Ultrafast photophysics of para-substituted 2,5-bis(arylethynyl) rhodacyclopentadienes: thermally activated intersystem crossing

Abstract

2,5-Bis(phenylethynyl) rhodacyclopentadienes (RCPDs), as a type of Rh(III) complex, exhibit unusually intense fluorescence and slow intersystem crossing (ISC) due to weak metal–ligand interactions. However, details on their ultrafast photophysics and ISC dynamics are limited. In this work, electronic relaxation upon photoexcitation of two substituted RCPDs with two –CO₂Me (A-RC-A) or –NMe₂/–CO₂Me (D-RC-A) end groups are comprehensively investigated using femtosecond transient absorption spectroscopy and theoretical analysis. Upon ultraviolet and visible excitation, dephasing of vibrational coherence, charge transfer, conformation relaxation, and ISC are observed experimentally. By calculating the spin–orbit coupling, reorganization energy, and adiabatic energy gap of plausible ISC channels, semi-classical Marcus theory revealed the dominance of thermally activated ISC (S₁ → T₂) for both D-RC-A and A-RC-A, while S₁ → T₁ channels are largely blocked due to high ISC barriers. With weak spin–orbit coupling, such differences in plausible ISC channels are predominately tuned by energetic parameters. Singlet oxygen sensitization studies of A-RC-A provide additional insight into the excited-state behavior of this complex.

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Introduction

Organometallic complexes have attracted attention for a wide range of applications in photocatalysis,^1–5 bioimaging,^6–8 sensing,^9,10 and organic light-emitting diode (OLED) devices.^11–14 The spin-forbidden nature of the singlet–triplet transition often leads to slow intersystem crossing (ISC) in organic systems. However, by incorporating heavy transition metals, the ISC rate constant (k_ISC) can be significantly increased to typically greater than 10¹⁰ s⁻¹,¹⁵ even up to 10¹³–10¹⁴ s⁻¹ in Ru(II) complexes,^16–19 leading to significant fluorescence quenching and enhanced phosphorescence emission. Efficient ISC can be primarily attributed to strong spin–orbit coupling (SOC) due to participation of the d-orbitals of heavy metals, which can significantly alter the photophysics due to strong metal–ligand interactions via metal-to-ligand charge transfer (MLCT) states that dominate electronic relaxation.^20–24

Unlike complexes with ultrafast ISC, 2,5-bis(phenylethynyl) rhodacyclopentadienes (RCPDs)^25–27 incorporating Rh(III) exhibit up to 69% fluorescence quantum yields (Φ_f) with k_ISC = 10⁷–10⁸ s⁻¹ which is several orders of magnitude slower than that in Ru(II) complexes.¹⁷ Intriguingly, by replacing Rh(III) with much heavier Ir(III), the corresponding iridacyclopentadienes²⁸ are still highly fluorescent. Such photophysics was attributed to weakened SOC due to low d-orbital participation in the frontier orbitals and an enlarged S₁–T₁ energy gap (ΔE_ST).^28,29 Meanwhile, the T₂ state was reported to be an ISC destination through a thermally activated mechanism in RCPDs,²⁸ which increased the complexity of their electronic relaxation. Investigations indicated that the fluorescence properties of RCPDs can be effectively tuned by introducing an electron donor (D) or acceptor (A) at the para-positions of the arylethynyl groups.^28,30,31 In particular, symmetric substitution with A/A groups (–CO₂Me or –BMes₂) (Mes = mesityl = 2,4,6-Me₃C₆H₂) at the para-positions leads to significantly higher Φ_f than corresponding D/A (–NMe₂/–CO₂Me) and unsubstituted RCPDs (see Table S1†). In a simple excited-state model, enhanced fluorescence emission can be attributed either to slow non-radiative relaxation of the S₁ state via dark states or suppressed ISC to the triplet state.^32,33 Although k_ISC of RCPDs was determined to be 10⁷–10⁸ s⁻¹ using picosecond time-resolved infrared spectroscopy,³⁰ a full picture of their S₁ relaxation remains unclear. Therefore, a comprehensive picture of the photophysics of RCPDs with weak metal–ligand interactions might be helpful for future rational design of fluorescent emitters.

In general, the ISC rate constant k_ISC between singlet (S_m, m ≥ 1) and triplet (T_n, n ≥ 1) excited states can be expressed via the Fermi golden rule,^34,35

in which k_ISC is determined by the SOC matrix element 〈S_m|Ĥ_SO|T_n〉, as well as the Franck–Condon-weighted density of states ρ_FC, which can be described in the framework of Marcus–Levich–Jortner theory:^36–39In a semi-classical approximation at high temperature T, with ℏω_eff ≪ k_BT, the Huang–Rhys factor (S) and effective frequency (ω_eff) of internal vibrational modes can be ignored. The density ρ_FC follows the standard Arrhenius-type equation and k_ISC can be obtained from the Marcus-theory equation:^40–43Here, 〈S_m|Ĥ_SO|T_n〉 describes the SOC matrix element,^44,45 while Γ and ΔE_ST represent the reorganization energy and adiabatic energy gap of the ISC (S_m → T_n, m, n ≥ 1) transition, respectively. Eqn (3) has been widely employed for estimating ISC and reverse ISC rates in medium-size organic molecules and complexes.^46–49

In cases of ultrafast ISC (k_ISC > 10¹² s⁻¹) of complexes with late transition metals, extremely high k_ISC is observed due to a large coupling term 〈S_m|Ĥ_SO|T_n〉 up to several thousands of cm⁻¹, which greatly amplifies the ISC rate associated with the ISC barrier (E_a) determined by Γ and ΔE_ST. However, RCPDs exhibit much slower ISC (k_ISC = 10⁸–10⁹ s⁻¹) due to the lack of strong metal–ligand interactions,³⁰i.e., 〈S_m|Ĥ_SO|T_n〉 in eqn (3) is expected to be small and relatively sensitive to para-substitution on the aryl ligand. It is hypothesized that the k_ISC may vary significantly with the reorganization energy and adiabatic energy gap subject to para-substitution, which determine the ISC barrier (E_a) thermodynamically and can be discussed within the framework of Marcus theory.

In this work, two para-substituted 2,5- bis(arylethynyl)rhodacyclopentadiene complexes (Scheme 1) were investigated by using excitation-wavelength-(λ_ex-)dependent femtosecond transient absorption (fs-TA) measurements and time-dependent density-functional theory (TD-DFT) calculations. Compared with A-RC-A (τ_S1 = 1.7 ns) substituted with two –CO₂Me groups, the D-RC-A with –CO₂Me/–NMe₂ substitution exhibits a shorter (τ_S1 = 0.8 ns) lifetime of the S₁ state in toluene solution.³¹ By resolving fs-TA data upon ultraviolet (UV) and visible excitation, the electronic relaxation channels of D-RC-A and A-RC-A are largely revealed. Moreover, by applying semi-classical Marcus theory, we determine that ISC of both D-RC-A and A-RC-A rely on a thermally activated S₁ → T₂ transition rather than the channel that directly populates the T₁ state. We also report studies of singlet oxygen, O₂(a¹Δ_g), sensitization by A-RC-A, which provides additional insight into the excited-state behavior of this complex.

Scheme 1 Chemical structures of investigated D-RC-A and A-RC-A. The Rh(III)–ligand core is illustrated in black while the peripheral groups are in gray. The phosphine ligand is PMe₃.

Results and discussion

Static absorption spectra

The static absorption spectra of D-RC-A and A-RC-A in THF are displayed in Fig. 1 along with the calculated vertical excitation energies and oscillator strengths, while the corresponding calculation results are listed in Table S2.† Note that the oscillator strength (f) here is not referenced to the transition probability for a freely oscillating electron in a single atom, but reflects only the transition dipole moment and the energy gap between two states of the RCPDs. For both D-RC-A and A-RC-A, the pronounced absorption in the 450–550 nm region can be attributed to the S₁ excited state, while higher singlet (S_m, m > 1) states comprise the intense absorption in the UV region. As a result, upon visible (λ_ex = 513 nm) and UV (λ_ex = 295 nm) optical excitation, direct population of the S₁ and S_m states can be expected in fs-TA experiments, as described in detail below.

Fig. 1 (a and b) Static UV/visible absorption spectra of D-RC-A ((a), blue) and A-RC-A ((b), red) in THF solution (10⁻⁵ mol L⁻¹), overlapped with spectra of UV (violet shaded) and visible (green shaded) excitation pulses employed in the fs-TA experiments. (c and d) TD-DFT-calculated vertical excitation energies and oscillator strengths of D-RC-A (c) and A-RC-A (d).

The observed S₁ band of D-RC-A exhibits less pronounced vibronic progression than that of A-RC-A. Reduced vibronic progression might be attributed to stronger solute–solvent interaction due to excited-state charge transfer (CT) between substituted D and A groups, which was confirmed by natural transition orbital (NTO) analysis of the S₁ state of both RCPDs. As illustrated in Fig. S1,† A-RC-A exhibits a symmetric distribution of both hole and electron density in the S₁ state, indicating its locally excited (LE) nature. However, clear CT character is observed in the S₁ state NTOs of D-RC-A, i.e., hole and electron density are asymmetrically distributed on D and A sides, respectively. A different S₁ character (CT or LE) of D-RC-A and A-RC-A can also affect the corresponding S₁ relaxation. The initially populated S₁ state undergoes rapid decay leading to the relaxed CT state, which is observed in the fs-TA signal of D-RC-A and absent for A-RC-A. Furthermore, NTO analysis on the triplet states indicates that the T₁ of D-RC-A is slightly mixed with CT character like the S₁ state, while the corresponding T₂ state and T₁/T₂ states of A-RC-A are all LE dominated.

On the other hand, NTO analysis indicates that the central Rh(III) in D-RC-A and A-RC-A is barely involved in the S₀ → S₁, S₀ → T₁, and S₀ → T₂ transitions, which is consistent with previous reports on electronic transitions of RCPDs,^28,31i.e., the low-lying S₁, T₁, and T₂ states of RCPDs are dominated by π–π* transitions of ligands with minimal contributions of Rh(III). The photophysics indicates the weak SOC of RCPDs, which is consistent with previous reports.^{25–28,30,31} Without pronounced metal–ligand interaction, ISC dynamics of RCPDs are largely determined by energetic parameters (Γ and ΔE_ST) and can thus be discussed in the framework of semi-classical Marcus theory.

Excitation-wavelength-dependent fs-TA

To acquire a full picture of electronic relaxation of RCPDs, we performed fs-TA experiments on D-RC-A and A-RC-A upon excitation by either UV (λ_ex = 295 nm) or visible (λ_ex = 513 nm) laser pulses as previously reported.⁵⁰ The resulting TA signal in the probe range of λ_pr = 320–670 nm was recorded for delay times up to Δt = 3.8 ns and are displayed in Fig. 2.

Fig. 2 Spectro-temporal maps of λ_ex-dependent fs-TA signals of D-RC-A upon UV (a) and visible (b) excitation as well as of A-RC-A upon identical UV (c) and visible (d) excitation. The spectral signatures of ISC-generated triplet states are highlighted by white dashed lines.

As shown in Fig. 2a and b, D-RC-A exhibits nearly identical fs-TA signals upon UV (λ_ex = 295 nm) and visible (λ_ex = 513 nm) excitation, respectively, in which at least three distinct bands can be distinguished. The negative band appears immediately after excitation in the λ_pr = 470–550 nm regime and agrees with the static absorption spectrum (S₀ → S₁), which can be attributed to the ground-state bleaching (GSB) signal. At the same time, two excited-state absorption (ESA) bands of the S₁ state appear in the λ_pr = 360–460 nm and >550 nm regimes which, subsequently, exhibit relaxation simultaneously with the decay of the GSB band. Meanwhile, slow formation of a new positive band is observed with a center at λ_pr = 580 nm, which is superimposed on the decay of the long-lived ESA band in the λ_pr > 550 nm region, probably corresponding to ESA of an ISC-generated triplet state. However, the final destination (T₁ or T₂) of the observed ISC process is difficult to identify by fs-TA data itself. Instead, ISC rates of S₁ → T₁ and S₁ → T₂ need to be calculated to assign the observed ISC process. Thus, we tentatively denote the triplet state generated as the T_n (n ≥ 1) state.

Unlike D-RC-A, A-RC-A exhibits λ_ex-dependent relaxation behavior. Upon UV excitation, a similar fs-TA signal as that for D-RC-A was recorded for A-RC-A, although the GSB displays a double peak at λ_pr = 500 nm and 535 nm, which is consistent with the pronounced vibronic progression exhibited in the static absorption spectrum. Meanwhile, triplet-state formation is also observed at λ_pr = 570 nm, with a substantially slower k_ISC than that of D-RC-A. As shown in Fig. S2,† preliminary fitting of triplet formation dynamics of D-RC-A (at λ_pr = 580 nm) and A-RC-A (at λ_pr = 570 nm) indicated that the observed ISC of D-RC-A (τ_ISC < 350 ps) is one order of magnitude faster than ISC of A-RC-A (τ_ISC > 3.5 ns). Thus, S₁ state relaxation of D-RC-A might be dominated by ISC as it is much faster than radiative and non-radiative S₁ → S₀ channels. In contrast, considering the observed fluorescence lifetime (∼1.7 ns), the radiative and non-radiative S₁ → S₀ decay of A-RC-A might be comparable with ISC to triplet states.

Intriguingly, upon visible excitation, the triplet band of A-RC-A is absent in the fs-TA data up to the maximum delay time (3.8 ns), while the decay of ESA bands and refilling of the GSB band are still observable. In general, upon UV excitation, rapid internal conversion (IC) from initially populated S_m states leads to a vibrationally hot S₁ state. Compared with the S₁ state directly populated by resonant visible excitation, excess vibrational energy of the S₁ state might be helpful to overcome the ISC barrier.^51–54 Therefore, we believe that the ISC barrier (E_a) for A-RC-A should be higher than that for D-RC-A, which is also indicated by a slower rise of the ISC band of A-RC-A compared to that of D-RC-A upon UV excitation.

Ultrafast electronic relaxation

To obtain details on the electronic relaxation of the RCPDs, we performed target analysis on the corresponding λ_ex-dependent fs-TA data. On ultrafast time scales, a sequential kinetic model including several independent species was employed for all fs-TA data, while a branched scheme was considered for the decay of the relaxed (CT and structural) S₁ state, corresponding to competition between relaxation to the S₀ state (S₁ → S₀) and ISC to triplet states (S₁ → T_n). As discussed above, S₁ relaxation of D-RC-A is dominated by the S₁ → T_n channel, for which the S₁ → S₀ channel was correspondingly ignored in target analysis (Fig. S3†). However, for A-RC-A upon UV excitation, both the S₁ → S₀ and S₁ → T_n channels were included in target analysis with a branch ratio of 0.5 (Fig. S3†). The extracted species-associated spectra (SAS) are displayed in Fig. 3, while the corresponding fitted time traces at selected λ_pr and the concentration evolution of each species can be found in Fig. S4 and S5,† respectively, in the ESI.†

Fig. 3 Target-analysis-extracted species-associated spectra (SAS) of λ_ex-dependent fs-TA signals of D-RC-A upon 295 nm UV (a) and 513 nm visible (b) optical excitation, as well as SAS of A-RC-A upon identical UV (c) and visible (d) excitation. Four or five independent species were employed to reproduce the fs-TA signals.

As mentioned above, D-RC-A exhibits similar relaxation dynamics upon UV and visible excitation. Upon UV excitation, the populated S_m states undergo rapid IC with a time constant of τ₁ = 206 fs to reach the Franck–Condon region of the S₁ state (S_m → S₁^FC), which is absent in the fs-TA data upon resonant visible excitation to the S₁ state. The subsequent SAS exhibits a spectral depletion in the range λ_pr = 570–670 nm, which is consistent with fluorescence spectra of D-RC-A and can be attributed to the stimulated emission (SE) band of the S₁ state. Pronounced solvatochromism of D-RC-A has been reported,³¹ implying CT character of the fluorescent bright state, which is also consistent with the NTO analysis mentioned above. Considering the observed SE signature in the SAS, we assigned the second SAS to the CT-relaxed S₁ state (noted as S₁^CT), corresponding to a local minimum on the S₁ potential energy surface (PES). Moreover, the fitted formation time of S₁^CT (S₁^FC → S₁^CT, ∼1 ps) is consistent with the reported formation time of the solvation-stabilized CT state of organic D–A-type chromophores in THF.^55,56

During the subsequent relaxation () with a ∼10 ps time constant, the SAS exhibit only minimal changes of spectral features, which might be explained by structural relaxation in the S₁ state. In order to obtain further details on S₁ relaxation, we calculated the optimized structures of both D-RC-A and A-RC-A in their S₁, T₁, and T₂ states to be compared with the S₀ structure. As shown in Fig. S6 and S7,† large S₀ → S₁ twisting is observed for the peripheral phenyl and D/A groups of RCPDs, which can be quantified by the calculated twisting angles listed in Table S3.† Apart from the twisting angles, contributions of S₀ → S₁ conformational relaxation can be generalized in reorganization energy (Γ^S₁→S₀).^57,58 By summing over contributions from each vibrational mode (Fig. S8†), Γ^S₁→S₀ of D-RC-A and A-RC-A were calculated to be 1519 cm⁻¹ and 1944 cm⁻¹, respectively. However, Γ^S₁→S₀ contributed by vibrational modes is not able to provide the relative contribution of each structural part of the RCPDs to conformational relaxation. Therefore, we further calculated the root-mean-square displacement (RMSD) in Cartesian coordinates of the optimized S₀ (x_i, y_i, z_i) and S₁ () state structures,

Summing over all atoms, i = 1, …, N. The calculation leads to RMSD^S₁/S₀ = 0.156 Å for D-RC-A which is lower than that for A-RC-A (0.207 Å), consistent with the calculated Γ^S₁→S₀. We further calculated the relative contributions of the peripheral groups (phenyls, C≡C, and D/A, gray part in Scheme 1) and Rh(III)–ligand core (black part in Scheme 1). For D-RC-A, the RMSD^S₁/S₀ was found to be dominated by twisting of the peripheral parts of the structure with ∼90% contribution. The rotational twisting around C–C single bonds has been widely reported to be nearly barrierless,^59,60 which is consistent with the observed efficient relaxation (, ∼10 ps). Intriguingly, we found that the Rh(III)-ligand core contributes ∼40% to the RMSD^S₁/S₀ of A-RC-A via its own framework distortion, which is comparable with the twisting of the peripheral parts (∼60%). Compared to the rapid twisting of the peripheral groups, the distortion of the molecular framework is normally much slower due to a high potential barrier. Therefore, a two-step conformational relaxation is expected to be observed in the fs-TA data of A-RC-A, which has been widely reported in organic fluorescent systems.^61–63

The extracted species corresponds to a global minimum on the S₁-state PES, which subsequently undergoes ISC leading to formation of a triplet state, featured by the rise of intense absorption centered at λ_pr = 580 nm and the disappearance of SE depletion (λ_pr = 570–670 nm). The formation time (, ∼300 ps) of the triplet state corresponds to the ISC rate constant (k_ISC) of D-RC-A, which is consistent with the relatively low fluorescence quantum yield (Φ_f = 0.22) and sub-nanosecond fluorescence lifetime (τ_S1 = 0.8 ns) observed in toluene solution.³¹ Note that relaxation of the S₁ state is contributed to by non-radiative decay to S₀ (k_NR^S), radiative decay to S₀ (k_R^S), and ISC to triplet states (k_ISC). Therefore, the S₁ ESA decay and GSB refilling dynamics could be largely different with formation of the triplet band, i.e., S₁ ESA and GSB include contributions of k_NR^S, k_R^S, and k_ISC, while rising of the triplet band is associated with k_ISC only. The full picture of the electronic relaxation of the RCPDs is summarized in Fig. 4.

Fig. 4 Electronic relaxation of D-RC-A (left two panels) and A-RC-A (right two panels) revealed by λ_ex-dependent fs-TA measurements.

In the fs-TA data for A-RC-A upon UV excitation, we observed electronic relaxation that is significantly different from D-RC-A. Without a D–A structure, the CT state signature was absent in the fs-TA of A-RC-A. After excitation, rapid IC (∼900 fs, S_m → S₁^FC) is followed by two-step conformational relaxation (), corresponding to a comparable contribution of the peripheral structure and metal–ligand core to the RMSD^S₁/S₀ of A-RC-A. The first step (, ∼9 ps) exhibits a time constant similar to that of the corresponding step in D-RC-A (, ∼10 ps), which was attributed to barrierless twisting of the peripheral structure. Note that the observed twisting with a ∼10 ps time constant is unobservable in our previous time-resolved IR investigation due to the limitation of low temporal resolution (10–20 ps).³⁰ The subsequent step (, ∼150 ps) accordingly corresponds to structural distortion of the Rh(III)–ligand framework. Furthermore, slower triplet formation (S₁′′ → T_n, ∼3.88 ns) in A-RC-A than in D-RC-A was observed upon UV excitation, corresponding to a long-lived (τ_f = 1.7 ns) S₁ state,³¹ which is discussed in detail below. Upon ∼25 fs visible excitation, A-RC-A exhibits largely different electronic relaxation (Fig. 3d) from the case with UV excitation (Fig. 3c). The target analysis extracted a short-lived species(noted as ) after excitation with a ∼400 fs time constant. As described above, rapid IC (∼900 fs, S_m → S₁^FC) was identified for A-RC-A upon UV excitation, while the observed visible-excitation-induced ∼400 fs relaxation obviously cannot be assigned to IC from S_m, as the visible excitation at λ_ex = 513 nm employed is resonant with the S₁ state of A-RC-A and, correspondingly, incapable of populating the S_m state. Moreover, as illustrated in Fig. S9,† we observed a beating behavior in the λ_pr = 400–550 nm wavelength regime of the fs-TA data, which is observed as an oscillatory modulation in both temporal (Fig. S4†) and frequency (Fig. S9†) domains. The beating-modulated TA spectra (Fig. S9†) observed in the initial few picoseconds are highly consistent with the extracted SAS of the species with a ∼400 fs relaxation. We therefore attribute relaxation to dephasing of the coherent vibrational wave packet (noted as ). The dephasing of was not recognized as an independent species in the target analysis of D-RC-A upon visible excitation, which might be associated with a less modulated spectral shape and faster dephasing (Fig. S9†) of D-RC-A due to intense solute–solvent interactions. We further extracted beating signals by subtracting the fitted exponential components from the measured fs-TA data. The Fourier transformed power spectra of the beating signals (Fig. S10†) revealed a dominant vibrational mode at ∼250 cm⁻¹ for both D-RC-A and A-RC-A. Considering that the beating frequency is independent of the 2,5-substitution, we speculate that the observed ∼250 cm⁻¹ mode might originate from a distortion of the metal–ligand core.

After rapid dephasing (), the S₁ state of A-RC-A subsequently undergoes a two-step conformational relaxation () nearly identical with that of A-RC-A upon UV excitation. However, the rise of the T_n band observed in the fs-TA of A-RC-A upon UV excitation is absent upon visible excitation. Instead, we observe an isosbestic point at λ_pr = 530 nm in the fs-TA data of A-RC-A upon visible excitation, indicating that the TA bands located on the blue (GSB, λ_pr = 430–530 nm) and red (ESA, λ_pr = 530–670 nm) sides of the isosbestic point belong to an identical process, i.e., S₁ relaxation. However, note that the fs-TA observation cannot fully exclude the existence of ISC of A-RC-A upon visible excitation due to the limitation of the fs-TA time window. Actually, upon visible excitation, slight spectral rising can be observed between 550 nm and 600 nm at long delays, which is consistent with the triplet band observed upon UV excitation. A plausible explanation is that visible excitation leads to an ultraslow ISC which is unobservable within our time window (3.8 ns).

By measuring the fluorescence quantum yield of A-RC-A upon UV (Φ_f^UV = 0.29) and visible (Φ_f^vis = 0.33) excitation in THF (Table S4†) and assuming an unchanged radiative decay rate constant (k_r) upon different excitation, the ISC time constant upon visible excitation was estimated to be ∼5.75 ns (ESI,† Section S4), which is accordingly unobservable in the fs-TA with time window of 3.8 ns. We also measured the fluorescence lifetime of A-RC-A upon UV (τ_S1^UV) and visible (τ_S1^vis) excitation, which leads to an unchanged lifetime of ∼1.6 ns (Fig. S11–S13†). However, quantitative estimation of the S₁ state decay (ESI,† Section S4) indicated that τ_S1^vis can be only <0.2 ns slower than τ_S1^UV, which can be easily concealed by different temporal profiles of excitation sources in the UV and visible regimes. Therefore, we believe an ultraslow ISC that is beyond our fs-TA time window leads to the absence of triplet ESA in the fs-TA of A-RC-A upon visible excitation, which corresponds to an inaccessible barrier for ISC. In the next section, we further analyze the ISC energetic diagram of D-RC-A and A-RC-A in the framework of Marcus theory to understand the fundamental mechanism that leads to the different ISC dynamics of D-RC-A and A-RC-A.

Marcus analysis of the ISC dynamics

As discussed above, upon identical excitation conditions, D-RC-A exhibited much faster ISC than A-RC-A, which is consistent with the reported lower Φ_f and shorter τ_S1 of D-RC-A compared to A-RC-A.³¹ For systems with weak SOC, i.e., 〈S_m|Ĥ_SO|T_n〉 ≪ E_a, ISC can be simplified as a transition between non-adiabatic states and described by semi-classical Marcus theory.^64–66 As the basis for our Marcus analysis, adiabatic excitation energies of the S₁ and T₂ states were calculated with TD-DFT for both D-RC-A and A-RC-A, while the corresponding T₁ states were calculated using unrestricted DFT (UDFT). UDFT has been reported to be reliable for calculating T₁ states of organic and organometallic complexes, but is inherently not able to treat higher lying triplet states.^67–69

Here, we first analyze the S₁ → T₁ channel that is regarded as the dominant ISC channel in common organic systems,^70,71 for which the adiabatic excitation energies of the S₁ and T₁ states are required. The ISC barrier of the S₁ → T₁ channel (E_a^S₁→T₁) was estimated by a reorganization energy (Γ^S₁→T₁) and corresponding adiabatic energy gap (ΔE_ST^S₁→T₁) within the framework of Marcus theory. As listed in Table 1, ΔE_ST^S₁→T₁ of RCPDs are comparable (0.829 eV for D-RC-A and 0.858 eV for A-RC-A) whereas D-RC-A features a higher Γ^S₁→T₁ (0.115 eV) than A-RC-A (0.062 eV), leading to E_a^S₁→T₁ for D-RC-A (1.103 eV) and A-RC-A (2.574 eV), which are comparable with the adiabatic energies of the corresponding T₁ states. Meanwhile, the SOC matrix elements 〈S₁|Ĥ_SO|T₁〉 of D-RC-A and A-RC-A were calculated to be 4.045 cm⁻¹ and 0.425 cm⁻¹, respectively. The large ISC barrier (>1 eV) leads to virtually forbidden transitions of the S₁ → T₁ channel of D-RC-A and A-RC-A.

Table 1 Summary of the calculated and experimentally measured photophysical parameters associated with plausible ISC channels of D-RC-A and A-RC-A

	D-RC-A	A-RC-A
a Adiabatic excitation energy calculated by TD-DFT. b Adiabatic excitation energy calculated by UDFT. c Calculated by adiabatic energies of optimized geometries of corresponding electronic states, the adiabatic energy gap of an exothermic process was defined to be positive. d Estimated by reorganization energy and adiabatic energy gap of the corresponding transition by Marcus theory. e Calculated by Ea^S1→T2 = Ea^T2→S1 + ΔETS^T2→S1.
S1 excitation energy^a/eV	1.952	1.939
T1 excitation energy^b/eV	1.123	1.081
T2 excitation energy^a/eV	2.022	2.213
RMSD^S1/S0/Å	0.156	0.207
RMSD^S1/T1/Å	0.377	0.302
RMSD^S1/T2/Å	0.853	0.325
Γ ^S1→S0/eV	0.188	0.241
Γ ^S1→T1/eV	0.115	0.062
Γ ^T2→S1/eV	0.558	0.257
ΔEST^S1→T1/eV	0.829	0.858
ΔEST^S1→T2/eV	−0.070	−0.274
ΔETS^T2→S1/eV	0.070	0.274
〈S1|ĤSO|T1〉/cm^−1	4.045	0.425
〈S1|ĤSO|T2〉/cm^−1	4.481	8.697
E a ^S1→T1/eV	1.103	2.574
E a ^T2→S1/eV	0.106	<0.001
E a ^S1→T2/eV	0.177	0.274
E a ^S1→T1/Ea^S1→T2	6.325	9.387
k ISC ^S1→T2 (cal. DA)/kISC^S1→T2 (cal. AA)	7.774
k ISC (exp.)/ps^−1	1/350	1/3900
k ISC (exp. DA)/kISC (exp. AA)	11.143

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Regarding the S₁ → T₂ channel, the calculated adiabatic energies of the S₁ and T₂ states indicate its endothermic nature with a negative ΔE_ST^S₁→T₂ for both D-RC-A (−0.070 eV) and A-RC-A (−0.274 eV). Nevertheless, the S₁ → T₂ transition of RCPDs can still be accessible through a thermally activated mechanism as long as E_a^S₁→T₂ is small enough (normally <0.2 eV), which has been observed via temperature-dependent experiments for RCPDs.²⁸ To estimate E_a^S₁→T₂, as illustrated in Fig. 5a, we calculated the reorganization energy (Γ^T₂→S₁) and adiabatic energy gap (ΔE_TS^T₂→S₁) of its reverse transition T₂ → S₁. As an exothermic process, E_a^T₂→S₁ can be estimated by Marcus theory, leading to E_a^T₂→S₁ = 0.106 eV and <0.001 eV for D-RC-A and A-RC-A, respectively. Thus, E_a^S₁→T₂ can be approximated by the sum of E_a^T₂→S₁ and the adiabatic energy gap (ΔE_TS^T₂→S₁), i.e., 0.177 eV and 0.274 eV for D-RC-A (Fig. 5b) and A-RC-A (Fig. 5c), respectively.

Fig. 5 (a) Simplified energetic diagram for calculating the ISC barrier of the S₁ → T₂ transition in the framework of Marcus theory, and energy diagrams for plausible ISC channels of D-RC-A (b) and A-RC-A (c), in which both T₁ and T₂ states are considered.

With the calculated ISC barriers and SOC matrix elements of plausible ISC channels, we can discuss the ISC dynamics of D-RC-A (Fig. 5b) and A-RC-A (Fig. 5c) in detail. For both D-RC-A and A-RC-A, E_a^S₁→T₁ is substantially higher than E_a^S₁→T₂ (E_a^S₁→T₁/E_a^S₁→T₂ = 6.325 for D-RC-A and 9.387 for A-RC-A), leading to S₁ → T₂ as the dominant ISC channel of both D-RC-A and A-RC-A. Although S₁ → T₂ ISC is an endothermic process, the thermally accessible barriers (∼0.2 eV) lead to ISC dynamics at room temperature, which is consistent with our previously observed temperature-dependence.²⁸ Furthermore, k_ISC^S₁→T₂ of D-RC-A were calculated to be ∼7.7 times faster than k_ISC^S₁→T₂ of A-RC-A, which is perfectly consistent with the ∼11 times faster ISC observed experimentally by fs-TA. The relatively fast ISC of D-RC-A also explains the lower Φ_f of D-RC-A than A-RC-A due to competition between radiative and non-radiative (including ISC) decay of the S₁ state. Meanwhile, the calculated ISC barrier (E_a^S₁→T₂) of D-RC-A and A-RC-A also explains the λ_ex-dependent fs-TA data of A-RC-A. For D-RC-A, the thermally accessible S₁ → T₂ channel at room temperature (E_a^S₁→T₂ = 0.177 eV) leads to the observed λ_ex-independent ISC signature in the TA-data. However, E_a^S₁→T₂ of A-RC-A (0.274 eV) is ∼0.1 eV higher than that for the ISC channel of D-RC-A, leading to a hindered ISC (S₁ → T₂) via a thermally activated mechanism. As discussed above, triplet ESA was consequently unobservable in the fs-TA of A-RC-A upon visible excitation due to its slow formation (∼5.8 ns). However, upon UV excitation, initial IC (S_m → S₁) decay may lead to more population being distributed in higher vibrational levels of the S₁ state, leading to faster ISC that can be observed in the fs-TA data. Note that values of all ISC barriers listed in Table 1 were estimated by Marcus theory based on the TD-DFT-calculated energies of S₁ and T₂ states, and unrestricted DFT (UDFT)-calculated T₁ state, which can have errors up to 0.3 eV. Thus, the S₁ → T₂ ISC barrier (E_a^S₁→T₂) can possibly be different between D-RC-A and A-RC-A, leading to different observations in the λ_ex-dependent fs-TA data.

Last but not least, note that although the T₂ state is heavily involved in the ISC dynamics of D-RC-A and A-RC-A, we believe that the observed triplet signal at λ_pr = 570–580 nm in the fs-TA data must be assigned to the T₁ rather than the T₂ state. Spin-allowed T₂ → T₁ transitions with ∼1 eV energy gaps are expected to be much faster than the corresponding S₁ → T₂ transitions, leading to limited accumulation of T₂ species. Thus, the observed ESA bands should be assigned to the T₁ states formed through rapid decay from the T₂ state. Similarly, the ISC populated T₂ states are energetically higher than the corresponding S₁ states of D-RC-A and A-RC-A, leading to potential exothermic reverse ISC (RISC, T₂ → S₁). However, such an RISC process cannot be the dominant decay channel of the T₂ state due to competition of spin-allowed internal conversion (T₂ → T₁).

Singlet oxygen sensitization

Having the above fs-TA and theoretical data in hand, we then examined the ability of photoexcited A-RC-A to sensitize singlet molecular oxygen, O₂(a¹Δ_g), and the associated kinetics for two reasons: (1) this would likely provide additional information on the formation of triplet states upon light irradiation, and (2) a compound which is both fluorescent and can generate O₂(a¹Δ_g) from its triplet state could be potentially useful for both bio-imaging and photodynamic therapy.^72,73 Moreover, using the fluorescence, one has the advantage of being able to insure that the sensitizing compound was localized at the desired location in a heterogeneous biological system.⁷⁴ We note that in our previous studies,^28,30 we found that several related complexes are capable of simultaneous fluorescence and O₂(a¹Δ_g) sensitization, with reasonable quantum yields for both processes, often summing to ca. 1.

Quantum yields of O₂(a¹Δ_g) production, Φ_Δ, were obtained by monitoring the intensity of the 1275 nm O₂(a¹Δ_g) → O₂(X³Σ_g⁻) phosphorescence in time-resolved experiments, as described previously.^75,76 Experiments were performed upon irradiation of A-RC-A at 417 nm. The integrated intensity of the time-resolved O₂(a¹Δ_g) phosphorescence signal, measured as a function of incident laser power, was normalized by the sensitizer absorbance and the O₂(a¹Δ_g) lifetime. Although a bleaching experiment indicates that A-RC-A can react with O₂(a¹Δ_g) (Fig. S14†), all data were recorded under conditions where A-RC-A bleaching was negligible.

We first performed experiments in toluene-h₈, using a solution that had been bubbled with a gas stream containing 2% oxygen and 98% N₂ (the reasons for using low concentrations of oxygen will become apparent below when discussing the kinetics of the time-resolved O₂(a¹Δ_g) phosphorescence signal). In this case, we performed one set of experiments using 1H-phenalenone (PN) in benzene as the reference O₂(a¹Δ_g) photosensitizer (Φ_Δ = 0.92 ± 0.03),^77,78 and another using m-tetraphenylporphyrin (TPP) in benzene as the reference photosensitizer (Φ_Δ = 0.66 ± 0.08).⁷⁹ The results yield a value of Φ_Δ for A-RC-A of 0.09 ± 0.01. The pertinent data are shown in Fig. S15 and S16.†

Singlet oxygen phosphorescence data recorded upon irradiation of A-RC-A show an increase in the value of Φ_Δ with increasing oxygen concentration (Table 2). In contrast, corresponding data from the PN-sensitized production of O₂(a¹Δ_g) do not show an increase in Φ_Δ with an increase in the oxygen concentration (Fig. 6a). These data indicate that, in the PN experiment, the lifetime of the O₂(a¹Δ_g) precursor (i.e., the PN triplet state) is sufficiently long that the entire ³PN population is effectively quenched at a low oxygen concentration, which is consistent with expectation. For the A-RC-A experiment, the data indicate that the O₂(a¹Δ_g) precursor, presumably the A-RC-A triplet state, is sufficiently short-lived that higher oxygen concentrations are needed to quench a larger fraction of the ³A-RC-A population.

Table 2 O₂(a¹Δ_g) quantum yields, Φ_Δ, for A-RC-A^a

Gas	Φ Δ
a Errors on ΦΔ are ± 10%. Data for the pertinent experiments are shown in Fig. 6.
2% O2	0.10
21% O2	0.18
40% O2	0.23
70% O2	0.32
100% O2	0.34

---

Fig. 6 (a) Integrated intensity of the O₂(a¹Δ_g) phosphorescence signal upon irradiation at 417 nm, normalized by the sensitizer absorbance and the O₂(a¹Δ_g) lifetime, plotted as a function of laser power and collected over a range of O₂ concentrations for both A-RC-A and for the reference standard, phenalenone (PN), in toluene-d₈. The O₂ concentration is represented as the percent of O₂ in the O₂/N₂ gas mixture bubbled through the solution. The slopes of the linear fits are proportional to the O₂(a¹Δ_g) quantum yield. Representative time-resolved O₂(a¹Δ_g) phosphorescence traces used to obtain the A-RC-A data are shown in (b and c). (b) The data from 100 μs to 2000 μs were fitted by a single exponential decay function (solid lines) to obtain the lifetime of O₂(a¹Δ_g) (i.e., 1/k_Δ). (c) Using k_Δ as a fixed parameter, eqn (5) was used as a fitting function (solid lines) to obtain values of k_T for a time domain where O₂(a¹Δ_g) was formed in the photosensitized reaction. (d) Plot of k_T, obtained from the fits shown in (c) for the A-RC-A data, against the concentration of dissolved oxygen. The slope, (1.3 ± 0.1) × 10⁹ M⁻¹ s⁻¹, is the bimolecular rate constant for oxygen quenching of the O₂(a¹Δ_g) precursor. The intercept yields a value of ∼9 μs for the lifetime of this O₂(a¹Δ_g) precursor in the absence of oxygen. Both of these numbers are consistent with expectation for oxygen quenching of a triplet state.^74,82

Given that the lifetime of the S₁ state of A-RC-A in oxygen-free toluene is 1.7 ns, the S₁ state is so short-lived that it cannot be quenched by oxygen, even in an oxygen-saturated solution at atmospheric pressure. This can be confirmed in a calculation where one accepts that the quenching will occur at the diffusion controlled limit (i.e., k_diff = 3 × 10¹⁰ M⁻¹ s⁻¹). As such, we infer that the O₂(a¹Δ_g) precursor will be the A-RC-A triplet state (vide infra). We then chose to obtain information about the kinetics of the O₂(a¹Δ_g) precursor, again presumably the A-RC-A triplet state, using our time-resolved O₂(a¹Δ_g) phosphorescence data, as described below.

For the triplet-state-photosensitized production of O₂(a¹Δ_g) in homogeneous solutions, the intensity, I(t), of the time-resolved 1275 nm O₂(a¹Δ_g) → O₂(X³Σ_g⁻) phosphorescence signal is generally modeled using a fitting function based on eqn (5)^74,75,81

In eqn (5), I_tot is proportional to the total integrated intensity of O₂(a¹Δ_g) phosphorescence, k_T is the decay rate constant for the O₂(a¹Δ_g) precursor (i.e., the reciprocal lifetime of the sensitizer triplet state) and k_Δ the rate constant for O₂(a¹Δ_g) decay (i.e., the reciprocal O₂(a¹Δ_g) lifetime). By performing the O₂(a¹Δ_g) phosphorescence experiment in toluene-d₈ as opposed to toluene-h₈, we take advantage of the large H/D solvent isotope effect on the O₂(a¹Δ_g) lifetime.⁷⁴ In this way, we can independently characterize k_Δ in a time domain where k_T does not appreciably influence the signal (Fig. 6b). Using this value of k_Δ as a fixed parameter, we can then re-fit the O₂(a¹Δ_g) phosphorescence data in the time domains where k_T influences the signal (Fig. 6c). We applied this procedure for experiments performed using a series of comparatively low oxygen concentrations to assess more accurately the decay rate constant of the O₂(a¹Δ_g) precursor.

In Fig. 6d, we plot the values of k_T thus obtained for A-RC-A against the oxygen concentration to yield the bimolecular rate constant for oxygen quenching of the O₂(a¹Δ_g) precursor. We determined oxygen concentrations using the mole fraction of oxygen in the bubbling gas (controlled by O₂ and N₂ flow meters) and Henry's Law constants published by Battino, et al.⁸² The value obtained for this quenching rate constant is (1.3 ± 0.1) × 10⁹ M⁻¹ s⁻¹. As an independent control for this study on A-RC-A, we performed the same experiment using PN as the O₂(a¹Δ_g) sensitizer (Fig. S17†), and the results obtained provide credence for our results on A-RC-A. Specifically, our data for the quenching of ³PN by oxygen yield a rate constant of (2.2 ± 0.2) × 10⁹ M⁻¹ s⁻¹, which is consistent with published data.⁷⁸

The data obtained from Fig. 6d are consistent with the following assignment: the O₂(a¹Δ_g) precursor upon irradiation of A-RC-A is a triplet state whose lifetime in the absence of oxygen is ∼9 μs.

From Fig. 6b, the values of the O₂(a¹Δ_g) lifetime obtained (i.e., k_Δ⁻¹ = 296 ± 3 μs) are shorter than what is expected for the solvent-mediated deactivation of O₂(a¹Δ_g ) in toluene-d₈. For the latter, we independently recorded a value of 326 ± 3 μs using PN as the sensitizer with the same batch of toluene-d₈ used for the A-RC-A experiments. Using eqn (6), and with the A-RC-A concentration of 1.7 × 10⁻⁵ M used in our experiments, we obtain a rate constant of ∼1.8 × 10⁷ M⁻¹ s⁻¹ for the deactivation/removal of O₂(a¹Δ_g) by A-RC-A. Given the magnitude of this rate constant, it is likely that the mechanism for A-RC-A-mediated deactivation of O₂(a¹Δ_g) involves some charge transfer from A-RC-A to O₂(a¹Δ_g).^74,80 Moreover, based on an A-RC-A bleaching experiment (Fig. S14†), a small component of this rate constant reflects a chemical reaction between A-RC-A and O₂(a¹Δ_g).

k^{obs.with A-RC-A}_Δ = k^{obs.without A-RC-A}_Δ + k_q[A-RC-A] (6)

We also considered the interesting possibility that the O₂(a¹Δ_g) precursor might possibly be the T₂ state. However, our data indicate that the O₂(a¹Δ_g) precursor upon irradiation of A-RC-A has quite a long lifetime (∼9 μs obtained from the intercept of the plot in Fig. 6d) and, as such, it must be the T₁ state, as spin-allowed internal conversion from T₂ to T₁ is expected to be quite rapid (vide supra).

Conclusions

We investigated the ultrafast photophysics and intersystem crossing (ISC) dynamics of two para-substituted 2,5-bis(phenylethynyl) RCPDs (D-RC-A and A-RC-A) using excitation-wavelength-dependent fs-TA measurements and TD-DFT calculations. The electronic relaxation channels of the S₁ state were revealed in detail, including charge transfer, conformational relaxation, vibrational dephasing, and ISC. By calculating the thermodynamic barrier and spin–orbit coupling, plausible ISC channels were revealed using semi-classical Marcus theory, i.e., ISC is dominated by the thermally activated S₁ → T₂ channel. With weak metal–ligand interactions, the plausible ISC channels of RCPDs are largely affected by ISC barriers. Studies of the sensitization of O₂(a¹Δ_g) by A-RC-A give quantum yields Φ_Δ of up to ∼0.3 at high oxygen concentrations, consistent with the rate of ISC being competitive with that of fluorescence. The relatively long lifetime of the triplet state responsible for sensitization of O₂(a¹Δ_g) of ∼9 μs indicates that it must be T₁, being formed rapidly from T₂. Our work, especially the paradigm on ISC dynamics, might provide useful insight into the behavior of other fluorescent emitters.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

Zilong Guo: conceptualization, methodology, investigation, data curation, formal analysis, visualization and writing original draft; Yaxin Wang: data curation, formal analysis and validation; Julia Heitmüller: data curation and formal analysis; Carolin Sieck: investigation and data curation; Andreas Prüfer: investigation and data curation; Philipp Ralle: investigation and data curation; Andreas Steffen: conceptualization, methodology, investigation, writing – review and editing; Petr Henke: methodology, data curation, formal analysis and validation; Peter R. Ogilby: methodology, supervision, and writing – review and editing; Todd B. Marder: conceptualization, formal analysis, funding acquisition, supervision, and writing – review and editing; Xiaonan Ma: conceptualization, formal analysis, funding acquisition, supervision, and writing – review and editing; Tobias Brixner: conceptualization, formal analysis, funding acquisition, supervision, and writing – review and editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

X. M. thanks the National Key R&D Program of China (No. 2020YFA0714603 and 2020YFA0714604) for funding. T. B. M. thanks the Julius-Maximilians-Universität Würzburg for support.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4sc04306e

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