The First Photoexcitation Step of Ruthenium-Based Models for

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J. Phys. Chem. B 2007, 111, 6078-6087

The First Photoexcitation Step of Ruthenium-Based Models for Artificial Photosynthesis Highlighted by Resonance Raman Spectroscopy Carmen Herrmann,† Johannes Neugebauer,*,† Martin Presselt,‡ Ute Uhlemann,‡ Michael Schmitt,‡ Sven Rau,§ Ju1 rgen Popp,‡ and Markus Reiher*,† Laboratorium fu¨r Physikalische Chemie, ETH Zu¨rich, Wolfgang-Pauli-Strasse 10, CH-8093 Zu¨rich, Switzerland, Institut fu¨r Physikalische Chemie, Friedrich-Schiller-UniVersita¨t Jena, Helmholtzweg 4, D-07743 Jena, Germany, and Institut fu¨r Anorganische Chemie, Friedrich-Schiller-UniVersita¨t Jena, August-Bebel-Strasse 2, D-07743 Jena, Germany ReceiVed: March 1, 2007

Ruthenium-polypyridine and related complexes play an important role as models for light-harvesting antenna systems to be employed in artificial photosynthesis. In this theoretical and experimental work, the first photoexcitation step of a tetranuclear [Ru2Pd2] complex composed of two ruthenium-bipyridyl subunits and two palladium-based fragments, {[(tbbpy)2Ru(tmbi)]2[Pd(allyl)]2}2+ (tbbpy ) 4,4′-di-tert-butyl-2,2′-bipyridine, tmbi ) 5,6,5′,6′-tetramethyl-2,2′-bibenzimidazolate), is investigated by means of experimental and theoretical resonance Raman spectroscopy. The calculated spectra, which were obtained within the short-time approximation combined with time-dependent density functional theory (TDDFT), reproduce the experimental spectrum with excellent agreement. We also compared calculations on off-resonance Raman spectra, for which a completely different theoretical approach has to be used, to experimental ones and again found very good agreement. The [Ru2Pd2] complex represents the probably largest system for which a quantum chemical frequency analysis and a calculation of conventional Raman as well as resonance Raman spectra with reasonable basis sets have been performed. A comparison between the resonance Raman spectra of the [Ru2Pd2] complex and its mononuclear [Ru] building block [(tbbpy)2Ru(tmbi)]2+ and a normal-mode analysis reveal that the [Ru2Pd2] resonance Raman spectrum is composed uniquely from peaks arising from the [Ru] fragment. This observation and an analysis of the Kohn-Sham orbitals mainly involved in the initial electronic excitation in the TDDFT description of the [Ru2Pd2] system support the hypothesis that the initial photoexcitation step of [Ru2Pd2] is a charge-transfer excitation from the ruthenium atoms to the adjacent butyl-2,2′-bipyridine ligands.

1. Introduction Light-harvesting antennae are essential building blocks in natural as well as artificial photosynthetic systems.1,2 They accomplish the first of four essential steps in photosynthesis,2 which are (1) the absorption of light by antenna systems, (2) the transfer of photoexcitation energy to the reaction center, (3) charge separation, and (4) exploiting charge separation for the synthesis of higher-energy compounds. Natural antenna systems mainly consist of extended supermolecular aggregates of chlorophyll a and b, i.e., of substituted tetrapyrroles coordinated to a central manganese atom, and of carotenoids.1 The analogues of chlorophyll in artificial photosynthesis are often either zinc porphyrin chromophores3,4 or ruthenium-polypyridine and related complexes. The latter play a central role as photoactive components in artificial solar energy conversion,5,6 e.g., in dye-sensitized photovoltaic devices,7,8 or as model compounds for energy-transfer and charge-separation processes.9 In the context of artificial photosynthesis, ruthenium-polypyridine complexes are of particular interest in combination with an electron-donating manganese cluster to mimic the function of the P680 complex in photosystem II of green plants.10 * Authors to whom correspondence should be addressed. E-mail: [email protected]; [email protected]. ch. † ETH Zu ¨ rich. ‡ Institut fu ¨ r Physikalische Chemie, Friedrich-Schiller-Universita¨t Jena. § Institut fu ¨ r Anorganische Chemie, Friedrich-Schiller-Universita¨t Jena.

Related applications include the photocatalytic generation of hydrogen at room temperature and in homogeneous solution by [RuPd] complexes.11,12 The initial steps involved in the photoexcitation of ruthenium-polypyridine complexes can in most cases be described as a transition from the singlet ground state to the first excited singlet state, followed by a very fast intersystem crossing to the lowest-lying triplet state.13 Investigations using femtosecond time-resolved spectroscopy suggest that a subsequent charge transfer from Ru to Pd takes place in systems containing one or more additional Pd center(s),13 such as the tetranuclear [Ru2Pd2] complex {[(tbbpy)2Ru(tmbi)]2[Pd(allyl)]2}2+ reported in ref 14 (tbbpy ) 4,4′-di-tert-butyl-2,2′bipyridine, tmbi ) 5,6,5′,6′-tetramethyl-2,2′-bibenzimidazolate; see the lower part of Figure 1 and Figure 2). The tetranuclear [Ru2Pd2] complex can therefore be regarded as a small model for an antenna system (the [Ru] subunits) linked to a possible reaction center (the [Pd] subunits) via a bibenzimidazolate bridge. Since the [Ru] subunits take part in the charge transfer, they may, in addition to their role as antennae, also be interpreted as a part of the reaction center. What makes the [Ru2Pd2] complex special compared to, for example, its flat [Ru2Cu2] analogue,14 is its rooflike structure, in which the two central [Pd] fragments constitute the roof ridge and are thus easily accessible for potential reactants. Although photocatalytic activity of the [Ru2Pd2] complex has not been shown yet, this system can serve as a a prototype for photo-

10.1021/jp071692h CCC: $37.00 © 2007 American Chemical Society Published on Web 05/10/2007

Ru-Based Models for Artificial Photosynthesis

Figure 1. Structures of the two ruthenium-bipyridyl systems under study: [(tbbpy)2Ru(tmbiH2)](PF6)2 (1; top) and {[(tbbpy)2Ru(tmbi)]2[Pd(allyl)]2}(PF6)2 (2; bottom).

Figure 2. Rooflike structure of [Ru2Pd2] (2). Structure optimization: BP86/RI, TZVP.

systems with exponated reactive centers for which our results are expected to be of significance. The goal of this study is to investigate the very first step in the photoexcitation of the tetranuclear {[(tbbpy)2Ru(tmbi)]2[Pd(allyl)]2}2+ complex, i.e., the transition to the excited singlet state. For this purpose, resonance Raman spectroscopy can be employed. This technique is a special form of Raman spectroscopy, where the energy of the incident laser beam is close to an electronic transition of the system under study.15 Thus, the intensities of vibrational modes located on chromophores under resonance are enhanced, which makes the technique optimally suited for selectively investigating chromophores in extended biological systems such as enzymes.16,17 Resonance Raman spectroscopy is often applied in studies on artificial or biological light-harvesting systems such as bacteriochlorophyll a18 or dendritic antenna systems,19 where electron or excitation energytransfer processes occur between different chromophores in a functional arrangement. It has also been used to investigate the spectroscopic properties of ruthenium-polypyridyl or related complexes (see ref 20 and references therein). In this work, experimental resonance Raman studies are complemented by first-principles quantum chemical calculations relying on density functional theory (DFT). For a review on first-principles approaches to resonance Raman and other selective types of spectroscopy to biologically relevant mol-

J. Phys. Chem. B, Vol. 111, No. 21, 2007 6079 ecules see, for example, ref 21. These calculations serve two purposes: First, the comparison of the calculated spectra to the measured ones provides an excellent means to assess the feasibility and reliability of the currently available quantum chemical methodology. This holds in particular for the capability of the short-time approximation in connection with timedependent DFT (TDDFT) to predict resonance Raman spectra of ruthenium-bipyridyl compounds. Second, and more important, the calculations provide insight into the electronic mechanisms involved in photoexcitation not avaliable in this detailed resolution from experiment. From theory, we hence gather detailed information on the interconnection between electronic structure and vibrational modes in the photoexcitation. Local contributions to the most intense resonance Raman peaks may be identified by inspecting the associated calculated normal modes, and the nature of the transition to the excited singlet state may be characterized by analyzing the electronic structure in terms of Kohn-Sham orbitals mainly involved in the description of the excitation by TDDFT. The quantum chemical calculation of resonance and offresonance Raman spectra are based on completely different intensity theories.15 To check the consistency of the established quantum chemical methodology for the description of different forms of Raman spectroscopy, calculated as well as measured off-resonance Raman spectra for the tetranuclear [Ru2Pd2] compound are also presented and compared to the resonance Raman results. The photoexcitation is supposed to be located uniquely on the [Ru] fragment; the resonance Raman spectrum of the tetranuclear [Ru2Pd2] complex is thus expected to be very similar to the one of its peripheral building block, the mononuclear complex [(tbbpy)2Ru(tmbiH2)]2+ (see the upper part of Figure 1). To test this assumption, resonance Raman spectra were also recorded and calculated for the smaller mononuclear [Ru] complex. Our work represents the first theoretical Raman study on molecular systems of the size of the tetranuclear [Ru2Pd2] complex using first-principles methods with basis sets of a reasonable size. We employ DFT methods using basis sets of a sufficient size and including polarization functions on all atoms, as is necessary for a reliable description of Raman spectra. This article is organized as follows: After outlining the theory of resonance Raman scattering in section 2, the quantum chemical and experimental methodology is summarized in section 3. In section 4, calculated and measured molecular structures and resonance Raman spectra are compared, while the next section provides a discussion of the calculated data. Finally, the results are summarized in section 5. The [Ru] and the [Ru2Pd2] complexes will be denoted as 1 and 2, respectively, in the following. 2. Theory Raman phenomena are described in terms of the KramersHeisenberg-Dirac formula for scattering tensor matrix elements.22,23 In the case of resonance with a particular excited electronic state, the original expression for the polarizability tensor matrix elements (see, for example, ref 24) can be simplified by assuming that only this excited state has to be considered and that only the term with an energy difference in the denominator will be important, since this term will dominate in the case of resonance. The simplified expression becomes25,26

Rf,i(ωL) )

∑k

〈f|µge(Q)|k〉〈k|µeg(Q)|i〉 , ωL - ωki + iΓik

(1)

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where |i〉 and |f〉 are initial and final vibrational states, respectively, of the electronic ground state, |k〉 is an intermediate vibrational state in the excited electronic state, µeg is an electronic dipole matrix element between the excited (e) and ground (g) electronic state, ωL is the laser frequency, ωki is the energy difference between the initial and the intermediate vibronic states, and Γik is the inverse lifetime of the wave packet in the intermediate state upon excitation from state |i〉; i.e., it is connected with the line width of the transition |i〉 f |k〉. Note that the above equation is of a symbolic nature, since the transition dipole moment and the polarizability matrix elements appear as scalar quantities, although they would have to be treated as first and second rank tensors, respectively. However, these tensor properties are usually eliminated by classical averaging over all possible orientations (see ref 25). In the timedependent theory of resonance Raman scattering, the energy denominator of the right-hand side of eq 1 is expressed as the half Fourier transform25

1 1 ) ωL - ωki + iΓ i

∫0∞ dt exp[i(ωL - ωki)t - Γt]

(2)

where a common inverse lifetime Γ is assumed for all vibronic transitions involved. The next steps are to explicitly write ωki ) ωk - ωi as a difference of the energy levels and to note that exp[- iωkt|k〉 ) exp[- iH ˆ ext/p]|k〉, where H ˆ ex is the Hamiltonian for the nuclear motion on the excited-state potential energy surface. With that, we obtain from eq 1

Rf,i(ωL) )

1

∞ dt exp[i(ωL + ωi)t - Γt]〈f|µge(Q) ∫ 0 i exp[-iH ˆ ext/p]∑ |k〉〈k|µeg(Q)|i〉 k

1 ) |µge(0)|2 i

∫0∞ dt exp[i(ωL + ωi)t - Γt] 〈χf|exp[-iH ˆ ext/p]|χi〉 (3)

In the last transformation, we used the closure relation ∑k |k〉〈k| ) 1 and the Condon approximation, µge(Q) ≈ µge(0). The functions |χi,f〉 are defined as products of the vibrational wavefunctions and the nuclear-coordinate-dependent part of the electronic transition moment, i.e.,

[

χi ) 1 +

∑j µ

1

( )

ge(0)

∂µge ∂Qj

]

Qj + ‚‚‚ |i〉

0

(4)

In a more compact notation, the initial vibrational wavepacket propagated by the excited-state vibrational Hamiltonian is often written as exp[-iH ˆ ext/p]|χi〉 ) |χ(t)〉. The resonance Raman scattering cross-section is proportional to

|Rf,i(ωL)|2 ) |µge(0)|4 | | ∞ | 0 dt exp[i(ωL + ωi)t - Γt]〈χf|χ(t)〉|2 (5) | |

∫

Under certain conditions, the time integral in this equation is determined by the dynamics of the system during a very short time after excitation in which the overlap 〈χf|χ(t)〉 is large. This is in particular the case if (1) the excitation is in preresonance, (2) the damping factor Γ is large enough so that the factor exp[-Γt] is sufficiently small to quench the overlap for longer times after excitation (e.g., by interactions with solvent molecules), or (3) there are many Franck-Condon-active vibrational

normal modes with considerably different frequencies.26,27 Heller et al. could show on the basis of an analysis of Gaussian wavepacket dynamics on classical excited-state potential energy surfaces26 that in these cases the polarizability tensor matrix element is determined to a good approximation only by the gradient of the excited-state potential energy surface. The relative resonance Raman intensities ij and ik for two (massweighted) normal modes Qj and Qk are then given by26

() ()

ij ν˜ k VQj 2 Vqj ) ) q ik ν˜ j VQ Vk k

2

(6)

where ν˜ j or ν˜ j are the wavenumbers of vibration j and k, respectively, and

VQj

( )

∂Eex el ) ∂Qj

.

(7)

Qj)0

Vqj is the corresponding excited-state gradient expressed in terms of the reduced (or dimensionless) normal coordinate qj ) Qjx2πcν˜ j/p. It should be noted that a more general version of the Placzek approximation polarizability has been proposed based on the short-time approximation, which reduces to the conventional Placzek approximation in the nonresonant case, and which has the advantage of automatically including all possible excited states, and compares well with experiment as well as to the short-time approximation.28,29 Although only valid within clearly defined conditions, the short-time approximation in combination with TDDFT has successfully been used in several studies on resonance Raman spectra (see, for example, refs 30-33 and 36). Resonance Raman spectra are often interpreted in terms of reorganization energies. Within the assumption that the groundand excited-state equilibrium positions are displaced but the vibrational frequencies are the same in both states, the reorganization energy in the excited state along a normal mode j can be calculated from the normal-mode displacement ∆qj of the excited-state minimum as follows34

λj )

ωj(∆qj )2 . 2

(8)

Within the “independent mode, displaced harmonic oscillator’’ (IMDHO) model,35,36 it is possible to calculate the reorganization energy from the excited-state displacements and vibrational frequencies of all normal modes. It should be noted, however, that the displacements ∆qj actually have two different interpretations within this model, which may not necessarily be the same in the real system. On the one hand, they are related to the gradients of the excited-state potential energy surface, which determine the short-time dynamics in the excited state. This is what Heller’s approach26 focuses on, which allows us to calculate resonance Raman intensities without making reference to the excited-state equilibrium structure. On the other hand, it can be interpreted as the displacement of the excited-state equilibrium structure and is, for example, calculated as such, i.e., by calculation of the geometric difference between the ground- and excited-state equilibrium structures within the transform-theory approach.37 A safe interpretation of the resulting resonance Raman spectrum would require that these two approaches are in agreement, as they should be for the IMDHO model.36

Ru-Based Models for Artificial Photosynthesis If conclusions about the reorganization energies in experiment shall be drawn on the basis of the calculation, then it is in general advisable to consider the solvent effect on the reorganization energy, since the total reorganization energy is a sum of all λj, i.e., also including all solvent degrees of freedom. Such a treatment would lead to an enormous increase in computational effort. For smaller molecules, the Car-Parrinello moleculardynamics-based approach outlined in ref 38 might offer a promising way in this respect. In most interpretations of experimental spectra, this problem is circumvented by going back to the explicitely time-dependent expression, eq 2, and by introducing a solvent-specific function gsolv(t) in the exponent. To mimic the solvent degrees of freedom, this function is often parametrized for a Brownian oscillator mode, which contains three parameters that can be adjusted to match both resonance Raman and optical absorption spectra.25 Since our main focus here is on the performance of the first-principles approach within the excited-state gradient approximation for the resonance Raman intensities, we refrain from analyzing the reorganization energies and the solvent contributions in detail. 3. Computational and Experimental Methodology Resonance Raman intensities were calculated by projection of the excited-state gradients onto the ground-state normal modes according to eq 6. For the seminumerical calculation of vibrational frequencies and normal modes, the vibrational spectroscopy program package SNF39 was used, which allows for high-efficiency massive parallelization and excellent restart facilities necessary for systems of the size under study here. Ground- and excited-state electronic structure, gradient and polarizability calculations, as well as geometry optimizations were performed with the quantum chemical suite of programs Turbomole40 using density functional theory and employing the BP86 functional41,42 in combination with the resolution-of-theidentity (RI) density fitting technique as implemented in Turbomole.43 Ground-state polarizabilities and excited-state gradients were calculated analytically based on TDDFT as implemented in Turbomole.44,45 For further references on the calculation of excited-state gradients within TDDFT, see refs 44 and 46-48. We used Ahlrichs’ TZVP basis set49 throughout, which features a valence triple-ζ basis set with polarization functions on all atoms. For the metal atoms, effective core potentials of the Stuttgart group were employed (which also account for the scalar relativistic effects).50 These potentials include 28 electrons of the inner shells of both ruthenium and palladium, i.e., the 16 (Ru) or 18 (Pd) electrons belonging to the 4s, 4p, 4d, and 5s shells are treated explicitly. Molecular structures and orbitals were visualized with the programs VMD51 and Molekel.52 For the graphical representation of the normal modes, Jmol53 was employed. The two PF6- anions were not included into the calculations, resulting in a charge of +2 for each of the two complexes under study. On an AMD Opteron 250 processor with 2400 MHz and 2 GB RAM, each single-point calculation needed for the Raman spectrum took 24 h on average. For the 272 atoms of the [Ru2Pd2] complex 2, 6 × 272 ) 1632 single-point calculations were needed when using a three-point formula for the numerical differentiations of the gradient and polarizability components along nuclear coordinates. Altogether, around 40 000 CPU hours were needed for the calculation of the Raman spectrum. The preceding structure optimization took approximately 1400 CPU hours, corresponding to 60 days or 2 months on a single processor. Due to the long wall time needed for the calculation of the spectra, reliable restart facilities as provided by Snf were mandatory.

J. Phys. Chem. B, Vol. 111, No. 21, 2007 6081 For the resonance Raman experiments the ruthenium complexes were dissolved in methylene chloride of spectroscopic purity. We prefered to measure the solution in favor of the solid state of the compounds to avoid decomposition of the samples upon irradiation, which can be better achieved in solution by rotation of the samples. The concentration of the solutions was optimized to obtain a maximum signal-to-noise ratio and was in the millimolar range. Off-resonance spectra were, however, recorded from a solid sample at 830 nm. To measure resonance Raman spectra of the ruthenium complexes in solution, the 458 nm line of an argon ion laser lying in the maximum of the metal-to-ligand charge transfer (MLCT) absorption band was used for excitation. The spectra were recorded in a 90° scattering geometry with a rotating cell to avoid degradation of the sample. The scattered light was focused onto the entrance slit of the spectrometer and analyzed with a double monochromator (Spex 1404, f ) 85 cm, 2400 grooves/mm). The dispersed Raman signal was recorded with a liquid-nitrogen-cooled CCD camera (Photometrics model RDS 200). Raman and resonance Raman spectra were recorded for the chemically significant wavenumber region between 200 and 1800 cm-1. The region of the C-H stretching modes at higher wavenumbers (in particular around 3000 cm-1), which may also be expected to contribute to the spectra, was discarded since these modes may be found in the spectra of virtually all organic molecules and residues and are thus not characteristic for the systems under study here. Self-absorption of the scattered light was minimized by focusing the laser light extremely close to the sample cell wall. Thus, the path length of the scattered light through the sample was minimized. Furthermore, the spectra were normalized according to the internal standard CH2Cl2 (solvent). 4. Results and Discussion Because of the size of the complexes under study, the efficient short-time approximation in connection with TDDFT36 is the method of choice for the calculation of the resonance Raman spectra. The comparatively small [Ru] complex 1 also serves as a test case for the dependence of calculated resonance Raman spectra on the choice of the density functional. The calculation of the resonance Raman spectrum may be divided into three steps: the optimization of the geometric structure, the calculation of the vibrational normal modes and frequencies, and the subsequent calculation of the resonance Raman intensities. For the structure optimization as well as for the calculation of vibrational normal modes and frequencies, the BP86 density functional was employed. The optimized structure is in reasonable agreement with the one obtained from X-ray crystallography.14 While bonding distances between the ruthenium centers and the ligands are reproduced very well, the bonding distances to palladium are overestimated by around 0.05 Å. In contrast to the B3LYP functional, BP86 has proven to yield harmonic vibrational normal modes in close agreement with fundamentals from experiment54-56 due to a fortunate error cancellation,54 which is true in particular for transition metal complexes.57-60 Therefore, no empirical scaling of the frequencies obtained with BP86 is necessary. For vertical TDDFT excitation energies and response properties, however, there are hints that pure functionals such as BP86 are likely to fail, whereas hybrid functionals such as B3LYP in general work better.61,62 This is in particular true for the description of charge-transfer excitations. TDDFT within the local density or the generalized gradient approximations is known to fail for longe-range charge-transfer excitations, i.e.,

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Figure 3. Comparison of experimental and calculated resonance Raman spectra of [(tbbpy)2Ru(tmbiH2)]2+ (1; calculation assuming excitation to the first singlet state). Calculated spectra plotted with Gaussian line-broadening, using a half-width of 20 cm-1. The assignments “BP86” and “B3LYP’’ refer to the density functionals employed for calculating the excited-state gradients needed for the resonance Raman intensities, while the vibrational normal modes and wavenumbers were obtained with BP86(RI)/TZVP in both cases. Accordingly, the vibrational wavenumbers in the BP86 spectrum (middle panel) are identical to those in the B3LYP one (upper panel).

if there is a spatial separation between the occupied and the unoccupied molecular orbitals involved in the transition. This can be partly corrected for by an admixture of exact exchange in the density functional.61,63-66 In our case, we are interested in MLCT excitations, where the relevant molecular orbitals are usually partially overlapping, so that the problems arising for long-range charge-transfer excitations may be expected to be of minor significance. Furthermore, vertical excitation energies are only needed to identify the excited state that is assumed to be in resonance. In the experiment, an excitation into the first absorption band was applied (laser wavelength of 458 nm, corresponding to 2.71 eV), which suggests that the calculation should be performed for the lowest (intense) singlet transition. This point will be discussed in detail below. To ensure that the calculated resonance Raman intensities are not affected by artifacts arising from the long-range chargetransfer problem, the resonance Raman spectrum of the [Ru] complex 1 was calculated using both BP86/RI and B3LYP, respectively, for the excited-state gradients. For the normal modes, BP86/RI was always employed. A comparison between the two calculations shows that despite the inability of BP86 to provide reasonable vertical excitation energies within a TDDFT framework, the resulting spectra indeed agree very well (Figure 3). This is due to the fact that in the short-time approximation only the shape of the excited-state potential energy surface at the ground-state equilibrium structure is relevant but not its vertical position. The excited-state gradient, which determines this local shape, is obviously described well with both functionals. This holds true, in particular, for the most characteristic part of the spectrum between 1200 and 1700 cm-1. Small discrepancies can be observed for the spectral features between 1000 and 1200 cm-1. Overall, the BP86 intensities are actually in better agreement with experiment than the B3LYP ones. Thus, the resonance Raman spectrum of the much larger tetranuclear [Ru2Pd2] complex 2 (containing 272 atoms) has

been calculated using the BP86 density functional for both the normal modes and the resonance Raman intensities. Also here, an excitation into the lowest excited state of significant oscillator strength (which is the second excited singlet state) was assumed (see discussion below). Figure 4 shows that also for the significantly larger tetranuclear complex 2 the calculated spectrum agrees very well with the experimental one. Owing to the efficient BP86 calculations and to a combination of good parallelization and restart facilities provided by our SNF vibrational spectroscopy package,39 it is thus now possible to calculate the full spectrum of normal modes and vibrational frequencies for compounds of the size of the tetranuclear complex under study with remarkable accuracy. The calculated spectrum is indeed dominated by the [Ru] fragment peaks. The most significant difference between the calculated spectra for the [Ru] complex 1 and the [Ru2Pd2] complex 2 is the peak around 1290 cm-1, which is considerably more intense in the spectrum of 2. This is mainly due to an amplification of resonance Raman scattering intensities associated with breathing-like vibrational modes of the RuN2C2 ring of the tmbi ligand (Figure 5). In the experimental spectra, however, this amplification is much less pronounced. Furthermore, the measured spectrum shows a large signal at around 700 cm-1 that is not reproduced by our quantum chemical calculation. This peak is an artifact of the solvent spectrum subtraction procedure. (The most intense Raman band of the CH2Cl2 solvent is centered around 713 cm-1.) It should be noted that in the present example there is not a single excited state that is energetically clearly separated in the calculation so that it can be unambigously identified as the excited state in resonance with the laser beam. In experiment, an excitation into the lowest-energy absorption band of 2 is applied with a laser wavelength of 458 nm (2.71 eV). This absorption band is broad and structureless and extends from approximately 550 to 450 nm (or 2.25 to 2.75 eV),13 so that the relative resonance Raman intensities may be expected to

Ru-Based Models for Artificial Photosynthesis

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Figure 4. Comparison of experimental and calculated resonance and off-resonance Raman spectra of {[(tbbpy)2Ru(tmbi)]2[Pd(allyl)]2}2+ (2). Calculation of resonance Raman spectrum assuming excitation to the second singlet state. Calculated spectra plotted with Gaussian line-broadening, using a half-width of 20 cm-1.

Figure 5. Normal modes responsible for two of the most intense peaks in the [Ru2Pd2] (2) resonance Raman spectra (BP86(RI)/TZVP). Hydrogen atoms have been left out for the sake of clarity.

be rather insensitive to the exact excitation energy. For the calculation, there are two main criteria that can be applied to identify states that may be important for the resonance Raman spectrum: (i) the calculated energy difference for a given

transition compared to the energy of the incident laser beam and (ii) its oscillator strength. The comparison of transition energies is hampered by the fact that the calculated vertical TDDFT excitation energies depend strongly on the density functional. In particular, some of the low-lying excitations in the [Ru2Pd2] complex 2 are clearly of the long-range chargetransfer type, for which generalized gradient approximation functionals such as BP86 are not suitable. As can be seen from Figure 6, there are pairs of nearly degenerate molecular orbitals (MOs) located on either side of the “roof ridge’’. The HOMO f LUMO (S1 in Figure 6) and the HOMO - 1 f LUMO + 1 (S3) transitions involve spatially separated orbitals with almost no (differential) overlap, and the calculated excitation energies are (nearly) equal to the difference in the orbital energies (Table 1 in the Supporting Information). This is a characteristic feature of the long-range charge-transfer problem in TDDFT calculations.63 In general, the excitation energies for such transitions are dramatically underestimated so that it is not likely that these states are in resonance under the experimental conditions employed here. In addition, pure long-range chargetransfer excitations also show a vanishing transition dipole moment (see, for instance, the first singlet transition in Table 1 in the Supporting Information) and are therefore neglected in the following. We are rather interested in the MLCT excitations, for example, HOMO f LUMO + 1 (S4) and HOMO - 1 f LUMO (S2). Transitions to both of these as well as to several other low-lying excited states have significant oscillator strengths (Table 1 in the Supporting Information) and could therefore be important for the resonance Raman spectrum. The excitation energy again is not a very good criterion for the selection of the state assumed in resonance: The BP86 results for the excitations denoted as S2 and S4 in Figure 6 are 1.23 and 1.26 eV, while the corresponding B3LYP excitation energies are 1.79

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Figure 6. Frontier molecular orbitals dominating the excitations to the four lowest excited singlet states (denoted by S1 to S4) in the [Ru2Pd2] complex 2 (BP86(RI)/TZVP). The corresponding orbital energies are given in parentheses. The orbital energies for the depicted pairs of occupied and unoccupied orbitals, respectively, indicate the somewhat imperfect Cs symmetry of the rooflike cluster, which was optimized without symmetry constraints. The small difference in these pairs of energies may be taken as an explanation for the localization of the orbitals on either half of the cluster.

TABLE 1: Measured and Calculated Raman Shifts of 1 and 2 for the Most Intense Peaks in the Resonance Raman (R) and Off-Resonance Raman (oR) Spectra. Raman shift/cm-1 1

2

exptl (R)

BP86(RI)/TZVP

exptl (R/oR)

BP86(RI) TZVP

1030 b 1316 b b 1479 b 1537 b 1581 b 1615

b b 1301 b b 1466 b 1508, 1511 b b b 1591

b 1031 (R)/1032 (oR) b 1317 (R)/1322 (oR) 1472 (oR) 1480 (R) 1535 (oR) 1537 (R) 1581 (oR) 1584 (R) 1611 (oR) 1615 (R)

b 1035 (R),1037 (R, oR) b 1292 (R), 1295 (R, oR) 1445 (oR) 1464 (2×, R) 1516 (oR) 1502, 1504 (R) 1562 (oR) b 1596 (oR) 1592,1594 (R)

assignmenta tmbi, coupled tbbpy tmbi, coupled tmbi, coupled tbbpy, one side tmbi, coupled tbbpy, one side tmbi, coupled tbbpy, one side tbbpy, one side

a Assignments are only given in unambiguous cases. The term coupled means that there are large contributions to the normal mode on both sides of the roof ridge, while one side denotes modes located on one of the sides of 2. b There is no mode in the frequency range of interest with considerable spectral intensity.

and 1.81 eV. Since these two excitations, which both have significant oscillator strengths (Table 1 in the Supporting Information), are spatially and energetically equivalent, we chose to concentrate on the S2 state. The choice of these two transitions is confirmed furthermore by the agreement of the

qualitative picture of a MLCT transition with chemical intuition as well as by the excellent prediction of the measured spectra. It may be anticipated, however, that the measured resonance Raman spectrum is composed of contributions arising from several energetically close-lying states in resonance. To elucidate

Ru-Based Models for Artificial Photosynthesis

Figure 7. Comparison of two similar vibrational modes of the [Ru] 1 (bottom) and the [Ru2Pd2] 2 (top) complexes. For the vibration in 2, a corresponding normal mode can be found located on the other half of the complex with an associated wavenumber of 1503 cm-1.

this point, we calculated spectra for six different low-lying excited states, which all give rise to similar individual resonance Raman spectra (see the Supporting Information for the spectra plots). In the literature, the photoexcitation of ruthenium-bipyridyl complexes is described as initiated by a MLCT.67,68 The four lowest-lying electronic singlet-to-singlet transitions are characterized predominantly by a transition from an occupied MO, which has mainly metal dz2-character, with contributions from the π system of the bibenzimidazolate ligand, to a virtual MO with negligible metal contribution, which is delocalized over the π system of the two bipyridyl ligands. This fits very well into the picture of an initial MLCT. As can be expected from the contributions of the bibenzimidazolate ligand atoms to the occupied MO involved in the lowest-lying electronic transition, the normal modes that show the highest resonance Raman intensity are not only located on the bipyridyl ligands (with wavenumbers around 15021505 cm-1 (see Figure 7 and the Supporting Information)), but also the two modes at 1292 and 1295 cm-1, which involve mainly motions of the bibenzimidazolate ligand atoms (Figure 5). Because of the near degeneracy of structurally similar modes and MOs, the excited-state gradients and thus the resulting resonance Raman spectra of the four lowest-lying excited singlet states are very similar, too. Calculations of the resonance Raman spectrum using any of the four excitations reproduces the experimental spectrum very well. Therefore, despite the difficulties to describe the excitation energies consistently with

J. Phys. Chem. B, Vol. 111, No. 21, 2007 6085 TDDFT, our calculations support the assumption that the MLCT is the first step in the absorption of photons by the tetranuclear [Ru2Pd2] complex (2). A closer look at the normal modes of the [Ru2Pd2] complex 2 and its mononuclear [Ru] building block 1 (Figure 7) also reveals why the [Ru] (1) peaks can be found nearly unaltered in the [Ru2Pd2] (2) resonance Raman spectrum: Many vibrational modes of the [Ru] (2) building block are preserved virtually unchanged in the tetranuclear complex, appearing in almost degenerate corresponding pairs located on either side of the “roof ridge’’. To verify that resonance Raman spectroscopy indeed results in a simplification of the vibrational spectrum in the case under study and to check the internal consistency of our methodology, the off-resonance Raman spectrum of the [Ru2Pd2] complex 2 was calculated within the commonly employed Placzek approximation69,70 and compared to the experimental one (Figure 4). In the region from 1800 to 800 cm-1, the calculation agrees very well with the experiment. Below 800 cm-1, no Raman peaks are predicted by the calculation, while the experimental spectrum shows a range of high Raman scattering intensities. This discrepancy is likely to be due to deficiencies in the theoretical description that may stem from method inherent difficulties of the electronic structure approach chosen here or from the fact that we investigate isolated complexes without considering environment effects. Both possibilities can hardly be overcome at present. As in the case of the resonance Raman spectra, the two peaks centered at 716 and 732 cm-1 in the experimental Raman spectrum, which are not reproduced by the calculations, may be attributed to artifacts of the solvent subtraction. With the same methodology as applied here, a comparable good agreement was achieved for off-resonance Raman spectra of 1,10phenanthroline57 and for a dinuclear diazene iron-sulfur complex with relevance to the biological nitrogen fixation problem.59 With respect to the comparison of the calculated Raman to the calculated resonance Raman spectrum (Figure 4) we note that the region below 1800 cm-1, where mostly vibrations of the aromatic rings are involved, is surprisingly similar for the spectra in and out of resonance. However, the most intense band in the Raman spectrum is located around 1295 cm-1, which involves the tmbi ligands, while in the resonance case the vibrations at higher wavenumbers with main contributions from the tbbpy ligands were the dominant ones. As can be seen from Table 1, although resonance and off-resonance spectra look similar at first glance, there are vibrational modes in the resonance Raman spectrum of 2 that do not have a counterpart in the off-resonance spectrum (with Raman shifts of 1464, 1502, 1504, 1592, and 1594 cm-1) and vice versa (1445, 1516, 1562, and 1596 cm-1). Except for the highest-wavenumber modes (1592/1594 and 1596 cm-1, respectively), the unmatched resonance Raman modes are always located on the tbbpy ligands, while the off-resonance Raman modes mainly involve the tmbi ligands. In particular, the additional peak in the offresonance Raman spectrum at 1561 cm-1 may be attributed to stretching vibrations of the central C-C bond in the tmbi ligands. The calculation of the Raman spectrum for the [Ru2Pd2] complex 2 is an enormous challenge for present-day quantum chemical methods. It represents the probably largest system for which a quantum chemical frequency analysis and a calculation of conventional Raman as well as resonance Raman spectra with reasonable basis sets have been performed. For the calculation

6086 J. Phys. Chem. B, Vol. 111, No. 21, 2007 of the resonance Raman spectrum within the short-time approximation, only a structure optimization, a calculation of normal modes and frequencies from the molecular gradients at displaced structures, and a calculation of the excited-state gradients at the equilibrium structure are needed. The transformation of the Cartesian excited-state gradients to a dimensionless normal-mode basis and the subsequent calculation of the resonance Raman spectrum was very quick. 5. Conclusion and General Discussion In this work, we studied a model for a small artificial lightharvesting antenna system, a tetranuclear [Ru2Pd2] complex, and its mononuclear [Ru] building block by means of experimental and theoretical resonance Raman and off-resonance Raman spectroscopy. The resonance Raman spectrum of the [Ru2Pd2] complex is dominated by vibrations located on the [Ru] building blocks. This result as well as an inspection of the Kohn-Sham molecular orbitals mainly involved in the TDDFT description of the vertical electronic excitations supports the assumption that the initial photoexcitation step in the [Ru2Pd2] system is a MLCT excitation on the [Ru] fragments. The calculated resonance Raman spectra agree very well with the experimental ones. They were obtained with a combination of DFT (BP86/ TZVP) for the ground-state normal modes and frequencies and TDDFT for the excited-state gradients from which within the framework of the short-time approximation the resonance Raman intensities could be computed. Such a good agreement with experiment employing a comparable theoretical methodology was also found for substituted pyrenes.31 The dependence of the calculated resonance Raman intensities on the choice of density functional was checked and found to be negligible. The off-resonance Raman spectrum of the [Ru2Pd2] complex, calculated within the Placzek approximation, also reproduced the experimental one very well. The ability to predict reliable resonance Raman spectra for ruthenium-polypyridyl complexes is of particular relevance, because ruthenium-based systems are among the most commonly employed and most intensely studied artificial lightharvesting antenna systems.5-11 Owing to recent advances in both quantum chemical methodology and computer hardware, quantum chemical calculations of resonance as well as conventional Raman spectra for systems of this type and size are now feasible. It may be anticipated that the methodology applied here will yield calculated resonance Raman spectra in very good agreement with measured ones also for other ruthenium-polypyridyl complexes. Its application to photoexcitable systems of other types will depend first of all on the requirement that the excitedstate dynamics of these systems must be described well by the short-time approximation. As discussed in section 2, large systems with many Franck-Condon-active normal modes (as the one studied here) will in general better fulfill this requirement. Provided the short-time approximation is valid, it is necessary to be able to compute accurate ground-state vibrational normal modes and frequencies and excited-state gradients (to calculate resonance Raman intensities). It turned out in numerous cases that the combination of density functional and basis set applied here (BP86/TZVP) provides harmonic vibrational frequencies in good agreement with fundamental ones due to a fortunate and apparently systematic cancellation of errors.54,56,57,59 Although some density functionals, such as BP86, may yield wrong vertical TDDFT excitation energies, the excited-state gradients may nonetheless be very accurate as witnessed in this work here (see also ref 36 for another example). Note that such

Herrmann et al. a conservation of shape of a potential energy surface calculated to be vertically at a wrong position in energy with different density functionals is known, for example, also for chemical reactions and even for those in states of different spin multiplicity (see refs 71 and 72 for examples). Then the vibrational spectra for a given minimum on a potential energy surface (of given spin) turn out to be quite similar with different density functionals. The experience gained with the calculation of resonance Raman spectra of very large polynuclear transition metal complexes so far may be extended first to other complexes with interesting photophysical properties and second to molecules in solution with explicit consideration of solvent effects. However, for systems of ever-increasing complexity it will then be important to employ focused and selective methods such as the mode-tracking protocol73,74 for the vibrational part and embedding techniques75,76 for the electronic structure part. Acknowledgment. C.H. gratefully acknowledges funding by a Chemiefonds-Doktorandenstipendium of the Fonds der Chemischen Industrie, and J.N. acknowledges funding by a LiebigStipendium of the FCI. This work was supported by the collaborative research center SFB 436 “Metal-Mediated Reactions Modeled after Nature’’ and by the Swiss National Science Foundation (Project No. 200021-113479). Supporting Information Available: Calculated resonance Raman spectra for the [Ru2Pd2] complex 2 assuming excitation to one of the six lowest-lying singlet states each, normal modes responsible for some of the most intense peaks in the [Ru2Pd2] (2) resonance Raman spectra calculated assuming different lowlying singlet excitations, further molecular orbitals important for the excitations to the lowest excited singlet states in the [Ru2Pd2] complex 2, and a list of the lowest-lying transitions for the [Ru2Pd2] complex 2. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Berg, J. M.; Tymoczko, J. L.; Stryer, L. Biochemistry, 6th ed.; W.H. Freeman: New York, 2006. (2) Artificial Photosynthesis: From Basic Biology to Industrial Application; Collings, A. F., Critchley, C., Eds.; Wiley VCH: Weinheim, Germany, 2005. (3) Kodis, G.; Liddell, P. A.; de la Garza, L.; Clausen, P. C.; Lindsey, J. S.; Moore, A. L.; Moore, T. A.; Gust, D. J. Phys. Chem. A 2002, 106, 2036-2048. (4) Kobuke, Y. Eur. J. Inorg. Chem. 2006, 12, 2333-2351. (5) Abrahamsson, M.; Wolpher, H.; Johansson, O.; Larsson, J.; Kritikos, M.; Eriksson, L.; Norrby, P.-O.; Bergquist, J.; Sun, L.; Åkermark, B.; Hammarstro¨m, L. Inorg. Chem. 2005, 44, 3215-3225. (6) Chen, M.; Ghiggino, K. P.; Thang, S. H.; Wilson, G. J. Angew. Chem., Int. Ed. 2005, 44, 4368-4372. (7) Nazeeruddin, M. K.; Gra¨tzel, M. Conversion and Storage of Solar Energy using Dye-Sensitized Nanocrystalline TiO2 Cells. In ComprehensiVe Coordination Chemistry II; McCleverty, J. A., Meyer, T. J., Eds.; Elsevier: Amsterdam, 2003; Vol. 9. (8) Hagfeldt, A.; Gra¨tzel, M. Acc. Chem. Res. 2000, 33, 269-277. (9) Bignozzi, C. A.; Schoonover, J. R.; Scandola, F. A Supramolecular Approach to Light Harvesting and Sensitization of Wide-Bandgap Semiconductors: Antenna Effects and Charge Separation. In Molecular LeVel Artificial Photosynthethic Materials; Meyer, G. J., Ed.; Wiley: New York, 1999. (10) Hammarstro¨m, L. Curr. Opin. Chem. Biol. 2003, 7, 666-673. (11) Rau, S.; Scha¨fer, B.; Gleich, D.; Anders, E.; Rudolph, M.; Friedrich, M.; Go¨rls, H.; Henry, W.; Vos, J. G. Angew. Chem., Int. Ed. 2006, 45, 6215-6218. (12) Rau, S.; Walther, D.; Vos, J. G. Dalton Trans. 2007, 915-919. (13) Dietzek, B.; Kiefer, W.; Blumhoff, J.; Bo¨ttcher, L.; Rau, S.; Walther, D.; Uhlemann, U.; Schmitt, M.; Popp, J. Chem.sEur. J. 2006, 12, 51055115.

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