New Cyanine Dyes or Not? Theoretical Insights for Model Chains

ARTICLE pubs.acs.org/JPCA

New Cyanine Dyes or Not? Theoretical Insights for Model Chains Denis Jacquemin* Laboratoire CEISAM - UMR CNRS 6230, Universit
e de Nantes, 2 Rue de la Houssiniere, BP 92208, 44322 Nantes Cedex 3, France

bS Supporting Information ABSTRACT: The quest of organic dyes presenting improved electronic features has been extremely active during the last decades, as new structures are necessary to build novel materials such as dye-sensitized solar cells, nonlinear optics commutators, or molecular photochromic switches. Cyanine derivatives occupy a key spot in that scene, as they present intense absorption bands and tunable colors, even when a relatively short πconjugated path is used. This behavior has often been interpreted as a consequence of a negligible bond length alternation. Recently, Thorley et al. have designed and characterized new cationic compounds that possess the cyanine electronic features, though presenting sizable bond length alternation (Angew. Chem. Int. Ed. 2008, 47, 70957098). In this contribution, I investigate, with quantum mechanical tools, the size dependence of these properties in model symmetric dyes displaying Thorley’s patterns. Extended chains are simulated in order to obtain insights into the chain length convergence, and the results are compared to those obtained at the same level of theory for classical cyanine architectures. This theoretical work is a step toward the rational development of more efficient π-conjugated compounds.

’ INTRODUCTION Classical cyanine derivatives, I, are cationic structures presenting a core that is schematized in Scheme 1. For these dyes, one notes a sharp decrease of the longest wavelength of maximal absorption when the distances between the two amino groups increases.1 In fact, for the first few oligomers, the evolution of the experimental absorption spectra of type-I derivatives almost perfectly fits the electron in the box approximation.2 This finding has been related to the (almost) equal carbon-carbon bond lengths, that is to the vanishing bond length alternation (BLA) at the center of the structures.2 Chemical variations of type-I compounds aiming at improving their properties are still actively searched for in several fields, including batteries, medical imaging, solar cells, and optical limitation:3-7 despite being used for many years, the potential of cyanines has not been fully explored. Recently, Thorley and co-workers have synthesized a molecule composed of two porphyrins linked together through a charged bridge of type II (as in Scheme 1 but with five carbon atoms).8 This structure presents cyanine-like electronic features, including very large nonlinear optics responses. This finding is quite astonishing, as a large BLA was also evidenced in the same molecule. Soon after, Ohira et al. proposed a first theoretical rationalization of the properties of Thorley’s cyanines by using relatively short model systems.9 In ref 9, DFT and semiempirical INDO-MRDCI approaches are applied to compute the ground-state geometrical parameters and the electronic (hyper)polarizabilties, respectively. Here, I investigate two series of model chains. On the one hand, the conventional cyanines, noted I-n, and, on the other hand, new structures, named II-n, with oligomers presenting from 1 to 41 carbon atoms (n) in order to get closer to the r 2011 American Chemical Society

convergence of both the structural and electronic properties. To allow calculations on long chains, only perfectly symmetric chains (C2v) have been used here for both families of cyanines. For classical chains, I-n, it has been shown by several authors6,10-12 that, in medium and long chains, a localized (symmetry-broken) geometry becomes favored, and this significantly modifies the shape of the absorption spectra and leads to a decrease of the transition energy to the first singlet excited state. Therefore, as in ref 9, we treat here model systems that correspond to the so-called cyanine limit.6,13 Our simulations relied on ab initio approaches accounting for electronic correlation effects (see the Method section). No previous theoretical work has been performed on II besides the study of Br
edas and collaborators.9 Their work, limited to smaller chain lengths (17 carbon atoms), actually called for the investigation of longer systems.

’ METHOD The Gaussian 09 program has been used throughout,14 and default algorithms/parameters have been selected except when noted. The geometry optimizations have been performed using the 6-31G(d) basis set that has been shown to provide accurate BLA estimates in π-conjugated systems (extra tests in the Supporting Information).15-17 As we wish to consider model systems in the present work, the C2v symmetry was systematically imposed during the geometry optimizations. The CCSD(T) force minimizations relied on numerical differentiation of energies and have been performed until the computed rms force Received: January 28, 2011 Published: March 01, 2011 2442

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The Journal of Physical Chemistry A Scheme 1. Representation of the two families of cyanine dyes for chains containing nine carbon atoms

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Table 1. CCSD(T) Bond Lengths (Å) Computed for Increasingly Long Cyanines, I-n and II-na 1.318

I-1 1.393

1.327

1.398

1.392

1.332

1.396

1.403

1.388

1.337

1.401

1.393

1.407

1.385

1.340

1.397

1.405

1.390

1.410

1.383

1.344

1.394

1.408

1.388

1.414

1.380

1.347

I-3 I-5 I-7 I-9 I-11 I-13 -4

was smaller than (at least) 10 au. These simulations have been the clear time-limiting step of the present investigation, as the computations on the longest chains containing 13 carbon atoms took several months (of real time) though the C2v point group was applied. MP2 optimizations have been carried out with analytic derivatives, and test calculations have shown that there is no major impact of using a larger basis set on the MP2 BLA (see the Supporting Information, 6-31G(d) bond lengths are systematically too large by ca. 5
10-3 Å, but the BLA are almost unchanged). Partial atomic charges are computed at the MP2/631G(d) level using the MK model that yields values consistent with the electrostatic potential. The transition energies and polarizabilities have been computed with the ωB97-XD functional, a range-separated hybrid with correct asymptotic behavior.18 RSH are known to be more accurate than conventional hybrids for (non)linear optic properties.19-22 The same basis as for the ground state has been selected, and test calculations using 6-311þþG(d,p) revealed no major variations compared to the diffuse-free atomic basis set (see the Supporting Information). TD-DFT simulations relied on the same ωB97XD/6-31G(d) approach. TD-DFT encounters several problems for cyanine transitions,21,23-26 but the goal is to compare the relative evolutions of the two series, not to provide accurate absolute values for transition energies.

’ RESULTS AND DISCUSSION In π-conjugated oligomers, it is well-known that the BLA is often a key geometrical parameter. As noted in ref 9, a simple analysis of the possible mesomeric forms in I and II allows one to conclude that the former (latter) should present a vanishing (large) BLA. As quantitative rather than qualitative estimates are searched for herein, the calculations started with the wave function reference method, namely, CCSD(T). These CCSD(T) distances are also useful to benchmark other methods. Indeed, recent investigations have demonstrated that the BLA may be very sensitive to the computational level.17,21,27 Results are displayed in Table 1, and one clearly notes the expected trends, with a central BLA close to zero (0.007 Å) for I-13 but 1 order of magnitude larger for II-13 (0.085 Å). For II, it turns out that MP2 yields very accurate estimates for the bond lengths. Indeed, for II-13, the differences with respect to the CCSD(T) reference are -0.001, -0.006, 0.000, -0.008, þ0.001, -0.007, and þ0.001 Å (following the same order as in Table 1). These discrepancies are much smaller than the differences between the two series of oligomers. Therefore, the MP2 method has been applied in the following to determine the ground-state BLA of long chains. Table S-II in the Supporting Information collates the full list of MP2 bond lengths obtained for n = 1, 5, 9, ... , 41, whereas Figure 1 compares the BLA for both types calculated for one medium and one large oligomer. In Thorley’s cyanines, the BLA

1.401

1.372

1.243

1.318 1.304

1.375

1.249

1.337

1.242

1.309

1.335

1.250

1.340

1.240

1.313

II-1 II-5 II-9 II-13

1.376

1.250

n is the number of carbon atoms included in the chain (see Scheme 1). The first (last) value of each row corresponds to the central CC (terminal CN) bond.

a

is large (ca. 0.010 Å), relatively constant along the chain, and almost unchanged for the two oligomer sizes. The present contribution therefore confirms that type-II dyes are constituted by a succession of single and triple bonds and that this statement holds for very long oligomers. On the contrary, the classical cyanine dyes present almost zero BLA at the center of the chain, but the alternation increases as one goes toward the terminal amino groups. Therefore, in the 41-atom chains, the BLA of I and II become more alike close to the capping NH2 moieties. This indicates that, in extremely large systems, the difference between the two families of dyes is maximal at the center of the chain. Note that the type-I systems are regularly bent; for the largest (N = 41), MP2 yields an angle of 167° considering the two extremities and the central carbon atom. An analysis of the partial atomic charges of I demonstrates that the positive charge is diluted, except for very short oligomers. Indeed, in I-13, each amino chain end bears only a þ0.05e charge, whereas the charge on the central CH is limited to þ0.09e. This contrasts with type-II dyes. Indeed, in that case, the amino groups are positive (negative) in short (long) chains, e.g., þ0.14e for II-5 but -0.11e for II-33, whereas the central CH unit is always significantly positive, e.g., þ0.29e for II-5 and þ0.33e for II-33. The charge patterns obtained for two chain lengths are compared in Figure 2, and it is clear that the alternation between successive carbon atoms is larger in type-II than in type-I. In short, the cationic charge is more localized and more alternating in Thorley’s structures than in classical cyanines. Table S-IV of the Supporting Information gathers the dipole moments and electronic polarizabilities computed for increasingly long oligomers. The total dipole moment of I first increases rapidly with chain length and then tends to a constant value in extended oligomers. On the contrary, consistently with the evolution of the charges carried by the amino chain ends, the dipole moment of II switches sign when the chain lengthens, so that the norm of the total dipole of the II-33 is almost perfectly zero. The isotropic polarizabilities, Rh = 1/3(Rxx þ Ryy þ Rzz), reported per carbon atom are displayed in Figure 3. These values have been computed with a range-separated hybrid to correctly account for long-range effects. For short oligomers, the polarizabilities of both systems are alike, and this statement holds up to n = 17. This conclusion is consistent with the only previous semiempirical investigation on the topic.9 However, in more extended dyes, the polarizability of classical cyanine retains a rapid polynomial progression, whereas it quickly saturates in 2443

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Figure 1. Comparisons between the successive MP2/6-31G(d) BLA computed for I and II chains having 21 (left) and 41 (right) carbon atoms. In all cases, the data at the left (right) of the graph correspond to the BLA measured at the center (periphery) of the cyanine.

Figure 2. Comparisons between the successive MP2/6-31G(d) MK partial atomic charges computed for I and II chains having 21 (left) and 41 (right) carbon atoms. The charges of the hydrogen atoms have been added to the one of the closest carbon (or nitrogen) atom for the sake of clarity.

Figure 3. Evolution with chain length of the polarizability per carbon atom (left) and vertical transition energies (right) computed with the ωB97-XD functional.

Thorley’s family. This is well illustrated in Figure 3: for the longest chains, the relative isotropic polarizabilities attain ca. 120 au for II but ca. 300 au for I. In other words, it is expected that typeII cyanines are competitive for short and medium sized compounds but become less polarizable when (very) long chains are considered. Nevertheless, it has to be emphasized that the results obtained for the longest molecules, that exceed 100 au per carbon

atom, remain very large. Indeed, in a recent investigation also using a range-separated hybrid, similar amplitudes have been predicted for the prototype polyacetylene and polydiacetylene polymers, that are both well-recognized as highly polarizable.28 In Figure 3, the transition energies of the first dipole-allowed state computed with TD-DFT are also reported. Contrary to the polarizability, the evolutions are very close for both series of dyes, 2444

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No. 2.4617.07, (2) the GENCI-CINES/IDRIS (Grant 2010x2010085117), and (3) the CCIPL (Centre de Calcul Intensif des Pays de Loire).

Figure 4. Frontier molecular orbitals (ωB97-XD) for the two longest chains investigated: I-41 (left) and II-41 (right). Contour threshold: 0.02 au.

though, for medium (long) chains, II (I) dyes present slightly smaller orbital transition energies (see the Supporting Information for a full list of data). In all cases, this first transition is dominated by the expected HOMO-LUMO orbital contribution, though other smaller contributions are also predicted to play a role in extended dyes. For the longest investigated systems, the topology of the frontier orbitals is displayed in Figure 4. The HOMO of I-41 is fully delocalized, whereas the LUMO is mainly located at the center of the chain where the BLA is minimal. For II-41, absorption of a photon implies a significant charge transfer from the negatively charged chain ends to the central electrondeficient moiety. Therefore, though the foreseen transition energies are alike for the two families of chromogens, the electronic reorganization induced by the electronic excitation differs.

’ CONCLUSIONS AND OUTLOOK This ab initio investigation confirms that Thorley’s structures possess several features of cyanine dyes, though they present a strong alternation between single and triple bonds. This general statement should however be nuanced, as the repartition of partial atomic charges, evolution with chain length of the electronic polarizabilities, as well as shapes of the frontier orbitals in long oligomers significantly differ in type-I and in type-II model dyes. For the polarizability, the discrepancies become notable only for chains having more than 17 carbon atoms, a threshold not yet reached experimentally. For such long chains, the structures of classical cyanines become nonsymmetric (see the Introduction), and the treatment of the localization effects in both families of structures certainly constitute the next step of theoretical research in that field. ’ ASSOCIATED CONTENT

bS

Supporting Information. Cartesian coordinates obtained for type-II cyanine at the CCSD(T) level. Complete list of bond lengths, dipole moments, polarizabilities, and transition energies computed with 6-31G(d) for both series of dyes. Basis set investigations for all properties. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

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*E-mail: [email protected].

’ ACKNOWLEDGMENT I am indebted to the R
egion des Pays de la Loire for financial support in the framework of a recrutement sur poste strat
egique. This research used resources of (1) the Interuniversity Scientific Computing Facility located at the University of Namur, Belgium, which is supported by the F.R.S.-FNRS under Convention 2445

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