Effects of metal–metal bonding in photosensitizers: red-shifted absorption and oscillator strength enhancement

Abstract

Metal–metal bonding of known bimetallic photosensitizers featuring Ru–Ru, Mo–Mo, Ag–Ag and Rh–Rh bonds was explored using computational modeling benchmarked by established experimental parameters. The analysis reveals that these metal–metal bonds facilitate (1) a red-shift in the maximum absorption wavelength (λ_max) and (2) an increase in the oscillator strength of the λ_max peak. A statistical analysis also reveals a strong correlation between the metal–metal bond order and the oscillator strength. These trends show that metal–metal bonds play a significant role in enhancing the photophysical properties of photosensitizers and inform future photosensitizer designs.

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Introduction

Photosensitizers are compounds that absorb light and after excitation, engage in transfer of energy or electrons.¹ Their applications span solar fuel cells,² light emitting devices,³ organic synthesis,^4,5 and photodynamic therapies.⁶ The prevalent paradigm in modern photosensitizer development is the monometallic design which utilizes metals such as iridium and ruthenium (Scheme 1a) which operate under high energy wavelengths.^4,5 While highly effective, the use of high-energy radiations such as ultraviolet (UV) and blue light leads to various drawbacks.⁷ For instance, due to their low penetration power, photodynamic therapies are limited to only the body surface or sites close to the surface and the scalability of photocatalytic reactions is also limited to smaller reaction vessels.⁸ High energy radiation also damages sensitive substrates limiting the substrate scopes of these photosensitizers and generates unwanted side effects in photodynamic therapies.⁹

Scheme 1 Photosensitizer paradigms and present work: effects of metal–metal bonding in photosensitizers.

Recently, bimetallic and multimetallic photosensitizers have emerged as an attractive alternative paradigm to monometallic photosensitizers (Scheme 1b).^10–14 Many bimetallic systems feature metal–metal bonds and exhibit photo reactivity^15–18 with low-energy wavelengths complementing the reactivity of the monometallic paradigm and overcome some of its limitations.^12,19 However, the role of metal–metal bonding in these photosensitizers and its influence on trends in photophysical properties with respect to their single metal congeners remains largely unexplored. Understanding these trends will likely lead to valuable insights that inform future photosensitizer designs and applications.^20,21

To this end, we used theoretical calculations to probe metal–metal bonding in bimetallic photosensitizers (Scheme 1c) developed by the Chisholm,¹¹ Campbell,¹³ Handa¹² (Fig. 1g, h and i) and Turro groups.^22–24 Our analysis revealed a red-shift in the maximum absorption wavelength and an enhancement of the oscillator strength in photosensitizers with metal–metal bonding in comparison to their monometallic analogues.

Fig. 1 Structures of the monometallic (a, b and c) and bimetallic (g, h and i) complexes and calculated UV-Vis spectra (d, e, and f) (monometallic: black, bimetallic: maroon).

Results and discussion

First, the symmetrical bimetallic photosensitizers containing second-row transition metals Mo, Ag, and Ru (Fig. 1g–i) were optimized, and their UV-Vis absorption spectra were simulated using time dependent-density functional theory (TD-DFT) methods (Fig. 1d–f) and benchmarked with experimental spectral data (Tables S1 and S2†). The scope of the benchmarking studies was limited to hybrid functionals in this analysis as they were sufficient to accurately predict the experimental data. More extensive electronic structure studies utilizing higher level multiconfigurational methods^25–28 are currently underway in our lab and will enrich our future models.

To eliminate the effects of metal–metal bonding, the bimetallic complexes were symmetrically deconstructed to obtain the corresponding monometallic model complexes (Fig. 1a–c).²⁹ Special care was taken to ensure that the ligand–metal interactions of each individual metal in the monometallic structure remained similar to the bimetallic structure. Any structures that could not be symmetrically broken down were excluded from the study to avoid convoluting ligand effects. These hypothetical monometallic structures were then theoretically analysed using identical conditions to their bimetallic counterparts.

Maximum absorption wavelength (λ_max)

The analysis of the simulated UV-vis spectra revealed that the maximum absorption wavelengths (λ_max) of the bimetallic complexes were observed at a higher wavelength in comparison to their monometallic analogues (Fig. 1 and Table 1). The highest red-shift was seen for the molybdenum complexes with multiple metal–metal bonds, where the λ_max was shifted from the UV region in the monometallic complex, [Mo-1], (290 nm, entry 1) to the visible region in the bimetallic complex, [Mo-2], (436 nm, entry 2). Both the ruthenium complexes showed maximum absorption peaks in the visible region. For the monometallic complex, [Ru-1], the maximum absorption was at 482 nm (entry 5) while for the bimetallic complex, [Ru-2], it was at 592 nm (entry 6). The λ_max values for the silver complexes were found to lie in the ultraviolet (UV) region. The maximum absorption for the monomer, [Ag-1] and the dimer, [Ag-2] were observed at 191 nm (entry 3) and 228 nm (entry 4) respectively.

Table 1 Calculated photophysical properties of the monometallic and bimetallic complexes: maximum absorption wavelength (λ_max)/nm, HOMO–LUMO gap/eV, molar absorptivity (ε)/10³ M⁻¹ cm⁻¹ and oscillator strength

Entry	Complex	Maximum absorption wavelength (λmax)/nm	HOMO–LUMO gap/eV	Molar absorptivity (ε)/10^3 M^−1 cm^−1	Oscillator strength
a Molar absorptivity matches the experimental value exactly.^11 b Experimental molar absorptivity = 23 × 10^3 M^−1 cm^−1.^13 c Experimental molar absorptivity = 6.73 × 10^3 M^−1 cm^−1.^12
1	[Mo-1]	290	4.706	46.0	0.468
2	[Mo-2]	436	4.616	46.0^a	0.763
3	[Ag-1]	191	6.293	19.0	0.232
4	[Ag-2]	228	5.359	22.0^b	0.622
5	[Ru-1]	482	α: 6.219	1.9	0.113
			β: 5.762
6	[Ru-2]	592	4.024	6.8^c	0.260

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We next used NBO calculations to determine the energies of the highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) for each complex. For all the three metals, the HOMO–LUMO gap was lower for the bimetallic complex in comparison to its monometallic complex (Table 1, column 3 and Fig. 3–5). This lower energy difference between the occupied and unoccupied bands in the bimetallic complexes causes the excitations to be lower in energy leading to the red-shift in wavelength.

Intensity of absorption & oscillator strength

The intensity of the absorptions for the highest absorption peaks were also evaluated using the simulated spectra (Table 1, columns 5 and 6). The calculated molar absorptivity values were consistent with the experimental values (Table 1).^11–13 The molar absorptivity (ε) was higher in bimetallic complexes in comparison to their respective monometallic analogues for both ruthenium and silver species, [Ru-2] and [Ag-2] (Table 1, column 4 and Fig. 1e and f). While the molar absorptivity of both the molybdenum complexes [Mo-1] and [Mo-2] was similar (Fig. 1d, Table 1, entries 1 & 2), the calculated oscillator strength, which expresses the probability of absorption for a particular transition,³⁰ was predicted to be higher for all the bimetallic complexes (Table 1, column 6) (see Fig. S1–S4† for visualizations).

Natural transition orbital analysis

Next, we performed a natural transition orbital (NTO) analysis to probe the molecular orbitals responsible for the electronic excitations leading to the maximum absorption transitions. In an NTO calculation, an ordinary orbital representation is transformed into a more compact form in which each excited state is expressed as a single pair of orbitals: the excited particle (occupied due to the excitation) and the hole (which is left empty due to the excitation).³¹ The particle–hole pair responsible for the λ_max excitation for each complex was determined.

The percentage metal contributions for each particle and hole were then computed to examine the contribution of the metals in these transitions (Table 2, Column 4). Overall, the general trend uncovered was that in the monometallic systems, both the particle and the hole had almost comparable metal contributions, i.e. 0, 10 and 16% differences (Table 2, Column 5), while in bimetallic systems, either the hole (in [Mo-2] and [Ag-2]) or the particle (in [Ru-2]) had more metal character in comparison (51, 32 and 53% differences, respectively) leading to strong metal-to-ligand or ligand-to-metal charge transfer transitions.

Table 2 Metal contributions in particle/hole transition orbitals for the maximum absorption wavelength (λ_max)

Entry	Complex	Natural transition orbital	Metal contribution/%	Δ|(Particle–Hole)| metal contribution/%
1	[Mo-1]	Hole	32	0
		Particle	32
2	[Mo-2]	Hole	67	51
		Particle	16
3	[Ag-1]	Hole	17	10
		Particle	7
4	[Ag-2]	Hole	42	32
		Particle	10
5	[Ru-1]	Hole	56	16
		Particle	60
6	[Ru-2]	Hole	0	53
		Particle	53

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While the NTO analysis is useful in extracting the total metal contributions in specific transitions, it is not as informative in qualitatively extracting the relevant molecular interactions. Only the net total orbital densities are captured in the orbital visualizations, and the overlapped orbitals are often too compact to deconvolute accurately (Fig. 2). Therefore, the exact orbital combinations with the highest contributions to the λ_max were extracted from the NTO analysis and visualized using NBO calculations to isolate the effects of metal–metal bonding on the transitions (see Table S3† for all the contributions).

Fig. 2 NTO orbitals of (a) [Mo-1]: particle (upper left) and hole (lower left) and (b) [Mo-2]: particle (upper right) andhole (lower right), visualized at iso value 0.03.

In the [Mo-1] system, the hole and the particle were mostly ligand-centred in character (∼70%) (Table 2, entry 1). This likely causes most of the excitations to be intra-ligand charge transfers (ILCT) while a lower amount of d–d, ligand-to-metal charge transfers (LMCT) and metal-to-ligand charge transfer (MLCT) transitions is also possible. The highest contribution to the λ_max (>50%) is from HOMO−4 → LUMO+1, HOMO−4 → LUMO and HOMO → LUMO+4 in the order of decreasing contribution (Table S3†). These orbitals mainly feature ligand-based π-bonding and π*-antibonding characteristics while limited metal–ligand bonding interactions are also seen in both donor and acceptor orbitals (Fig. 3).

Fig. 3 Calculated molecular orbital diagrams for [Mo-1] and [Mo-2] with primary electronic transitions at λ_max and visualizations of the corresponding molecular orbitals at iso value = 0.03.

In contrast, in the [Mo-2] system, the hole is primarily metal-based in character (67%) while the particle is primarily ligand-based in character (84%) (Fig. 2). This is consistent with strong (metal–metal)-to-ligand charge transfers ((MM)LCTs), which have been reported for these complexes.^11,32 The calculations show that the highest contribution to λ_max (67%) is from the HOMO to LUMO transition (Fig. 3) as has been established previously.¹¹ The HOMO is mainly metal-based (67%) due to strong δ (Mo–Mo) bonding interactions and the LUMO is mainly ligand-based (97%). This is consistent with the previously described electronic structure for [Mo-2].¹¹ Thus, strong (MM)LCT transitions (δ (Mo–Mo) → π* (ligand)) cause the excitations to be of high oscillator strength (Table 1, entry 2).

Similar to [Mo-1], the hole and the particle are mostly ligand-based in character in the [Ag-1] complex (∼83–93%) (Table 2, entry 3), causing most of the excitations to be intra-ligand charge transfers. The primary transitions to the λ_max are from HOMO → LUMO+6, HOMO−1 → LUMO+5, and HOMO → LUMO+7 in the order of decreasing contribution. As is the case with [Mo-1], all the donor and acceptor orbitals mainly show ligand-based π-bonding and π*-antibonding. However, some minor metal–ligand interactions are also present in the HOMO and HOMO−1 (Fig. 4).

Fig. 4 Calculated molecular orbital diagrams for [Ag-1] and [Ag-2] with primary electronic transitions at λ_max and visualizations of the corresponding molecular orbitals at iso value = 0.03.

The molecular orbital diagrams for transitions of [Ag-2] in the visible region have been reported in detail previously.¹³ Our NTO analysis for the maximum absorption wavelength reveals that in the [Ag-2] system, the hole is more metal-based in character (42%) compared to the particle (10%). The highest contribution to λ_max (58%) were from the transitions HOMO−14 → LUMO, HOMO−9 → LUMO+1, and HOMO−8 → LUMO+1 (Fig. 4). LUMO and LUMO+1 show heavy ligand based π- and π*-character. All the highest contributing donor orbitals involved feature metal–metal interactions. HOMO−14 shows strong π (Ag–Ag) bonding interactions while both HOMO−8 and HOMO−9 show strong π* (Ag–Ag) antibonding interactions consistent with strong (metal–metal)-to-ligand charge transfers ((MM)LCT) consistent with previously reported data for [Ag-2].¹³

In the [Ru-1] system, more than half of both the hole and the particle were metal-based (56–60%) in character (Table 2, entry 5). This likely leads the excitations to be mainly of d–d transitions, resulting in lower molar absorptivity and oscillator strength. The highest contribution to λ_max (∼99%) was from HOMO to LUMO (Fig. 5).

Fig. 5 Calculated molecular orbital diagrams for [Ru-1] and [Ru-2] with primary electronic transitions at λ_max and visualizations of the corresponding molecular orbitals at iso value = 0.03.

In the [Ru-2] system, the hole had no contributions from the metal while more than half of the particle had metal character (53%) (Table 2, entry 6). This is consistent with strong ligand-to-metal charge transfers³³ (LMCT) as previously been reported for these complexes.^12,34–36 The calculations show the highest contribution to λ_max (97%) is from the HOMO−2-to-LUMO transition (Fig. 5). The HOMO−2 orbital is entirely ligand-based preventing any weak d–d transitions, and the LUMO shows prominent δ* (Ru–Ru) character as previously demonstrated for this system.¹² Thus, strong LMCT transitions (π (ligand) → δ* (Ru–Ru)) cause the excitations to be of high molar absorptivity and oscillator strength (Table 1, entry 6).

To summarize, the NTO study of the above three examples illustrates that there is a prominent metal presence in either the hole or the particle for bimetallic systems leading to strong MLCT or LMCT absorptions. The NBO analysis reveals that strong metal–metal interactions are responsible for this high metal occupancy. These observations clearly demonstrate that metal–metal interactions contribute significantly to the molecular orbitals involved in high-intensity absorptions.

Multivariate linear regression (MVR) analysis

We next performed a multivariate linear regression analysis to map out the factors that influence the absorptions of bimetallic photosensitizers. We also expanded our bimetallic scope to include other Mo₂, Ag₂ and Rh₂ photosensitizers developed by Chisholm,¹¹ Campbell,¹³ Turro^19,22–24 and co-workers (Fig. 6). This enabled us to keep the number of data points ≥3N (N = number of parameters in the MVR plots) to avoid overfitting. These photosensitizers were excluded from the above study as attempts to deconstruct them in a meaningful manner to form their respective monometallic analogues without adding or losing extra ligand effects were unsuccessful. Out of the absorption peaks in the calculated spectra, we limited our scope to the maximum absorption wavelength (λ_max) peaks. Oscillator strength of absorption was set as the independent variable, y.

Fig. 6 Dimolybdenum, disilver and dirhodium complexes used for MVR analysis.

First, a two-parameter correlation was attempted using only metal related descriptors. The first parameter was picked out of the formal shortness ratio (FSR),³⁷ Wiberg bond Index (WBI), Natural Atomic Orbital (NAO) bond order and Molecular Orbital (MO) bond order to describe the metal–metal bond order. The second parameter was picked out of the metal percentage in the hole (M_H), the metal percentage in the particle (M_P), and the metal percentage difference between the hole and the particle (M_|H–P|) to describe the metal contributions involved in the transitions. The two-parameter combination that provided the best fit was the Molecular Orbital bond order (BO_MO) and the metal percentage in the hole (M_H) (R² = 0.63, eqn (S1), Fig. S13†). This weak correlation with the metal-only parameters indicated that additional factors contribute to the oscillator strength.

The energy of the transitions likely influences the strength of the absorption. Therefore, we added the HOMO–LUMO energy gap (ΔE_HOMO–LUMO) as a parameter. This improved the fit slightly (R² = 0.69; eqn (S2), Fig. S14†). The influence of solvent on the intensity of absorption has long been established.^38,39 Therefore, the dielectric constant (ε) of the solvent was added next as a parameter for the regression analysis. This improved the correlation further (R² = 0.74, eqn (S3), Fig. S15†).

Since the coefficient of the metal percentage in the hole, M_H showed a positive correlation consistent with MLCT transitions and since the [Ru-2] photosensitizer exhibited LMCT absorptions while the rest of the photosensitizers exhibited MLCT absorptions, we rationalized that [Ru-2] would be an outlier skewing the data and thus removed it as a data point. This improved the correlation significantly giving us the best fit (R² = 0.9; eqn (1), Fig. 7).

Fig. 7 Multivariate correlation plot relating oscillator strength to solvent dielectric constant (ε), the HOMO–LUMO energy gap (ΔE_HOMO–LUMO), metal percentage in the hole (M_H) and MO bond order (BO_MO) in bimetallic photosensitizers featuring MLCT transitions.

When the metal related descriptors in eqn (1) were removed one at a time, the R² value decreased (Fig. S16 and S17†). The worst outcome (R² = 0.1) was seen when the MO bond order was removed indicating that the oscillator strength had the highest correlation with the MO bond order. The influence of the other parameters in eqn (1) have been established previously in the context of monometallic photosensitizers.^8,38–41

We next performed a leave-one-out-cross-validation (LOOCV) test on the best fit (eqn (1)) to test for overfitting. In a LOOCV test, a single data point is left out of the data set and the model is trained on the remaining points.⁴² The process is repeated for all the data points. The R² values for the LOOCV analysis remained robust and within 0.85–0.94 for our model. While there is room for the model to be improved with more data as the field of bimetallic photosensitizers evolves, we propose that this model is sufficient to qualitatively indicate that metal–metal bonding shows a positive correlation with the oscillator strength and thus can be utilized to enhance photosensitizer reactivity.

Conclusions

Using computational modelling, we studied the effects of metal–metal bonding in known bimetallic photosensitizers containing Ru–Ru, Mo–Mo, Ag–Ag and Rh–Rh bonds. Our analysis reveals that metal–metal bonds affect (1) maximum absorption wavelength and (2) oscillator strength of absorption. TD-DFT calculations reveal that metal–metal bonding causes a red-shift in the maximum absorption wavelength. NTO and NBO studies reveal that either the donor or the acceptor orbitals responsible for the highest absorption transitions contain strong metal–metal interactions, and an MVR analysis reveals that the metal–metal bond order strongly correlates with the oscillator strength. These trends show that metal–metal bonds play a vital role in tuning photophysical properties of bimetallic photosensitizers and inform future photosensitizer designs.

Computational details

All calculations were performed using density functional theory (DFT) in Gaussian 16.⁴³ Geometry optimizations and vibrational frequency calculations were performed using cam-B3LYP functional in gas phase with LANL2DZ basis set.⁴⁴ All the structures were optimized to a ground-state minima with no imaginary frequencies. Time-dependent DFT (TD-DFT) calculations^45–47 were performed on the geometry-optimized structures using cam-B3LYP/LANL2DZ and the polarizable continuum model (PCM) with the solvents; acetonitrile, dichloromethane, tetrahydrofuran, ethyl acetate and dimethylformamide to match the experimental conditions for the bimetallic complexes (Tables S1 and S2†). UV-Vis absorption spectra were visualized using Gaussview.^48,49 Analysis of simulated UV-vis absorption spectra, and orbital and atomic contributions to the natural transition orbitals (NTOs) were carried out using Chemissian.³¹ Natural Bond Order (NBO) calculations⁵⁰ were performed to determine the Wiberg bond indices, natural atomic orbital (NAO) bond orders, molecular orbital (MO) bond orders and frontier molecular orbitals. The orbitals were visualized using Avogadro (Version 1.2.0)⁵¹ and Chemissian. Multivariate linear regression (MLR) analysis was performed using OriginPro (OriginLab Corporation, version 2021b).

Data availability

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

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Funding for this project was provided by the Department of Chemistry and the President's Research Fund at Saint Louis University. Calculations were performed at the High-Performance Computing Cluster (HPC) at Saint Louis University. We thank the professors Neal P. Mankad, Keary M. Engle and Peng Liu for their valuable feedback.

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Footnote

† Electronic supplementary information (ESI) available: Computational details and cartesian coordinates of optimized geometries (PDF). See DOI: https://doi.org/10.1039/d4qi02131b

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