J. Phys. Chem. B 2010, 114, 511–520
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Investigation of the Resonance Raman Spectra and Excitation Profiles of a Monometallic Ruthenium(II) [Ru(bpy)2(HAT)]2+ Complex by Time-Dependent Density Functional Theory Julien Guthmuller,*,†,‡ Benoıˆt Champagne,† Ce´cile Moucheron,§ and Andre´e Kirsch - De Mesmaeker§ Laboratoire de Chimie The´orique, Faculte´s UniVersitaires Notre-Dame de la Paix (FUNDP), Rue de Bruxelles 61, B-5000 Namur, Belgium, and SerVice de Chimie Organique et Photochimie, UniVersite´ Libre de Bruxelles, AVenue F. D. RooseVelt 50, CP 160/08, B-1050 Bruxelles, Belgium ReceiVed: August 24, 2009; ReVised Manuscript ReceiVed: October 1, 2009
The resonance Raman (RR) properties of the [Ru(bpy)2(HAT)]2+ (where bpy ) 2,2′-bipyridine and HAT ) 1,4,5,8,9,12-hexaazatriphenylene) complex have been investigated by means of time-dependent density functional theory calculations employing the hybrid B3LYP-35 XC functional and by including the effects of the solvent within the polarizable continuum model approach. Analysis of the electronic excited-state energies has demonstrated that mainly four different metal-to-ligand charge-transfer excitations contribute to the first absorption band in vacuo and water. The simulation of the absorption spectra by including the vibronic structure of the states has shown a general agreement with the experimental spectrum recorded in water. Furthermore, significant variations of the excited-state energies and compositions have been found when the effects of the solvent are included. Calculation of the short-time-approximation RR spectra has provided the vibrational signature of each contributing state and has shown that considering only one excited state is not sufficient to accurately simulate the RR spectra for excitation frequencies in resonance with the first absorption band. A comparison of the RR spectra calculated using the vibronic theory for different excitation wavelengths with the measured spectra at 514 and 458 nm has demonstrated that inclusion of the solvent effects in the simulation scheme leads to substantial improvements of the RR intensity patterns, which allow assignment of the vibrational bands. In particular, the calculations are able to reproduce the variations of the HAT and bpy RR intensities as illustrated by their RR excitation profiles, highlighting the strong dependence of the RR intensities with respect to the excitation frequency. 1. Introduction Over the last decades, increasing attention has been devoted to the photochemical, photophysical, and electrochemical properties of ruthenium-based transition-metal complexes.1–4 Besides their fundamental relevance, the interest for such compounds resides in their potential applications in artificial photosynthesis, light-driven catalysis, dye-sensitized solar cells, organic light-emitting diodes, and nonlinear optical materials. For example, ruthenium polypyridine complexes have been employed to photoinduce the splitting of water into hydrogen and oxygen5–7 as well as to design efficient photoelectrochemical cells composed of semiconductor electrodes with wide band gaps.8 Moreover, with a view to develop DNA markers9 and therapeutic agents or biomolecular tools, several studies have shown that ruthenium complexes can inhibit DNA transcription10 or can be applied in gene silencing when chemically attached to oligonucleotide probes.11,12 All of those potential applications require a deep understanding of the photophysical properties of the complexes. In particular, the investigation of their electronic and structural properties, which determine the energy and charge-transfer processes occurring upon photoexcitation, is of special importance to allow for the design of new compounds with desired * To whom correspondence should be addressed. † FUNDP. ‡ Current address: Institut fu¨r Physikalische Chemie, Friedrich Schiller Universita¨t Jena, Helmholtzweg 4, 07743 Jena, Germany § Universite´ Libre de Bruxelles.
properties and functions. To this aim, the use of absorption spectroscopy and resonance Raman (RR) spectroscopy can provide much interesting information, as has been demonstrated by a number of experimental studies.13,14 However, because of the inherent complexity of the electronic and vibrational structures of the complexes, the understanding of their photophysical properties can be hampered by difficulties arising from interpretation of the experimental results. In that way, the use of well-designed theoretical models and of accurate first principles calculations can reveal the fundamental parameters determining the properties of the compounds and allow an interpretation of the measurements.15 Moreover, the development of reliable theoretical approaches is also of interest to predict the photophysical properties of a family or a set of compounds and, consequently, to propose from the computational studies new compounds with suitable functions. Several recent investigations4,16–21 have reported on the calculation of the singlet and triplet electronic excited states of ruthenium complexes. The most commonly employed method is time-dependent density functional theory (TDDFT) because of its good compromise between accuracy and computational cost. Some studies have also used semiempirical approaches22 or even the more expensive post-Hartree-Fock method23 CASSCF/CASPT2. Despite the well-known deficiencies of TDDFT to describe the long-range charge-transfer excited states,24,25 it is generally recognized that this method can provide accurate transition energies of metal-to-ligand charge-transfer (MLCT) states, that is, energies and excited-state properties
10.1021/jp908154q 2010 American Chemical Society Published on Web 10/19/2009
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Guthmuller et al. orientations of the molecule and integrating over all directions and polarizations of scattered light, is given by52–55
Ig0fg1l(ωL) ∝ ωL(ωL - ωl)3
Figure 1. Structure of the [Ru(bpy)2(HAT)]2+ complex corresponding to the enantiomer Λ and Cartesian coordinate system.
allowing an interpretation of the photophysical data. This is particularly the case provided that hybrid exchange-correlation (XC) functionals are employed and provided that the effect of the surroundings (usually the solvent) is included.4 A number of computational studies have also focused on the simulation of RR spectra26–44 for different kinds of compounds. Such approaches have shown several successes for the interpretation and understanding of experimental results. However, up to now, only a few first principles applications have dealt with transition-metal complexes. The most relevant investigations in this area are probably the ones reported by Petrenko et al.45 using TDDFT and ab initio calculations as well as the work of Herrmann et al.,46 in which the Raman and RR spectra of a tetranuclear complex of ruthenium and palladium have been simulated. As outlined before, first principles calculations can be very useful because they allow the determination of all electronic and structural properties of the compounds. This is particularly the case when several electronic excited states provide a contribution to the absorption and RR properties. In such situations, the modeling and interpretation of the experimental spectrum is more complicated because the signs of ∆, representing the dimensionless displacements along the normal coordinates occurring upon excitation, should be known47,48 to evaluate the interferences between the Raman amplitudes of the different states. The purpose of this contribution is to investigate the application of TDDFT-based approaches to the monometallic ruthenium [Ru(bpy)2(HAT)]2+ complex and to assess the vibronic effects beyond the short-time approximation. This compound has already been studied experimentally in a water solution using absorption and RR spectroscopy14 and is known to behave as a good DNA intercalator49 or as an attractive synthetic precursor for heterometallic edifices.50 The enantiomer Λ of the complex is depicted in Figure 1 and is composed of two 2,2′-bipyridine (bpy) ligands and one 1,4,5,8,9,12-hexaazatriphenylene (HAT) ligand. One of the interests in the HAT ligand originates from its ability to act as a unique symmetric bridging ligand for polymetallic complexes.49–51 This study concentrates thus on the simulation and interpretation of the RR properties of the complex at excitation frequencies in resonance with the first absorption band, which corresponds to the experimental situation. In particular, in this contribution, the RR excitation profiles are determined by including the vibronic structure of the excited states because they describe the dependence of the RR intensities with respect to the excitation wavelength. Furthermore, the impact of interaction with a solvent is also considered using the polarizable continuum model. 2. Theory and Computational Methods 2.1. Vibronic Theory of RR. Within the Born-Oppenheimer approximation and assuming that the molecule is initially in its electronic and vibrational ground state, the total Raman intensity for a fundamental transition, obtained after averaging over all
∑ |(RRβ)g0fg1 |2 l
R,β
(1)
where ωL is the frequency of the incident light, ωl is the frequency of the lth normal vibrational mode, and (RRβ)g0fg1l is the Raman polarizability tensor for a transition from the electronic and vibrational ground state |g0〉 to the vibronic state |g1l〉. Then, if ωL is in resonance with several electronic excited states, the Raman polarizability tensor is given by
(RRβ)g0fg1l )
1 p
(µg1l,eu)R(µeu,g0)β
∑ ∑ ωeu,g0 - ωL - iΓ e
(2)
u
where e represents a summation over all electronic excited states contributing to the RR scattering, u describes a summation over the vibrational states of a given electronic state e, (µg1l,eu)R is a component of the transition dipole moment between the states |g1l〉 and |eu〉, ωeu,g0 is the transition energy of the vibronic state |eu〉, and Γ is a damping factor describing a homogeneous broadening. The following additional assumptions are made: (1) only Condon scattering is considered, which corresponds to the A term contribution of Albrecht,52 (2) the ground- and excitedstate potential energy surfaces are harmonic, (3) the excitedstate potential surfaces are only displaced with respect to the ground-state equilibrium geometry (the vibrational frequencies of the ground and excited states are the same, and there are no Duschinsky rotations). Under these approximations, the transition polarizability tensor can be written in the following form:56 (RRβ)g0fg1l )
1 p
∑ (µ
ge)R(µge)β
e
∆e,l
√2
{Φe(ωL) - Φe(ωL - ωl)}
(3) where (µge)R is a component of the electronic transition dipole moment evaluated at the ground-state equilibrium geometry, ∆e,l is the dimensionless displacement for the lth normal coordinate going from the ground to the excited state (e) potential minimum, and the function Φe(ωL) is given by the expression 3N-6
Φe(ωL) )
∑ u
∏ |〈χg0 |χeu 〉|2 i 3N-6
ωe0,g0 +
i
i
(4)
∑ ujωj - ωL - iΓ j
The summation over u is taken over all of the vibrational quantum numbers ui of the electronic excited state (e), ωe0,g0 is the origin transition, and 〈χg0i|χeui〉 is the one-dimensional Franck-Condon (FC) overlap integral between the ground state g and the excited state e for the ith normal mode. Additionally, the absorption spectrum is obtained by summing the imaginary part of the functions Φe(ωL) weighted by the square of the electronic transition dipole moments
A(ωL) ∝ ωL
∑ (µge)2Im Φe(ωL) e
(5)
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2.2. Computational Methods. A program developed locally is employed to calculate the RR intensities and absorption spectra. This is performed through evaluation of eqs 1 and 5 and requires computation of the dimensionless displacements ∆e,l for all normal coordinates of each contributing electronic excited state. Because the potential energy surfaces correspond to displaced harmonic oscillators, the displacements ∆e,l were determined from the partial derivatives of the excited-state electronic energy along the normal coordinates evaluated at the ground-state equilibrium geometry (eq 6).
∆e,l ) -
1
√pωl3/2
( ) ∂Ee ∂Ql
(6)
0
These derivatives were obtained by a two-point numerical differentiation procedure from the vertical excitation energies, which were computed for distorted structures resulting from the addition or subtraction of a finite displacement along the normal coordinates to the equilibrium geometry. Furthermore, the values of ∆e,l allow the calculation of the FC overlap integrals appearing in the function Φe(ωL) and were evaluated by using an analytical expression.32 Quantum chemical calculations were performed with the Gaussian03 program,57 which provides the structural and electronic data necessary for simulation of the RR and absorption spectra. The geometry, vibrational frequencies, and normal coordinates of the ground state were obtained by means of DFT using the XC functional B3LYP-35. B3LYP-35 is a modified version of the Becke three-parameter hybrid XC functional58 that contains 35% of Hartree-Fock exchange and that has recently been successfully applied for determination of the absorption and RR properties of the julolidinemalononitrile push-pull chromophore in different solvents.32 The LANL2DZ double-ζ basis set was used for the ruthenium atom in association with the 28-electron relativistic effective core potential;59,60 that is, 4s, 4p, 4d, and 5s electrons are treated explicitly, whereas the three first inner shells are described by the core pseudopotential. The 6-31G* double-ζ basis set with d polarization functions on carbon and nitrogen was employed for the ligands. Additionally, RR intensities for several modes were also calculated with the 6-311G* basis set and showed negligible differences in comparison to 6-31G*. Therefore, to reduce the computational cost, only the 6-31G* basis set was considered in the entire study. To correct for the lack of anharmonicity and the approximate treatment of electron correlation,61 the harmonic frequencies were scaled by the factor 0.94. The vertical excitation energies and electronic transition dipole moments were obtained from TDDFT calculations within the adiabatic approximation with the same XC functional, pseudopotential, and basis set. The effects of interaction with a solvent (water) on the geometry, frequencies, and excitation energies were taken into account by the integral equation formalism of the polarizable continuum model62 (IEFPCM). The nonequilibrium procedure of solvation was used for calculation of the excitation energies, which is well adapted for processes where only the fast reorganization of the electronic distribution of the solvent is important. The molecular orbitals (Figure 2) and normal coordinates (Figure 9) were viewed and drawn using the graphical tool Gabedit.63 3. Results and Discussion 3.1. Excited States. The vertical excitation energies of the 30 lowest singlet excited states have been computed in vacuo
Figure 2. Molecular orbitals involved in the dominant configurations of the states responsible for the absorption and RR properties of the complex. The depicted orbitals were computed with the B3LYP-35 XC functional in water. Because the orbitals in vacuo show similar shapes, their orbital numbering is given in square brackets.
and water using the ground-state geometries optimized in the corresponding environment. Because the RR measurements14 and simulations (section 3.3) are performed with excitation wavelengths of 458 and 514 nm in resonance with the first absorption band, only the excited states participating with this band will be considered and described. Among these states, several of them are found with a small oscillator strength (f < 0.025) and can therefore be neglected because they provide a negligible contribution to the absorption spectrum and, consequently, to RR scattering (eq 3). Finally, under these conditions, only four states (states 6, 14, 15, and 21) remain significant in vacuo as well as in water (states 3, 6, 11, and 14). The vertical excitation energies, oscillator strengths, transition dipole moments, and singly excited configurations are given in Table 1 for the four states that dominate the absorption spectrum in vacuo. The main orbitals involved in the transitions are depicted in Figure 2 in addition to their numbering in vacuo, which is given in square brackets. All excited states correspond to MLCT excitations, which are associated with transitions from d orbitals of the ruthenium atom to π* orbitals of the HAT and bpy ligands. More precisely, the two lowest excited states (6 and 14) have the largest oscillator strengths with values of 0.101 and 0.114, respectively, and involve a charge transfer to the HAT ligand for state 6 and to the bpy ligand for state 14. Moreover, the next two states (15 and 21) have smaller oscillator strengths with values of 0.053 and 0.050, respectively, and are composed of several transitions to the HAT and bpy ligands, with a dominant contribution given by a transition to the HAT ligand for state 21. Furthermore, it can be noted that transitions to states 6, 15, and 21 present a transition dipole moment oriented along the X axis connecting the ruthenium atom to the HAT ligand (Figure 1), whereas state 14 has a transition dipole moment oriented along the Y axis.
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TABLE 1: Vertical Excitation Energies, Oscillator Strengths, Transition Dipole Moments and Singly-Excited Configurations with Weights Larger than 8% of the Main Excited States Contributing to the First Absorption Banda state no.
transition
6
dRu(147) f π*HAT(150)
78
3.57
0.101 µx ) -1.08 µy ) 0.00 µz ) 0.00
14
dRu(148) f π*bpy(151) dRu(147) f π*bpy(152) dRu(146) f π*bpy(151)
37 26 25
3.84
0.114 µx ) 0.00 µy ) 1.10 µz ) 0.02
15
dRu(149) dRu(147) dRu(146) dRu(148) dRu(148)
f f f f f
π*HAT(153) π*bpy(151) π*bpy(152) π*bpy(152) π*HAT(153)
29 19 15 11 8
3.89
0.053 µx ) -0.74 µy ) 0.00 µz ) 0.00
dRu(148) dRu(149) dRu(146) dRu(148)
f f f f
π*HAT(153) π*HAT(153) π*HAT(153) π*bpy(152)
30 16 12 8
4.15
21
weight Evert (%) (eV)
f
(µge)R(au)
0.050 µx ) -0.70 µy ) 0.00 µz ) 0.00
Figure 3. Absorption spectrum of [Ru(bpy)2(HAT)]2+ calculated in vacuo according to eq 5 (black line). Oscillator strengths (black sticks) and absorption spectra (dashed lines) of the individual electronic states contributing to the first absorption band. The experimental spectrum (gray line) in water is taken from ref 14. The theoretical spectra are computed with a damping factor Γ fixed at 1200 cm-1 and are shifted so that experimental and theoretical maxima coincide. The wavelengths of 514 and 458 nm correspond to the wavelengths at which the RR experiments were performed.
a The calculations are performed at the TDDFT level of approximation with the B3LYP-35 XC functional in vacuo.
TABLE 2: Vertical Excitation Energies, Oscillator Strengths, Transition Dipole Moments, and Singly Excited Configurations with Weights Larger than 8% of the Main Excited States Contributing to the First Absorption Banda state no.
transition
weight Evert (%) (eV)
3
dRu(147) f π*HAT(150)
78
3.32
6
dRu(149) f π*HAT(151)
76
3.57
11
dRu(148) f π*HAT(151) dRu(149) f π*bpy(154)
55 13
3.75
14
dRu(147) f π*bpy(154) dRu(148) f π*bpy(153)
51 39
3.89
f
(µge)R(au)
0.097 µx ) -1.09 µy ) 0.00 µz ) 0.00 0.051 µx ) -0.76 µy ) 0.00 µz ) 0.00 0.101 µx ) -1.05 µy ) 0.01 µz ) 0.00 0.115 µx ) 0.01 µy ) 1.10 µz ) 0.03
a
The calculations were performed at the TDDFT level of approximation with the B3LYP-35 XC functional in water (IEFPCM).
Table 2 presents the excited-state properties calculated in water using the IEFPCM approach. The comparison between vacuum and water shows that interaction with the solvent has a large impact on the energies, ordering of the states, and orbital transitions. The lowest excited state (state 3) presents properties similar to those of state 6 in vacuo and corresponds to a transition to the HAT ligand. Similarly, state 14 has orbital composition, oscillator strength, and transition dipole moment comparable to those of state 14 in vacuo, and both states involve charge transfer to the bpy ligands. However, states 6 and 11 present no strict concordance with states 15 and 21 in vacuo. It can be noted that these pairs of states exhibit a main contribution from a transition to the same HAT orbital (151 in water and 153 in vacuo) but that the mixing with transitions to the bpy orbitals is less pronounced in the case of water. The large differences in the excited-state properties between vacuum and water can be understood from modification of the molecular orbital energies and ordering. Indeed, the effect of the solvent leads to a stronger stabilization of the HAT orbitals with respect
Figure 4. Absorption spectrum of [Ru(bpy)2(HAT)]2+ calculated in water according to eq 5 (black line). Oscillator strengths (black sticks) and absorption spectra (dashed lines) of the individual electronic states contributing to the first absorption band. The experimental spectrum (gray line) in water is taken from ref 14. The theoretical spectra are computed with a damping factor Γ fixed at 1200 cm-1 and are shifted so that experimental and theoretical maxima coincide. The wavelengths of 514 and 458 nm correspond to the wavelengths at which the RR experiments were performed.
to the bpy orbitals. As a consequence, when going from in vacuo to water, the two HAT orbitals 151 and 152 become lower than the two bpy orbitals 153 and 154. One consequence of the latter is the fact that the three lowest excited states in water (3, 6, and 11) correspond mainly to excitations to the HAT ligand, whereas in vacuo, only one excitation to the HAT ligand (state 6) is found with energy lower than state 14, which involves a transition to the bpy ligands. Finally, it can be observed that the orbital π*HAT(152) in water (π*HAT(154) in vacuo), which is mainly localized at the end of the HAT ligand, provides no significant contribution to the excited states participating with the first absorption band. 3.2. Absorption Spectra. The normalized absorption spectra in vacuo and water are depicted on Figures 3 and 4, respectively. These spectra were computed from eq 5 by including the vibronic structure (FC factors) of each contributing state and are compared to the experimental absorption spectrum recorded in water (further information concerning the experimental
Investigation of [Ru(bpy)2(HAT)]2+ procedure can be found in ref 14). In order to reproduce the experimental broadening, a damping factor Γ equal to 1200 cm-1 was assumed in the simulation. Other values of Γ comprised between 1000 and 1500 cm-1 were tested but had negligible effects on the absorption and RR spectra and, therefore, do not affect the subsequent analysis and conclusions. Additionally, the relative positions of the origin transitions (ωe0,g0) were approximated by the relative energies of the vertical excitations given in Tables 1 and 2. Furthermore, to correct for the absolute error in reproducing the position of the first absorption band, the simulated spectra have been shifted so that the theoretical and experimental maxima coincide. Figures 3 and 4 show the contributions of the different excited states to the absorption spectrum as well as the amplitudes of their oscillator strengths. The absorption spectrum simulated in vacuo (Figure 3) presents a general agreement with experiment. Indeed, a shoulder is found between 475 and 500 nm with an intensity that is partially underestimated in comparison to the experimental spectrum. This shoulder mainly arises from the contribution of state 6, which involves an excitation to the HAT ligand. However, the central part of the absorption band is obtained from a superposition of the states 6, 14, 15, and 21 and therefore involves contributions from excitations to both HAT and bpy ligands. Similarly to that of in vacuo, the spectrum simulated in water (Figure 4) displays a shoulder at longer wavelengths (between 475 and 550 nm). The fact that this shoulder is more pronounced is in agreement with the experiment, but its width and position are overestimated in comparison to the experimental spectrum. In this case, the shoulder mainly results from the two lowest transitions to the HAT ligand and its width originates from the large energy gap between states 3 and 6. Finally, in water the transition to the bpy ligands (state 14) only provides a contribution to the shorter-wavelength part of the absorption band. By comparison of the shapes of the simulated absorption spectra in vacuo and water with the experimental spectrum, it can hardly be concluded whether the inclusion of interaction with the solvent in the computational scheme improves the agreement with the experiment or not. Indeed, both simulated spectra show a general agreement with the experiment while the differences concern reproduction of the shoulder at longer wavelengths. Nevertheless, it can be noted from Tables 1 and 2 that taking into account the solvent leads to a decrease of the energies for the states involving a transition to the HAT ligand. Such an effect provides a correction to the overestimation obtained with the XC functional B3LYP-35 on the absolute position of the absorption maximum. This is in agreement with recent DFT investigations of charge-transfer excited states of transition-metal complexes (ref 4 and references cited therein), which concluded that accurate excitation energies can be obtained using hybrid XC functionals and including the effect of the solvent. Additionally, to correctly predict the RR spectrum for different excitation wavelengths, an accurate determination of the absolute position of the absorption band is not sufficient. It can even be of lesser importance if the exact position of the band in resonance is known from the experiment because in this case an overall correction can always be applied to the computed energies to fit the experimental conditions. However, a proper description of the absorption band shape, which is determined by the relative energies, intensities, and orbital decompositions of the excited states, is mandatory to appropriately reproduce the dependence of the RR spectrum with respect to the excitation wavelength. In that sense, the large modifications induced by the interaction with the solvent on
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Figure 5. RR spectra in resonance with each electronic excited state contributing to the first absorption band in vacuo. The spectra are calculated within the short-time approximation (Ie,g0fg1l ) ωl2∆e,l2) and are normalized with respect to the most intense band. A Lorentzian function with a full width at half-maximum (fwhm) of 10 cm-1 is employed to broaden the transitions.
Figure 6. RR spectra in resonance with each electronic excited state contributing to the first absorption band in water. The spectra are calculated within the short-time approximation (Ie,g0fg1l ) ωl2∆e,l2) and are normalized with respect to the most intense band. A Lorentzian function with a fwhm of 10 cm-1 is employed to broaden the transitions.
the excited states contributing to the first absorption band are significant and their effect can be studied in more detail by investigating the RR properties. 3.3. RR Spectra. The theoretical simulation of RR spectra has often been performed in the literature within the so-called short-time approximation, in which the dependency of the RR intensities on the excitation frequency is not taken into account (Ie,g0fg1l ) ωl2∆e,l2). This approximation can be appropriate under some conditions53,56,26 and provided that the excitation frequency is in resonance with a single excited state. However, if several excited states are in resonance and display different RR signatures, their respective contributions should be included to determine the Raman polarizability tensor (eq 2). Nevertheless, analysis of the short-time-approximation RR spectra is still of interest because it provides the particular vibrational signature of each contributing state. The short-time-approximation RR spectra calculated in vacuo and water for each excited state in resonance are depicted on Figures 5 and 6, respectively. To allow an easier comparison of their vibrational signatures, the spectra have been normalized with respect to their most intense band. Figures 5 and 6 indicate that the vibrational signatures of states 6 and 14 in vacuo show
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Figure 7. RR spectra in vacuo simulated according to eq 1 for different excitation wavelengths (black line). The experimental spectra recorded in water at 514 and 458 nm (gray line) are taken from ref 14. The spectra are normalized with respect to the most intense band, and a Lorentzian function with a fwhm of 10 cm-1 is employed to broaden the transitions. The assignments (solid line) of the five most RR-active bands measured at 514 nm in the 1100-1450 cm-1 frequency range are reported.
strong similarities with those of states 3 and 14 in water, respectively. This is in agreement with the orbital decompositions of the states as provided in Tables 1 and 2. However, because of significant differences in the excited-state properties, the spectra of states 15 and 21 in vacuo are strongly different from those of states 6 and 11 in water. Actually, in vacuo the spectrum of state 15 shows some similarities with the spectra of states 14 and 21. This is related to the fact that state 15 involves dominant transitions to the π*HAT(153) orbital, contributing to state 21, as well as to the π*bpy(151) and π*bpy(152) orbitals, contributing to state 14. Moreover, in water states 6 and 11 have comparable RR signatures because both states mainly involve a dominant transition to the π*HAT(151) orbital. It is also interesting to notice the differences between the RR spectra obtained for resonances with states 3 and 6 (in water), which both correspond to dRu f π*HAT transitions. Of course, the differences come from the states that are involved, emphasizing the richness of RR spectroscopy. Finally, because of the large differences found between the short-time-approximation RR spectra of each contributing states, it can be concluded that considering only one electronic excited state is not sufficient to simulate the RR spectrum for excitation wavelengths in resonance with the first absorption band. In this direction, the RR intensities have then been calculated beyond the short-time approximation by using eqs 1-4 for several excitation wavelengths in resonance with the simulated absorption band. The corresponding normalized RR spectra in vacuo and water are depicted on Figures 7 and 8, respectively. It can be noted that, in order to fit the experimental conditions, the RR spectra (and excitation profiles in section 3.4) were simulated by employing the shifted excitation energies used to reproduce the absorption maximum (section 3.2). Additionally, the theoretical RR spectra are compared to the experimental RR spectra14 recorded in water for excitation wavelengths of 514 and 458 nm. It can be seen from Figure 7 that there is a strong dependence of the RR spectrum with respect to the value of the excitation wavelength. For the spectra simulated in vacuo at 514 and 480 nm, the excitation wavelength is mainly in resonance with state 6 (see Figure 3) and, consequently, the calculated spectra for these two wavelengths present strong similarities with the short-time-approximation RR spectrum
Guthmuller et al.
Figure 8. RR spectra in water simulated according to eq 1 for different excitation wavelengths (black line). The experimental spectra recorded in water at 514 and 458 nm (gray line) are taken from ref 14. The spectra are normalized with respect to the most intense band, and a Lorentzian function with a fwhm of 10 cm-1 is employed to broaden the transitions. The assignments (solid line for HAT vibrations and dotted line for bpy vibrations) and mode numbering are reported.
obtained for state 6 (see Figure 5). However, for shorter excitation wavelengths (458 and 430 nm), closer to the maximum of absorption, there is a stronger contribution of the other states. Therefore, the resulting RR spectra are significantly different from any of the short-time-approximation RR spectra reported in Figure 5. Furthermore, some qualitative agreement is observed when comparison is made between the theoretical results and the experimental spectra at 514 nm and to a lesser extent at 458 nm. Indeed, five main RR-active vibrations are found in the 1100-1450 cm-1 frequency range, which can most probably be assigned to the five most RR-active experimental bands measured at 514 nm in this frequency domain. Moreover, in agreement with the experimental findings, the relative intensities of almost all of these bands, except the one with a frequency slightly lower than 1300 cm-1, decrease for excitation wavelengths that approach the maximum of absorption. In both experiment and simulations, the strongest RR-active bands are found between 1450 and 1650 cm-1. Nevertheless, because of noticeable differences in the frequency positions and relative intensities between the calculated and measured spectra, an unambiguous assignment is not straightforward in the 1450-1650 cm-1 domain. Finally, it can be seen that considering an excitation wavelength closer to the maximum of absorption (430 nm), which reduces the contribution from the underestimated shoulder (Figure 3), does not improve the agreement with the experimental spectrum at 458 nm. The RR spectra simulated for different excitation wavelengths by including the effects of the solvent with the IEFPCM approach are given in Figure 8. Similarly to those of in vacuo, the RR spectra calculated in water display a strong dependence with respect to the excitation wavelength. However, the RR spectra in water show also significant differences with respect to the spectra simulated in vacuo. This is particularly the case for excitations at shorter wavelengths (458 nm and, to a lower extent, 480 nm) and for the vibrational bands in the 1450-1650 cm-1 frequency range. At longer wavelengths (530 and 514 nm) the calculated RR spectra present, as expected, strong similarities with the short-time-approximation spectrum computed for state 3 (Figure 6) because this state provides the main contribution at such excitation wavelengths. It can be noted that an excitation wavelength of 530 nm has been considered to probe the rededge part of the large simulated absorption shoulder (Figure
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TABLE 3: Theoretical Vibrational Mode Numbering, Type, Frequency (cm-1), and ∆ Values of the Four Excited States Contributing to the First Absorption Banda modes
frequencies
∆l
no.
type
theory
exp.
state 3
state 6
123 125
HAT HAT
1180 1237
-0.23 0.34
0.30 0.21
0.23 0.22
0.08 -0.02
133 136 140 142 151 152 154 155 158 162
HAT bpy HAT HAT HAT bpy HAT HAT bpy HAT
1281 1290 1360 1392 1468 1475 1512 1547 1559 1578
1182 1236 1282 1307 1322 1398 1430 1488 1496
-0.38 -0.07 -0.33 0.28 -0.54 -0.01 -0.26 -0.47 0.01 -0.11
-0.24 -0.12 -0.17 0.47 0.04 -0.14 0.03 0.50 -0.07 0.32
-0.18 -0.16 -0.17 0.44 0.05 -0.18 0.06 0.37 -0.09 0.24
-0.02 -0.47 0.01 0.02 0.02 -0.64 0.09 0.02 -0.41 -0.04
1534 1566 1602
state 11
state 14
a The calculations were performed with the B3LYP-35 XC functional in water. The experimental frequencies were taken from ref 14.
4). On the other hand, significant differences are found between the spectra computed at shorter excitation wavelengths (480 and 458 nm) and those simulated within the short-time approximation for states 6, 11, and 14 (Figure 6). This highlights again the importance of considering the contribution of all relevant excited states to simulate the RR spectrum at a given excitation frequency. Moreover, from a general point of view, it can be seen that the agreement with the experiment is substantially improved by taking into account interactions with the solvent and that this agreement appears now to be sufficient to assign the vibrational modes over the whole 1100-1650 cm-1 frequency range. In doing so (Figure 8), the five modes 123, 125, 133, 140, and 142 (the numbers correspond to the numbering resulting from the quantum chemical calculations) are assigned to the five strongest RR-active bands in the 1100-1450 cm-1 frequency domain of the experimental spectrum recorded at 514 nm. Furthermore, in agreement with the experiment, their relative intensities decrease when the excitation wavelength is progressively reduced to 458 nm. Moreover, considering the solvent effects, the intensity pattern in the 1450-1650 cm-1 frequency range is improved in comparison to the simulation in vacuo. The experimental bands are thus assigned to the three modes 151, 155, and 162. Besides, it is proposed that the mode 154 can be assigned to the shoulder of the experimental band at 1534 cm-1. The calculated frequencies of these modes are reported in Table 3 and are compared to the experimental frequencies. Additionally, it can be noted that all of the modes mentioned previously correspond to in-plane motions of the HAT ligand (Figure 9), except mode 125, which also presents a smaller motion of the bpy ligands. Therefore, their RR activity arises from the contributions of states 3, 6, and 11, which mainly involve transitions to the π*HAT(150) and π*HAT(151) orbitals localized on the nearest aromatic cycles connected to the ruthenium atom (Figure 2). Then, when the excitation wavelength goes from 530 to 458 nm, some additional bands show a nonnegligible RR intensity in the simulated spectra. These bands correspond to bpy vibrations, and their RR activity mainly arises from the contribution of state 14. Three bpy vibrations (Figure 9), namely, 136, 152, and 158, were assigned to experimental bands appearing in the spectrum recorded at 458 nm. In particular, the experimental bands at 1488 and 1496 cm-1 are assigned to the HAT mode 151 and the bpy mode 152, respectively, whereas the band at 1566 cm-1 can be assigned
Figure 9. Pictorial representation of the HAT vibrational normal modes 123, 125, 133, 140, 142, 151, 154, 155, and 162 and of the bpy vibrational normal modes 136, 152, and 158, calculated in water. The Cartesian frame is represented for the modes 123 and 136.
to the bpy vibration 158. Moreover, even if some bpy vibrations were found in the calculations with nonzero RR intensities (mode 130 at 1246 cm-1 and mode 132 at 1266 cm-1) close to 1250 cm-1, the experimental band at 1282 cm-1 was not assigned. Finally, the deviations between the calculated and experimental frequencies are lower than 40 cm-1 with a mean absolute deviation equal to 20 cm-1. The largest deviations are found for the frequencies of modes 140 and 142, which are underestimated by 38 cm-1. From eq 3 it can be seen that the Raman polarizability tensor depends on the ∆ values, on the transition dipole moments, and on the frequency-dependent part determined by the Φe(ωL) function. Depending on the signs of these different terms, the summation over e in eq 3 can lead to interferences, which can be constructive or destructive. Therefore, the correct prediction of these signs is mandatory to simulate the RR spectrum and its dependency with respect to the excitation frequency. Table 2 provides the transition dipole moment components, while Table 3 lists the ∆ values of the RR-active modes for each contributing state. Thus, it is seen that at longer wavelengths the Raman polarizability tensor is dominated by the (RXX)g0fg1l component because the low-lying excited states 3, 6, and 11 all have a transition dipole moment oriented along the X axis in the same direction (negative sign). Then, as another illustration, analysis of the ∆ values shows that the smaller RR intensity obtained for mode 155 at 530 nm in comparison to the intensity of mode 151 can be related to a destructive interference occurring between the contributions of states 3 and 6, which have ∆ values amounting to -0.47 and 0.50, respectively. It should be emphasized that the assignment of the HAT and bpy vibrations proposed in this study is mostly in agreement with the ones based on the experimental analysis initially reported by Kirsch - De Mesmaeker et al.14 The comparison between both assignments is summarized in Figure 10 for the two excitation wavelengths at 514 and 458 nm. An agreement is found for the seven HAT vibrations 125, 133, 140, 142, 151,
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Figure 10. Comparison of the assignments performed in the present study (black) with those obtained from ref 14 based on experimental considerations (gray) for the RR spectra simulated/recorded in water at 514 and 458 nm. The solid (for HAT vibrations) and dotted (for bpy vibrations) lines represent agreements between both assignments. A single asterisk denotes bpy vibrations, and two asterisks denote overlapping of the bpy and HAT vibrations. The spectra are normalized with respect to the most intense band, and a Lorentzian function with a fwhm of 10 cm-1 is employed to broaden the transitions.
Figure 11. RR excitation profiles in water simulated according to eq 1 for the vibrational modes 151, 152, 155, and 162. The excitation wavelengths (530, 514, 480, and 458 nm) employed in Figure 8 are represented by vertical dotted lines.
155, and 162 (represented as solid lines) as well as for the two bpy vibrations 136 and 152 (represented as dotted lines). The principal difference concerns the experimental band at 1182 cm-1, which is assigned to the HAT mode 123 in the present calculations instead of a bpy vibration. Additionally, the computations reveal that the experimental band at 1496 cm-1, which was assigned to a superposition of HAT and bpy vibrations in ref 14, corresponds to the overlap of the HAT mode 151 and the bpy mode 152. Furthermore, it is also suggested by the simulations that the shoulder of the experimental band at 1534 cm-1 could be assigned to mode 154. Finally, the experimental band at 1282 cm-1 (Table 3) corresponds most probably to a bpy vibration, as is suggested from experimental deductions.14 Nevertheless, as discussed above, no bpy vibrations with sufficient RR activity were found in the calculations to allow an unambiguous assignment of this band. 3.4. Excitation Profiles. Figures 11 and 12 present the RR excitation profiles computed in water for several representative vibrational modes. These profiles were simulated according to eq 1 by calculating the evolution of the RR intensity as a function of the excitation frequency ωL for a single vibrational
Guthmuller et al.
Figure 12. RR excitation profiles in water simulated according to eq 1 for the vibrational modes 133, 136, 140, and 142. The excitation wavelengths (530, 514, 480, and 458 nm) employed in Figure 8 are represented by vertical dotted lines.
mode. It is seen that the variation of the relative RR intensities with respect to the excitation wavelength is noticeably different between the various modes. Figure 11 shows that the intensity of the HAT vibration 151 is maximal for a wavelength close to 500 nm. This is in agreement with the fact that its RR activity mainly arises from the contribution of state 3 (see Figures 4 and 6). Moreover, the RR excitation profiles of the HAT modes 155 and 162 reveal that these modes have the strongest RR intensity for wavelengths ranging between 425 and 450 nm because the three lowest excited states 3, 6, and 11 provide contributions to their RR activity. Additionally, the intensity of the bpy vibration 152 is large for shorter wavelengths with its maximum close to 400 nm. As is apparent in Figure 6, this vibration becomes RR-active mainly from the contribution of state 14. Consequently, if a comparison is made between the RR excitation profiles and the RR spectra simulated for successive excitation wavelengths going from 530 to 458 nm (Figure 8), the following observations can be drawn: (i) the intensity of the mode 151 strongly decreases in comparison to the intensities of modes 155 and 162; (ii) the relative intensity of modes 155 and 162 is nearly constant because their RR excitation profiles display a similar shape; (iii) only the bpy vibration 152 presents a significant RR intensity at shorter excitation wavelengths. Figure 12 presents the RR excitation profiles of the vibrational modes 133, 136, 140, and 142. The excitation profiles of the HAT vibrations 133 and 140 have a comparable shape, which shows two maxima between 550 and 400 nm. The RR intensity of mode 142 is largely increased at shorter wavelengths because of the fact that both states 6 and 11 provide a significant contribution to its RR activity. Finally, the bpy mode 136 has an excitation profile similar to that of the bpy mode 152 (Figure 11) with a maximum of intensity close to 400 nm. 4. Conclusions The RR properties of the [Ru(bpy)2(HAT)]2+ complex have been investigated by means of DFT and TDDFT calculations employing the hybrid B3LYP-35 XC functional and by including the effects of the solvent within the IEFPCM approach. Analysis of the electronic excited-state energies has demonstrated that mainly four different MLCT excitations contribute to the first absorption band in vacuo and water. Simulation of the absorption spectra by including the vibronic structure of the states has shown a general agreement with the experimental
Investigation of [Ru(bpy)2(HAT)]2+ spectrum recorded in water. The main differences between vacuum and water concern the intensity and width of the shoulder at longer wavelengths. Furthermore, significant variations of the excited-state energies and compositions have been found when the effects of the solvent are included. The calculation of the short-time-approximation RR spectra has provided the vibrational signature of each contributing state and has shown that considering only one excited state is not sufficient to accurately simulate the RR spectra for excitation frequencies in resonance with the first absorption band. Within the vibronic theory, comparison of the calculated RR spectra at different excitation wavelengths with the measured spectra at 514 and 458 nm has demonstrated that inclusion of the solvent effects in the simulation scheme leads to substantial improvements of the RR intensity patterns. Even if some deviations between theory and experiment remain, the theoretical results allow interpretation of the experimental spectra and assignment of the vibrational bands. Moreover, in agreement with the experiment, the calculations are able to reproduce the variations of the HAT and bpy RR intensities when the excitation wavelength scans the first absorption band. This is also illustrated by the RR excitation profiles, which highlight the strong dependence of the RR intensities with respect to the excitation frequency. On the one hand, such theoretical investigations (i) provide structural information about the excited states contributing to the absorption spectrum, (ii) reveal the ligands involved in the charge-transfer excitations, and (iii) help to understand and interpret the experimental findings. On the other hand, such studies also provide a challenging test of the computational approaches because many aspects (electronic energies, transition dipole moments, structures of the ground and excited states, vibrational frequencies, and solvent effects) entering the simulation procedure should be described in a balanced way to reproduce and/or predict the RR properties of transition-metal complexes. Acknowledgment. This work was supported by research grants from the Belgian Government (IUAP No. P06-27 “Functional Supramolecular Systems”). J.G. thanks the Fund for Scientific Research (FRS-FNRS) for his postdoctoral grant under convention No. 2.4.617.07.F. B.C. thanks the FRS-FNRS for his research director position. Calculations have been performed on the Interuniversity Scientific Computing Facility (ISCF) installed at the University of Namur-FUNDP, for which the authors gratefully acknowledge financial support of the FRSFRFC and “Loterie Nationale” under Contract 2.4.617.07.F and of the FUNDP. References and Notes (1) Balzani, V.; Juris, A.; Venturi, M. Chem. ReV. 1996, 96, 759. (2) Ortmans, I.; Moucheron, C.; Kirsch - De Mesmaeker, A. Coord. Chem. ReV. 1998, 168, 233. (3) Daniel, C. Coord. Chem. ReV. 2003, 238-239, 143. (4) Vlcˇek, A., Jr.; Za´lisˇ, S. Coord. Chem. ReV. 2007, 251, 258. (5) Brown, G. M.; Chan, S. F.; Creutz, C.; Schwarz, H. A.; Sutin, N. J. Am. Chem. Soc. 1979, 101, 7638. (6) Kirch, M.; Lehn, J. M.; Sauvage, J. P. HelV. Chim. Acta 1979, 62, 1345. (7) Yamauchi, K.; Masaoka, S.; Sakai, K. J. Am. Chem. Soc. 2009, 131, 8404. (8) Hagfeldt, A.; Gra¨tzel, M. Chem. ReV. 1995, 95, 49. (9) Erkkila, K. E.; Odom, D. T.; Barton, J. K. Chem. ReV. 1999, 99, 2777. (10) Pauly, M.; Kayser, I.; Schmitz, M.; Dicato, M.; Del Guerzo, A.; Kolber, I.; Moucheron, C.; Kirsch - De Mesmaeker, A. Chem. Commun. 2002, 1086. (11) Jacquet, L.; Davies, R. J. H.; Kirsch - De Mesmaeker, A.; Feeney, M.; Kelly, J. M. J. Am. Chem. Soc. 1997, 119, 11763.
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