Novel Pathways for Enhancing Nonlinearity of Organics Utilizing Metal

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Novel Pathways for Enhancing Nonlinearity of Organics Utilizing Metal Clusters Zilvinas Rinkevicius,† Jochen Autschbach,‡ Alexander Baev,| Mark Swihart,§,| Hans Ågren,† and Paras N. Prasad*,‡,| Department of Theoretical Chemistry, Royal Institute of Technology, Roslagstullsbacken 15, S-106 91 Stockholm, Sweden, and Department of Chemistry, Department of Chemical and Biological Engineering, and The Institute for Lasers, Photonics and Biophotonics, State UniVersity of New York at Buffalo, Buffalo, New York 14260 ReceiVed: March 17, 2010; ReVised Manuscript ReceiVed: June 11, 2010

We show that ultrasmall metallic nanoparticles can be combined with large second- and third-order response organic chromophores to enhance the overall third-order response of the system. This approach can be used in combination with microscopic cascading to generate exceptionally large third-order response. Intermolecular charge-transfer coupling between the molecules and the metal clusters enhances the real part of the nonlinearity at telecommunication wavelengths, while avoiding plasmonic enhancement of one- and two-photon absorption, and minimizing optical losses. The results of density functional calculations for a molecule with large secondorder response, (para)nitroaniline, show that use of a gold cluster as a link between molecular entities enhances third-order nonlinearity. Varying size and shape of the metal cluster as well as the distance between the clusters and the molecules allows fine-tuning of nonlinear response over a large range of magnitudes. 1. Introduction Application of π-conjugated organic chromophores to alloptical switching has long been of great interest because of high values of their third-order nonlinearities (second hyperpolarizability, γ, of molecules and corresponding χ(3) of materials). In particular, the real part of the nonresonant degenerate thirdorder susceptibility determines the intensity dependent refractive index (IDRI) of a medium, the basis for a number of applications including all-optical switching. A number of approaches have emerged that can help increase the third-order nonlinear response, for example, multidimensional electronic delocalization in multibranched dendritic structures,1 resulting in cooperative enhancement of nonlinearities. Modifying the molecular geometry via synthetic approaches to change the electronic properties has also been proposed. Recently synthesized twisted chromophores2 that have particularly large β and γ are highly promising targets in the search for materials with enhanced χ(3). Further, the concept of microscopic cascading has recently been introduced3 as a means to enhance high-order nonlinear responses by exploiting strong lower-order responses. Firstprinciples calculations of cascaded third-order nonlinearities have been reported,4 which show that microscopic cascading can be used to achieve a strong third-order response using aggregates of organic chromophores with large second-order nonlinearity. In this paper we investigate another approach to attaining enhanced values of third-order nonlinearities: The use of small metallic clusters. Most prior work on this subject has focused on local field enhancement in the vicinity of plasmonic particles, and opportunities remain to exploit other mechanisms. While a * Corresponding author. E-mail: [email protected]. † Royal Institute of Technology Stockholm. ‡ Department of Chemistry, State University of New York at Buffalo. § Department of Chemical and Biological Engineering, State University of New York at Buffalo. | The Institute for Lasers, Photonics and Biophotonics, State University of New York at Buffalo.

few previous studies achieved promising results using either nanostructured silver fractals or spherical nanoparticles,5 the modest enhancements in χ(3) appear to be offset by increased optical loss. There are three general mechanisms through which metal nanostructures can contribute to optical nonlinearity: (i) through their own inherent optical nonlinearity; (ii) by acting as donors or acceptors with respect to organic chromophores conjugated to them; (iii) through plasmonic local field enhancement. While the third effect is expected to be strongest for metallic particles large enough to support a plasmon resonance, particularly at wavelengths near that resonance, the other two may also contribute significantly and must be considered in particular for ultrasmall metal clusters. On the basis of these premises, we suggest the following strategy for achieving greater enhancement in χ(3) of organics, while minimizing absorption losses: chemical linking of ultrasmall metal nanoparticles or clusters with organic χ(3) chromophores. Mechanistically, this enhancement can result from charge transfer, electron sharing, or hybridization of molecular orbitals between the metal cluster and chromophore. It is worthwhile to note that this effect does not depend on plasmon resonances, and in fact, clusters in this size range are too small to support plasmon modes.6 Thus, optical losses are not expected to be an issue at the wavelengths of interest (1300-1550 nm). 2. Theory For the smallest particles, which range from well-defined clusters of 4, 11, 20, 25, or 38 gold atoms7 to a few hundred atoms, both the absorption and field enhancement become increasingly sensitive to the environment, and the concept of field enhancement based on plasmonic behavior and the Drude model breaks down. Moreover, the effect of the metal nanoparticles will not be field enhancement alone, as they can act as donors or acceptors for attached molecules. Figure 1 depicts our model systems: gold Au4 and Au20 nanoclusters bound to a well-known second-order nonlinear organic molecule (para)nitroaniline (PNA). Electron donation to, or withdrawal from, the

10.1021/jp102438m  2010 American Chemical Society Published on Web 06/29/2010

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Figure 1. PNA in the vicinity of Au4 and Au20 clusters.

metallic particle in turn affects the field enhancement by changing the effective number of free electrons in the particle. It is worthwhile to note here that superatom Au20 superatom was previously used by Schatz’s group as a model for plasmonic gold nanoparticles8 and was observed experimentally in the gas phase9 and in solution.10 On the other hand, thiolated Au25 gold clusters are well characterized experimentally and are stable materials.7 Nevertheless, we chose nonstabilized gas-phase Au20 for our model system, mainly because of computational considerations. To assess the role of small metal clusters on nonlinear response of the systems of interest, quantum chemical calculations of molecular hyperpolarizabilities are needed. The power series expansion of the induced dipole moment in the staticfield limit reads

µi ) RijEj +

1 1 β E E + γijklEjEkEl + ... 2! ijk j k 3!

(1)

where Rij is microscopic molecular polarizability, associated with the macroscopic first-order (linear) response of a medium, βijk is the molecular first hyperpolarizability, associated with the macroscopic second-order nonlinear response of a medium, and γijkl is the molecular second hyperpolarizability, associated with the third-order nonlinear response of a medium. The static and dynamic second hyperpolarizability tensor γ of a molecule can be described using the response theory in which γijkl is given by the cubic response function

γijkl ) -〈〈µˆ i;µˆ j,µˆ k,µˆ l〉〉ω′;ω1,ω2,ω3

(2)

where µˆ m is the Cartesian component of the dipole moment operator (m ) i, j, k, l) and the combination of frequencies (ω′;ω1,ω2,ω3) is dependent on the nonlinear process investigated. For example, in the case of third harmonic generation this combination becomes (-3ω;ω,ω,ω). As already mentioned in the Introduction, in the present work we are interested in γijkl(-ω;ω,-ω,ω), the real part of which determines intensity dependent refractive index (IDRI) of a medium. The response function of eq 2 can be computed using an analytical approach, which is the computational method adopted in this work. Alternatively, a sum-over-states (SOS) approach is sometimes adopted. In the SOS the response function is transformed into its spectral representation and an explicit summation is carried out over a truncated set of excited states to evaluate the second hyperpolarizability tensor components.11

The accuracy of the latter approach is strongly dependent on the number and types of excited states included in the summation, as well as on the computational model used to calculate approximate excited state wave functions, and the accuracy of this approach therefore strongly varies when going from one to another molecular system. For example, accounting for a few of the lowest excited states is sometimes sufficient to obtain an acceptable approximation of the full sum-over-states expansion for selected organic charge-transfer dyes.12 More generally, the summation is often ill-convergent, and inclusion of a sufficiently large number of states in the SOS to make accurate predictions is computationally unfeasible. Analytical response theory methods are therefore generally preferable in computation of second hyperpolarizability tensors. These methods for computations of hyperpolarizabilities and a variety of other molecular properties have been implemented in the Dalton13 and in the ADF14 quantum chemistry programs at the time dependent density functional theory (TDDFT) level. 3. Computational Details A subset of the computations were performed with the Amsterdam density functional package (ADF),14 employing the PBE15 nonhybrid generalized gradient approximation (GGA) functional. For analytic response calculations of hyperpolarizability tensors, the “aoresponse” module of ADF, described in refs 16 and 17 was used. A triple-ζ Slater-type atomic orbital (STO) basis set with polarization functions for all atoms (TZP) from the ADF basis set library was used for the PNA moiety, along with the default set of density-fitting functions accompanying this basis. For PNA, a basis set of this flexibility and the functionals as used here have previously been shown to yield reasonable agreement with experiment for first- and second-order nonlinear response tensors,16,17 although the use of additional diffuse functions would be beneficial.17 An optimized geometry for PNA was taken from ref 16. An optimized geometry for the Au20 cluster was taken from ref 8. We did not reoptimize the geometry of the complex but instead varied the distance between PNA and Au20 to assess the role of intermolecular charge transfer. A double-ζ 4f frozen-core STO basis (DZ) was used for gold atoms. The zeroth-order regular approximation (ZORA) relativistic Hamiltonian in its spin-free form was used in the ADF computations to describe the sizable relativistic electronic structure effects of the gold atoms. The importance of using a relativistic method is demonstrated in Figure 2 where a comparison of the excitation spectra of Au20 cluster, obtained with and without ZORA, is presented (see also refs 8, 18). The spectra were Gaussian broadened, with σ ) 7.5ν˜ 1/2, where ν˜ is the excitation wavenumber in cm-1. The remainder of the computations were performed with Dalton,13 with which responses were obtained using the Coulomb attenuated B3LYP (CAM-B3LYP) functional,20 the 6-311+G* Gaussian-type orbital (GTO) basis set on the H, C, N, O atoms, and a double-ζ GTO basis set based on the Stuttgart small effective core pseudopotential (ECP) for the gold atoms. This combination of basis sets and ECP allows us to incorporate the scalar relativistic effects into the calculation at the minimal cost and provides an efficient way to study large systems of this kind. 4. Results and Discussion Computationally, PNA has formed the main test-bed for calculations of hyperpolarizabilities of charge-transfer systems.16,17,19 Results indicate that density functional theory can match high level coupled cluster theory on a qualitative,

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Figure 3. Dispersion of second hyperpolarizability of the Au20-PNAtip system computed with the PBE functional. Figure 2. Excitation spectrum of the Au20 cluster computed with the PBE functional.

TABLE 1: Orientationally Averaged Degenerate First and Second Hyperpolarizabilities of Different Configurations of PNA Molecule and Au20 Cluster Computed with PBE Functional system PNA Au20-PNA-tip Au20-PNA-face PNA Au20 Au20-PNA-tip Au20-PNA-face

βav (103 au) a. At 1300 nm 1.97 22.53 b. At 2000 nm 1.73 0.00 13.77 18.03

γav (103 au) 23.29 -7231.95 -18870.87 20.12 19.96 6894.08 45317.56

sometimes semiquantitative, level using conventional functionals, while quantitatively there is a need for specially designed so-called Coulomb attenuated functionals20 that have the proper asymptotic dependence for long-range interaction and thus are most suitable for applications of NLO effects in charge-transfer systems.21,22 We have therefore made complementary calculations of the cubic response functions (eq 2) using Coulomb attenuated functionals as implemented in the program package Dalton.13 For the nonhybrid time dependent density functional theory (TDDFT) computations with ADF we found a substantial enhancement of the degenerate γ(ω;ω,-ω,ω) of the cluster system, depicted in the lower half of Figure 1, at the telecommunication wavelength of 1300 nmsmore than 2 orders of magnitude greater than the isolated PNA value, and almost 1 order of magnitude greater than the isolated Au20 cluster value (see Tables 1a,b, Au20-PNA-tip entry). Even greater enhancement factors were found for a system of a PNA molecule attached to one of the facets of tetrahedral Au20, but as will be shown below, the value is too close to a resonance to be reliable. The dispersion data presented in Figure 3 indicate a resonance at around 1300 nm, where the calculated γ(ω;ω,-ω,ω) diverges. We attribute this behavior to a two-photon resonance. Indeed, the excitation spectrum of the Au20 cluster reveals a noticeably strong absorption band at 620 nm. Since we expected the nonhybrid DFT computations to somewhat underestimate the excitation energies, we applied a wavelength correction (i.e., the rest of calculations were performed at 2000 nm) in subsequent calculations with the PBE functional to stay off resonance. The difference in energy (hc [1/1300 - 1/2000]

Figure 4. Excitation spectra of the Au20 cluster/PNA systems computed with the PBE functional.

TABLE 2: Orientationally Averaged Degenerate Second Hyperpolarizability of PNA Attached to the Au20 Cluster (Au20-PNA-tip) versus the Distance between Them (TDDFT Computations with PBE Functional at 2000 nm) distance (Å)

γav (103 au)

3 4 5

6894.08 2707.47 468.08

nm-1) is 0.33 eV, which is not an uncommonly large correction for TDDFT when using standard functionals. A stronger enhancement obtained for the Au20-PNA-face system indicates that either the local field generated by the Au20 cluster at its facet is particularly strong or that the charge-transfer mechanism (vide infra) is more effective (likely a combination of effects causes the differences). Indeed, the calculated excitation spectra of Au20-PNA-tip and Au20-PNA-face systems, shown in Figure 4, reveal larger oscillator strengths for the latter along with an additional resonance at 966 nm, which could contribute by a two-photon process to the second hyperpolarizability and push the calculated γ into the strongly dispersive regime. The results of our calculations obtained for a number of distances between the Au20 cluster tip and PNA molecule (Table 2) strongly support the suggested charge-transfer mechanism of enhancement described below. This is very promising

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TABLE 3: Orientationally Averaged Degenerate First and Second Hyperpolarizabilities of Different Configurations of PNA Molecule and the Au20 Cluster Computed with the CAM-B3LYP Functional at 1300 nm system

γav (103 au)

PNA Au4-PNA-face Au4-PNA-2 Au20-PNA-2

29.00 569.00 781.00 6330.00

because one may be able to fine-tune the interaction in a composite system to achieve maximal enhancement at minimal loss. The enhancement factors obtained for a smaller Au4 cluster system with the hybrid CAM-B3LYP functional (Table 3) are smaller though substantial (still more than 1 order of magnitude). It is interesting to note that the enhancement factor for a larger Au20 system is more than 5 times that of a smaller Au4 system, which probably means that the number of gold atoms in the cluster, NAu, can be optimized for greater enhancement. This aspect is currently being investigated. Our results suggest that resonant coupling of chromophores with different size gold clusters, resulting in an effective pool of delocalized electrons, has the potential to push χ(3) to magnitudes far exceeding the current limit. It is worthwhile to briefly comment here on our choice of functionals. In this work we used two exchange-correlation functionals: CAM-B3LYP and PBE. The selection of the CAM functional was motivated by its ability to describe the charge-transfer excitations and consequently to predict polarizabilities and hyperpolarizabilities of charge-transfer systems. As we can see from Tables 1 and 3, the two functionals predict the same order of magnitude enhancements of these quantities after considering the wavelength correction described above. The CAM-B3LYP functional predicts γ for PNA molecule to be around 30% larger than γ obtained using the PBE functional. The main reason for this difference is the improved description of charge-transfer excitations in the PNA molecule by the asymptotically well behaved CAM-B3LYP functional compared to that by the PBE functional. This property of CAM-B3LYP functional makes it likely more suitable for describing chargetransfer processes occurring in gold clusters and PNA complexes. Besides, density functional theory has been rather thoroughly benchmarked for the first hyperpolarizability of PNA; see ref 19b, for example. In particular, DFT calculations with B3LYP functional overshoot coupled-cluster single-double (CCSD) calculated values by roughly 10%, while local density approximation (LDA) functionals overshoot CCSD values by 50%. Figure 5 shows a schematic representation of molecular orbitals of the combined Au4 + PNA cluster and separated

Figure 5. Molecular orbitals of the composite Au4 + PNA cluster and their relation to the parent systems as computed with the CAMB3LYP functional in Dalton.

subsystems (from Dalton calculations). Similarly to the case for typical charge-transfer dyes, the HOMO of PNA is localized on the donor group of the molecule (-NH2) and the LUMO is localized on the acceptor group (-NO2). The charge-transfer excitation, which is responsible for large NLO response of PNA occurs between these two orbitals. In the combined Au4 + PNA system, three orbitals of the Au4 cluster (HOMO, LUMO, LUMO+1) are energetically located between the HOMO and LUMO orbitals of PNA (see Figure 4). This phenomenon, which normally does not occur in organic “clusters”, drastically changes the electronic structure and properties of the Au4 + PNA cluster compared to those of its constituents. In this respect, we note that hybridization between the Au4 orbitals and the PNA orbitals in the combined system is relatively insignificant and mostly the HOMO and LUMO of the PNA unit are affected. An analysis of the excited states in this system indicates that the most important change in transitioning from the PNA molecule to the combined system is the opening of two new charge-transfer excitation channels: (a) charge transfer from the donor group of PNA (HOMO-1 in combined system) to the Au4 cluster unoccupied orbitals; (b) charge transfer from the Au4 cluster HOMO to LUMO of the PNA cluster. Analysis of the excited states of the combined system indicates that the latter excitation channel is responsible for the large enhancement of the second hyperpolarizability observed in Au4 + PNA cluster compared to that for a single PNA unit, since the transition dipole moment for charge-transfer excitation localized in the PNA molecule is only slightly affected by the presence of the Au4 cluster. The PNA molecule with its donor group close to gold receives much less charge transfer (with a transition dipole of opposite sign), making the net effect large. Therefore, we conclude that additional charge-transfer channels located below the typical PNA charge-transfer excitation are responsible for the large second hyperpolarizability observed in the PNA + Au4 gold cluster complex. Calculations with a larger gold cluster indicate the same qualitative behavior. The suggested mechanism of enhancement correlates with the obtained dependence of γ on the distance between the PNA molecule and the Au20 cluster (see Table 2). The rapid decrease of γ with the distance confirms that the main contribution to the enhanced γ comes from the overlap between the corresponding molecular orbitals of the cluster and the PNA (see the discussion below). The larger cluster introduces a richer density of states and a smaller HOMO(cluster)-LUMO (PNA) gap. A salient difference is also that charge transfer from gold to PNA takes place over a longer distance, leading to a larger transition dipole element. In the framework of a few-state model for γ, these features easily rationalize the strong enhancement of the cubic response function by linking with metal clusters. The electronic excitations of the systems studied in this paper can be classified according to the overlap of the occupied and unoccupied molecular orbitals involved in the excitation process. According to Peach et al.20 measure Λ of the spatial overlap of orbitals is given by the normalized square weighted sum of excitation vector components (for details see ref 20). For the isolated PNA molecule this measure, Λ equals 0.57 for the charge-transfer, HOMO-LUMO, excitation as computed at the TDDFT level with the CAM-B3LYP long-range corrected functional. This indicates that there is a significant overlap between the donor (HOMO) and the acceptor (LUMO) orbitals in this case. In the combined system, Au4 + PNA cluster, the overlap of this charge-transfer excitation remains almost unchanged as compared to that for the isolated PNA molecule. The new charge-transfer band, which corresponds to a charge

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Rinkevicius et al. by a grant from the Swedish Infrastructure Committee (SNIC) for the project “Multiphysics Modeling of Molecular Materials”, SNIC 022/09-25. References and Notes

Figure 6. PNA dimer linked through Au20.

transfer from the Au4 cluster HOMO to the PNA LUMO, shows a smaller, albeit significant overlap of 0.28 between the acceptor (Au4 cluster) and donor (NO2 group in PNA) orbitals. In this work we also studied a system composed of two PNA molecules linked via tetrahedral gold Au4 and Au20 clusters, as shown in Figure 6. Similar to findings for the simpler systems of Figure 1, there were substantial enhancements of second hyperpolarizabilites (see Table 3) in hybrid (CAM-B3LYP, Dalton) TDDFT calculations. The agreement between the results obtained with nonhybrid and hybrid calculations for the Au20PNA-2 system was not good. One reason could be a resonance in the nonhybrid excitation spectrum of Au20-PNA-face system which, unless some form of damping is incorporated in the calculations, results in numerical divergence. 5. Conclusion We have suggested a strategy for enhancing the nonlinear optical third-order response of π-conjugated organics based on supramolecular organization mediated by metallic clusters. The strategy was tested by means of cubic response calculations of the second hyperpolarizability of systems with (para)nitroanaline (PNA), a traditional prototype for studies of charge-transfer excitations, with gold clusters of different sizes. We found that additional charge-transfer channels located below the typical intramolecular PNA charge-transfer excitation are responsible for the large second hyperpolarizability observed in the PNA-gold cluster complexes. The organization of a high density of cluster states of the larger complexes with enhanced transition dipole matrix elements of excitations involving charge transfer over longer distances, and a narrowed energy gap, account for strong enhancement of polarizability and hyperpolarizability. These findings motivate our strategy of using metal clusters for generating large molecular γ, where the cluster size is too small to support sizable plasmon excitations. It is worthwhile to note here that Au11, Au25, and Au38 clusters can be prepared experimentally.7 There may also be particular clusters at the low end of the cluster size range where there is a particularly advantageous trade-off between enhancement due to resonant coupling and one and two-photon absorption losses. Acknowledgment. This work was supported by a seed grant from the office of Vice President for Research at the University at Buffalo. We are grateful to Dr. Ruth Pachter of Air Force Research Laboratory, Wright-Patterson AFB, Ohio, and to Prof. Marek Samoc´ of University of Technology, Wrocław, for valuable discussion. J.A. thanks the National Science Foundation for financial support of his research. H.A. acknowledges support

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