Optical Properties of Chiral Plasmonic Tetramers ... - ACS Publications

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Optical Properties of Chiral Plasmonic Tetramers: Circular Dichroism and Multipole Effects Zhiyuan Fan, Hui Zhang, and Alexander O. Govorov* Physics and Astronomy Department, Ohio University, Athens, Ohio 45701, United States S Supporting Information *

ABSTRACT: Chiral metal nanoparticle assemblies exhibit plasmonic circular dichroism (CD) in the visible spectral interval. It was found previously that the circular dichroism signals can be induced by dipolar interactions between nanoparticles in a chiral assembly. In order to enhance plasmonic circular dichroism response, one can take advantage of multipole effects and anisotropy of nanostructures. We calculate the plasmonic circular dichroism of several nanoparticle (NP) assemblies using the interacting point-dipole approach and the purely numerical method based on the discrete dipole approximation (DDA). We found that the multipole effects revealed by the DDA calculations are crucial to describe and understand CD responses of tightly packed assemblies. The chiral equilateral tetrahedral 4-NP complexes are especially interesting because they do not have the dipolar contribution to the CD signal. Therefore, CD signals of equilateral tetrahedral 4-NP complexes originate solely from the multipole interactions. The strength of CD signals rapidly decreases with the particle−particle distance as 1/R9.7 for the helices and as 1/R18.1 for the equilateral tetrahedral 4-NP complexes, where R is a particle−particle distance. We show that the CD spectra are much more sensitive to the geometry of a plasmonic complex compared to the extinction spectra. Small variations in geometry can result in large changes in CD responses. This study can be used to design nanostructures with strong CD for optical and sensor applications.

1. INTRODUCTION Chirality is also called handedness. In nature, many biomolecules are chiral. The biological stereoselectivity is such that the chemical properties of two enantiomers may be dramatically different. Enantiomers are molecules of opposite handedness. For example, in drug development, one enantiomer may not be desired because sometimes this enantiomer may be inactive or even cause adverse effects in a treatment. Circular dichroism (CD), which is the difference in absorption of left circularly polarized (LCP) light and right circularly polarized (RCP) light by chiral molecules, is very sensitive to molecular conformations and chirality. Generally, the CD effect is weak but very characteristic. The CD spectroscopy is widely used in the sensing of biomolecules. It often requires ultraviolet light to see molecular CD because most natural biomolecules absorb in the ultraviolet wavelength region. Recently in the lab, a plasmonic CD in the visible spectral interval was observed in a solution with metal nanoclusters incorporating chiral ligands.1,2 More experiments and physical models of ligand-protected nanoclusters were reviewed previously.3,4 In 2006, another study demonstrated CD in the plasmon band of 10-nm silver nanoparticles that were grown on a DNA template.5 Nanomaterials involving well-defined metal nanoparticles (NPs) showed the potential of both transferring a CD signal to the visible band and modifying molecular CD signals that are mostly in the UV region. The © XXXX American Chemical Society

interest in such artificial chirality is growing quickly. Mechanisms of artificial plasmonic chirality include dipolar, molecule−plasmon, and electromagnetic interactions in nanoscale structures composed of biomolecules and metal nanocrystals.6−10 In the mechanism coming from the molecule− plasmon Coulomb interaction, structural anisotropy8 and plasmonic hotspot11,12 effects can enhance plasmonic CD signals. The mechanisms mentioned above can be used to explain a number of experimental observations.11,13−24 Purely plasmonic chirality comes from the plasmon−plasmon interactions in a nanocrystal assembly7,21,25 or from chiral shapes of individual nanocrystals.9,14 Several experimental papers reported NP bioassemblies with chiral geometries.17,21,26−32 The CD mechanism induced by the dipole plasmon−plasmon interaction is often used to explain experimental data for chiral nanoscale assemblies. Potential application of chiral metal nanostructures is in the sensing of biomolecules. The enhancement of electromagnetic fields from chiral lithographic plasmonic structures 33−38 is another approach to develop chiral biosensing with plasmons. Our previous calculations of CD of chiral nanoparticle assemblies were performed for the dipolar regime of Received: May 21, 2013 Revised: June 26, 2013

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dx.doi.org/10.1021/jp404987v | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Models of chiral nanoparticle assemblies studied previously.7,25 The optical anisotropy factor is defined as g = εCD/εabs, where εCD is the CD signal and εabs is the absorption. Generally, the anisotropy factor of helical assemblies is the largest, and the next is the assembly with other asymmetric frames. Asymmetric tetrahedrons with symmetric frames show relatively small CD responses, and equilateral tetrahedral 4-NP complexes show the smallest signals. The equilateral tetrahedral complexes have negligible CD in the dipole limit.7 However, as it will be shown below, tightly packed equilateral tetrahedral assemblies may have noticeable CD signals due to the multipolar interactions.

interparticle interaction.7,25 In this regime, we compared CD signals of different metal nanoparticle assemblies. In particular, we considered a helix, both symmetric and asymmetric pyramidal structures, and an equilateral tetrahedron with NPs of different sizes on its vertices. Our conclusion was that the strongest CD signals appear in complexes with asymmetric frames, whereas NP assemblies with symmetric frames give weaker CD signals. In addition, we made an observation that a chiral equilateral tetrahedral assembly (4 different NPs on the vertices of an equilateral tetrahedron) has a vanishing CD response in the dipolar model. This is due to the highly symmetric frame of an equilateral tetrahedral assembly. Figure 1 illustrates the assemblies studied in previous work.7,25 Here, we show that the role of multipoles becomes very important in tightly packed nanoassemblies. The plasmons interact more effectively through dipolar, as well as multipolar, near-fields when the distance between NPs is reduced. This electromagnetic problem can be solved using a Mie theory or a multiple-scattering formalism applied to the multisphere geometry.39,40 Alternatively, in this study we have computed the CD response using a numerical tool called DDSCAT 7.2.2, which was developed by Draine and Flatau.41 This numerical tool is based on the discrete dipole approximation (DDA) and can be conveniently applied to nonspherical objects. The convergence of the simulation has been carefully checked. We believe that this method is capable to predict a magnitude of CD response with a good accuracy. In the dipolar regime, we have shown that a stronger NP−NP interaction may lead to a larger CD response described by a power law (CD ∼ R−α, where R is a characteristic particle−particle distance),7,17 whereas from the DDA simulations, we see that the NP−NP interaction in the multipolar regime gives a red-shifted CD spectrum, as well as an extra enhancement of the CD signal compared to the point-dipole model.7,25 Here, we will give results for a helical structure, an elliptic helical structure, an asymmetric tetrahedron with an asymmetric frame, and an equilateral tetrahedral structure (Figure 3). The nanocrystal assemblies with strong plasmon−plasmon interactions are actively studied.42−45 These interactions lead to characteristic splittings and shifts in the extinction spectra of NP complexes. In contrast to the extinction spectra, the CD

spectra include, in addition to spectral shifts and splittings, high sensitivity to the geometry of a plasmonic assembly because this response depends on asymmetries of the interaction between NPs.7 In particular, the CD response decreases very rapidly with the NP−NP separation and is strong only in tightly packed assemblies.

2. MATHEMATICAL FORMALISM 2.1. General Equations of Interacting Dipoles. A system of N particles is described by a set of dipoles {p⃗i}i=1,...,N induced by an external field and interactions. The equation for a dipole moment of the i-th NP is ⃗ i+ pi ⃗ = αi (Eext,

∑ Ej⃗ → i) (1)

j≠i

where E⃗ ext,i is an external field, αi is an isotropic polarizability of the i-th NP, and the fields due to neighboring NPs46 are ⎧ iω ε0 rji ⎞ 3rjî ·pj⃗ rjî − pj⃗ ⎪⎛ 1 Ej⃗ → i = ⎨ − ⎜ ⎟ ⎪ c rji 3 ⎠ ⎩⎝ + ε0

⎫ ω 2 pj⃗ − rjî ·pj⃗ rjî ⎪ iω ⎬e ⎪ rji c2 ⎭

ε0 rji / c

(2)

The NP polarizability can be defined in the usual way: αi(ω) = a3NP,i(εAu − ε0)/(εAu − 2ε0), where εAu(ω) is the Au dielectric function and ε0 is the dielectric constant of a matrix. The ⃗ external field varies at different sites by a phase factor eik·r⃗. The set of linear equations (eq 1) can be solved self-consistently for all 3N dipole moments. Then, the total absorption and extinction can be calculated using the following equations: Q abs = Q ext =

1 ωε0 2

⎛ p⃗ *

⎞ ·pi ⃗ ⎟ ⎝ αi* ⎠

∑ Im⎜ i

i

(3)

1 ⃗ i *·p ⃗ ) ωε0 ∑ Im(Eext i 2 i

(4) 41,47,48

2.2. Discrete Dipole Approximation (DDA). In nature, all materials are composed of atoms of various kinds. B



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When the wavelength of light is much longer than the atomic spacing, the dielectric properties of a substance can be described using Maxwell’s equations, which are written for a continuous medium. On the other hand, the dielectric properties of a substance with a cubic lattice can be related to the polarizability of individual atoms. The DDA technique was inspired by this argument. To approximate a continuous medium, a target (i.e., a nanocrystal) can be replaced by a set of 3N polarizable dipoles defined on a cubic lattice, assuming that the wavelength is longer than the lattice period. The oscillating dipole moments {p⃗i}i=1,...,N are excited by an incident monochromatic field. The polarizability αi and the lattice of dipoles can be defined following the method given in a previous study.47 Then, the dipoles become iteratively computed from eq 1. Finally, the absorption and extinction cross sections can be calculated from {p⃗i}i=1,...,N. 2.3. Point Dipole Approximation (PDA). When nanoparticles are located far from each other, the electrodynamics problem can be simplified by introducing a set of point dipoles to represent each individual NP of an assembly.49,50 The dipolar approach is valid when a spacing between NPs is large enough and the size of each single NP is small enough so that the multipole fields become weak.50,51 Mathematically, the set of equations can be similar to the DDA method, although the PDA approach is applied to a different physical system. 2.4. Plasmonic Circular Dichroism. Circular dichroism is defined as the difference in absorption or extinction of LCP and RCP light. The directional CD for an incident light beam associated with a particular wavevector k⃗ is CDk ⃗ = Q + − Q −

Figure 2. Schematic of a pair of right circularly polarized light beams traveling in the opposite directions. A chiral object is shown in blue.

3. RESULTS AND DISCUSSION 3.1. Geometry of Nanostructures. Systematically, we have studied a series of nanoassemblies using DDA. They are a helical structure, an elliptic helical structure, an asymmetric tetrahedron structure with an asymmetric frame, and an equilateral tetrahedral structure. The sketches of these nanoassemblies are shown in Figure 3a. The size is chosen to be 5 nm in radii for NPs in a helix, an asymmetric tetrahedron, and an elliptic helix. In an equilateral tetrahedral complex, the asymmetry comes from NPs of different sizes; the sizes of NPs are 3 nm, 4 nm, 5 nm, and 6 nm. To begin with the following investigation, we start with assemblies in which NPs are close to each other and choose the minimum surface to surface gap within the assembly to be only 1 nm, as shown in Figure 3a. The parameter η = 1 for the structures is shown in Figure 3a. Then, we expand the structure by multiplying the coordinates of each NP with a parameter of η ≥ 1. In other words, the coordinates of NPs in our complexes will be ri,α (η) = η·r0i,α, where r0i,α is the α-coordinate of the i-th NP for η = 1. Table 1 shows the case of η = 1. The coordinates and radii of NPs are given in the following form: [x,y,z, radius]. In Figure 3b, we show the computed extinction spectra for the structures with η = 1. For small AuNPs, the total extinction is roughly proportional to the total volume of AuNPs. With the geometric parameters chosen, we can predict that the total extinction of those nanoassemblies is generally of the same magnitude, although some variations of extinction appear in the spectra due to the interaction between NPs. 3.2. Helix and Elliptic Helix. In a previous study, we found that helical nanoparticle assemblies create strong CD signals.7 This is because a helical chain of nanoparticles possesses a chiral collective excitation that comes directly from the geometry of the frame. The anisotropy factor g = εCD/εabs is the largest of all chiral geometries that we have studied. However, one can optimize the CD strength by varying geometrical parameters of a helix.25 In this present study, we first fixed the radius of a helical assembly made of four NPs. Then, the pitch was chosen to obtain the maximal CD. Then, using the packing parameter η, we can compress or expand the geometry. The elliptic helices are shown in Figure 3a. This structure is similar to the complex designed and described previously.33 If we place the first NP in the center of coordinates, the second NP will be displaced in the x-direction by a distance d. Then, we start with the position of the second NP and make a displacement in the y-direction by the same distance. This will be a position for the third NP. The position for the fourth NP is obtained by a displacement from the third one in the z-direction.

(5)

where Q refers to extinction. In colloidal systems, the nanostructures are randomly oriented in a solution and averaging over orientations is needed. Mathematically, averaging can be performed by assuming that the light comes from all directions. Then, ⟨CD⟩ = ⟨Q + − Q −⟩Ωk ⃗

(6)

Instead of numerical averaging for all directions, we use the following equation that is valid for small objects:9 ⟨CD⟩ =

CD+x + CD−x + CD+y + CD−y + CD+z + CD−z 6 (7)

The proof of this equation is given in ref 9 and is also available in the Supporting Information (SI). In fact, one can show that CD+n = CD−n (see the Supporting Information), and therefore, the averaging can be done over three perpendicular directions: CD =

CD+x + CD+y + CD+z 3

(8)

Figure 2 illustrates two right circularly polarized beams propagating in the opposite directions and a chiral object. Because we are using a method of local dielectric function, we need to define the dielectric constants of the components. For gold NPs, we have used the data for εAu(ω) from a previous experiment.52 For the matrix material, we assume that for water ε0 = 1.8. C



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Figure 3. (a) Models of chiral nanoparticle assemblies. (b) Extinction spectra computed from DDA for closely packed chiral nanoparticle assemblies. The coordinates and sizes of NPs can be found in Table 1 for a packing parameter η = 1. The packing parameter reflects the NP−NP separations, Rij. When we increase the size of a complex, we simply assume larger NP−NP separations according to the equation η·Rij with η ≥ 1.

from NPs of different radii. The dipolar interactions between plasmons in an equilateral tetrahedral 4-NP complex are not able to create CD responses even though the complex is chiral.7 This has been confirmed numerically by using both DDA and PDA for equilateral tetrahedral complexes with relatively large separations between NPs. This interesting property of a chiral equilateral tetrahedral complex can be also demonstrated analytically (see Supporting Information). Interesting phenomena are observed when the AuNPs are pushed closer to each other when the multipole fields become stronger. A moderate CD signal with g ∼ 10−5 is observed when the surface-tosurface gap is decreased to 1 nm. The results of simulations for several packing parameters are shown in Figure 6a. These CD responses are extra sensitive to the interparticle separation in comparison to the other chiral nanostructures studied here. 3.5. Multipole Effects. As we have previously shown,7 for the dipolar regime CD ∝ a12/R8 for small structures composed of nanoparticles with the same size, where a is the radius and R is the dimension of the nanostructure. Intuitively, the strength of CD is directly related to the strength of interaction and dipole moments; the stronger the interaction, the stronger the CD signal. The exponent of 12 shows the power of enhancing the CD signal by simply increasing the size of NPs. A previous experiment was able to confirm this relation by increasing the sizes of NPs in a well-defined DNA-assembled nanostructure.17 However, it was unclear whether a dipolar model can accurately describe the relationship between the size and the magnitude of the CD signal, especially when the NPs are nearly touching. Noticeably, both experiments and dipolar simulations have shown enormous CD enhancement with the increase of NP size. Here, DDA simulations allow us to look beyond the dipole interaction between NPs. The simulated dipolar CD for closely packed AuNP helical assemblies shows enhancement in CD, as well as a larger red shift, which is qualitatively consistent with the experiment. In Figures 4d, 5d, and 6b, we plot the CD strength as a function of the packing parameter in logarithmic scale. In these figures, we also show the linear fits. A CD strength is chosen as the peak-dip difference in the spectra. The slopes obtained in the PDA model are as follows: −8.83 for the helix and −8.03 for the asymmetric tetrahedron. Then from DDA, we obtained −9.67 for the helix and −9.08 for the asymmetric tetrahedron. These faster decay rates can be

Table 1. Coordinates and Radii of NPs in a Chiral Assembly with η = 1 coord and radii (nm)

x

y

z

radius

equilateral tetrahedron

4.2426 −4.2426 4.2426 −4.2426 0 0 11 0 7.188 0 −7.188 0 7.78 0 0 0

4. 2426 −4.2426 −4.2426 4.2426 0 11 0 11 0 7.188 0 −7.188 0 11.67 −7.78 0

4.2426 4.2426 −4.2426 −4.2426 0 0 0 11 0 4.193 8.386 12.579 0 0 0 11.67

3 4 5 6 5 5 5 5 5 5 5 5 5 5 5 5

elliptic helix

helix

asymmetric tetrahedron

The comparison of CD computed using DDA and PDA is presented in Figure 4. From the geometry in Figure 3a, we can easily tell that the helix is right handed and the elliptic helix is left handed in our simulation. The CD responses are the same order, but the shapes are roughly flipped due to the opposite handedness of the assemblies. At η = 1.5 and 2, simulations give similar results for DDA and PDA, which confirms that the point-dipole model is valid for diluted chiral nanostructures. When η = 1, the CD magnitude computed from DDA is significantly different from that obtained within the PDA model. It indicates that the multipole effects are becoming important. Simultaneously, the CD bands of closely packed complexes are red shifted, which is also attributed to a stronger interaction between plasmonic NPs. 3.3. Asymmetric Tetrahedron. For asymmetric tetrahedrons, we take asymmetric frames. Such asymmetry is created by introducing arms of different length in the complex, as shown in Figure 3a. The coordinates of Au NPs for η = 1 can be found in Table 1. 3.4. Equilateral Tetrahedron. An equilateral tetrahedral complex has a highly symmetric frame. The chirality comes D



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Figure 4. (a−c) Comparison of CD spectra computed using DDA and PDA for a helix and an elliptic helix; the packing parameter η = 1, 1.5, and 2.0. (d) The normalized CD strength as a function of η for the helix. The plot is in the logarithmic scale.

Figure 5. (a−c) Comparison of CD spectra computed using DDA and PDA for an asymmetric tetrahedron with packing parameter η = 1, 1.5, and 2.0. (d) The normalized CD strength as a function of η. The plot is in logarithmic scale.

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Figure 6. (a) CD spectra computed using DDA for the equilateral tetrahedral structures with various packing parameters of η. (b) The normalized CD strength as a function of η. The plot is in logarithmic scale.

Figure 7. Directional CD from PDA simulation of nanostructures for a helix (a), an elliptic helix (b), an asymmetric tetrahedron (c), and an equilateral tetrahedral complex (d). The coordinates are taken from Table 1, and the packing parameter η = 2.

tetramers with symmetric frames can be strong only when NPs are very densely packed. 3.6. Directional CD. Orientated nanostructures are able to demonstrate stronger CD signals than those that are randomly orientated and floating in colloidal solutions. This can be seen in Figure 7: The averaged CD signals are much weaker than the directional CD. It is even possible to induce optical chirality in symmetric nanostructures.53,54 The emerging asymmetric interaction between the nanostructures and circularly polarized optical fields is because the geometry of the combined system (nanostructure + light) is chiral.36 Circular dichroism in this sense is more common than the isotropic optical activity of 3D chiral objects in a solution. In the dipolar regime, we show in

qualitatively attributed to the multipole interactions; the multipole fields induced by NPs decay faster than the dipolar fields. From our observation, we found that the dipole effect is still a critical factor in CD of assemblies with asymmetric frames. However, in the equilateral tetrahedral complexes with a highly symmetric frame, we see that the decay of CD is much faster; the slope obtained from the linear fit is about −18. Importantly, the dipolar interaction will give no contribution to a CD response in the equilateral tetrahedral structures, and therefore, the corresponding decrease of CD(η) in Figure 6b is much steeper compared to that of other structures. This suggests that the plasmonic CD response in nanoparticle F



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(4) Gautier, C.; Bürgi, T. Chiral Gold Nanoparticles. ChemPhysChem 2009, 10, 483−492. (5) Shemer, G.; Krichevski, O.; Markovich, G.; Molotsky, T.; Lubitz, I.; Kotlyar, A. B. Chirality of Silver Nanoparticles Synthesized on DNA. J. Am. Chem. Soc. 2006, 128, 11006−11007. (6) Govorov, A. O.; Fan, Z.; Hernandez, P.; Slocik, J. M.; Naik, R. R. Theory of Circular Dichroism of Nanomaterials Comprising Chiral Molecules and Nanocrystals: Plasmon Enhancement, Dipole Interactions, and Dielectric Effects. Nano Lett. 2010, 10, 1374−1382. (7) Fan, Z.; Govorov, A. O. Plasmonic Circular Dichroism of Chiral Metal Nanoparticle Assemblies. Nano Lett. 2010, 10, 2580−2587. (8) Govorov, A. O.; Fan, Z. Theory of Chiral Plasmonic Nanostructures Comprising Metal Nanocrystals and Chiral Molecular Media. ChemPhysChem 2012, 13, 2551−2560. (9) Fan, Z. Y.; Govorov, A. O. Chiral Nanocrystals: Plasmonic Spectra and Circular Dichroism. Nano Lett. 2012, 12, 3283−3289. (10) Govorov, A. O.; Gun’ko, Y. K.; Slocik, J. M.; Gerard, V. A.; Fan, Z.; Naik, R. R. Chiral Nanoparticle Assemblies: Circular Dichroism, Plasmonic Interactions, and Exciton Effects. J. Mater. Chem. 2011, 21, 16806−16818. (11) Gerard, V. A.; Gun’ko, Y. K.; Defrancq, E.; Govorov, A. O. Plasmon-Induced Cd Response of Oligonucleotide-Conjugated Metal Nanoparticles. Chem. Commun. 2011, 47, 7383−7385. (12) Zhang, H.; Govorov, A. O. Giant Circular Dichroism of a Molecule in a Region of Strong Plasmon Resonances between Two Neighboring Gold Nanocrystals. Phys. Rev. B 2013, 87, 0754101− 0754108. (13) Slocik, J. M.; Govorov, A. O.; Naik, R. R. Plasmonic Circular Dichroism of Peptide-Functionalized Gold Nanoparticles. Nano Lett. 2011, 11, 701−705. (14) Maoz, B. M.; van der Weegen, R.; Fan, Z.; Govorov, A. O.; Ellestad, G.; Berova, N.; Meijer, E. W.; Markovich, G. Plasmonic Chiroptical Response of Silver Nanoparticles Interacting with Chiral Supramolecular Assemblies. J. Am. Chem. Soc. 2012, 134, 17807−13. (15) Pandoli, O.; Massi, A.; Cavazzini, A.; Spada, G. P.; Cui, D. Circular Dichroism and UV−Vis Absorption Spectroscopic Monitoring of Production of Chiral Silver Nanoparticles Templated by Guanosine 5′-Monophosphate. Analyst 2011, 136, 3713−3719. (16) Oh, H. S.; Liu, S.; Jee, H.; Baev, A.; Swihart, M. T.; Prasad, P. N. Chiral Poly(Fluorene-Alt-Benzothiadiazole) (Pfbt) and Nanocomposites with Gold Nanoparticles: Plasmonically and Structurally Enhanced Chirality. J. Am. Chem. Soc. 2010, 132, 17346−17348. (17) Kuzyk, A.; Schreiber, R.; Fan, Z.; Pardatscher, G.; Roller, E.-M.; Hogele, A.; Simmel, F. C.; Govorov, A. O.; Liedl, T. DNA-Based SelfAssembly of Chiral Plasmonic Nanostructures with Tailored Optical Response. Nature 2012, 483, 311−314. (18) Xie, J.; Duan, Y.; Che, S. Chirality of Metal Nanoparticles in Chiral Mesoporous Silica. Adv. Funct. Mater. 2012, 22, 3784−3792. (19) Qi, H.; Shopsowitz, K. E.; Hamad, W. Y.; MacLachlan, M. J. Chiral Nematic Assemblies of Silver Nanoparticles in Mesoporous Silica Thin Films. J. Am. Chem. Soc. 2011, 133, 3728−3731. (20) Wang, R.-Y.; Wang, H.; Wu, X.; Ji, Y.; Wang, P.; Qu, Y.; Chung, T.-S. Chiral Assembly of Gold Nanorods with Collective Plasmonic Circular Dichroism Response. Soft Matter 2011, 7, 8370−8375. (21) Rosi, N. L.; Song, C.; Blaber, M. G.; Zhao, G.; Zhang, P.; Fry, H. C.; Schatz, G. C. Tailorable Plasmonic Circular Dichroism Properties of Helical Nanoparticle Superstructures. Nano Lett. 2013, DOI: 10.1021/nl4013776. (22) Lu, F.; Tian, Y.; Liu, M.; Su, D.; Zhang, H.; Gorovov, A.; Gang, O. Discrete Nano-Cubes as Plasmonic Reporters of Molecular Chirality. Nano Lett. 2013, DOI: 10.1021/nl401107g. (23) Liu, W.; Zhu, Z.; Deng, K.; Li, Z.; Zhou, Y.; Qiu, H.; Gao, Y.; Che, S.; Tang, Z. Gold Nanorod@Chiral Mesoporous Silica Core− Shell Nanoparticles with Unique Optical Properties. J. Am. Chem. Soc. 2013, DOI: 10.1021/ja312327m. (24) Ma, W.; Kuang, H.; Wang, L.; Xu, L.; Chang, W.-S.; Zhang, H.; Sun, M.; Zhu, Y.; Zhao, Y.; Liu, L.; Xu, C.; Link, S.; Kotov, N. A. Chiral Plasmonics of Self-Assembled Nanorod Dimers. Sci. Rep. 2013, DOI: 10.1038/srep01934.

Figure 7 that the directional CD appears in many nanostructures, including the equilateral tetrahedral complexes which exhibit negligible dipolar isotropic CD. The directional CD signals are typically stronger than the signals averaged over the orientation of a complex. This suggests that orientated nanostructures are another approach toward biosensing applications. Interestingly, a similar conclusion was previously made for systems incorporating a single molecule and a single nanosphere.55

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CONCLUSION In conclusion, we have compared the simulated spectra from the discrete dipole approximation (DDA) and the interacting point-dipole approach (PDA). Both methods are consistent in the dipolar regime. However the PDA method is a faster method of computation. In the multipolar regime, when the NPs are closely packed, the DDA simulations are able to reveal extra effects. A larger red shift of the CD band is observed compared to dipolar CD band. The red shift can be attributed to a stronger interaction between plasmonic NPs. In the dipolar regime, chiral collective excitations of plasmonic NPs assembled on an asymmetric chiral frame are the cause of the CD response. Due to the multipole interactions, an asymmetry in the sizes of NPs starts to play an equally important role. Hence, the equilateral tetrahedral structures are also good candidates for an observation of the plasmonic CD effect. However, concerning the fabrication, these equilateral tetrahedral 4-NP structures should be densely packed in order to show an essential CD response. Overall, our investigation demonstrates that the plasmonic CD effect is very sensitive to the geometry of a chiral assembly. Plasmonic CD can be used as a sensitive tool to characterize the morphology and sizedispersion of three-dimensional nanostructures in a solution.

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ASSOCIATED CONTENT

* Supporting Information S

The proof of eqs. 7 and 8. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.O.G. acknowledges the Science Foundation Ireland. This work was supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF-12-1-0407 and by the Volkswagen Foundation (Germany). We also thank Dr. Stephan Gray for the discussions.

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