Computational Studies of the Interaction between Ruthenium Dyes

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J. Phys. Chem. C 2010, 114, 15165–15173

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Computational Studies of the Interaction between Ruthenium Dyes and X- and X2-, X ) Br, I, At. Implications for Dye-Sensitized Solar Cells Ching-Han Hu,*,† Abu Md. Asaduzzaman,‡ and Georg Schreckenbach*,‡ Department of Chemistry, National Changhua UniVersity of Education, Changhua 50058, Taiwan, and Department of Chemistry, UniVersity of Manitoba, Winnipeg, MB, Canada, R3T 2N2 ReceiVed: January 20, 2010; ReVised Manuscript ReceiVed: July 15, 2010

Quantum chemistry in the form of relativistic density functional theory (DFT) combined with a continuum solvation model has been applied to study the interaction of two prototypical ruthenium dyes (N3 and its chlorinated form) and redox mediators X- and X2-, X ) Br, I, At, with a view at the elementary reactions within a dye-sensitized solar cell (DSSC). Along the series Br, I, and At, increasing bond lengths of X2, X2-, and X3- are found, as well as an increasing reducing power of the X-/X3- redox couple. Inner-sphere sevencoordinate complexes between the dye and the redox species do not exist; however, the dyes form outersphere complexes with the X- and X2- species. The thermodynamics of a recently proposed mechanism [J. Phys. Chem. C 2007, 111, 6561] involving a [dye+X-] intermediate are probed, and the existence of the intermediate and the elementary steps of the process are confirmed. The dye regeneration is thermodynamically more favorable for the N3 dye than its chlorinated counterpart. The regeneration of the neutral dye is favored for At, followed by the iodine and bromine systems (At > I > Br). This may be related to the observed superior performance in actual DSSCs of the iodide/triiodide redox couple over the alternative bromide/ tribromide couple. Introduction 1-6

Dye-Sensitized Solar Cells (DSSCs), also known as Gra¨tzel cells, have generated and continue to generate an enormous amount of interest in the scientific literature and beyond.7 For instance, the original report on the operating principle of DSSCs by O’Regan and Gra¨tzel8 is the 18th most cited paper of the journal Nature for the time span since 1955.9 This interest is not really surprising given the urgent need to “power the planet”10 while stabilizing the global atmospheric CO2 content. DSSCs hold the promise of cheap and efficient conversion of solar energy into electrical energy or fuels. Nevertheless, in order to realize this potential, the efficiency of DSSCs has to be increased dramatically, and a large part of the current literature in the field is targeting this goal. Indeed, while the maximum (thermodynamic) solar conversion efficiency η of DSSCs, known as the Shockley-Queisser limit,11 is about 32% (not counting ideas such as stacking of multiple DSSCs with different band gaps,12 tandem DSSCs,13 or multiple-electron generation by singlet fission14,15 or quantum dots16,17), the current efficiency record is approximately 11%.18,19 Thus, a major gap in efficiency remains to be bridged. Moreover, the efficiency record has not changed appreciably for the last 15 or so years (see, e.g., the review by Hamann et al.5 and references cited therein). This is quite astonishing, given the amount of effort put into studying DSSCs, and one might conclude, in the words of Lewis,20 that “we don’t understand how these things work”. DSSCs consist of several principal components that are combined to form a rather complex system.2 A layer (film) of TiO2 semiconductor nanoparticles has a sensitizer dye21 attached * To whom correspondence should be addressed. E-mail: chingkth@ cc.ncue.edu.tw and [email protected]. † National Changhua University of Education. ‡ University of Manitoba.

to it that functions to absorb the incoming light and to inject a photoelectron into the conduction band of the semiconductor. The TiO2 is connected to a transparent electrode (conductive mechanical support) that, in turn, is connected to the counter electrode (typically Pt) by way of the external load. A solution containing the I-/I3- redox couple completes the circuit. Typically, polar organic solvents are applied. However, solidstate devices that do not require a liquid electrolyte have been investigated also.22,23 Clearly, each of the cell components will have some kind of influence on the overall efficiency. The overall cell efficiency η can be determined as5

η)

JSC · VOC · FF Pin

Here, Pin is the power input, JSC is the short-circuit current density, VOC is the open-circuit photovoltage, and FF is the fill factor, defined as the ratio of the maximum power obtainable from the DSSC to the product of VOC and JSC. Efforts to improve the DSSC efficiency need to concentrate on VOC and/or JSC.5 The open-circuit voltage VOC is determined by the difference between the I-/I3- potential and the quasi-Fermi level of the semiconductor. Since there is a considerable gap between the I-/I3- potential and that of the dye, it would be desirable to use an alternative redox mediator instead of the iodide/triiodide couple. However, for reasons that are not fully understood, any other redox mediator dramatically reduces the cell performance.5 It is evident, then, that the I-/I3- redox couple and its interactions with all the cell components;including interactions with the dye during dye regeneration;play a unique role in the functioning of the DSSC. In a recent paper, Clifford et al.24 presented a study of the kinetics and thermodynamics of the dye regeneration. They propose that the regeneration (or, in the words of the paper the

10.1021/jp100572f  2010 American Chemical Society Published on Web 08/16/2010

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SCHEME 1: Schematic Structures of the Dye Molecules N3 (left) and 4 (right)

“re-reduction”) reaction “proceeds via a transient [dye+-iodide] intermediate complex formed by reaction of photogenerated dye cations with one iodide ion.” (quoted from Clifford et al.24) Furthermore, they find that this complex subsequently reacts with a second iodide ion to form I2-. This second step appears to be the limiting reaction, both kinetically and thermodynamically. Hence, the nature of the intermediate complex might be important for understanding;and possibly improving;some of the factors that limit the efficiency of current DSSCs. Consequently, the authors hypothesize about the nature of the proposed [dye+-I-] complex, noting that it could either be a seven-coordinate ruthenium complex (inner-sphere coordination) or a 1:1 adduct (outer-sphere complex.) The purpose of the present article is to apply the tools of computational quantum chemistry to studying aspects of the dye regeneration process, following the work of Clifford et al.24 Specifically, we look at the thermodynamics of the proposed reaction mechanism for the dye regeneration reaction, including the [dye+-I-] complex. To be able to handle the complexities of the system, we build a model containing just two components of the DSSC, i.e. the dye and the redox shuttle. This model system is embedded into a continuum solvation model25 that accounts for the effects of the polar organic solvent in an approximate, average manner. We have chosen two typical ruthenium-based dyes, the N3 dye19 that serves as the de facto standard for DSSCs [Ru(dcbpy)2(NCS)2; dcpby ) 4,4′-dicarboxy-2,2′-bipyridyl], as well as a variant thereof,19 i.e. dye 4 from the paper of Clifford et al.24 [Ru(dcbpy)2Cl2]. For these two dyes, we have studied the neutral (N3 and 4, respectively; structures shown in Scheme 1) and cationic forms (N3+ and 4+, respectively), as well as complexes between N3+ and 4+ and X- and 2X-. Here, X represents the redox mediator. In addition to the experimentally used iodide couple, X ) I, we have also included its neighbors immediately above and below in the periodic table, viz. X ) Br and At. Of these, bromine has been used in previous experimental setups.26 Of course, it is quite likely that no practical device with an astatine-containing redox mediator will ever be built, due to the radioactivity of this element. However, studying the periodic trends in going from bromine to iodine and astatine might help us better understand the unique role of the iodide redox couple. Also, studying periodic trends within the periodic table of elements is an interesting objective in and of itself. Computational

chemistry is well suited for investigating hypothetical compounds such as, in this case, components of an astatine-based DSSC. Finally, we briefly mention two very recent experimental papers that are closely related to the current study, but are outside its scope. O’Regan et al.27 studied structure/function relationships for a number of ruthenium dyes, including a discussion of the dye-(poly-)iodide interactions. The article by Gardner et al.28 provides evidence for a regeneration mechanism involving iodine atoms as intermediates instead of iodide ions. This idea, while clearly relevant in the given context, is nevertheless outside the scope of the current study. Work is in progress to address it separately, using similar computational tools. Previous Theoretical and Computational Studies. Theoretical and computational approaches have been used to elucidate aspects of DSSCs, though there are perhaps still relatively few studies compared to the sheer volume of the experimental literature.4 Naturally, due to the complexity of the DSSC, such theoretical studies tend to concentrate on some aspect of the system, rather than the whole setup. Gorlov et al.29 have calculated properties of mixed halogen compounds such as IBr2-, using a computational approach that is relatively similar to the one employed in our study. Several studies focus on the different dyes, their attachment (adsorption) to the TiO2 surface, and their frontier orbitals.13,30-45 Among those, we mention the work of Qin et al., who have studied organic dyes for potential applications in p-type DSSCs.13 The dynamics at the TiO2-dye interface for organic dyes have been investigated.46-48 Labat et al. published a study on the interactions between a ZnO semiconductor and an organic dye.49 The, already mentioned, idea of singlet fission for pushing the thermodynamic limit of DSSCs has been pursued.14 Several studies focus on the electron transport in the semiconductor and, more generally, the properties of the TiO2 bulk.4,30,31,35,41,50-52 In related work, we have studied various adsorbates on the semiconductor surface and their influence on the band edge.53,54 Ogiya et al.55 published a report on their development of a “multiscale simulator for a dye-sensitized TiO2 nanoporous electrode” that is based on semiempirical tight-binding density functional theory. Few details on performance or accuracy are given in that paper. Finally, we need to mention a very recent paper by Privalov et al.56 that came to our attention only after completing an initial

Interaction between Ru Dyes and Redox Mediators draft of the current paper. This work comprises a DFT study of the interaction between the N3 dye and I-, I2-, and I3-, with a view of the experimental work of Clifford et al.24 that, as mentioned, is also the starting point of our study. Geometries and spin densities are discussed, whereas energetics (thermodynamics) are not reported. While there are some similarities between the two studies (for instance, the optimized gas-phase structures of the N3 dye are similar), we note important differences also. In terms of methodology, Privalov et al.56 use large-core ECPs (LC-ECP) for iodine, which, as a relativistic method, is problematic, see below. Moreover, in our study, solvation effects are included. Regarding systems beyond outersphere complexes that are considered by us as well, Privalov et al. have also looked at six-coordinate inner-sphere complexes where the incoming I- either replaces an NCS- ligand or reduces the coordination of a dcbpy ligand from bidentate to monodentate. Computational Details. Density functional theory57 (DFT) was used for all calculations. We applied the B3LYP exchangecorrelation functional.58-60 Unrestricted calculations were performed if appropriate. Unless otherwise noted, the SDD (smallcore) effective core potentials (SC-ECPs) and accompanying VDZ basis sets were used for Ru, Br, I, and At,61-63 whereas all other atoms were described with the 6-31G* basis sets. These basis set settings should provide an adequate balance between accuracy (convergence with respect to basis set level) and computational cost. Test calculations were also performed with large-core ECPs (LC-ECP). The use of the SDD ECPs ensures that scalar relativistic effects are included; the ECP method has been shown to be a valid relativistic approximation.64,65 Spin-orbit effects have been neglected. Recently, we65 and others66 have shown that spin-orbit has a strong influence on properties such as the enthalpy of formation of I2. However, the focus of the current work is on the binding of dye molecules with X- and X2-, a less stringent property as compared to enthalpies of formation. Thus, the neglect of spin-orbit should be justified. All calculations were done with the Gaussian03 suite of programs.67 The standard, “fine” integration grid was used, after a test for one case using the “ultrafine” grid showed essentially identical results, while significantly increasing the computational cost. Optimizations were performed in the gas phase. A systematic search has been carried out for N3+I- local energy minima structures. We have obtained structures b, e, and z as the three lowest local energy minima among all N3+Istructures. Among them, two other N3+I- structures, where the I- binds to the S atom of an NCS group, were very close to the b, e, and z in terms of total energy. However, binding of I- to an NCS group induces huge structural distortions. For instance, the Ru-N-C angle is bending by as much as 25° upon binding of I- with NCS. Therefore, we have not presented these types of structures in this paper. For each ruthenium complex, structures b, e, and z (see below for a further discussion of these structures) were determined as local minima on the potential energy surface. Also, several attempts were made to locate seven-coordinate Ru complexes, in accordance with the hypothesis of Clifford et al.24 However, any such attempt failed in that these optimizations invariably led to six-coordinated complexes with the extra X- ligand bound in the outer sphere. We will discuss this point in some more detail below. Likewise, some “floppy” structures (X- on top of a phenyl ring) were attempted. The energies are much higher for such structures, and many of them are very difficult to converge. Harmonic vibrational frequencies were calculated for the gas-phase optimized structures in order to verify the nature of each stationary point and to obtain the thermochemistry.

J. Phys. Chem. C, Vol. 114, No. 35, 2010 15167 TABLE 1: Gas-Phase Optimized Bond Lengths of X2, X2-, and X3- from This Work and Selected Literature Values Including Experiment (Å) molecule

method

ref

Br

X2 X2 X2 X2 X2 X2 X2 X2X2X2X3X3X3-

scalar LC-ECP B3LYP scalar SC-ECP B3LYP scalar SC-ECP BP86 scalar SC-ECP B3LYP spin-orbit SC-ECP BP86 spin-orbit SC-ECP B3LYP experiment scalar LC-ECP B3LYP scalar SC-ECP B3LYP scalar LC-ECP B3LYPb scalar LC-ECP B3LYP scalar SC-ECP B3LYP scalar LC-ECP B3LYP

a a b b b b c a a d a a d

2.451 2.336 2.317 2.315 2.320 2.318 2.281 3.061 2.989

I

2.852 2.731 2.694 2.697 2.715 2.716 2.666 3.465 3.383 3.462 2.731 3.131 2.637 3.024 3.137

At 2.932 2.914 2.875 2.878 3.025 3.027 3.551 3.524 3.213 3.182

a This work. b Mitin and van Wu¨llen,66 quadruple-ζ polarized basis sets (AVQZ in the article). c NIST chemistry webbook;72 Huber and Herzberg.73 d Privalov et al.56

Solvation effects were modeled with the PCM model,68 using acetonitrile (CH3CN) as the solvent. Atomic radii from the UFF force field were used (RADII)UFF).69,70 Unlike the (default) United Atom (UA) model, in which hydrogen atoms are enclosed in the sphere of the atom to which they are bonded, we applied explicit hydrogen radii; this choice was motivated by convergence difficulties encountered with the UA approach. Solvation calculations were done as single points. The ∆∆G of solvation obtained in this way was added to the gas phase free energies. The free energies for redox half reactions of the general form A f A+ + e- were calculated as ∆G ) G(A+) - G(A), i.e. with the free energy of e- set to zero. This approach is appropriate since the free energy of the solvated electron cancels out in charge balanced redox reactions. Mulliken charges have been calculated and used for qualitative interpretations of the results. Atomic charges are not quantum-mechanical observables, and thus are inherently model dependent. Mulliken charges, in particular, have been criticized because of their basisset dependence and problems for very large basis sets.71 However, for the given purpose of qualitative interpretations of certain trends, they should be appropriate, particularly for the modest basis sets used. Results and Discussion 1. Structural Properties. a. Halogen Molecules X2, X2-, and X3-. The computed geometries for X2, X2-, and X3- for X ) Br, I, and At are collected in Table 1. The values for the iodine species agree with those obtained in our earlier study,65 keeping in mind differences in the methodological details. In Table 1, we have also included some of the recent results by Mitin and van Wu¨llen66 as well as experimental values for Br2 and I2.72,73 Our data are very similar to the scalar relativistic calculations of Mitin and van Wu¨llen. Remaining differences are probably a result of the much larger basis sets used by these authors. Also interesting in Mitin’s data is the importance of spin-orbit, particularly for At2. However, as discussed already in the Computational Details, we feel that the neglect of spin-orbit is still acceptable in the context of this study. Finally, we have included in Table 1 calculations using large-core ECPs (LC-ECP), including those used by Privalov et al.56 for I2- and I3-.74 These show consistently much longer bond lengths, and hence the agreement with the available experiment deteriorates considerably. This finding is in accordance with our experience for f-block compounds.64,75

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Hu et al. TABLE 2: Optimized Geometries of the Naked Complexes, Key Geometry Parameters, from This Work and Privalov et al.56 (Bond Lengths in Å)a bond lengths complex Ru-Cl Ru-N(CS) N-C C-S N3 N3c N3+ 4 4+

Figure 1. Optimized bond lengths (Å) of X2 (bottom, blue), X2- (red, top), and X3- (green, middle), X ) Br, I, and At.

Our (SC-ECP) structural data are also presented in Figure 1 that serves, in particular, to illustrate the periodic trends in going from Br to I to At as well as between the different species for a given atom. The most prominent feature of the bond lengths graphs is the slight leveling-off of the curves for the heaviest compounds, i.e. those of At. This can be understood as a consequence of the combined effects of the lanthanoid contraction and scalar relativistic effects.76,77 Relativistic effects are very roughly proportional to the atomic number squared,77 and are therefore much more pronounced for astatine than for either iodine or bromine. (We note, however, that inclusion of spin-orbit effects leads to a lengthening of the bond, Table 1, which would somewhat offset the effect.) The bond length trends can also be compared to trends along a transition metal triad (3d to 4d to 5d). There, it is typically the case that the 4d species has the longest and weakest bonds.78 b. Uncomplexed Dye Molecules. The optimized structure of the neutral dye molecule 4 is shown in Figure 2a. Its ionized form (4+) as well as N3 and N3+ have qualitatively very similar optimized structures. Key geometry parameters are provided in Table 2, as well as in Scheme S1 of the Supporting Information. For the neutral N3 dye, we can compare our results to those of Privalov et al.,56 Table 2. The metal-to-ligand bond lengths are generally longer for the latter studies, in accordance with the much smaller Ru basis set used by these authors.

2.031 2.066 1.978 2.425 2.338

Ru-N(dcpbyb)

1.185 1.625 2.065, 2.066 1.187 1.630 2.090, 2.091, 2.086, 2.084 1.192 1.607 2.109, 2.087 2.051, 2.064 2.113, 2.097

a Essentially the same data are also provided in the context of structural drawings in the Supporting Information, Scheme S1. b dcpby ) 4,4′-dicarboxy-2,2′-bipyridyl. c LC-ECP calculations, Privalov et al., ref 56.

Going from the neutral dye to its cationic form leads to a significant shortening of the Ru-Cl and Ru-N(CS) bond lengths, respectively, in accordance with the ionic character of these bonds. At the same time, the Ru-N(dcpby) bond lengths increase significantly, which can be related to the covalent bonding mechanism between the metal and the ligand. While a good portion of the extra positive charge is delocalized over the ligands (see Tables S1 and S2 of the Supporting Information for calculated Mulliken charges), the ruthenium atom has formally one less electron available for back-donation to the dcpby ligand, weakening the bond. c. Complexes between the Dyes and X- and X2-. For each of the redox couples tested in this study (viz. X ) Br, I, At), we have optimized structures b, e, and z (see below) for both, the N3 and 4 dyes, and with X- as well as X2- attached. Specifically, we optimized neutral species N3+X- or 4+X- for the complexes between X- and a cationic dye+, and anionic species N3X2- or 4X2- with an overall charge of minus one for the complexes between the neutral dye and X2-. Mulliken charges (Tables S1 and S2, Supporting Information) confirm the picture of neutral dye plus X2- and cationic dye+ + X-, respectively: The calculated charges on X or X2 are roughly -0.9 in all cases. Among these, the z-structures of X- have

Figure 2. Optimized structures of (a) the dye molecule 4, as well as the complexed dye molecules (b) 4+I-(b), (c) 4+I-(e), and (d) 4I2-(z). Color scheme: Ru, brown; N, blue; C, gray; H, light blue; O, red; Cl, green; and I, purple.

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SCHEME 2: Schematic Structures of the Different Complexes between N3+ and I2-a

a

The structures of 4+, as well as those with different adsorbates are similar.

Figure 3. Optimized structure and selected bond lengths (Å) of (a) N3+Br-(z) and (b) N3Br2-(z). Color scheme: Ru, brown; N, blue; C, gray, H; light blue; O, red; S, yellow; and Br, light red.

the lowest X- charges at -0.86 to -0.88, which can be directly related to interactions with the aromatic rings, to be discussed later. As mentioned, all attempts failed to optimize seven-coordinate (inner-sphere) Ru complexes, in accordance with the hypothesis of Clifford et al.24 (although inner-sphere six-coordinate complexes have been found by Privalov et al.56 where the I- or I2replaces one NCS ligand of N3). The three structures that we were able to obtain in each case, b, e, and z, represent outersphere complexes. They differ by their point of attachment of the X- or X2-, respectively. Structures b and e refer to attachment to the carboxylic groups cis and trans, respectively, to the NCS or Cl groups of the dye. Structures of type z have the halogen moiety placed between, and interacting with the aromatic rings. Similar z-type structures have been considered by Privalov et al.56 also. The three types of attachment are illustrated in Scheme 2 where we show, by way of example, the different complexes between 4+ and I2-. All other complexes have qualitatively very similar structures. Additional structural drawings are provided in the Supporting Information (Schemes S2-S7). Examples of optimized structures are shown in Figures 2 and 3 also; the other complexes have qualitatively similar geometries. Figure 3, in particular, illustrates how the X- or

the X2- in the z structures is placed between the aromatic rings of the dcpby ligands. Key geometry parameters for the iodine-containing complexes are provided in Tables 3 and 4 as well as in Schemes S4 and S5 of the Supporting Information. The corresponding data for X ) Br and At are provided in the Supporting Information (Tables S3 and S4 and Schemes S2-S7). The dyes are desymmetrized by the attachment of either Xor X2- as compared to the naked species (Tables 3/S3 (Supporting Information) and 4/S4 (Supporting Information) in comparison to Table 2.) The Ru-N(CS) bond lengths in the various N3 complexes reflect the cationic or neutral status of the dye: longer bond lengths around 2.04 Å for the neutral complexes, and shorter ones around 2.01 Å for the cationic ones, in complete analogy to the naked dyes (as discussed above) and in accordance with the ionic character of these bonds. A comparable statement can be made regarding the C-S bond lengths (about 1.63 Å for the neutral complexes; 1.62 Å for the cationic ones), while the N-C bond lengths show little variation throughout the series, Tables 3 and S3 (Supporting Information). The trend in C-S bond lengths can be related to the calculated Mulliken charges. While the carbon charge is relatively close to zero in all cases, the charge of the adjacent sulfur parallels

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TABLE 3: Optimized Geometries of the N3+I- and N3I2- Complexes, Key Geometry Parameters (Bond Lengths in Å)a bond lengths complex

Ru-N(CS)

+ -

N3 I (b) N3+I-(e) N3+I-(z) N3I2-(b) N3I2-(e) N3I2-(z)

2.014, 2.010, 1.198, 2.039, 2.036, 2.045,

N-C

2.014 2.016 1.195 2.032 2.041 2.040

1.186, 1.186, 1.188, 1.183, 1.184, 1.183,

C-S

1.186 1.186 1.188 1.184 1.184 1.183

1.622, 1.621, 1.614, 1.633, 1.630, 1.633,

1.621 1.622 1.615 1.629 1.631 1.632

Ru-N(dcpbyb) 2.080, 2.077, 2.083, 2.071, 2.068, 2.070,

2.082, 2.087, 2.092, 2.064, 2.082, 2.070,

2.077, 2.079, 2.082, 2.066, 2.054, 2.068,

H-I 2.073 2.074 2.083 2.061 2.061 2.061

Ru-I

I-I

2.507 2.494 5.268 2.682 2.607 5.406

3.353 3.382 3.326

The corresponding data for X ) Br and At are provided in Table S3, Supporting Information. Essentially the same data are also provided in the context of structural drawings in the Supporting Information, Schemes S2 to S7. b dcpby ) 4,4′-dicarboxy-2,2′-bipyridyl. a

TABLE 4: Optimized Geometries of the 4+I- and 4I2Complexes, Key Geometry Parameters (Bond Lengths in Å)a

TABLE 5: Free Energies in Solution (∆G) for Reactions of X-, X2-, and X3- (kcal/mol)

bond lengths complex 4+I-(b) 4+I-(e) 4+I-(z) 4I2-(b) 4I2-(e) 4I2-(z)

Ru-Cl 2.388, 2.384, 2.369, 2.433, 2.431, 2.444,

2.388 2.391 2.365 2.424 2.440 2.439

Ru-N(dcpbyb) 2.086, 2.081, 2.087, 2.081, 2.064, 2.068,

2.077, 2.081, 2.092, 2.054, 2.071, 2.051,

2.077, 2.074, 2.080, 2.042, 2.038, 2.049,

2.077 2.079 2.089 2.052 2.058 2.057

H-I Ru-I

I-I

2.514 2.487

2X- f X2- + eX2- f 1/2(X- + X3-) 2X- f 1/2(X- + X3-) + e-

Br

I

At

121.50 -7.06 114.44

115.05 -6.77 108.28

107.72 -6.83 100.89

5.278 2.487 2.459 5.661

3.367 3.372 3.339

The corresponding data for X ) Br and At are provided in Table S4, Supporting Information. Essentially the same data are also provided in the context of structural drawings in the Supporting Information, Schemes S2 to S7. b dcpby ) 4,4′-dicarboxy-2, 2′-bipyridyl. a

the overall charge of the complex, -0.44 to -0.45 for the complexes of the neutral dye, and -0.27 to -0.28 for those of N3+. Very similar observations apply to the Ru-Cl bond lengths in the 4 and 4+ complexes, Tables 4 and S4 (Supporting Information). They are again shorter for the cationic dyes that have a larger positive charge on the ruthenium metal than their neutral counterparts. The Ru-N(dcpby) bond lengths are shorter in the X2complexes that contain a neutral dye than in the corresponding X- complexes which feature a cationic dye. This trend is again similar to the one in naked dyes, Table 2, that also show shorter Ru-N(dcpby) bond lengths in the neutral forms of the dyes. Interestingly, the Ru-N(CS) bond lengths are shorter by about 0.1 Å for the z structures of X- as compared to the corresponding b or e structures. A similar trend exists for the Ru-Cl distances in the complexes of 4 or 4+. At the same time, the Ru-N(dcpby) distances are considerably elongated for the z structures. In the z structures of X-, the X- interacts strongly with the aromatic rings of the dcpby ligands, resulting in weaker interactions between the ruthenium center and the dcpby ligand, and thus stronger interactions between Ru and the remaining NCS or Cl ligands. For the 2X- cases, the interaction between the X2- and the dcpby appears to be much weaker. Moreover, steric effects come to play; the space between the two dcpby ligands appears to be insufficient to accommodate the X2-. The X-X bond lengths in the X2- complexes are significantly shorter (by as much as 0.1 Å or so) than those for the free species. This can be readily understood from the significant interactions between the negatively charged X2- and the positively charged hydrogen atom (b and e structures) or the aromatic rings of the dye (z structures), respectively. These interactions delocalize and strongly stabilize the negative charge of X2-. The shortest X-X bonds are found for the z structures that are also the most stable gas phase conformers in each case. (We will separately discuss the relative stabilities of the different isomers below.)

In the z structures, there are significant interactions with the neighboring aromatic rings of the dye, allowing for a delocalization and stabilization of the charge. This is exemplified in Figure 3 for the N3 structures with Br- and Br2-, respectively. While it is difficult to quantify these interactions, we notice that the sum of the van der Waals radii79 of neutral Br and C amounts to 3.55 Å, which is longer than several of the distances in the Br- complexes shown in Figure 3. Thus, this illustrates that there are significant interactions as expected. The distances in the Br2- case are slightly longer than those for the Br- case; however, anionic Br- should be significantly larger than neutral Br, and hence, there should be significant interactions here as well. The situation is similar for the iodine and astatine z complexes. 2. Energetics. a. Halogen Molecules. Table 5 contains the energetics (free energies in CH3CN solution, ∆G) for some reactions of X- and X2- that are relevant for the dye regeneration processes. In going from Br to I to At, we observe a decreasing energy for the formation of X2- and X3- from X-, whereas the energy for the X2- disproportionation is essentially unchanged across the series. In particular, the reducing power of the electrolytes (X3-/X-), as shown by the reaction 2X- f 1 /2(X- + X3-) + e-, follows the order At > I > Br. Finally, we note that the energetics in continuum solvation models of such small, charged species should not be overinterpreted as they depend strongly on the choice of radii in the solvation model.80,81 b. Uncomplexed Dye Molecules; RelatiWe Stability of Isomers. Starting with the naked, uncomplexed dyes, the calculated ionization potentials (free energies in CH3CN for the following reaction: dye f dye+ + e-) of N3 and 4 are 115.38 and 109.33 kcal/mol, respectively. We now turn to the complexes between dye molecules and X- or X2- and their different isomers. The relative energies of the different isomers (b, e, and z structures) are provided in Table 6. In the gas phase, the most stable isomer for the X- complexes is z. This can be understood from the stabilizing interactions between the X- species and the neighboring aromatic rings. The interaction and stabilization of the system is larger than that for the b or e species where the X- interacts only with a hydrogen atom of the neighboring carboxylic group. For the X2- gas phase complexes, however, this effect is more than offset by the larger steric demands of the X2- species, and the z structure is least stable in each case. This situation is changed if the effects of the polar solvent are included. Now, the dye+X- complexes have b or e as their

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TABLE 6: Relative Gibbs Free Energies (in kcal/mol) of the e and z Isomers with Respect to Their b Counterparts in the Gas Phase (∆G), and in CH3CN Modeled with PCM (∆Gsol) ∆G +

-

N3 Br (b) N3+Br-(e) N3+Br-(z) N3Br2-(b) N3Br2-(e) N3Br2-(z) N3+I-(b) N3+I-(e) N3+I-(z) N3I2-(b) N3I2-(e) N3I2-(z) N3+At-(b) N3+At-(e) N3+At-(z) N3At2-(b) N3At2-(e) N3At2-(z)

∆Gsol

0.0 -1.17 -6.69 0.0 -3.80 4.95 0.0 -1.45 -4.84 0.0 -1.78 5.83 0.0 -0.35 -2.49 0.0 v1.37 4.86

0.0 0.02 12.15 0.0 -7.46 2.70 0.0 -0.96 9.30 0.0 -4.22 2.14 0.0 0.17 8.27 0.0 -1.72 1.66

+

-

4 Br (b) 4+Br-(e) 4+Br-(z) 4Br2-(b) 4Br2-(e) 4Br2-z 4+I-(b) 4+I-(e) 4+I-(z) 4I2-(b) 4I2-(e) 4I2-(z) 4+At-(b) 4+At-(e) 4+At-(z) 4At2-(b) 4At2-(e) 4At2-(z)

∆G

∆Gsol

0.0 -1.59 -7.63 0.0 -1.81 7.15 0.0 -1.25 -5.36 0.0 -1.90 6.09 0.0 -2.94 -6.81 0.0 -4.79 0.60

0.0 0.58 12.22 0.0 -0.31 8.82 0.0 0.15 12.96 0.0 -0.73 7.99 0.0 -2.21 4.08 0.0 -6.51 -0.36

most stable isomer, and z as the least stable one. We can use the Mulliken charges (Tables S1 and S2, Supporting Information) for a qualitative understanding of the charge distribution that underlies these effects. As discussed already, X- bears a charge of -0.9 or so in all cases. More generally, the charge distribution over the different atoms is approximately similar across the three isomers in each case. The strong negative charge of the X- is directly exposed to the solvent in the b and e structures, leading to very strong stabilizing interactions and relative energies that are very close to each other, Table 6. As a result, z, where this charge is largely shielded from the polarizable solvent, is least stable in solution. The situation is more complex and less straightforward for the dye+X2complexes where, for instance, the X2- adsorbed species is closer to the solvent in the z isomers than in the related Xcases. Also, in these cases, the dominating effect for the solvation free energy is the interaction of the net negative charge (concentrated on the X2-) with the polarizable solvent. Overall, a balance between various factors, charges, sterics, gas-phase stability, and so on leads to the calculated energetic ordering of the isomers, with e being most stable in solution for all of the dye+X2- cases. c. Reactions. In this section, we will discuss the complexed dye species and their reactions. In Table 7, we have collected the energetics (∆G in CH3CN solution) for relevant reactions involved in the dye regeneration processes. Together with the reactions in Table 5, they provide a picture of the thermodynamics. We note in passing that a simpler energetic approach using “∆E + ∆∆Gsolv” instead of the proper ∆G (thus avoiding expensive frequency calculations) provides a qualitatively similar picture in this case, Table S5 (Supporting Information).

Considering the net regeneration reaction (dye+ + 2X- f dye + 1/2(X- + X3-), it is energetically more favorable for N3 than for 4. This could be related to the electronegativity difference between the Cl- and NCS- groups. The former has a higher electronegativity, resulting in 4+ forming stronger bonds with X2- than N3+. Hence, complexes of the latter decompose more easily. Moreover, for a given dye, the regeneration of the neutral dye is favored for the At system (At > I > Br). Indeed, for X ) Br, the reaction is endothermic for 4, and only marginally exothermic for N3. This thermodynamic trend can be related to the trend in the reducing power of the redox couples as discussed above (Table 5), and it may also be related to the experimental observation that the bromide/tribromide redox couple generally performs much worse in actual DSSCs than its normally used iodide/triiodide counterpart. In the 2007 paper by Clifford et al.,24 it was suggested that the second step of the regeneration reaction, N3+X- + X- f N3X2-, is kinetically and thermodynamically the rate limiting step. Our data generally agree with this proposal for N3 as well as for 4 on the thermodynamics aspect: In most cases, this reaction is less exothermic (or more endothermic) than the first and third steps, dye+ + X- f dye+X- and dyeX2- f dye + X2-, respectively. The only exceptions to the statement are the z structures of X ) I and At for which the first step is somewhat more endothermic than the second step. In this connection, we recall that the z structures of X2- are generally least stable in solution, as discussed above. The third step, the dissociation of the dye+X2- complex, is exothermic in all cases, and strongly exothermic for X ) I and At. Privalov et al.56 suggest three possible pathways for the dye regeneration by I-: (i) interaction of the I- with the aromatic rings, i.e., via structures similar to our z structures, (ii) an outersphere mechanism where the I- interacts with the NCS ligand, and (iii) an inner-sphere mechanism involving ligand exchange between I- and NSC-. Of these, we have studied pathway i, although pathway ii could be viewed as qualitatively similar. However, we have chosen not to pursue this pathway due to the structural distortions induced in the case of N3+I-, as already discussed. To assess the feasibility of, in particular, pathway iii, thermodynamics and kinetics (transition states), using a realistic solvent model, would be required. This is clearly outside the scope of the current investigations. Conclusion In this study, we have used the tools of quantum chemistry to investigate a key step in the functioning of DSSCs, the regeneration of the dye by the redox couple. Specifically, we have probed the mechanistic proposal of Clifford et al.,24 employing two different but closely related ruthenium dyes. For each combination of dye and redox species, we found different possible outer-sphere complexes. However, inner-sphere, sevencoordinate complexes do not exist. Differences in structures and

TABLE 7: Free Energies in Solution (∆G) for Reactions of the dyes (kcal/mol) Br dye reaction +

-

+

-

N3 + X f N3 X N3+X- + X- f N3X2N3X2- f N3 + X2N3+ + 2X-f N3 + 1/2(X- +X3-) 4+ + X- f 4+X4+X- + X- f 4X24X2- f 4 + X24+ + 2X- f 4 + 1/2(X-+X3-)

I

At

b

e

z

b

e

z

b

e

z

-1.38 21.97 -14.47 -0.94 -1.75 18.41 -4.49 5.11

-1.37 14.49 -7.00 -0.94 -1.17 17.53 -4.19 5.11

10.77 12.52 -17.17 -0.94 10.47 15.02 -13.32 5.11

0.67 14.17 -15.17 -7.11 0.15 12.33 -6.77 -1.06

-0.30 10.92 -10.95 -7.11 0.30 11.45 -6.03 -1.06

9.97 7.01 -17.31 -7.11 13.11 7.36 -14.75 -1.06

-0.46 4.32 -11.52 -14.49 1.96 7.01 -10.59 -8.44

-0.28 2.42 -9.80 -14.49 -0.25 2.72 -4.08 -8.44

7.81 -2.29 -13.18 -14.49 6.04 2.58 -10.23 -8.44

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relative stabilities of the complexes can be understood from a qualitative discussion of the electronic structure. We confirm the proposal by Clifford et al. that the reaction N3+X- + Xf N3X2- is the rate limiting step thermodynamically. The dye regeneration is favorable for N3+, i.e. N3+ is more easily regenerated than 4+. It is clear, though, that the overall functioning of a DSSC involves a delicate balance of various thermodynamic and kinetic factors. Theory is uniquely able to probe hypothetical species that are difficult or impossible to study experimentally. We have made use of this capability by extending the previously tested redox couples X ) Br and X ) I to X ) At also. Along this series, we find periodic trends of, for instance, increasing bond lengths and increasing reducing power. The comparatively low reducing power of the bromide/tribromide redox couple appears to be related to its overall bad performance in actual DSSCs. Astatine, on the other hand, might be a more powerful redox mediator than the standard iodide/triiodide couple;though, of course, its radioactivity precludes any practical application. As already discussed, Privalov et al.56 have recently published a paper that is relatively closely related to the current work. Therefore, it is worthwhile to recap the comparison between our work and the earlier paper. In terms of methodology, we have applied a different and apparently superior82 relativistic method in the form of SC-ECPs. The two papers differ most in their goals and resulting scope: Privalov et al.56 aim to identify the possible complexes between dye and redox couples. On the other hand, we focus mainly on the energetics (thermodynamics) for each step in the dye regeneration mechanism. In addition, we offer comparisons from Br to I and At, and from the standard N3 dye to a less efficient dye 4. Acknowledgment. G.S. would like to thank Peter Budzelaar for valuable suggestions and Nate Lewis for his tremendous inspiration in taking up this research area, as well as for his support. G.S. and A.M.A. acknowledge financial support from The EJLB Foundation, the Natural Sciences and Engineering Council of Canada (NSERC), and The University of Manitoba (University Research Grants Program URGP). C.H.H. acknowledges the National Center for High-Performance Computing in Taiwan for computer time and facilities. Supporting Information Available: Full citations for refs 18, 36, 37, 39, 55, and 67; schematic structures containing key geometry parameters for the various complexes (Schemes S1-S7); calculated Mulliken charges (Tables S1 and S2); optimized geometries of the N3+X- and N3X2- complexes, key geometry parameters (Table S3); optimized geometries of the 4+X- and 4X2- complexes, key geometry parameters (Table S4); “∆E + ∆∆Gsolv” values for the dye reactions (Table S5); and Cartesian coordinates for all of the optimized complexes. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Bisquert, J.; Cahen, D.; Hodes, G.; Ruhle, S.; Zaban, A. J. Phys. Chem. B 2004, 108, 8106–8118. (2) Gra¨tzel, M. Inorg. Chem. 2005, 44, 6841–6851. (3) Meyer, G. J. Inorg. Chem. 2005, 44, 6852–6864. (4) Peter, L. M. J. Phys. Chem. C 2007, 111, 6601–6612. (5) Hamann, T. W.; Jensen, R. A.; Alex., B. F.; Martinson, A. B. F.; Hal Van Ryswykac, H. V.; Hupp, J. T Energy EnViron. Sci. 2008, 1, 66– 78. (6) Goncalves, L. M.; Bermudez, V. D.; Ribeiro, H. A.; Mendes, A. M. Energy EnViron. Sci. 2008, 1, 655–667. (7) E.g.: http://en.wikipedia.org/wiki/Gra¨tzel_cell. (8) O’Regan, B.; Gra¨tzel, M. Nature 1991, 353, 737–740.

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