TDDFT and CIS Studies of Optical Properties of Dimers of Silver

Article pubs.acs.org/JPCA

TDDFT and CIS Studies of Optical Properties of Dimers of Silver Tetrahedra Gyun-Tack Bae and Christine M. Aikens* Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506, United States ABSTRACT: The absorption spectra for dimers of Ag4+2 and Ag8 clusters at various interparticle distances are examined using time-dependent density functional theory (TDDFT) and configuration interaction singles (CIS) calculations. With TDDFT calculations employing the SAOP functional, minor peaks for Ag4+2 and Ag8 dimers appear as the interparticle distance decreases; these peaks are suggested to be charge transfer artifacts on the basis of CIS and TDDFT (CAM-B3LYP) calculations. The relationship of the absorption peak locations to the distance and orientation between Td Ag20 dimers is also investigated. TDDFT calculations using the SAOP functional are used to determine excitation absorption spectra for eight different orientations of Ag20 dimers. Although the Ag20 Td monomer has a sharp peak, each dimer absorption spectrum is split due to lower symmetry. This splitting increases as the center of mass distance decreases. As the interparticle distance between the monomers decreases, the initially strong peaks decrease in intensity and red or blue shift depending on symmetry, while the minor peaks increase in intensity and red shift.

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Ag9+ cluster27,28 and an ab initio study of the absorption spectra of neutral Agn (n = 2−8) as well as cationic Agn (n = 2−4) was performed in the framework of the linear response equation-ofmotion coupled-cluster (EOM-CC).29,30 Several time-dependent density functional theory (TDDFT) studies have been undertaken for Ag1131 and Agn (n = 4, 6, and 8)32 with the PW91 functional and AgmNip (5 ≤ m + p ≤ 8) clusters33 with the BP86 functional. Recently, the electronic and optical excitations in silver clusters (Agn, n = 1−8) have been analyzed using density-functional and many body theories within an ab initio pseudopotential framework34 and TDDFT calculations have been employed to examine the optical absorption of Agn with n = 4−22.23 The pyridine−Ag20 model system,35 the pyridine between Ag20 dimer36 and Ag20 tetrahedral clusters37 have been investigated using TDDFT. TDDFT has also been successfully employed for larger tetrahedral, rod-like, cubic, octahedral, and icosahedral systems.37−41 Dimers of metal nanoparticles, usually of Ag or Au, have been researched experimentally and theoretically.42−69 A dimer of nanoparticles can play a key role in the understanding of hybridized plasmons in complex nanostructures and provide a simple system for systematic studies of plasmon interactions. These studies showed that there is red shift of the longitudinal plasmon resonance as the interparticle distance decreases in the nontouching regime, whereas it will start to blue shift when the two particles touch.46,47,53−58 In 2008, Lassiter et al. investigated the plasmon interaction of individual pairs of nanoshells in the adjacent and touching regimes using environmental scanning electron microscopy (ESEM) exper-

INTRODUCTION Metal nanoparticles such as gold and silver have recognized importance in chemistry, physics, and biology because of their unique optical, electrical, and photothermal properties.1−4 Surface plasmon excitations which are collective excitations of the electrons of metal nanoparticles are currently studied for a variety of applications including surface-enhanced spectroscopy5,6 and biological and chemical sensing.7,8 The optical properties of silver nanoparticles have also been used in medical diagnostics and therapeutics1 and biological imaging.2,9,10 The morphology (size, shape, and surface structure) of silver nanoparticles is very important because of their physical, chemical, and optical properties.11−15 Small silver particles have been studied experimentally and theoretically. The optical spectra of small cationic silver clusters Ag9+ and Ag21+ were first obtained in experiment at very high temperature (about 2000−3000 K).14,16 Afterward, the optical absorption spectra of neutral Agn clusters (n = 5, 7−9, 11, 13, and 15−21) embedded in solid argon were measured at low temperature.15,17 Experiments were also performed to investigate the fluorescence properties of Ag8 and Ag9 clusters.18−21 Recently, the absorption spectra of silver clusters Agn (n = 4− 22) were investigated by UV−vis absorption22,23 and matrix effects of small silver nanoclusters (Ag7, Ag9, and Ag11) were studied at a temperature of 28 K.24 A variety of theoretical methods have been employed to examine absorption spectra. For large nanoparticles, Mie theory is widely used for the extinction spectra of spherical and spheroidal shapes25 and numerical continuum electrodynamics methods such as discrete dipole approximation (DDA) can be used for more complex structures.26 Time-dependent localdensity approximation (TDLDA) was used to investigate the optical response of silver clusters including Agn (n = 2−8) and © 2012 American Chemical Society

Received: May 31, 2012 Revised: July 6, 2012 Published: July 27, 2012 8260

dx.doi.org/10.1021/jp305330e | J. Phys. Chem. A 2012, 116, 8260−8269

The Journal of Physical Chemistry A

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imentally and the boundary element method (BEM) simulation theoretically.57 They found that a new plasmon mode is enabled at a close distance between the two particles. In this region, a new plasmon resonance that involves electrons flowing between two particles is due to the charge transfer plasmon (CTP).57,58 Similarly, Vincenot et al. examined the absorption spectra of Ag19+1 dimers with tip-to-tip distances of 5.659−9.659 Å using TDDFT.70 They determined how the energies and intensities of the dimer peaks change and new excitation peaks grow as the distance decreases. Recently, ab initio density functional theory has been used to study the electronic coupling between silver nanoparticles of different sizes and with different relative orientations.67−69 Over the past decade, TDDFT has been become one of the most popular theoretical tools to calculate excitation energy calculations. However, TDDFT errors for charge transfer (CT) states were reported and appear to be especially problematic at long-range.71−73 Investigations for accurate CT have been attempted using TDDFT.74,75 TDDFT yields errors for charge transfer excitations76−78 as well as long-range charge transfer.76,79 However, configuration interaction with single electron excitation (CIS)80 is also a useful tool for calculating excitation energies. CIS can improve the problem of charge transfer at a long and short-range as well as correct asymptotic behavior but has the drawback of no dynamic electron correlation.73 Although corrected xc-functional such as LB94 81 and SAOP82,83 lead to a substantial improvement in asymptotic behavior for Rydberg states, these functionals were not necessarily designed for CT states. In density functional theory, the Coulomb-attenuated method (CAM-B3LYP) by Handy and co-workers is a long-range corrected version of the B3LYP functional.84 CAM-B3LYP has been found to provide good results for intermolecular charge transfer transitions.85 In this paper, we report a theoretical study of the TDDFT and CIS absorption spectra for Ag4+2 and Ag8 cluster dimers with various separation distances. The new plasmon modes, called minor peaks in this work, are examined at short interparticle distance and depend on the level of theory. Then, we investigate the relationship of the peak locations to the distance and orientation between two tetrahedral Ag 20 monomers.

with a full width at half-maximum (fwhm) of 0.2 eV. The ADFGUI program is used for orbital visualization. A total of eight different dimer orientations of Ag20 tetrahedra were constructed by fixing a second monomer at a given distance from the first. For these dimers, the longest COM interparticle distance considered is 20 Å between centers of mass. At this distance, the dimers are essentially noninteracting. The eight dimers consist of tip-to-tip (dimers A and B), face-to-face (dimers C and D), tip-to-face (dimers E and F), and edge-to-edge (dimers G and H). Figure 1 shows the

METHODS The excitation energies of the Ag4+2 and Ag8 cluster dimers are calculated using the GAMESS program86 with the CIS method and the SBKJC effective core potential (ECP)87 basis set and the CAM-B3LYP functional with SBKJC-ECP; calculations are also performed using the Amsterdam Density Functional (ADF) 2010.01 program88 with the SAOP/DZ level of theory. The center-of-mass (COM) interparticle distance ranges from 20 to 4 Å between Ag4+2 monomers and 14 to 6 Å between Ag8 monomers. Monomer coordinates are held fixed to optimized geometries calculated with the gradient-corrected BeckePerdew (BP86) exchange-correlation functional89,90 and a double-ζ (DZ) Slater type basis set. The geometries of Ag4+2 and Ag8 cluster dimers are not reoptimized in this work. All Ag20 calculations are performed using the ADF program. The Ag20 monomer geometry is the same as in ref 37. TDDFT calculations are performed to calculate excited states using SAOP/DZ. The tolerance is set to 10−8 and the orthonormality is set to 10−10. A total of 200 dipole-allowed transitions are evaluated for the optical absorption spectrum. The smoothed spectra shown in the figures are convoluted with a Lorentzian

Figure 1. Structures for dimers of tetrahedral Ag20 clusters.

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structures of eight Ag20 dimers. The COM interparticle distance between monomers ranges from 20 to 13.5 Å (dimers A and B), 7 Å (dimers C and D), 10.5 Å (dimers E and F), and 9.5 Å (dimers G and H). We have calculated the optical absorption spectrum decreasing the COM interparticle distance 0.5 Å between each dimer.

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RESULTS AND DISCUSSION The Ag4+2 dimer is calculated with a tip-to-tip orientation. The excitation energies are calculated as the COM interparticle distance decreases in increments of 1 Å from 20 to 4 Å between centers of mass. In the SAOP/DZ calculations in Figure 2, there are initially two strong peaks at a long COM interparticle distance of 20 Å. These correspond to a splitting of the T2 excitation peak of the Ag4+2 monomer due to symmetry lowering. Dipole allowed irreducible representations of D3d symmetry are A2u and Eu. Two peaks lie at 4.72 eV (A2u symmetry) and 4.74 eV (Eu symmetry) with oscillator strengths of 0.50. The primary transitions located at 4.72 eV are HOMO8261



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Figure 2. Absorption spectra of Ag4+2 dimer as a function of distance using SAOP/DZ, CIS/SBKJC, and CAM-B3LYP/SBKJC levels of theory.

1 (S-like orbital) → LUMO+1 (P-like orbital) and HOMO (Slike orbital) → LUMO (P-like orbital). The primary transitions located at 4.74 eV are HOMO (S-like orbital) → LUMO+2 (Plike orbital) and HOMO-1 (S-like orbital) → LUMO+3 (P-like orbital). As the interparticle distance decreases, the gap between the two initial peaks becomes wider; the initial peak located at 4.72 eV red shifts significantly until the COM interparticle distance reaches 5 Å, then blue shifts from 5 to 4 Å; in contrast, the initial peak located at 4.74 eV blue shifts. A minor peak at 3.58 eV appears starting from the COM interparticle distance of 5 Å with the SAOP/DZ level of theory. At the shortest COM interparticle distance considered here (4 Å, which corresponds to a closest interparticle Ag−Ag distance of 3.50 Å), the minor peak lies at 3.01 eV with A2u symmetry (oscillator strength f = 0.42). The primary transition is HOMO (S-like orbital) → LUMO (P-like orbital). The minor peak red shifts and the oscillator strengths increase from 0.02 to 0.42 at COM interparticle distances from 5 to 4 Å in Figure 2. We also calculated excitation energies of the Ag4+2 dimer with the CIS/SBKJC and the CAM-B3LYP/SBKJC models to analyze the appearance of a minor peak when the distance between monomers decreases. The excitation spectra of the Ag4+2 dimer with COM interparticle distances of 20 to 4 Å are also shown in Figure 2. When the CIS/SBKJC model was used, two initially strong peaks lie at 5.09 (f = 1.09) and 5.11 eV ( f =

1.09). As the interparticle distance decreases, the gap between the initial peaks becomes wider. The initial peak located at 5.09 eV red shifts significantly, while the initial peak located at 5.11 eV blue shifts slightly. The excitation spectra using the CIS/ SBKJC model are much cleaner than those of the SAOP/DZ model at a short COM interparticle distance. In addition, no minor peaks appear as the interparticle distance decreases. Two initial peaks are located at 4.75 eV ( f = 0.49) and 4.78 eV ( f = 0.48) using the CAM-B3LYP/SBKJC model at a COM interparticle distance of 20 Å. Like the CIS/SBKJC model, the gap between the two initial peaks becomes wider with decreasing interparticle distance; the initial peak located 4.75 eV strongly red shifts and another initial peak located at 4.78 eV blue shifts slightly. However, a small peak arises at 5.31 eV at a COM interparticle distance of 5 Å. The peak red shifts, increases in peak intensity, and leads to a broad spectrum at higher energy as the interparticle distance decreases. As in the CIS/SBKJC calculations, there are no minor peaks at a short interparticle distance. The three models at a long interparticle distance exhibit similar results in that there are initially two peaks. However, the absorption peaks using the CIS/SBKJC model lie higher in energy than those of the SAOP/DZ and CAM-B3LYP/SBKJC models. As the interparticle distance decreases, the initial peaks split because one red shifts and another blue shifts in all three 8262



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Figure 3. Absorption spectra of Ag8 dimer as a function of distance using SAOP/DZ, CIS/SBKJC, and CAM-B3LYP/SBKJC levels of theory.

As the interparticle distance between monomers decreases, the peak located at 3.39 eV red shifts, while the peaks located at 3.41 and 3.42 eV blue shift; the peak located at 4.58 eV red shifts, while the peaks located at 4.61 eV blue shift. In addition, a small peak arises at 3.82 eV at the COM interparticle distance of 9 Å and red shifts as the interparticle distance decreases. Minor peaks appear around 2.55 eV when the COM interparticle distance reaches 8 Å. The minor peaks red shift from the COM interparticle distance of 9 to 6 Å. At the shortest COM interparticle distance examined in this work (6 Å; 2.86 Å between the closest Ag atoms), there is one strong minor peak at 2.44 eV (f = 0.57) in Figure 3. The primary transitions of minor peaks are HOMO − HOMO-2 (P-like orbital) → LUMO, LUMO+2, LUMO+3, and LUMO+8 (Dlike orbitals). We also calculated excitation energies of Ag8 dimer with the CIS/SBKJC and CAM-B3LYP/SBKJC models to examine whether minor peaks appear at a short COM interparticle distance between monomers. In the CIS/SBKJC model, there are three peaks at 2.88 eV (f = 0.31), 2.89 eV (f = 0.24), and 3.15 eV ( f = 0.14); three peaks at 4.19 eV (f = 4.41), 4.27 eV (f = 4.16), and 4.29 eV (f = 4.26); two peaks at 5.05 eV ( f = 0.96) and 5.07 eV ( f = 1.15) at the COM interparticle distance of 14 Å. The peaks located around 3.0 eV red shift and increase in intensity as the distance decreases. The peak located at 4.19 eV

levels of theory. However, an additional minor peak appears in the SAOP calculations at short interparticle distance, while only the initial peaks are maintained in the CIS/SBKJC and CAMB3LYP/SBKJC models. This suggests that the minor peak may arise due to CT artifacts that are not present in CIS and CAMB3LYP models. The larger Ag8 cluster dimer (which has D2h symmetry formed from two Td monomers) is also investigated to calculate excitation energies using 14 to 6 Å COM interparticle distances with the SAOP/DZ, CIS/SBKJC, and CAM-B3LYP/SBKJC levels of theory. Two sharp peaks lie at 3.41 and 4.60 eV for the Ag8 monomer in the SAOP/DZ excitation spectra. These monomer peaks have T2 symmetry, so each contains three degenerate excited states. The two T2 peaks split in the dimer because this system has a lower symmetry (D2h). We have calculated the optical absorption spectrum for intervals of 1.0 Å between monomers. In Figure 3, three strong peaks lie at 3.39 eV (f = 0.68), 3.41 eV (f = 0.62), and 3.42 eV (f = 0.60) and three strong peaks lie at 4.58 eV ( f = 1.64), 4.61 eV (f = 1.56), and 4.61 eV (f = 1.56) with the SAOP/DZ model at a long COM interparticle distance of 14 Å. The primary transitions of three peaks around 3.41 eV are HOMO (P-like orbital) → LUMO − LUMO+2 (D-like orbitals and Slike orbital) and the main transition responsible for peaks near 4.60 eV is HOMO (P-like orbital) → LUMO+2 (D-like orbital). 8263



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properties of nonspherical systems. We investigate the relationship of the peak locations to the distance and orientations between two tetrahedral Ag20 monomers. For the tetrahedral Ag20, the optical-absorption spectrum in solid argon is measured at 3.70 eV15 and the excitation spectrum was previously calculated with several basis sets and density functionals.37 A single sharp peak in the excitation spectra of the tetrahedral Ag20 monomer calculated at the SAOP/DZ//BP86/DZ(froz) level of theory lies around 3.39 eV. Because of the size of this system, CIS and CAM-B3LYP calculations are not practical. Thus, we focus primarily on the behavior of the strong peaks, although the minor (possibly artifactual) peaks are also briefly described. This peak has T2 symmetry, so it contains three degenerate excited states. Two tetrahedral Ag20 monomers have a lower symmetry, which causes the T2 peak to split. This behavior agrees with previous results on isotropic dimers such as spheres. Table 1 shows the overall symmetry and the peak symmetries that correlate to the T2 state for the Ag20 dimers. The optical absorption spectra with various distances and orientations for Ag20 dimers are presented in Figures 4 and 5. Each absorption spectrum exhibits a split peak at around 3.4 eV at long interparticle distances, and minor peaks at lower energy increase in intensity as the interparticle distance decreases. At long COM interparticle distances (20 Å), there are two (dimers A−F and H) or three (dimer G) initially strong peaks in Figures 4 and 5. The primary orbital transitions are D → F, S → P, D → S or D → P in all dimers. The absorption spectra of dimers A and B with D3h and D3d symmetry, respectively, resemble each other in that there are two initially strong peaks at a long interparticle distance and two minor peaks grow as the interparticle distance decreases in Figure 4. At long COM interparticle distance (20 Å), the two initially strong peaks arising from the split T2 peak are A2′′ at 3.37 eV ( f = 2.45) and E′ at 3.40 eV (f = 2.13) in dimer A and A2u at 3.37 eV ( f = 2.45) and Eu at 3.40 eV (f = 2.16) in dimer B (Figure 4). The energy difference between the initially strong peaks becomes wider as the interparticle distance decreases. Usually, the red-shifted peak displays polarization along the interparticle axis (z) and the slightly blue-shifted peak displays polarization perpendicular to the interparticle axis (x and y).91 Therefore, the peak corresponding to the z-component symmetries located at 3.37 eV red shifts and the peak related to the (x,y)-component located at 3.40 eV blue shifts significantly as the interparticle distance decreases. The intensities of minor peaks increase as the distance decreases, while the intensities of two initially strong peaks decrease in dimers A and B. In dimer A (A2′′ symmetry), two minor peaks appear at 1.56 and 1.81 eV at a COM interparticle distance of 13.5 Å (Figure 4). In dimer B, there are three minor peaks at 1.58, 1.81, and 1.84 eV at a COM distance of 13.5 Å (corresponding to a nearest interparticle distance of 3.28 Å; Figure 4). Dimers A and B have a broad spectrum at a short COM interparticle distance of 13.5 Å. The absorption spectra of dimers C (D3h symmetry) and D (D3d symmetry) have two initially strong peaks at a long distance and one strong minor peak at a short interparticle distance in Figure 4. The initially strong peaks lie at 3.39 eV (f = 2.32; A2′′ symmetry) and 3.40 eV (f = 2.12; E′ symmetry) in dimer C and at 3.39 eV (f = 2.30; A2u symmetry) and 3.41 eV ( f = 2.11; Eu symmetry) in dimer D at a COM distance of 20 Å.

red shifts, while the peaks located at 4.27 and 4.29 eV blue shift as the interparticle distance decreases. In the CAM-B3LYP/SBKJC model, there are the three peaks at around 3.20 and 4.07 eV at the COM interparticle distance of 14 Å. The three peaks located at 3.19 eV (f = 0.38), 3.20 eV (f = 0.33), and 3.20 eV ( f = 0.31) red shift, while one of three peaks located at 4.04 eV (f = 2.36) red shifts and two of the three peaks located at 4.09 eV ( f = 2.27 and f = 2.28) blue shift slightly. At a long interparticle distance, the absorption peaks located around 3.41 eV using the SAOP/DZ model lie at higher energies than those located around 2.97 and 3.20 eV of the CIS/SBKJC and CAM-B3LYP/SBKJC models. The three peaks around 3.41 eV using the SAOP/DZ model and around 2.97 eV using the CIS/SBKJC model arise from HOMO to LUMO − LUMO+2. The primary transitions are P → S and P → D. In the CIS/SBKJC and CAM-B3LYP/SBKJC models, the minor peak does not appear at a short distance between monomers unlike the SAOP/DZ model, which suggests that it is a potential artifact. TDDFT calculations with SAOP/DZ give reasonable results for dimers with a long interparticle distance between monomers when we compare with the CIS and CAMB3LYP models even though artifact peaks appear to occur at short interparticle distances between monomers. It appears that TDDFT calculations with SAOP/DZ or similar functionals may be useful for describing the shifts in the main peaks of the optical absorption spectra of nanoparticle dimers, but caution must be taken not to overanalyze the importance of the minor peaks. SAOP/DZ is more efficient than either CIS or CAMB3LYP and thus may be more easily employed for larger systems; as shown in Table 2, the CPU time required is an order of magnitude less for SAOP/DZ than CAM-B3LYP/ SBKJC. Table 1. Dimer Symmetries and Irreducible Representations for Split Peaks of Ag20 Dimers dimers

symmetry

split peak symmetries

A B C D E F G H

D3h D3d D3h D3d C3v C3v D2h D2d

A2′′ + E′ A2u + Eu A2′′ + E′ A2u + Eu A1 + E A1 + E B1u + B2u + B3u B2 + E

Table 2. Comparison of CPU Time of Ag4+2 and Ag8 Dimers dimer (COM)

methods

CPU time (s)

Ag4+2 (20 Å)

CIS/SBKJC CAM-B3LYP/SBKJC SAOP/DZ CIS/SBKJC CAM-B3LYP/SBKJC SAOP/DZ

1317.3 7192.6 753.16 195675.5 250845.0 25824.47

Ag8 (14 Å)

The optical absorption spectrum of the Ag20 tetrahedral monomer at the BP86/DZ.4p level of theory has a single sharp peak at 3.59 eV, similar to the plasmon resonance of larger nanoparticles.37 For this reason, this Ag20 tetrahedral cluster is a good system for studying aggregation effects on the absorption 8264



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Figure 4. Absorption spectra for dimers A−D with varying distances.

The z-component peaks located at 3.39 eV (dimers C and D) red shift and the x,y-component peaks located at 3.40 eV (dimer C) and 3.41 eV (dimer D) blue shift as the interparticle distance decreases in Figure 4. Like dimers A and B, the intensities of two initial peaks decrease while the intensities of minor peaks increase. The strong minor peaks located at 2.92 eV (dimer C) and 2.96 eV (dimer D) are evident in Figure 4 at a COM interparticle distance of 7 Å; at this distance, the initially strong peaks create a broad spectrum. In dimers E and F, there are two strong peaks with A1 and E symmetries at long COM distances (20 Å) in Figure 5. The absorption spectra between dimers E and F are the same. Dimers E and F both have C3v symmetry. The initial strong peaks of A1 and E symmetries in dimer E lie at 3.38 (f = 2.36) and at 3.40 eV (f = 2.11) at the COM distance of 20 Å. One of two initial peaks located at 3.38 eV (z-component) red shifts and another peak located at 3.40 eV (x-component) blue shifts significantly as the interparticle distance decreases. The initial

peaks have a broad spectrum at a short COM distance of 10.5 Å. The intensities of two initial peaks decrease while the intensities of minor peaks increase. Dimer F has the same properties as dimer E. Dimers G and H have D2h and D2d symmetries, respectively. There are three split peaks at 3.38 eV (f = 2.35), 3.39 eV (f = 2.17), and 3.40 eV (f = 2.12) in dimer G with B3u, B2u, and B1u symmetries, respectively; for dimer H, two split peaks occur at 3.38 ( f = 2.34) and 3.40 eV (f = 2.15) with B2 and E symmetries, respectively, at a long COM interparticle distance of 20 Å (Figure 5). In dimer G, the z-component peak located at 3.38 eV red shifts and the x,y-component peaks located at 3.39 and 3.40 eV blue shift slightly as the interparticle distance decreases. In dimer H, the z-component peak located at 3.38 eV red shifts and the peak located at 3.40 eV blue shifts as the interparticle distance decreases. As the interparticle distance decreases, five strong minor peaks appear at 2.28 eV ( f = 0.56), 2.42 eV (f = 0.32), 2.74 eV 8265



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Figure 5. Absorption spectra for dimers E−H with varying distances.

Figure 6. Absorption spectra of (a) dimer A (black line) and dimer B (red line) at a COM distance of 13.5 Å, (b) dimer C (black line) and dimer D (red line) at a distance of 7 Å, (c) dimer E (black line) and dimer F (red line) at a distance of 10.5 Å, and (d) dimer G (black line) and dimer H (red line) at a distance of 9.5 Å. 8266



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Figure 7. Plots of peak intensity vs COM distances between monomers.

(f = 0.96), 2.92 eV ( f = 1.48), and 3.05 eV (f = 0.91) with B3u symmetry in dimer G and three strong minor peaks lie at 1.45 eV (f = 0.13), 1.87 eV ( f = 0.14), and 2.49 eV ( f = 0.28) in dimer H. The intensities of the two initial peaks decrease while the intensities of minor peaks increase in Dimers G and H similar to the other dimers. The absorption spectra for related shapes of the tetrahedral Ag20 cluster dimers have significant similarities. Figure 6 shows the comparison of absorption spectra between similar dimers at the COM distances of 13.5 Å (dimers A and B), 7 Å (dimers C and D), 10.5 Å (dimers E and F), and 9.5 Å (dimers G and H). The nearest interparticle Ag−Ag distances are 3.28 Å for dimers A and B, 3.25 Å for dimers C and D, 3.51 Å for dimers E and F, 3.35 Å for dimer G, and 3.88 Å for dimer H. Few changes to the absorption spectra appear between dimers A and B and dimers C and D. At a short interparticle distance, the absorption spectra of dimer B blue shifts a little with respect to dimer A, while dimer D also blue shifts with respect to dimer C for the minor peaks (Figure 6). The absorption spectra are almost the same between dimers E and F. However, the absorption spectra between dimers G and H are quite different in comparison to the absorption spectra of other dimers. Minor peaks of dimer H blue shift more than those of dimer G at the COM interparticle distance of 9.5 Å. This may occur in part because there are significant structural

differences between dimer G and dimer H. Dimer G is the parallel structure and dimer H is the perpendicular structure for the edge-to-edge arrangement. The structural change between dimer G and dimer H is greater than the other dimers and leads to quite different absorption spectra at the same COM interparticle distance; these differences remain even if the calculations are performed at the same nearest Ag−Ag distance (3.88 Å, not shown). Figure 7 shows the plots of peak intensity as a function of COM distance between monomers in dimers A, C, E, and G. Initial peak intensities decrease while minor peak intensities increase as the COM distance decreases. In dimers A and E, initial peak intensities decrease suddenly around the COM interparticle distance of 17 Å (tip-to-tip interparticle distance of 6.78 Å) and 13.5 Å (tip-to-face interparticle distance of 6.51 Å), respectively. However, the peak intensities of dimers C and G decrease gradually while minor peak intensities grow suddenly at the COM interparticle distance of 9 Å (dimer C, face-to-face interparticle distance of 5.25 Å) and 11.5 Å (dimer G, edge-toedge interparticle distance of 6.85 Å). Therefore, the changes in the peak intensities start at interparticle distances of around 5− 7 Å between monomers. 8267



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CONCLUSIONS In this study, the absorption spectra of dimers of Ag4+2 and Ag8 clusters using the SAOP/DZ, CIS/SBKJC, and CAM-B3LYP/ SBKJC models have been studied. In Ag4+2 and Ag8 dimers, the initial peaks split at a long interparticle distance using all three models; minor peaks appear as the interparticle distance decreases only for the SAOP/DZ level of theory and not for CIS/SBKJC nor CAM-B3LYP, which suggests that these peaks may be charge transfer artifacts. This work demonstrates that caution must be employed when using TDDFT to analyze the “charge transfer plasmon” that arises when two nanoparticles nearly touch, which is an issue of current interest both theoretically and experimentally. We have presented a theoretical investigation of the absorption spectra of Ag20 dimers using SAOP/DZ calculations. The dimers have the following characteristics in common: (1) the initial peak splits at a long interparticle distance between monomers; (2) the gap of the initially strong peaks becomes wider as the interparticle distance decreases, because the zcomponent of the initial strong peaks red shifts while the x- or y-component is slightly blue-shifted; and (3) initially strong peaks decrease in intensity, while minor peaks increase in intensity. The primary excited states of initially strong peaks are D → F, S → P, D → S, and D → P at long interparticle distances in all dimers. Spectra for the tip-to-tip (dimers A and B), face-to-face (dimers C and D), and tip-to-face (dimers E and F) orientations are very similar within the dimer pairs, whereas the parallel and perpendicular edge-to-edge arrangements (Dimers G and H) lead to substantial differences in absorption spectra. At the SAOP/DZ level of theory, oscillator strengths for the initial peaks decrease while minor peaks grow at an interparticle distance between 5 and 7 Å.

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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 This material is based upon work supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-09-1-0451. C.M.A. thanks the Alfred P. Sloan Foundation for a Research Fellowship (2011-2013) and the Dreyfus Foundation for a Camille Dreyfus Teacher-Scholar Award (2011-2015).

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TDDFT and CIS Studies of Optical Properties of Dimers of Silver

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