Nature of the Ultrafast Interligands Electron Transfers in Dye-Sensitized Solar Cells

Abstract

Charge-transfer dynamics and interligand electron transfer (ILET) phenomena play a pivotal role in dye-sensitizers, mostly represented by the Ru-based polypyridyl complexes, for TiO₂ and ZnO-based solar cells. Starting from metal-to-ligand charge-transfer (MLCT) excited states, charge dynamics and ILET can influence the overall device efficiency. In this letter, we focus on N3^4– dye ( [Ru(dcbpy)₂(NCS)₂]^4–, dcbpy = 4,4′-dicarboxy-2,2′-bipyridine) to provide a first direct observation with high time resolution (<20 fs) of the ultrafast electron exchange between bpy-like ligands. ILET is observed in water solution after photoexcitation in the ∼400 nm MLCT band, and assessment of its ultrafast time-scale is here given through a real-time electronic dynamics simulation on the basis of state-of-the-art electronic structure methods. Indirect effects of water at finite temperature are also disentangled by investigating the system in a symmetric gas-phase structure. As main result, remarkably, the ILET mechanism appears to be based upon a purely electronic evolution among the dense, experimentally accessible, MLCT excited states manifold at ∼400 nm, which rules out nuclear–electronic couplings and proves further the importance of the dense electronic manifold in improving the efficiency of dye sensitizers in solar cell devices.

Charge-transfer excited states, and in particular metal-to-ligand charge-transfer (MLCT), are essential for photoexcited energy transfer steps in many natural and artificial light-harvesting processes and photocatalysis.¹⁻⁶ Charge-transfer dynamics and interligand electron transfer (ILET) phenomena play a pivotal role in these emerging technologies and applications. ILET can potentially lead to a random mixture of charge-localized MLCT states, independent of which ligand the initial excitation localized the charge. This can influence the rate and the fate of the subsequent injection step in the substrate materials used in solar cell applications and, thus, the overall light-harvesting performances. For these reasons, the investigation of the charge injection mechanisms for dye–semiconductors has been the focus of several studies, with a particular attention on the related injection rates.⁷⁻¹² Among the most studied and employed nanostructured systems in this field are the dye sensitizers for TiO₂ and ZnO-based substrates for solar cells, mostly represented by the Ru-based polypyridyl complexes. In this regard, [Ru(dcbpy)₂(NCS)₂]^4–, dcbpy = (4,4′-dicarboxy-2,2′-bipyridine), or “N3^4–” (please see Figure S1 in the Supporting Information for N3^4– molecular structure), belongs to a broad class of transition-metal compounds undergoing rapid and complex charge-transfer dynamics, potentially correlated with both a structural rearrangement and the polar environment (the solvent).^2,13−25 Electron–nuclear couplings and the electronic structure at the dye–substrate interface are believed to play key roles in determining the device function.²⁶⁻³² An additional layer of complexity is added because the general consensus is that N3 and its charged variants are characterized by complex dynamics that can involve multiple electronic states from the singlet initial ¹MLCT photoinduced state(s) in the visible range to the long-lived final triplet ³MLCT, both in solution³³⁻³⁸ and on semiconductor substrates.^1,39−45 Time-resolved studies in the infrared and terahertz regimes have identified remarkable differences between the dynamic response of dye–ZnO and dye–TiO₂ interfaces.^{26,28−32,46−48} However, a complete understanding of the role (or not) of nuclear–electronic couplings in the early stage of MLCT before injection is difficult to achieve since the ultrafast ILET charge dynamics (<100 fs, where nuclear vibrations are not involved yet in a predominant way) cannot be directly observed because of the still limited time resolution of experimental techniques.^7,26 Investigation of the occurrence or not of the ILET process in the ultrafast regime is the first step for disentangling (or not) the role in ILET of the nuclear vibrations from the ultrafast electronic dynamics of the dye sensitizer excited state electronic manifold. This is very important to understand, since ligands anchored on the substrate can be further stabilized by coordination with the Ti/Zn atoms of the substrates, which creates an even larger driving force for ILET to the proximal ligand and, thus, decreases the ILET barrier.

Time-dependent electronic structure theories can model the evolution in time of photoinduced excited electronic states from first principles. The wide adoption of density functional theory (DFT) and its time-dependent (TD) formulation has opened the doors in the recent years, indeed, to the ab initio characterization of both ground and excited-state properties for large macromolecular systems, such as those of biological⁴⁹⁻⁵⁷ and materials⁵⁸⁻⁷⁰ interest and their transient behavior.⁷¹⁻⁷³ DFT and TDDFT have shown to be effective for the theoretical characterization of many Ru complexes in different environments⁷⁴⁻⁹⁸ and the vibrational dynamics of transient species.⁹⁹⁻¹⁰⁴ Among nonperturbative approaches to mean-field quantum electronic dynamics (ED), real-time time-dependent density functional theory (RT-TDDFT) has been proven to be very powerful and provides a molecular interpretation of the interplay between initial photoexcited states and exciton and polaron formation,^{102,105−108} also including relativistic effects.^109,110 In this letter, we present the ultrafast hole–electron dynamics of two experimentally relevant N3^4– photoinduced charge-transfer excited states (belonging to the 372 nm band¹¹¹), where the system is characterized and propagated both in water solution and in gas-phase, which demonstrates the crucial role of the dense electronic manifold of metal complexes for the initial ultrafast ILET, even before the nuclear-electron couplings have a substantial impact on the CT dynamics.¹¹² Such states, called ¹MLCT_A and ¹MLCT_B and respectively found around 24 400–24 700 cm^–1 (410–405 nm) and 25 000–25 300 cm^–1 (400–395 nm), were previously shown to be those most vibronically coupled with the final triplet one.¹¹¹ Both states are characterized by an important electronic density redistribution from the Ru(NCS)₂ moiety toward the dcbpy rings, with a transition electric dipole moment predominantly located on the N3^4– equatorial plane.¹¹¹

Effects by solvation and structural distortions from the symmetric, minimum energy structure (due to finite temperature and the environment) on photoinduced MLCT states and subsequent ultrafast charge rearrangements were considered. No explicit effects of temperature were included in the electronic degrees of freedom. In this work, we are not limited to the vertical excitation picture from the minimum of the ground state, and the distortions due to the environment and thermal fluctuations are indeed included, although in an average manner, by employing a representative configuration, given also the high computational cost related to RT-TDDFT simulations. The excited electronic density was, in fact, propagated via RT-TDDFT on a representative configuration extracted from a previously collected ab initio molecular dynamics (AIMD) trajectory in water solution, hereafter referred to as D-W structure (see Figure S7 in the Supporting Information). Additionally for interested readers, please refer to Section 5 and to Section 2 in the Supporting Information, along with ref (113), for RT-TDDFT electronic dynamics and AIMD computational details, respectively. The chosen configuration features relevant Ru(II) coordination structural parameters (Figure S3), overall symmetry distortion in water from an ideally C₂ configuration (Figure S5), as well as ligands’ solvation with a proper number of explicit solvent molecules (Figure 1 and Figure S4) that are representative of room temperature structural equilibrium, controlling also the NCS ligands’ coordination, given their lability in solution, as witnessed by inspecting AIMD structural distributions (please refer to Section 2 and Figures S3–S5 of the Supporting Information and ref (113)).

Figure 1.

¹MLCT_A and ¹MLCT_B excited states characterized by NTOs (D-W structure). Hole and electron isodensity plots (0.02 isovalue) are reported on left and right panels, respectively. NTOs are calculated to provide a simpler orbital interpretation of electronic excitations, which results in a hole–electron pair of orbitals.¹¹⁴

We first analyzed the nature of the excited states by linear-response (LR-) TD-DFT calculations (please refer to Table S1 in the Supporting Information). Two main effects of the symmetry lowering in aqueous solution were observed on the nature of the photogenerated MLCT states: (i) excited states were more accessible compared with the ones that appear dark in the C₂ gas-phase optimized arrangement (hereafter called M-G structure) and (ii) the photoexcited electrons in MLCT states were now more localized. In fact, the ¹MLCT_A state appeared brighter in the vibrationally distorted, water-solvated, D-W structure, whereas it was dark in the M-G symmetric arrangement, representative of the gas phase. The photoelectron localization could be gauged by inspecting a direct spatial representation of the hole–electron charge redistribution by Natural Transition Orbital analysis¹¹⁴ [NTOs, reported in Figure 1 for ¹MLCT_A (upper panels) and ¹MLCT_B (lower panels)]. In both CT excitations, electron density is always removed from a combination of NCS^– π* and Ru d orbitals to relocate on the whole dcbpy ligands (¹MLCT_A) or more on the dcbpy aromatic rings (the dcbpy portions labeled with 1b or 2b in Figure S1) in a trans orientation with respect to the NCS^– ligands (¹MLCT_B).

Then, the ultrafast CT electronic dynamics through RT-TDDFT were analyzed. The electronic densities to be propagated, resembling an electronic excitation, were prepared according to a well-established procedure.^{71,107,108,115−117} In brief, the orbitals’ population is adjusted by promoting an electron from a selected occupied molecular orbital to another one that is unoccupied in the ground state (“Koopman excitation”). Koopman excitation is a very easy procedure for preparing an initial state resembling an electronic excitation via a nonstationary superposition of excited states.¹¹⁸ Although specific and experimentally tailored approaches have been also proposed over the years for mimicking excitations,^119−121 the procedure used in this work is very effective given the size of the system and the resulting affordable computational cost. Electromagnetic radiation instantaneously induces exciton formation in N3^4–; therefore, the subsequent hole–electron dynamics can be analyzed as time-dependent charge differences with respect to the equilibrium ground state, S₀. In particular, we report in Figure 2 the evolution in time of the charge differences localized on dcbpy1 and 2, NCS1 and 2, and Ru molecular fragments, together with spatial distributions of the positive and negative charge differences since they provide an immediate view of the hole–electron formation and dynamics. The hole and electron positions can be taken as the barycenters of the positive and negative atomic charges, respectively.

Figure 2.

Electronic dynamics of ¹MLCT_A (left) and ¹MLCT_B (right) states for D-W N3^4– structure in water solution. Top: hole (in red) and electron (in blue) barycenter spatial distributions. Hole/electron RMS distances are also reported in the figure. Bottom: time-dependent fragment charges (with respect to the S₀ state). Hole and electron RMS velocities are 0.777 and 0.766 Å fs^–1 for ¹MLCT_A state and 0.838 and 0.760 Å fs^–1 for ¹MLCT_B state, respectively.

Concerning ¹MLCT_A excitation, the hole barycenter is located between NCS2 and Ru, while the electron one is found nearly between dcbpy2 rings (Figure 2, top left panel). Regarding the time evolution of the electronic density, we can observe the charge migration from the NCS2 and dcbpy1 ligands onto both dcbpy2 rings (Figure 2, bottom left panel). The charge carriers appear quite separated and show a 3.100 Å average distance. Their mobility is moreover comparable (0.777 and 0.766 Å fs^–1 hole and electron average velocities, respectively). While NCS1 density is almost constant along the simulation, the hole is shared between NCS2 and Ru center at a fast 16 012 cm^–1 exchange frequency. Nevertheless, the hole appears more localized on the Ru center and not equally shared. After the ¹MLCT_A photoexcitation, the electron appears instead to be moderately stable on the dcbpy2 ligand, because no major charge transfer between the two dcbpy ligands is observed.

Similarly to ¹MLCT_A, we observe that the initial ¹MLCT_B excitation (t = 0) asymmetrically places the photoexcited electron from NCS2 and NCS1 mainly onto one dcbpy ligand (dcbpy2) (Figure 2, bottom right panel). The hole barycenter, again located near the (NCS)₂Ru moiety, now is more symmetrically found between the two NCS^– ligands (Figure 2, top right panel). On the contrary, the electron barycenter explores a wider region, moving from dcbpy2 in the first part of the trajectory (near the dcbpy2a axial ring), toward the dcbpy1b equatorial ring on the other acceptor ligand (after ∼15 fs). Similar hole/electron RMS distance (2.759 Å), hole (0.838 Å fs^–1), and electron (0.760 Å fs^–1) RMS velocities are found. The hole is shared between NCS2 and Ru(II) at 16 012 and 20 015 cm^–1 frequencies, in a less clear way than in ¹MLCT_A (Figure 2, bottom right panel). Again, the hole is more concentrated on the Ru center. In contrast to ¹MLCT_A, the ¹MLCT_B photoinduced electron is hosted by dcbpy2 for ∼15 fs and then completely transferred to dcbpy1 within the simulated 25 fs time. An ultrafast ILET process based upon an intrinsic electronic dynamics is therefore observed for the ¹MLCT_B N3^4– state in water solution at finite temperature.

Electron–nuclear couplings and effects of environmental phonons can potentially induce charge localization during the charge dynamics. Such relaxation processes based upon internal conversion and intersystem crossing, which occur on ∼50–100 fs time scales, have been previously investigated both from an experimental and computational point of view.^33,122−124 On ultrafast time scales, nuclei can instead be considered fixed, and from the results in this letter, it appears that pure electron couplings within electronic states are responsible for the observed ultrafast ILET in solution, which causes charge randomization on the acceptors on a time scale faster than nuclear motions, thereby potentially already promoting subsequent ultrafast charge injection into the substrate. Excited states characterization and electronic dynamics were also performed on the gas-phase, symmetric, and optimized M-G structure, excluding any structural distortion and solvation effects, to rule out the indirect effects induced by dynamics in water at finite temperature and to further assess the purely electronic nature of ILET processes in transition metal compounds like N3^4–. As expected, the structural C₂ symmetry is reflected in ¹MLCT_A and ¹MLCT_B NTOs spatial distributions. In particular, the photoexcited electron is symmetrically distributed between the two acceptor ligands (Figure 3), placed on both axial and equatorial rings (¹MLCT_A) or only on the equatorial rings, trans to the NCS^– ligands (¹MLCT_B). The hole is symmetrically found on both the NCS^– ligands, as well.

Figure 3.

¹MLCT_A and ¹MLCT_B excited states characterized by NTOs (M-G structure). Hole and electron isodensity plots (0.02 isovalue) are reported on left and right panels, respectively.

As matter of fact, the t = 0 initial states of both electronic dynamics are, thus, symmetric (no indirect effects on photoinduced hole–electron density induced by the environment). In ¹MLCT_A state propagation, the hole and the electron barycenters oscillate along the C₂ symmetry axis (Figure 4, top left panel) but with different mobility (1.223 and 0.684 Å fs^–1 RMS velocities, respectively). In particular, the photoexcited electron remains symmetrically spread between the two acceptor dcbpy ligands along all the simulation (Figure 4, bottom left panel). As previously observed in water, an ultrafast ILET process is triggered by the ¹MLCT_B equatorial excitation, although in this case it cannot by ascribed to distortions induced by the finite temperature and solvation because of the highly symmetric structure. In particular, the ¹MLCT_B electronic dynamics on the symmetric M-G structure features a lowering of the symmetry of the initial photoexcited electron spatial distribution, starting from ∼15 fs (Figure 4, bottom right panel), whose barycenter deviates from the symmetry axis (Figure 4, top right panel). The electron mobility appears moreover increased (0.939 Å fs^–1). Several movies of CT dynamics are provided as additional Supporting Files to better display the hole–electron ¹MLCT_A and ¹MLCT_B dynamics on N3^4– D-W and M-G structures.

Figure 4.

Electronic dynamics of ¹MLCT_A (left) and ¹MLCT_B (right) states for M-G symmetric, gas-phase N3^4– structure. Top: hole (in red) and electron (in blue) barycenter spatial distributions. Hole/electron RMS distances are also reported in the figure. Bottom: time-dependent fragments’ charges (with respect to the S₀ state). Hole and electron RMS velocities are 1.223 and 0.684 Å fs^–1 for the ¹MLCT_A state and 1.190 and 0.939 Å fs^–1 for the ¹MLCT_B state, respectively. Note that for the ¹MLCT_A state, the dcbpy1 and dcbpy2 time-dependent charges are equal along the entire simulation and, thus, are completely superimposed.

RT-TDDFT electronic dynamics simulations are used as a mean-field approach to study ultrafast photoinduced charge dynamics and are capable of capturing randomization of the charge transfer on the acceptor ligands. Thus, in this letter, we clearly observe an ILET process on an ultrafast time-scale that is within 15 fs. The intricate electronic manifold can, indeed, induce a randomization of the initial localized excitation via ILET. This process occurs faster than vibrations can start to play an important role, and thus, the charge injection into the substrate can happen before that nuclear motions can further localize the excitations. This was possible by analyzing the RT-TDDFT electronic dynamics simulations, which are capable of disentangling electronic and nuclear effects on such short (not easily experimentally accessible) time scales. Previous experimental works already suggested that ILET processes can occur in the Franck–Condon region or in the ¹MLCT excited state(s), i.e., before the intersystem crossing toward the ³MLCT state, for the extensively studied Ru(bpy)₃²⁺,^20,125−131 as well as for N3^4–.²⁶ However, an ultrafast time-scale of ILET could be only indirectly inferred from experimental measurements, which in fact can only actually probe the final triplet state. This work is, instead, the first direct observation of ultrafast electron exchange between bpy-like ligands in N3^4– dye with such ultrafast time resolution. Remarkably, the ILET mechanism appears to be based upon a purely electronic evolution among the dense, experimentally accessible, MLCT excited state manifold at ∼400 nm, which rules out nuclear–electronic couplings. Specific CT excitations (such as ¹MLCT_B state) seem to actually promote ILET at ∼15 fs after the photoexcitation. As a practical consequence, our study predicts that ILET does not necessarily require nuclear motions to occur and cannot be a rate-limiting step for following electron injection into the semiconductor substrate. The deep comprehension of the dynamic behavior of the MLCT states and the dense electronic manifold is relevant for photoharvesting and can be useful to improve the efficiency of dye sensitizers in solar cell devices. We believe that this work will motivate other groups to utilize RT-TDDFT simulations for testing and designing better performing dye sensitizers to exploit the role of symmetry, electronic nature of ligands, and the nature of the environment in the ultrafast charge dynamics that rule the charge injection into substrates.

Methods

LR- and RT-TDDFT calculations were performed using a development version of the Gaussian suite of programs.¹³² N3^4– electronic structures were obtained by solving the Kohn–Sham equations employing the B3LYP exchange–correlation functional^133−135 with the def2-SVP¹³⁶ basis set and corresponding electronic core potential (ECP) for Ru.¹³⁷ Such level of theory was already validated in previous studies about N3^4– S₀ and T states structural characterization in solution, electronic, and X-ray transitions.^{68,79,113,138}

All the electronic dynamics trajectories were simulated for 25 fs. The modified midpoint unitary transformation (MMUT) method was employed to propagate the RT-TDDFT equations.¹³⁹ Please refer to Section 5 in the Supporting Information for details about the integration procedure and the main text for the preparation of the initial density reproducing the excitation. A time step of 1 as (N3^4– M-G structure) or 2 as (D-W structure) was chosen, which allowed an energy conservation within 10^–6 hartree.

Supporting Information Available

The following files are available free of charge: The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.2c00556.

• N3^4– structure and fragments partition, N3^4–ab initio molecular dynamics in explicit water solution, N3^4– structure for electronic dynamics, N3^4– excited states, and real-time time-dependent density functional theory (PDF)

• rt_hole_el_dw_a.mpg: movie of hole–electron barycenters dynamics, A state, D-W structure (MPG)

• rt_hole_el_dw_b.mpg: movie of hole–electron barycenters dynamics, B state, D-W structure (MPG)

• rt_hole_el_mg_a.mpg: movie of hole–electron barycenters dynamics, A state, M-G structure (MPG)

• rt_hole_el_mg_b.mpg: movie of hole–electron barycenters dynamics, B state, M-G structure (MPG)

Author Present Address

^# Scuola Superiore Meridionale, Largo San Marcellino 10, I-80138 Napoli, Italy

Author Contributions

CRediT: Fulvio Perrella data curation, formal analysis, investigation, writing-original draft, writing-review & editing; Xiaosong Li methodology, software, writing-review & editing; Alessio Petrone conceptualization, methodology, software, supervision, validation, writing-original draft, writing-review & editing; Nadia Rega conceptualization, funding acquisition, methodology, supervision, writing-original draft, writing-review & editing.

The authors declare no competing financial interest.