels.^29–32 Therefore, pronounced lifetimes of the charge-separated “trap state” (e.g., ³ILCT and ³LLCT) can be realized as these ³ππ* states are only weakly coupled to the singlet ground state.

In previous joint synthetic–spectroscopic–theoretical investigations, we focused on unraveling the Franck–Condon photophysics of such dyads that combined inorganic and organic chromophores as well as on the description of ISC processes along ^1/3MLCT gateway states for a series of triphenylamine-donor-ligand Rh(I) and Pt(II) complexes^33–35 and a Ru(II)-based dye incorporating a thiazole push–push ligand.³⁶ The nature of the ^1/3MLCT gateway was tuned systematically by structural modification at the metal center,³³ the triphenylamine-donor-ligand³⁴ as well as by solvent effects.³⁵ Consequently, remote control of excited state relaxation channels within the triplet manifold was rationalized, leading to either short-lived ³MLCT or long-lived ³ILCT states.

In the scope of the present work, we aim to elucidate the light-driven processes and excited state relaxation cascades associated with the population of such charge-separated triplet states localized away from the metal center in a series of Ru(II)-terpyridyl push–pull triads by means of quantum chemical simulations. Along this series of dyes, one terpyridyl (tpy) ligand is substituted with an electron donating 10-methylphenothiazinyl (PTZ) moiety, while the substitution pattern of the second tpy ligand is systematically modified from the parent ligand architecture (R = H; RuH) by a phenyl (RuPh), tolyl (RuTol), anisyl (RuAn) or by a C₆₀ fullerene (RuC₆₀), see Fig. 1(b). The effect of the substitution pattern is particularly interesting as previous experimental studies highlighted the potential to remotely control photoinduced electron transfer kinetics by means of structural modification. Based on ns-transient absorption spectroscopy and electrochemistry, it was shown that photoinduced electron transfer (ET) kinetics are mainly modulated by electronic coupling (V_DA) between the donor (D) and acceptor (A) states and to a lesser extent by the underlying thermodynamic properties, such as the driving force (ΔG) and reorganization energy (λ).³⁷ 

In this study, quantum chemical methods, i.e., density and time-dependent density functional theory (DFT and TDDFT) as well as multiconfigurational simulations, are utilized to investigate light-driven processes for the series of RuR push–pull triads. Prominent excited state relaxation channels involved in the population transfer from the singlet to the triplet manifold are investigated by means of scalar-relativistic TDDFT (SR-TDDFT), while the focus of the present computational study is to address the substitution effect on the subsequent ET kinetics among key ³MLCT, ³LLCT, and ³ILCT states based on semi-classical Marcus theory. Thereby, we follow our recently introduced protocol to assess the kinetics of intramolecular ET processes along efficient reaction coordinates within the Marcus picture as benchmarked with respect to (dissipative) quantum dynamics.^38–40 

All quantum chemical calculations, if not stated otherwise, were performed utilizing the Gaussian 16 program.⁴¹ The singlet ground state equilibrium structures and electronic properties of the Ru(II) complexes as ruthenium(II)-based triads, i.e., RuH, RuPh, RuTol, RuAn, RuC₆₀, were obtained at the density functional level of theory (DFT) using the B3LYP^{33,34,42–45} exchange–correlation (XC) functional in association with the def2-SVP^46,47 basis set as well as the respective core potentials. Subsequently, a vibrational analysis was carried out for each optimized ground state structure to verify that a (local) minimum on the 3N-6 dimensional potential energy (hyper-)surface was obtained. The effects of interaction with the dichloromethane solvent (CH₂Cl₂: ε = 8.93, n = 1.4070) were taken into account by the solute electron density (SMD) variant of the integral equation formalism of the polarizable continuum model (IEFPCM).^48,49 All calculations were performed including D3 dispersion correction with Becke–Johnson damping (D3BJ).⁵⁰ 

Thereafter, time-dependent DFT (TDDFT) calculations were performed for these five complexes using the same XC functional and basis set as mentioned above in the preceding ground state calculations. These TDDFT simulations aim to provide insight into the exited state properties, i.e., excitation energies, oscillator strengths, transition dipole moments, and electronic characters of the 100 lowest excited singlet states as well as of the 20 lowest triplet states within the Franck–Condon region. Solvent effects on the Franck–Condon photophysics, where only the fast reorganization of the solvent is important, were addressed by the non-equilibrium procedure of solvation. This computational protocol was already successfully applied to elucidate the ground and excited state properties of structurally closely related Ru(II) complexes and allows a balanced description of metal-to-ligand charge transfer (MLCT), intra-ligand charge transfer (ILCT), ligand-to-ligand charge transfer (LLCT) as well as local intra-ligand states.^38,51–58 Furthermore, to confirm the order of the low-lying singlet excited states in the Franck–Condon point, the 50 lowest energy singlet transitions of RuH were evaluated using the double-hybrid SOS-wPBEPP86 functional⁵⁹—also in association with as the def2-SVP basis set and respective core potentials as implemented in Orca 5.0. Solvent effects were included using the conductor-like polarizable continuum model (CPCM)⁶⁰ for CH₂Cl₂.

While dynamic correlation, i.e., the close-range interaction between neighboring electrons, is typically well described by (TD)DFT, static correlation stemming from near-degenerate electronic configurations (Slater determinants) is insufficiently treated by (TD)DFT methods due to its single-determinant nature. To account for static correlation, multiconfigurational methods, e.g., the complete active space self-consistent field (CASSCF) approach,⁶¹ are the methods of choice. The application of multiconfigurational simulations provides an unbiased description of the photophysics of small to medium sized chemical systems, e.g., the light-driven charge transfer processes for the given set of Ru(II)-based triads. Yet, the computational demand quickly increases with the size of the active space (AS). In the case of RuH (smallest triad), an appropriate active space (AS) would include a Ru-centered AS comprising ten electrons in seven molecular orbitals, (10,7), a (18,18) with the $πtpy/πtpy*$ system of each terpyridine (tpy) ligand, as well as a (16,14) containing the $πPTZ/πPTZ*$ orbitals of the 10-methylphenothiazinyl moiety (including sulfur’s and nitrogen’s lone pairs in the aromatic plane). Consequently, an AS (62,57) is obtained for RuH, which is unfeasible without further restrictions. To restrict the number of configuration state functions (CSFs) in the CASSCF methodology, several approaches have been introduced, e.g., the restricted active space (RAS)SCF^62–64 method, which allows the computational demand to be reduced by splitting the AS into three subspaces. RAS1 holds mostly doubly occupied orbitals with a predefined number of maximal electron holes, while the RAS3 subspace contains mostly unoccupied orbitals where a defined number of electrons are allowed to be excited into. Finally, a full configuration interaction calculation is performed within RAS2—equivalent to the AS in the CASSCF method. To label the RAS calculations, the notation RAS (n,l,m;i,j,k)⁶⁵ is used. Here, the index n indicates the number of active electrons, l labels the maximum number of holes in the RAS1, and m is the maximum number of electrons in the RAS3. The labels i, j, and k refer to the number of active orbitals in the RAS1, RAS2, and RAS3 subspaces, respectively. All RASSCF calculations were performed as implemented in OpenMolcas 22.02^66,67 using the singlet ground state geometry of RuH obtained at the B3LYP level of theory. The 6-31G(d) double-ζ basis set⁶⁸ as well as the MWB28⁶⁹ relativistic core potential were applied.

The RAS partitioning of RuH was built based on our experience with a structurally related push–pull Ru(II)-based polypyridyl dye combining inorganic and organic chromophores.³⁶ In order to provide a proper description of MLCT, ILCT, and LLCT states of interest, the RAS comprises the (10,7) of the ruthenium atom including two pairs of σ/σ* orbitals and the three t_2g orbitals (d_xy, d_xz, and d_yz), four pairs of $πtpy/πtpy*$ orbitals (four orbitals per tpy ligand), three pairs of $πPTZ/πPTZ*$ orbitals as well as one nonbonding orbital of the chelating nitrogen atoms, which showed pronounced mixing σ orbitals of the coordination environment. Thereby, RAS2 contains the three t_2g orbitals, the highest occupied molecular orbital of PTZ group, and the lowest unoccupied molecular orbital of each tpy ligand. The remaining either occupied or unoccupied orbitals within the Hartree–Fock reference wavefunction were distributed over the RAS1 and RAS3 subspaces, accordingly. In consequence, a RAS (26, 2, 2; 9, 6, 7) is obtained, see Fig. 5, which spans over almost 700 000 and more than 1.2 × 10⁶ CSFs in singlet and triplet multiplicity, respectively. State-average (SA-)RASSCF calculations were carried out considering the first nine singlet and triplet roots, respectively. The transition dipole moments were obtained at the SA-RASSCF level of theory using the CAS state interaction method exclusively for the singlet roots.⁷⁰ 

To assess scalar-relativistic effects and their potential impact on the subsequent excited state relaxation pathways accessible upon intersystem crossing (ISC) within the Franck–Condon region, scalar-relativistic TDDFT calculations were performed utilizing Orca 5.0 using the scalar-relativistic zeroth-order regular approximation (SR-ZORA). DFT and TDDFT calculations were performed using the B3LYP (“Gaussian version”) XC functional;⁷¹ the SARC-ZORA-TZVP⁷² basis set was utilized for ruthenium, while all other atoms were described using the respective def2-TZVP basis sets (with the corresponding SARC/J auxiliary basis set).⁷³ The 20 lowest singlet–singlet and singlet–triplet excitations were obtained, while spin–orbit couplings (SOCs) between these states and the singlet ground state were obtained at the SR-ZORA-TDDFT level of theory. The effects of interaction with CH₂Cl₂ were taken into consideration at the CPCM level of theory.

Furthermore, equilibrium geometries of three specific excited states involved in the subsequent excited state relaxation cascade within the triplet manifold, i.e., of the low-lying ³MLCT as well as of the ³LLCT and ³ILCT states, were optimized for all ruthenium complexes. These states were fully relaxed at the TDDFT level of theory using our external optimizer pysisyphus⁷⁴—interfaced in the present case, with Gaussian 16 for gradient and energy calculations. Wavefunction overlaps⁷⁵ were utilized to track excited state characters (i.e., ³MLCT, ³LLCT, and ³ILCT) along the course of the optimization. The equilibrium procedure of solvation SMD was applied for all optimizations.

This computational approach was lately introduced in the scope of photoinduced intramolecular ET processes in photocatalysis^38,58,77 as well as to assess the competitive energy and electron transfer processes in light-harvesting antennae.⁷⁸ 

Additionally, the electronic couplings were obtained based on the GMH method as well as with the fragment charge difference (FCD) approach, which are widely applied to study intermolecular and intramolecular electron transfer processes.^79–84 These simulations were performed at the B3LYP/def2-SVP level of theory using Q-Chem.⁸⁵ Solvent effects (CH₂Cl₂) were taken into account using the conductor-like polarizable continuum model.

Section III A addresses the light-driven processes for the present set of Ru(II)-based triads as predicted at the (scalar-relativistic) time-dependent density functional level of theory (SR-TDDFT). Initially, structural and electronic properties within the Franck–Condon point as well as the nature of the electronic transitions underlying the UV–vis absorption bands are carefully evaluated and compared with respect to the substitution pattern. Furthermore, multiconfigurational simulations—based on the restricted active space self-consistent field methodology—were utilized to benchmark the cost-efficient TDDFT simulations. Subsequently, the population transfer channels among the optical accessible excited singlet states and energetically close-lying triplet states are identified. Finally, the kinetics of the photoinduced electron transfer processes, populating the (long-lived) charge-separated species, are simulated within the semi-classical Marcus picture. These simulations assess the charge separation efficiency of excited states governed by the thermodynamical properties and the electronic coupling of the involved donor and acceptor states.

Initially, the Franck–Condon photophysics of the Ru(II) complex RuH, Fig. 1(b), were carefully evaluated using TDDFT as well as by means of multiconfigurational simulations. Figure 2 shows the experimental electronic absorption spectrum in CH₂Cl₂ alongside the simulated spectra obtained by spin-free (SF-)TDDFT as well as by means of SR-TDDFT using the B3LYP hybrid functional.

In the case of the spin-free simulations as performed using Gaussian 16,⁴¹ the visible region of the electronic absorption spectrum of RuH is dominated by a low-lying and strongly dipole-allowed ILCT excitation at 2.13 eV (S₁ at 582 nm) as well as by a set of MLCT transitions. Excitation into the MLCT states S₉, S₁₁, and S₁₂ (at 2.71, 2.85, and 2.86 eV; and 457, 435, and 343 nm, respectively) leads to a population transfer from the t_2g orbitals (d_xy, d_xz, and d_yz) into the low-lying $πtpy*$ orbitals of both coordinating terpyridyl ligands, while S₁₆ (3.20 eV; 395 nm) is of mixed ILCT/MLCT character and localizes its excited electron density primarily on the PTZ-tpy ligand. Consistently, the spin–orbit (SO) picture provided by SR-TDDFT reveals one low-lying ILCT transition (into SO₁₀) at 2.21 eV (561 nm), which is mainly of ¹ILCT (S₁) character with slight ³ILCT, ³MLCT, and ³LLCT contributions associated with T₃ and T₄ within the spin-free picture, see Table I.

The higher-lying spin–orbit states SO₄₉, and SO₅₂ and SO₅₃ are of MLCT nature and feature an increased ratio of triplet character. These MLCT transitions can be related to the three MLCT transitions obtained using spin-free TDDFT involving both tpy ligands (S₉, S₁₁, and S₁₂). Finally, SO₇₅ at 3.21 eV (387 nm) is almost entirely of singlet character and represents the formerly discussed mixed ILCT/MLCT transition into S₁₆. Thus, spin-free and scalar-relativistic TDDFT simulations draw a consistent picture. Both methods predict a dipole-allowed low-lying ILCT transition at ∼570 nm as well as several optically active MLCT transitions in the range between 470 and 390 nm. However, the absorption band of the experimental UV–vis spectrum is centered at ∼500 nm. Therefore, the TDDFT results are at first glance not in good agreement with the experimental reference. A closer look into the experimental data reveals a weakly absorbing shoulder at ∼450 nm—in agreement with the MLCT band of the [Ru(tpy)₂]²⁺ parent compound.^86,87 Therefore, the main absorption band of RuH at roughly 500 nm cannot stem exclusively from MLCT_tpy transitions. In agreement with the low-lying and optically allowed ILCT (π_PTZ/$πtpy*$⁠) and higher-lying MLCT_tpy excitations, the resonance Raman data show a decrease in Raman intensity of PTZ-related vibrational modes from 515 to 476 nm and further decrease with 458 nm excitation, while characteristic tpy modes are observed at all three excitation wavelengths.³⁷ The energetic order of ILCT and MLCT transitions was also confirmed by employing the double-hybrid functional SOS-wPBEPP86,⁵⁹ which also predicts the ILCT state well below the MLCT states of interest, see Fig. S1(a). Unfortunately, all excitation energies are hypsochromically shifted with respect to the experimental data. Finally, the presence of the ILCT state in addition to the MLCT states was confirmed by the restricted active space self-consistent field (RASSCF) method employing a restricted active space (RAS) of (26,2,2;9,6,7), which leads to a multiconfigurational space spanning over almost 700 000 configuration state functions (CSFs), see Fig. 3.

The performed state-average procedure takes the nine lowest singlet roots into account and yields two dipole-allowed MLCT excitations (f = 0.905 and 0.084), the one optical accessible ILCT transition of interest (f = 0.146) as well as the singlet ground state and five (mostly) inaccessible states (four MLCTs and one LLCT; f ≈ 0). It is noteworthy that RASSCF predicts the ILCT with 4.36 eV at a higher excitation energy than the accessible MLCT states at 2.70, 2.97, 3.01, and 4.05 eV, respectively, (Table S5). However, based on the constructed active space, the MLCT states are better described than the ILCT state as merely one π_PTZ orbital is set to the RAS2 subspace. In general, the RASSCF energies are overestimated with respect to the experimental data as well as the TDDFT results. This deviation is not surprising and can be ascribed to the lack of dynamic electron correlation in RASSCF. The dynamic electron correlation can be included upon applying second-order perturbation theory on the RASSCF reference wavefunction (i.e., RASPT2). Unfortunately, multistate RASPT2 calculations could not be performed for the present transition metal complex due to their enormous computational demand. Furthermore, solvent effects were not included in the multiconfigurational simulations. Detailed information regarding the setup of the multiconfigurational simulations as well as regarding the composition of the active space is presented in Sec. II.

In summary, the computational results draw a conclusive picture. The Franck–Condon photophysics of RuH are dominated by one low-lying ILCT transition (⁠$πPTZ/πtpy*$⁠) as well as by several slightly higher-lying MLCT transitions populating $πtpy*$ orbitals of both terpyridyl ligands.

Finally, the population transfer from the excited singlet states to the triplet manifold upon intersystem crossing (ISC) was exemplarily evaluated for RuH by means of SR-TDDFT—employing the scalar-relativistic zeroth-order regular approximation (SR-ZORA).⁸⁸ The electronic absorption spectrum as obtained by SR-TDDFT is visualized in Fig. 2. As reflected by the composition of the SO transitions discussed above (Table I), the ¹ILCT state (S₁) is weakly coupled to the triplet states T₃ (78 cm⁻¹) and T₄ (63 cm⁻¹), which are of mixed ³LLCT/³MLCT and ³ILCT/³MLCT character, respectively. Even smaller spin–orbit couplings (SOCs) are predicted with the higher-lying MLCT states T₁₄ (12 cm⁻¹), T₁₅ (18 cm⁻¹), and T₁₆ (8 cm⁻¹). However, significantly stronger SOCs are calculated between the ¹MLCT states (S₉, S₁₀, S₁₁, and S₁₇) and the energetically close-lying triplet states, i.e., triplet states of pronounced ³MLCT nature. Of particular interest is the interaction between the strongly dipole-allowed and pure ¹MLCT transition (see Orca S₁₁ and Gaussian S₁₂ in Table I) and the energetically close triplet states. SR-TDDFT yields SOCs of 216 and 242 cm⁻¹ between this ¹MLCT and the ³MLCT states T₁₄ and T₁₅. Considerably smaller SOCs are observed among the ¹MLCT states and triplet states of dominant ³ILCT or ³LLCT (i.e., T₃ or T₄) character, see Table II for details. These findings agree with previous theoretical studies and show that an efficient singlet-to-triplet population transfer is only possible along ^1/3MLCT gateway states.^{23,33–35,89}

Upon thoroughly investigating the Franck–Condon photophysics of the RuH parent compound, the TDDFT-based computational protocol was adapted to unravel the nature of electronic transitions underlying the electronic absorption bands of RuPh, RuTol, RuAn, and RuC₆₀ in the visible and UV regions. In agreement with the experimental data, the simulated UV–vis absorption spectra of RuPh, RuTol, and RuAn closely resemble the spectrum of the unsubstituted RuH species as predicted by TD-B3LYP, see Figs. S2(a)–S2(c) and Tables S1–S3. The ¹ILCT excitation is consistently predicted to occur in the narrow range between 2.13 and 2.15 eV. This is not surprising as the structural modification is localized at the other terpyridyl ligand. In a similar fashion, the energic positions of these ¹MLCT states are barely affected by the structural modification. In the case of RuC₆₀, the ILCT excitation is split into two transitions (i.e., S₇ and S₈ at 2.12 and 2.13 eV) due to mixing with an LLCT state from the 10-methylphenothiazinyl moiety to the electron withdrawing fullerene, see Table S4. Likewise, the MLCT properties of RuC₆₀ are slightly altered by the impact of $πC60*$ orbitals. However, all five complexes feature a low-lying ILCT absorption band and a higher-lying MLCT band in a consistent manner, which was further confirmed by applying the SOS-wPBEPP86 double-hybrid functional (Fig. S1).

Later discussion will focus on the electron transfer pathways available upon ISC for RuH, RuPh, RuTol, and RuAn. Due to the influence of the fullerene moiety on the electronic structure of RuC₆₀, the predicted excited state relaxation pathways and electron transfer kinetics are addressed separately for RuC₆₀.

In the following, we investigate the excited state relaxation for the five push–pull triads RuR by means of quantum chemical simulations. Herein, we focus on the ET branching channels from the lowest energy ³MLCT state (accessible upon ISC, see Sec. III A) to the ³LLCT as well as to the ³ILCT state. A previous experimental investigation based on excited state spectroscopy and electrochemistry revealed similar thermodynamic properties, i.e., driving forces (ΔG) and reorganization energies (λ) regarding electron transfer from a ³MLCT donor state to a ligand-based acceptor state for the series of compounds.³⁷ Experimental evidence also suggests that the introduced substitution pattern allows the electronic coupling (V_DA) to be remotely controlled for the given pairs of donor and acceptor states in RuR. The kinetics of the underlying ET processes are also addressed quantum chemically. Hence, our approach yields driving forces, reorganization energies, and electronic couplings based on our lately introduced computational protocol to predict (light-driven) intramolecular charge transfer phenomena in the semi-classical Marcus picture.^38–40 In order to achieve this, the respective ³MLCT donor state (D) and the ligand-based acceptor states (A; ³LLCT and ³ILCT) are fully relaxed at the TDDFT level of theory. Subsequently, a linear-interpolated internal coordinate (R_ET) is constructed to connect ³MLCT equilibria with the respective ³LLCT and ³ILCT structures. Potential energy curves (PECs) are simulated along these efficient coordinates for the states of interest. Subsequently, our lately introduced external optimizer pysisyphus—also aware of excited states—was applied.⁷⁴ The diabatization factors were obtained based on the generalized Mulliken–Hush (GMH)⁹⁰ method within the crossing region of two diabatic states. Finally, electronic couplings are calculated via the GMH and fragment charge difference (FCD)⁹¹ approaches as well as by virtue of the minimum energy splitting between the involved adiabatic states. Further information on the computational protocol is collected in Sec. II.

All investigated dyes show only a minor structural rearrangement upon relaxation into the ³MLCT donor state equilibrium from the Franck–Condon point. More pronounced structural changes occur upon ³LLCT optimization. As illustrated for RuH in Fig. 4(a), structural relaxation mainly involves the PTZ donor moiety. This is attributed to the photooxidation of this group, which leads to partial planarization in the vicinity of the nitrogen atom due to the decreased sp³ character. In a similar fashion, structural equilibration of the ³ILCT state mainly involves partial planarization of the PTZ group, see Fig. 5(a). All optimized and interpolated structures are available from the online repository Zenodo via Ref. 76.

Finally, the ET kinetics from the ³MLCT donor to the ³LLCT acceptor states were evaluated within the semi-classical Marcus picture for the given set of Ru(II)-based compounds. In the case of the parent compound RuH, a driving force of −0.09 eV is obtained. Very similar reorganization energies of 0.35 and 0.37 eV are predicted for the donor and acceptor states (λ_D and λ_A), respectively, which yields an average reorganization energy (λ_AVG) of 0.36 eV; see Table III.

The almost identical reorganization energies indicate that the parabolic diabatic PECs of D and A possess curvatures that are a near perfect match. Hence, the PECs are merely displaced along R_ET and offset in energy, making the applied LIIC a suitable reaction coordinate within the Marcus picture. In addition, similar values of λ_AVG are obtained for the structurally modified triads RuPh (0.28 eV), RuTol (0.38 eV), and RuAn (0.38 eV). However, a slight systematic decrease in ΔG is predicted with increasing electron donating character of the applied substitution pattern at the tpy acceptor ligand. While the ³MLCT–³LLCT electron transfer is still slightly exergonic, (ΔG = −0.03 eV) for RuPh, the driving force is further decreased to +0.03 and +0.08 eV in the case of RuTol and RuAn, respectively. In general, this range of driving forces ([-0.09 eV; +0.08 eV]) suggests an equilibrium between the two states. In the case of RuC₆₀, the predicted driving force of −0.44 eV is significantly stronger in comparison to the other systems. This is accompanied by an increase in reorganization energy to roughly 0.46 eV. As mentioned previously, these changes in thermodynamic properties are related to a pronounced mixing of the ³LLCT state (into $πtpy*$⁠) of interest with a charge transfer to the electron accepting fullerene (⁠$πC60*$⁠), see Fig. 4(f).

In addition to ΔG and λ, the electron transfer processes are governed by electronic communication between the involved diabatic states described by electronic coupling (V_DA). As shown previously by means of excited state spectroscopy, the applied substitution pattern at the acceptor tpy ligand allows one to remotely control the magnitude of V_DA, yielding couplings of 1.17 × 10⁻², 1.12 × 10⁻², 9.17 × 10⁻³, and 4.60 × 10⁻² eV for RuH, RuPh, RuTol, and RuAn, respectively. In the case of RuC₆₀, an electronic coupling of 1.95 × 10⁻² eV was determined.³⁷ Computationally, V_DA was obtained for the present set of Ru(II)-based dyes by virtue of the GMH and the FCD approaches, see Eqs. (3)–(5) in Sec. II. Both methods allow the calculation of V_DA via the gap between the adiabatic states and by means of the diabatization factor. The diabatization factor is defined for the states of interest either by permanent and transition dipoles (GMH) or by charge distribution (FCD). Figures 4(b)–4(f) depict the diabatization factors in the vicinity of the crossing region along R_ET. Again, the symmetric shape of the calculated diabatization factors suggests that the LIIC is a suitable coordinate to study the present ET reaction. As expected, the largest values (close to 1) are obtained if both states are quasi-degenerate and a mixing angle (θ) of ∼45° is obtained. Therefore, the electronic coupling at this geometry is governed almost entirely by the energy splitting of the respective adiabatic states [Eq. (6)]. Based on the performed TDDFT simulations and in combination with the GMH methodology, small electronic coupling values of merely 4.5 × 10⁻⁴, 4.5 × 10⁻⁴, 7.5 × 10⁻⁴, 11.5 × 10⁻⁴, and 10.5 × 10⁻⁴ eV are determined for RuH, RuPh, RuTol, RuAn, and RuC₆₀, respectively, see Table III. Numerically identical values were calculated based on the FCD approach (Table S11). The magnitude of V_DA indicates a weak interaction between the ³MLCT donor and the ³LLCT acceptor states, which is attributed to the large distance between the involved redox centers. In agreement with the experimental data, the strongest couplings are predicted for RuAn and RuC₆₀, while RuH, RuPh, and RuTol feature rather similar V_DA values. However, the theoretically derived electronic couplings are more than one order of magnitude smaller than the experimental values.

Finally, the rate constants for electron transfer from the ³MLCT donor state to the ³LLCT acceptor state were calculated within the Marcus picture based on ΔG, λ_AVG, and V_DA (Table III). In the case of RuH, a rate constant of 6.71 × 10⁸ s⁻¹ is obtained at the TDDFT level of theory. The magnitude of k indicates a medium–fast ET processes in the case of Ru(II)-polypyridyl-based complexes. For comparison, slightly lower rates of ∼10⁷ s⁻¹ are predicted for ³MLCT via triplet metal-centered (³MC) states in Ru(II)-based photocatalysts,⁴⁰ while much faster ET kinetics of up to ∼10¹³ s⁻¹ have been reported for ³MLCT to ³MMCT (metal-to-metal charge transfer) processes in Ru(II)–Co(III)-based dyads.³⁸ While the driving force slightly decreases from RuH to RuPh, RuTol, and RuAn, no significant differences are observed for the reorganization energy and electronic coupling. As a result, the ET rates decrease from RuH (6.71 × 10⁸ s⁻¹) to 5.77 × 10⁸, 1.31 × 10⁸, 8.87 × 10⁷ s⁻¹ for RuPh, RuTol, and RuAn, respectively. In the case of RuC₆₀, the ET kinetics are faster by two orders of magnitude (2.80 × 10¹⁰ s⁻¹), which is mainly a consequence of the more favorable driving force (recall the influence of the $πC60*$ orbitals). Experimentally, all ET rates were determined to be in the order of magnitude of 10¹¹ s⁻¹ (Table III). In agreement with the simulated data for the ³MLCT–³LLCT channel, the fastest rate was observed for RuC₆₀. However, in contrast to the computational results, this enhanced rate constant was associated with an increased electronic coupling and not with a larger driving force.

The calculated potential energy curves, electronic couplings, and therefore the ET rates are subject to deviations in the TDDFT-predicted excitation energies as obtained by singlet–triplet transitions. Therefore, the PECs and electronic couplings have been evaluated also based on the Tamm–Dancoff approximation (TDA). However, the TDA results are qualitatively identical to the TDDFT results for the present systems, see the supplementary material and Table 12 for details.

In an analogous manner to that described above for the ³MLCT–³LLCT relaxation pathway, we investigated the second excited state relaxation channel that is available from the ³MLCT donor state, i.e., to a ³ILCT acceptor state, see Fig. 5.

In the case of the ³MLCT–³ILCT pathway, only minor changes of the driving force are observed for all five Ru(II) complexes, see Table III. The largest ΔG was obtained for RuH (−0.33 eV), decreasing to −0.24 eV for RuPh and RuTol, and finally to −0.21 eV for RuAn. Once again, the more favorable driving force for RuC₆₀ (−0.30 eV) results from the contribution of $πC60*$ orbitals. Likewise, almost identical reorganization energies spanning merely the range from 0.41 to 0.46 eV were predicted at the TDDFT level of theory along the reaction coordinate. The electronic couplings, as obtained by means of the GMH method, were calculated in the crossing region of the diabatic donor (³MLCT) and acceptor (³ILCT) states. The respective diabatization factors are illustrated in Figs. 5(b)–5(f). For this pair of redox states, the simulated V_DA values are ∼1.5 orders of magnitude larger than for ³MLCT–³LLCT pathway(s) as the involved redox centers are relatively close. In the case of RuH, a coupling of 1.29 × 10⁻² eV was obtained, which is in very good agreement with the experimentally derived V_DA of 1.17 × 10⁻² eV. However, a pronounced impact of the substitution pattern—as seen by time-resolved experimental spectroscopic techniques—was not observed. In fact, the quantum chemical simulations yield almost identical electronic couplings for RuPh (1.29 × 10⁻² eV), RuTol (1.26 × 10⁻² eV), and RuAn (1.27 × 10⁻² eV). Only in the case of the fullerene substituted dye, a slightly smaller value, i.e., 1.05 × 10⁻² eV, was calculated. Again, this finding can be explained by the contribution of $πC60*$ orbitals, which reduces the overlap of the respective wavefunctions. Due to favorable driving forces and larger electronic couplings, the ET kinetics along the ³MLCT–³ILCT pathway (∼10¹² s⁻¹, Table III) are by approximately four orders of magnitude faster than the ET kinetics of the previously discussed ³MLCT–³LLCT channel. Therefore, the TDDFT-predicted ET rates along the ³MLCT–³ILCT cascade are in general in good agreement with the experimental rate constants as obtained by time-resolved spectroscopy (∼10¹¹ s⁻¹, Table III). However, the marginal variation of simulated V_DA values along the series of compounds does not allow one to rationalize the trend of ET rates as observed experimentally.

Finally, the performed quantum chemical simulations map the competitive excited state relaxation cascades as visualized in Fig. 6 for RuH.

The initial photoexcitation in the visible spectral region leads to the population of ¹ILCT (S₁) as well as ¹MLCT (S₉, S₁₁, and S₁₂) excited states. Subsequently, efficient ISC occurs from the ¹MLCT states to the energetically close-lying ³MLCT states, provided by the substantial SOC. Afterward, internal conversion to the lowest energy ³MLCT state follows; see T₂ in Fig. 6(b). Finally, fast ET (4 × 10¹² s⁻¹) from the equilibrated ³MLCT donor state (T₂) to the ³ILCT acceptor state (T₁) is simulated based on semi-classical Marcus theory, while et along the ³MLCT–³LLCT pathway is approximately four orders of magnitude slower (7 × 10⁸ s⁻¹). In good agreement with the theoretically predicted fast ³MLCT–³ILCT conversion, time-resolved absorption studies yielded a slightly slower rate constant of ∼2 × 10¹¹ s⁻¹ for the ET from the ³MLCT donor state to the ligand-based acceptor state.

Therefore, the performed quantum chemical simulations highlight the importance of the ILCT transition involved in the initial light-activation and also in the (triplet) excited state relaxation cascade.

In the present quantum chemical study, a series of five Ru(II)-based photoactive complexes incorporating a 10-methylphenothiazinyl electron donating moiety (RuH, RuPh, RuTol, RuAn, and RuC₆₀) were investigated with respect to their excited state properties and relaxation cascades. The strategy of combining inorganic and organic chromophores thereby allows for the localization of the excited electron density away from metal center. As a result, efficient ISC as well as—upon further excited state relaxation—the population of a long-lived triplet state on the organic chromophore are achieved. In particular, the focus was on addressing the impact of the substitution pattern at the electron accepting terpyridyl ligand. The Franck–Condon photophysics of the parent compound, RuH, were thoroughly investigated using time-dependent density functional theory as well as multiconfigurational simulations. These calculations consistently predict a strongly dipole-allowed low-energy ILCT transition to be involved in light-harvesting in addition to higher-lying MLCT transitions. However, scalar-relativistic TDDFT clearly reveals that the subsequent intersystem crossing from accessible singlet states to the triplet manifold proceeds almost exclusively via ^1/3MLCT gateway states. In agreement with previous experimental investigations, the substitution pattern at the accepting terpyridyl ligand has a marginal impact on the Franck–Condon photophysics. However, introduction of the fullerene leads to a pronounced contribution of $πC60*$ orbitals to electronic transitions.

Subsequently, the electron transfer kinetics of thermally equilibrated lowest-lying ³MLCT (donor) state to the ³LLCT (acceptor) state vs ET to the ³ILCT (acceptor) state were investigated within the semi-classical Marcus picture along a linear-interpolated internal coordinate—connecting the optimized equilibrium structures of the donor and acceptor states. The performed simulations reveal a slow ET from the ³MLCT to the ³LLCT state, which is rationalized by the small driving forces in the range of −0.09 to +0.09 eV and the minor electronic coupling between these states (∼10⁻⁴ eV). Contrastingly, the favorable ΔG ([−0.3 eV: −0.2 eV]) and V_DA values (∼10⁻² eV) for ³MLCT–³ILCT process lead to fast ET processes along this pathway. Thus, the theoretical results clearly reveal that charge separation occurs on the PTZ-substituted terpyridine ligand. Only in the case of RuC₆₀ competitive charge separation processes might take place as the population of the ³ILCT state is only two orders of magnitude slower than the population of the ³LLCT state.

On the one hand, the performed quantum chemical simulations could rationalize—in agreement with previous experimental studies—a pronounced effect and trend of the substitution pattern on the underlying electronic coupling along the ³MLCT–³LLCT channel, the absolute value of these couplings deviates by more than one order of magnitude. On the other hand, the absolute values of the coupling along the ³MLCT–³ILCT pathway were determined to be independent with respect to structural modifications, yet in magnitude, they were in excellent agreement with the experimental observations, i.e., for RuH 1.29 × 10⁻² eV (theory) vs 1.17 × 10⁻² eV (experiment). We speculate that the measured remote control effect of the structural substitution pattern on the electronic coupling might originate from interference effects between the involved excited states, in particular between the ³MLCT, the ³LLCT, and the ³ILCT states.

Future computational studies will elaborate on different methods to approximate the reaction coordinate in the excited state. Furthermore, we will evaluate such possible interference effects between these three states of interest (³MLCT, ³LLCT, and ³ILCT) using dissipative quantum dynamics simulations that also allow description of superexchange phenomena and incomplete population transfer. Furthermore, the capability to tune electron transfer processes by virtue of the underlying electronic coupling will be explored for structurally closely related systems in a joint synthetic–spectroscopic–theoretical fashion.

See the supplementary material for details on spin-free and spin–orbit states contributing to the Franck–Condon photophysics of all complexes, multiconfigurational simulations, and electron transfer kinetics as obtain using the Tamm-Dancoff approximation.

Dedicated to Professor Wolfgang Weigand on the occasion of his 65th birthday.

We thank Philipp Traber for scientific discussions. Financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Projektnummers 456209398 and 448713509 as well as Projektnummer 364549901, TRR 234 [A1 and A4]—is gratefully acknowledged. All calculations were performed at the Universitätsrechenzentrum of the Friedrich-Schiller-University Jena.

The authors have no conflicts to disclose.

S.K. and B.D.-I. performed the conceptualization and the project-administration. G.Y. and C.Z. performed quantum chemical simulations. G.Y. and S.K. prepared the figures, the writing of the original draft was performed by G.Y., G.E.S., and S.K. All authors contributed to the writing by reviewing and editing of the original draft.

Guangjun Yang: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Georgina E. Shillito: Conceptualization (supporting); Formal analysis (equal); Supervision (supporting); Visualization (supporting); Writing – original draft (lead); Writing – review & editing (equal). Clara Zens: Conceptualization (supporting); Data curation (equal); Formal analysis (equal); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (equal). Benjamin Dietzek-Ivanšić: Conceptualization (lead); Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (lead). Stephan Kupfer: Conceptualization (lead); Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead); Visualization (equal); Writing – original draft (lead); Writing – review & editing (lead).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request. The data that support the findings of this study are openly available in Zenodo, Ref. 76.