Time-Dependent Density Functional Theory ... - ACS Publications

Subscriber access provided by UNIV MASSACHUSETTS BOSTON

Article

Time-Dependent Density Functional Theory Studies of Optical Properties of Au Nanoparticles: Octahedra, Truncated Octahedra, and Icosahedra Gyun-Tack Bae, and Christine M. Aikens J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b05978 • Publication Date (Web): 14 Sep 2015 Downloaded from http://pubs.acs.org on September 25, 2015

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Time-Dependent Density Functional Theory Studies of Optical Properties of Au Nanoparticles: Octahedra, Truncated Octahedra, and Icosahedra Gyun-Tack Bae¶,* and Christine M. Aikens† Department of Chemistry Education, Chungbuk National University, Cheongju 361-763, Korea † Department of Chemistry, Kansas State University, 213 CBC Building, Manhattan, Kansas 66506 *[email protected] ¶

Abstract The optical absorption properties of gold nanoparticles are investigated theoretically. A timedependent density functional theory (TDDFT) approach is employed to determine excitation energies for a set of three structural shapes: octahedra, truncated octahedra, and icosahedra (Aun, n=6-85) in several charge states that correspond to electronic shell closings. Octahedral Aun clusters with n = 6-85; truncated octahedral Aun clusters with n = 13-79; and icosahedral Aun clusters with n = 13-55 are examined. The optimization calculations use the BP86/DZ.4f level of theory and the excitation energy calculations employ the LB94 functional. The ADF code was used for all calculations. Keywords: TDDFT, Gold Nanoparticles, Size and Shape Dependence, Octahedra, Truncated Octahedra, Icosahedra Introduction Gold is one of the most important metals in the fields of physics, chemistry, biology, medicine, and material science due to its potential technological applications in catalysis, biosensing, and electronic, photonic, and sensor devices.1-3 For biomedical applications, targeted gold nanoparticles can reduce the laser energy necessary for selective tumor cell destruction.4 Much of the interest in gold nanoparticles has been driven by their fascinating optical properties, related to a surface plasmon resonance (SPR) which gives rise a very strong absorbance in the visible.5 The optical response of gold nanoparticles depends strongly

ACS Paragon Plus Environment

1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 37

on their size, shape, and their dielectric environment.6-8 For example, the peak of the surface plasmon band absorption of hollow gold nanospheres can be controlled by tuning particle size and wall thickness.9 Nanoparticles with fewer faces and sharper vertices show resonances over a wider range of wavelengths.10 For these purposes, it is necessary to control the size and shape of nanoparticles. As a result, these attractive optical properties have led to extensive research regarding synthetic approaches for gold nanoparticles. Recently, various well-defined gold nanoparticles have been successfully synthesized including truncated tetrahedra,11 truncated cubes,12 cubes,11-15 triicosahedra,12 bipyramids,16 octahedra,12, 14, 17-19 truncated octahedra,12 cuboctahedra,12 decahedra,11,

18

icosahedra,11 nanowires,20 nanorods,21 nanobars,22-23 and

nanoplates.24-25 The plasmonic absorption of metal nanoparticles has been studied theoretically for many years. Mie found the solution for the extinction spectra of a sphere of arbitrary size in a homogeneous medium and subjected to a plane monochromatic wave using Maxwell’s equations in 1908.26 However, Mie theory for nonspherical particles is not straightforward. In the last few years, advanced electrodynamic methods for complex shapes and large sizes of nanoparticles have been adopted that solve Maxwell’s equations numerically, such as the discrete dipole approximation (DDA)7, 10, 27-28 and the finite-difference time-domain method (FDTD).29-31 Time-dependent density functional theory (TDDFT) can describe optical properties in smaller nanosystems. For example, the effect of the size and shape of a series of silver nanoparticles in various charge states on their optical absorption properties has been investigated with up to 85 atoms using TDDFT.32 Recently, a number of TDDFT studies have examined bare gold nanoparticles33-38 with a variety of sizes and shapes as well as thiolate-stabilized gold nanoclusters.39-47 In one of the earliest studies of the optical properties


2

Page 3 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of small gold nanoparticles, the optical excitations of Au64+, Au444+, and Au1462+ were investigated at the scalar relativistic time dependent density functional theory level.33 Later, DFT/TDDFT calculations were carried out for a series of silver and gold nanorod clusters (Agn, Aun, n = 12 – 120).38 The TDDFT approach has also been employed to examine the optical properties of larger cuboctahedral, icosahedral, and cubic Au clusters35 as well as alloyed Ag-Au octahedral nanoclusters.34 Other researchers studied the optical absorption spectra of magic number nanoparticles Au13 and Au55.36 In 2014, TDDFT was used to calculate the optical absorption spectra of gold clusters of 20 to 171 atoms,48 the dependence of localized surface plasmon resonance (LSPR) with size for gold nanoclusters with up to 1414 atoms,49 and the surface-plasmon resonance in small spherical gold nanoparticles.37 In this study, we investigate the effect of the size and shape of octahedral, truncated octahedral, and icosahedral gold nanoparticles on their absorption spectra using TDDFT, and we analyze the bands of transitions that occur in these systems. Computational Method All density functional theory calculations have been performed using the Amsterdam Density Functional (ADF) program.50 The gradient-corrected Becke-Perdew (BP86) exchange-correlation functional is used for optimization of the molecular structures of all neutral and charged clusters. It should be noted that generalized gradient approximation (GGA) calculations are known to slightly overestimate the gold-gold distances in bare gold cluster calculations,51 which can have minor effects on the excited state energies due to differences in electron density although these effects are not expected to change the qualitative results for these systems. A double-ζ (DZ) Slater type basis set is used in the optimization with frozen core orbitals up through 4f (denoted here as DZ.4f). The zerothorder regular approximation (ZORA) is applied to incorporate scalar relativistic effects in the calculations. The SCF convergence threshold is 10-8. A gradient convergence criterion of at


3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 37

least 10-3 and an energy convergence criterion of at least 10-4 are utilized to obtain wellconverged geometries. Excited states are calculated using TDDFT. We employ the LB94 functional,52 which is an asymptotically correct model potential. In addition, the LB94 functional is computationally efficient with frozen core basis sets such as DZ.4f. Comparisons to excited state energies calculated using BP86 are provided for some of the systems examined in this work. The tolerance and orthonormality settings used are 10-8 and 10-10, respectively. The Fock matrix and energy terms are integrated numerically; the accuracy of this is increased to 10-6 (10-8 for small clusters). The excitation energies and their corresponding oscillator strengths are convoluted with a Lorentzian with a full width at half-maximum of 0.2 eV to yield the smoothed spectra shown in the figures. All spectra are convoluted with the same function. Spectra are not normalized and all calculations have the same units, so the y-axes of the figures are comparable; values on the y-axis are proportional to oscillator strength for the excited states. Results and Discussion Octahedral Clusters The theoretical absorption spectra of octahedral Au6, Au19, Au44, and Au85 clusters are considered. Charged clusters from removing or adding electrons to make a closed shell are investigated such as Au6-2, Au6+4, Au19-1, Au19+1, Au44-2, Au44+4, Au85-1, Au85-5, and Au85+5. For instance, Au6 clusters can have two electrons added or four electrons removed in the 6t1u orbital (HOMO) so that it is completely filled or unfilled, respectively. The closest spherical symmetry representation for this orbital is P. The orbitals for the Au6-2 cluster are shown in Figure 1. For octahedral systems, the spherical symmetry representations are reasonable approximations, but the octahedral field splits the orbitals. The unoccupied orbitals include a set of doubly degenerate orbitals with


4

Page 5 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


approximate D symmetry (LUMO), a singly degenerate orbital with approximate S symmetry (LUMO+1), and a set of triply degenerate orbitals with approximate D symmetry (LUMO+1). The absorption spectra of Au6-2 and Au6+4 clusters are displayed in Figure 2. For the octahedral Au6-2 cluster, the strongest peaks lie at 2.34 eV, ~4.10 eV, 5.10 eV and 5.61 eV with the LB94 functional, whereas these peaks lie at 2.15 eV, 3.49 eV, 4.50 eV, 5.31 eV, and 5.60 eV with the BP86 functional (Figure 1S). In previous work on tetrahedral silver clusters, the LB94 functional was found to overestimate excited state energies compared to BP86 and SAOP functionals relative to experiment;53 on the other hand, LB94 has been found to be in good agreement with experiment and with SAOP for thiolate-protected gold nanoparticles, whereas GGA functionals such as BP86 typically underestimate the excited state energies.42 Since experimental data is not available for the clusters in this work, we have selected the LB94 functional as our primary functional for this work but provide comparison with BP86 results for several systems. Overall, the LB94 functional predicts excited state energies that are blue-shifted compared to BP86 calculations, as expected. According to the selection rule ∆L = ±1 for spherical symmetry, P → D or P → S transitions should be allowed in the Au6-2 cluster with eight electrons. Table 1 shows peak energies, oscillator strengths, and orbital transitions of octahedral Au6-2 and Au6+4 clusters. In the Au6-2 cluster, the first peak at 2.34 eV (oscillator strength f = 0.094) arises to a HOMO → LUMO (P → D) transition, the second set of peaks around 4.10 eV (f = 0.059 and 0.12) arise from mixed transitions that are the HOMO → LUMO+1 (P → S) and HOMO → LUMO+2 (P → D), and the third small peak at 5.10 eV (f = 0.075) is calculated to primarily arise from the HOMO → LUMO+2 (P → D) transition. The fourth strong peak at 5.61 eV (f = 0.42) is also calculated to arise from the HOMO → LUMO+2 (P → D) transition. (Figure 1 and Table 1). In the Au6+4 cluster, there are three strong peaks in Figure 2. These peaks lie at


5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 37

4.04 eV, 4.32 eV, and 5.50 eV (Figure 2 and Table 1) with the LB94 functional and 3.18 eV, 4.13 eV, and 4.91 eV with the BP86 functional. All of these peaks arise from interband transitions from d-based orbitals into the sp-based P orbital. The interband transitions in gold clusters are stronger than those in related silver clusters.32 The next larger octahedral clusters are the Ag19 and Au44 clusters. Au19 has one electron in the HOMO (10a1g orbital), so adding and removing one electron forms the Au19-1 and Au19+1 clusters, respectively. The octahedral Au44 clusters would have four electrons in a triply degenerate 34t1u orbital (HOMO). We make the Au44-2 cluster and Au44+4 cluster by adding two electrons and removing four electrons, respectively. In the octahedral Au19 and Au44 clusters, the absorption spectra may be decomposed into contributions from sp←sp intraband transitions, sp←d interband transitions, p←sp interband transitions, and p←d interband transitions. The sp←d transitions form a broad background in the spectra. These spectra are interesting in that the lower excitations and higher excitations are dominated by sp←sp intraband transitions and p←d transitions, respectively (Figures 3 and 4). Many more peaks are apparent in the absorption spectra of these systems than in those of related silver systems.32 In Au19 clusters, multiple small peaks lie from 2.0 eV to 5.0 eV with the LB94 functional. Five strong peaks lie at 4.28 eV (f = 0.15), 4.30 eV (f = 0.19), 4.45 eV (f = 0.15), 4.69 eV (f = 0.20), and 4.84 eV (f = 0.19) in the Au19-1 cluster and two strong peaks lie at 4.43 eV (f = 0.27) and 4.86 eV (f = 0.22) in the Au19+1 cluster (Figure 3). In the BP86 functional calculations, five strong peaks lie at 3.75 eV, 3.89 eV, 4.83 eV, 5.05 eV, and 5.77 eV in the Au19-1 cluster and three strong peaks lie at 3.30 eV, 4.10 eV, and 5.25 eV in the Au19+1 cluster. Again, the LB94 functional predictions are somewhat blue-shifted compared to BP86 predictions. Future benchmarking studies on large gold clusters are needed.


6

Page 7 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


In the Au44-2 cluster, three strong peaks arise at 4.00 eV, 4.39 eV, and 5.47 eV. The excitation spectrum of the Au44+4 cluster is broad and appears similar to that of the Au44-2 cluster (Figure 4). For this system, 40 electrons does not represent a strong magic number as it does for spherical systems. Due to the octahedral environment, the G orbitals (which would be unoccupied in a 40 electron spherical system) are split, and the HOMO and HOMO-2 orbitals of this system arise from the G orbitals, whereas the 2P orbitals (which are occupied in a 40 electron spherical system) are the LUMO for Au44+4. Due to the dramatic splitting of the spherical shells in e.g. the octahedral environment, the approximate spherical representations are not discussed throughout the remainder of this paper. Overall, as the size of the cluster increases, the absorption spectra appear to become less sensitive to the charge state of the system; in contrast, the spectra of the smallest Au6 cluster exhibit marked changes with charge state due to differences in orbital occupation. The largest octahedral cluster examined in this work is Au85 cluster, which would have five electrons in the triply degenerate 51t2g orbital (HOMO). Adding one electron makes the Au85-1 cluster; adding five electrons yields the Au85-5 cluster (which also has a filled 46eg orbital); removing five electrons yields the Au85+5 cluster. The excitation spectra of Au85-1, Au85-5, and Au85+5 are shown in Figure 5. These spectra are very similar to each other and the transitions of the spectra are also similar to those of the spectra of smaller octahedral gold clusters except there are essentially no sp←sp interband transitions. The sp←d transitions form a broad background in the spectra of three Au85 clusters. These spectra show increasing broadening with increasing cluster sizes.36 Overall, for small gold nanoparticles the interband excitations play a principal role in the absorption spectra, whereas the spectra of silver nanoparticles are generally dominated by the intraband excitations. In the Au6-2 cluster, the HOMO→LUMO transition of the first peak at 2.34 eV has a weight of 91.0% in the excited state. Other transitions are HOMO→LUMO+1 (3.64%),


7


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 37

HOMO-3→LUMO (2.40%), and HOMO→LUMO+2 (1.56%). In the Au19+1 cluster, the peak located at 4.43 eV arises from a mixture of HOMO-12→LUMO+2 (weight of 32.5%, dipole moment -0.16), HOMO-14→LUMO+1 (7.33%, 0.65), and HOMO→LUMO+5 (5.46%, 0.85), among others. (We report only those transitions with |dipole moment| > 0.50 or a weight > 30%.) In the Au44-2 cluster, one of the three strong peaks (at 4.00 eV) can be assigned to a constructive mixture of the HOMO-26→LUMO+2 (38.7%, 0.57) and HOMO-16→LUMO+2 (6.00%, -0.47), the second peak (4.39 eV) can be described as a constructive mixture of the HOMO-34→LUMO+3 (28.0 %, -0.41), HOMO-59→LUMO (18.5 %, 0.10), and HOMO43→LUMO+1 (10.2%, -0.16), and the third strong peak (5.47 eV) can be calculated to arise from HOMO-31→LUMO+7 (14.5%, 0.15) and HOMO-33→LUMO+6 (12.2%, -0.13) transitions. (For this cluster, we report transitions with |dipole moment| > 0.45 or a weight > 10%.) There are multiple peaks to analyze for the Au85-1 cluster. We choose two strong peaks (f > 0.20). The first strong peak located at 3.69 eV (f = 0.21) is a mixture of the HOMO8→LUMO+9

(11.6%,

0.025),

HOMO-26→LUMO+6

(11.8%,

-0.13),

HOMO-

43→LUMO+4 (10.4%, -0.11), and HOMO-25→LUMO+6 (3.88%, 0.22). The second strong peak (5.40 eV) arises in part from HOMO-48→LUMO+15 (12.3%, 0.22). (We report transitions for this cluster with |dipole moment| > 0.20 or a weight > 10%.) Thus, with increased cluster size the percentage contribution of each individual transition decreases, and the transitions are more mixed. Truncated Octahedral Clusters Next, truncated octahedral clusters Au13, Au38, Au55, and Au79 have been optimized. We remove low-coordinated atoms from the octahedral clusters to yield these structures. For example, the octahedral Au13 cluster is formed by removing the six vertex atoms of the octahedral Au19 cluster. We again investigate charged clusters with completely filled and


8

Page 9 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


unfilled orbitals. The Au13 cluster is considered with three charge states of -1, -5, and +5. The neutral Au13 cluster has five electrons in the triply degenerate 9t2g orbital in the HOMO. For the Au13-1 cluster, we add one electron to fill the HOMO. Adding one electron in the 9t2g orbital and four electrons in the 8eg orbital forms the Au13-5 cluster. In addition, we remove five electrons from the HOMO to make a charge state of +5. The excitation spectra of the Au13-1, Au13-5, and Au13+5 clusters are shown in Figure 6. The types of transitions apparent in the Au13-5 cluster (sp←sp, p←sp, sp←d, and p←d) are very similar to those of the smaller octahedral clusters. In the Au13-1 cluster, the lower energy excitations are decomposed into contributions from sp←sp intraband and sp←s(d) interband, and the sp←d interband transitions form a broad background. It should be emphasized that any given molecular orbital is hybridized and contains a percentage of atomic s, p, and d character. The notation s(d) indicates that s and d are hybridized with a greater contribution from atomic s orbitals. In the Au13-1 cluster, the p←sp transitions lie around 4 - 5 eV. It is interesting that there are no sp←sp intraband transitions in the Au13+5 cluster. The peak at 2.43 eV can be assigned to a HOMO → LUMO (P → D) transition in the Au13+5 cluster. (Figure 6). The next larger truncated octahedral cluster is Au38. Excitation energies are calculated for charge states of -2 and +4. The neutral Au38 cluster has four electrons in the triply degenerate 29t1u orbital (HOMO). Addition of two electrons to fill the HOMO yields the Au38-2 cluster; removing four electrons in the 29t1u orbital forms the Au38+4 cluster. The optical absorption spectra for Au38-2 and Au38+4 are shown in Figure 7. The low-energy excitations are dominated by sp←sp intraband transitions and p←sp transitions (Au38-2) and sp←sp intraband transitions and sp←s(d) interband transitions (Au38+4), although the sp←d


9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 37

interband transitions also play a role in Au38 clusters. The higher excitations are ruled by p←d interband transitions. The next truncated octahedral cluster Au55 has five electrons in the triply degenerate 25t1g orbital (HOMO). The charge states -1 and +5 of the Au55 cluster are made by adding one electron or removing five electrons so that the 25t1g orbital is completely filled or unfilled. Because the Au55-3 cluster would have 58 electrons, a spherical magic number, we also consider a system in which a total of three electrons are added in the 25t1g and 21a1g orbitals. The transitions of the three spectra (Figure 8) are similar in that the low-energy excitations are dominated by sp←sp intraband transitions (as well as sp←s(d) intraband transitions in the Au55+5 cluster) and higher-energy excitations are dominated by p←d interband transitions. In addition, sp←d interband transitions play a significant role. The overall shape of the spectrum is not greatly affected by charge state, unlike the smaller Au13 cluster. Au79 is the largest truncated octahedral gold cluster studied in this work. The charge states of -7 and +5 of the Au79 cluster are made adding and removing electrons in the triply degenerate 57t1u orbital, which has five electrons in the neutral cluster. The -7 charge state had to be considered instead of the -1 charge state because a second triply degenerate orbital was essentially degenerate with the 57t1u orbital. The optical absorption spectra for Au79-7 and Au79+5 are shown in Figure 9. The two Au79 spectra are dominated by sp←d interband transitions. The p←d interband transitions ruled the higher energy excitations. In the Au79-7 cluster, low-energy excitations are dominated by sp←sp intraband transitions; in the Au79+5 cluster, low-energy excitations are dominated by sp←sp intraband transitions, sp←s(d) interband transitions, and p←sp interband transitions. As for the octahedral systems, interband transitions in the gold nanoparticles are much stronger than those for related silver systems.32


10

Page 11 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Icosahedral clusters Icosahedral clusters are more similar to spheres than the octahedral and truncated octahedral shapes. Because of this, icosahedral clusters have more facets than octahedral and truncated octahedral clusters of a similar size. Thus, we expect a relationship between the excitation spectra and the more spherical shape. The first icosahedral gold cluster is Au13, which was calculated using D5d symmetry since the full Ih symmetry is not available in ADF. Throughout this work, D5d and C5v symmetries will be used depending on how close ADF recognizes the geometries to being to the full Ih symmetry. The Au13-5 and Au13+5 clusters are magic number clusters because they have 18 electrons and 8 electrons, respectively. Tables 2-3 show the symmetries, peak energies, oscillator strengths, and primary Kohn-Sham independent-particle transitions responsible for the peaks of the Au13-5 and Au13+5 clusters. The primary transitions of the Au13-5 cluster are from HOMO-HOMO-4, HOMO-11-HOMO-12, and HOMO-16 to LUMOLUMO+3. The primary transitions of the Au13+5 cluster are from HOMO, HOMO-5, HOMO7-HOMO-8, HOMO-10, and HOMO-16 to LUMO-LUMO+1. Dipole allowed irreducible representations of D5d symmetry are A2u and E1u. Each peak appears as two degenerate peaks in the tables and spectra (Figure 10) due to splitting because D5d has lower symmetry than Ih. The non-magic number cluster Au13-1 exhibits many more peaks and a much broader spectrum than the spectra of the magic number clusters (Figure 10). The next size icosahedral gold cluster is Au43, which was calculated using C5v symmetry. This cluster is built by removing the 12 vertex atoms from the icosahedral Au55 cluster. The excitation energies of charge states of -1 and +3 are examined. The transition of the magic number cluster Au43+3 with 40 electrons are decomposed into contributions from sp←sp intraband transitions, sp←d interband transitions, and p←d interband transitions (Figure 11). The peaks of the Au43+3 cluster again appear as two degenerate peaks (with A1


11


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 37

and E1 symmetries) in the spectrum due to the splitting of peaks because C5v has lower symmetry than Ih. The non magic number Au43-1 cluster with 44 electrons has less defined peaks than those of the magic number cluster (Figure 11); however, it should be noted that the overall features of the spectra including a first peak around 3.0 eV, a second strong peak around 4.0 eV, and a third broad peak around 5.0 eV are consistent within the two spectra. Au55 is the next larger icosahedral cluster. It is calculated with C5v symmetry. Excitation energies of clusters with charge states of -3 and +1 are calculated. The magic number cluster, Au55-3 (58 electrons), exhibits much clearer peaks than those of non-magic number cluster, Au55+1. Again, the overall features of the spectrum are similar. In the Au55-3 cluster, the sp←d interband transitions play a role and sp←sp intraband transitions are responsible for the low-energy excitations. In addition, p←d interband transitions rule the high-energy excitations (Figure 12). Similar to the octahedral and truncated octahedral systems, the gold nanoparticles have much stronger interband transitions than comparably sized silver systems.32 In calculations of the HOMO-LUMO gaps, gaps for non-magic number clusters are usually smaller than the gaps of magic number clusters because icosahedral clusters are relatively spherical and thus the spherical magic numbers play a strong role (Table 4). The energy gaps of the magic numbers Au13+5 (2.17 eV) with 8 electrons and Au13-5 (0.69 eV) with 18 electrons are significantly larger than the HOMO-LUMO gap for the Au13-1 cluster (0.11 eV). The magic clusters Au43+3 with 40 electrons and Au55-3 with 58 electrons also have much larger HOMO-LUMO gaps than non-magic clusters Au43-1 and Au55+1, as shown in Table 4. In general, HOMO-LUMO gaps tend to decrease with the size of the cluster for all of the shapes considered here, but it should be stressed that this trend is not monotonic because the gap depends on the orbitals filled for each charge state for a given cluster size. Comparison of Nanoparticle Sizes and Shapes


12

Page 13 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The spectra of octahedral, truncated octahedral, and icosahedral nanoparticles are shown together in Figure 13. From Figure 13, it can be observed that the peak location maxima of octahedral and truncated octahedral clusters are red-shifted with increasing size of the cluster. In contrast, the peak location maxima of icosahedral clusters are somewhat blueshifted as the cluster becomes larger. However, this behavior is somewhat complex because although the large peak around 3.75 eV for Au13+5 shifts to about 4.1 eV for Au55-3, it also broadens so that some strong peaks are observed at energies around 3.1-3.3 eV. Normally, a red-shift with increasing size would be expected. Furthermore, the peak intensities increase as the cluster becomes larger for octahedral, truncated octahedral, and icosahedral clusters (Figure 13). The intensity results are in good agreement with a combined experimental and theoretical study.54 However, the size dependence for icosahedral clusters is not in agreement with experimental work that shows a red-shift in peak locations as the cluster becomes larger.55 This discrepancy may be due to the small size of the nanoclusters examined in this work, or in the spectral range considered; for example, if only peaks below 4 eV are considered, the absorption maxima of icosahedral clusters appears to red-shift with increasing cluster size. To investigate the shape dependence, absorption spectra for truncated octahedra and icosahedra with the same charges are compared in Figure 14. The icosahedral Au13-5 cluster has peaks that are red-shifted with respect to truncated octahedral ones; the icosahedral Au13-1 and Au13+5 clusters have blue-shifted peaks with respect to truncated octahedral ones. In the Au55-3 cluster, the icosahedral cluster has a peak maximum that is blue-shifted with respect to the truncated octahedral spectrum. In the experimental extinction spectra of aqueous solutions of octahedral, truncated octahedral, cuboctahedral, truncated cubic, cubic, and trisoctahedral gold nanoparticles,12 the truncated octahedral gold nanoparticles are blueshifted with respect to octahedral ones. The absorption spectra are thought to depend on


13


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 37

factors such as the number of facets and edges of the polyhedra.12 We predict that the absorption peaks of icosahedral clusters that have more facets than octahedral clusters will be blue-shifted. In our results, the trends in the absorption spectra of truncated octahedral and icosahedral Au13-1, Au13+5, and Au55-3 clusters are in good agreement with the experimental data shown in Ref. 12. Weissker et al. previously showed using TDDFT that the absorption peak locations are red-shifted with increasing cluster size for cuboctahedral shapes (13 and 55 atoms) and truncated octahedral shapes (38 and 140 atoms), and the absorption peak locations of cubo shapes (Au13 and Au55) are red-shifted with respect to icosahedral ones.36 In addition, in silver nanoparticles the peak locations are blue-shifted as the shape changes from octahedral to icosahedra and are red-shifted as the cluster size increases.32 Thus, the results from our current study agree with findings from other experimental and theoretical studies. Conclusions In this article, the optical absorption spectra of octahedral, truncated octahedral, and icosahedral gold nanoparticles Aun (n = 6 - 85) have been studied. TDDFT is employed to calculate excitation energies using LB94/DZ.4f after optimizing the cluster structures using BP86/DZ.4f. The number of electrons in the cluster is considered so that each cluster has filled electronic shells. The charge state affects the optical absorption spectrum, especially for smaller systems. As expected for the magic number clusters, their absorption spectra are sharper than those of non-magic clusters. In addition, they have larger HOMO-LUMO gaps. Overall, the spectra are typically composed of many peaks rather than the sharp plasmon resonance of larger gold nanoparticles. Most excitation spectra of gold nanoparticles may be decomposed into contributions from sp←sp intraband transitions, sp←d interband transitions, p←sp interband transitions, and p←d interband transitions. We find that the absorption peak locations are red-shifted as


14

Page 15 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the cluster size increases for octahedral and truncated octahedral clusters. In addition, the absorption peak locations are a little blue-shifted with increased cluster size for icosahedral clusters. The absorption peak locations of truncated octahedral clusters are red-shifted with respect to icosahedral ones. These results agree with other experimental and theoretical studies. Acknowledgments This work was supported by the research grant of the Chungbuk National University in 2013. This material is also based upon work supported by the Air Force Office of Scientific Research under AFOSR Award NO. FA9550-09-1-0451.


15


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 37

Table 1. Strong Optical Absorption Peaks in the Spectrum of Octahedral Au6 Clusters: The Clusters, Peak Energies, Oscillator Strengths, Orbitals, and Primary Transitions Responsible for These Peaks

Au6-2

Au6+4

Peak Energy

Oscillator Strength

2.34 4.07

0.094 0.059

4.13 5.10 5.61 3.40

0.12 0.075 0.42 0.003

3.49 4.04

0.004 0.023

4.32 5.05

0.096 0.038

Orbital

Transition from Occupied Orbital

Transition from Unoccupied Orbital

P→D P→S P→D P→S P→D P→D d-like → P d-like → P d-like → P d-like → P d-like → P d-like → P d-like → P d-like → P

HOMO HOMO HOMO HOMO HOMO HOMO HOMO-4 HOMO-1 HOMO-7 HOMO-5 HOMO-9 HOMO-7 HOMO-7 HOMO-8

LUMO LUMO+1 LUMO+2 LUMO+1 LUMO+2 LUMO+2 LUMO LUMO LUMO LUMO LUMO LUMO LUMO LUMO


16

Page 17 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Strong Optical Absorption Peaks in the Spectrum of Icosahedral Au13-5 Clusters: The Clusters, Peak Energies, Oscillator Strengths, Orbitals, and Primary Transitions Responsible for These Peaks Transition to Peak Oscillator Transition from Symmetry Unoccupied Energy Strength Occupied Orbital Orbital A2u 2.01 0.13 13a1g (HOMO) 12a2u (LUMO+1) 12e2g (HOMO) 11e2u (LUMO+1) E1u 2.01 0.13 12e2g (HOMO) 11e2u (LUMO+1) 11e2u (LUMO+1) 13e1g (HOMO) 12a2u (LUMO+1) 13e1g (HOMO) 13e1u (HOMO-1) 14a1g (LUMO) A2u 2.70 0.063 14a1g (LUMO) 11a2u (HOMO-1) E1u 2.70 0.063 13e1u (HOMO-1) 14a1g (LUMO) A2u 13a2u (LUMO+2) 3.65 0.29 13a1g (HOMO) 13e1g (HOMO) 14e1u (LUMO+2) 12a1g (HOMO-3) 12a2u (LUMO+1) 10e2g (HOMO-3) 11e2u (LUMO+1) E1u 3.65 0.29 12e2g (HOMO) 14e1u (LUMO+2) A2u 4.68 0.20 10a1g (HOMO-11) 12a2u (LUMO+1) 13e1g (HOMO) 15e1u (LUMO+3) 7e2g (HOMO-11) 11e2u (LUMO+1) E1u 4.68 0.20 12e2g (HOMO) 12e2u (LUMO+3) A2u 5.19 0.33 7a2u (HOMO-16) 14a1g (LUMO) 11e1g (HOMO-4) 14e1u (LUMO+2) 13e1g (HOMO) 15e1u (LUMO+3) 6e2g (HOMO-12) 11e2u (LUMO+1) E1u 5.19 0.33 7e1u (HOMO-16) 14a1g (LUMO) 12e2g (HOMO) 12e2u (LUMO+3) A2u 5.82 0.44 11e1g (HOMO-4) 14e1u (LUMO+2) 11e2g (HOMO-2) 12e2u (LUMO+3) 13e1g (HOMO) 15e1u (LUMO+3) E1u 5.83 0.44 11e1g (HOMO-4) 13a2u (LUMO+2) 2a2g (HOMO-4) 14e1u (LUMO+2) 3a2g (HOMO-2) 15e1u (LUMO+3) 10e2g (HOMO-3) 14e1u (LUMO+2)


17


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 37

Table 3. Strong Optical Absorption Peaks in the Spectrum of Icosahedral Au13+5 Clusters: The Clusters, Peak Energies, Oscillator Strengths, Orbitals, and Primary Transitions Responsible for These Peaks Symmetry

Peak Energy

Oscillator Strength

Transition from Occupied Orbital

Transition to Unoccupied Orbital

A2u

3.00

0.12

E1u

3.00

0.12

A2u

3.75

0.064

E1u

3.75

0.064

A2u

4.02

0.17

E1u

4.02

0.17

A2u

4.33

0.062

E1u

4.33

0.062

A2u

4.73

0.050

E1u

4.73

0.050

A2u

5.68

0.17

E1u

5.68

0.17

A2u E1u

5.91 5.91

0.14 0.14

11a2u (HOMO) 13e1u (HOMO) 9e2u (HOMO-5) 13e1u (HOMO) 11a2u (HOMO) 11a2u (HOMO) 10a2u (HOMO-7) 8e2u (HOMO-7) 13e1u (HOMO) 8e2u (HOMO-7) 10a2u (HOMO-7) 8e2u (HOMO-7) 10a2u (HOMO-7) 8e2u (HOMO-7) 8e2u (HOMO-7) 8e2u (HOMO-7) 13e1u (HOMO) 13e1u (HOMO) 11a2u (HOMO) 7e2u (HOMO-8) 10e1u (HOMO-8) 2a1u (HOMO-8) 10e1u (HOMO-8) 7e2u (HOMO-8) 10e1u (HOMO-8) 9a2u (HOMO-10) 9e1u (HOMO-10) 9a2u (HOMO-10) 9e1u (HOMO-10) 9a2u (HOMO-10) 7a2u (HOMO-16) 7e1u (HOMO-16) 9e1u (HOMO-10) 7a2u (HOMO-16) 7e1u (HOMO-16) 9a2u (HOMO-10) 9e1u (HOMO-10)

13a1g (LUMO) 13e1g (LUMO) 12e2g (LUMO) 12e2g (LUMO) 13e1g (LUMO) 14a1g (LUMO+1) 13a1g (LUMO) 12e2g (LUMO) 14a1g (LUMO+1) 12e2g (LUMO) 13e1g (LUMO) 13e1g (LUMO) 13a1g (LUMO) 12e2g (LUMO) 13e1g (LUMO) 12e2g (LUMO) 14a1g (LUMO+1) 12e2g (LUMO) 13e1g (LUMO) 12e2g (LUMO) 13e1g (LUMO) 13e1g (LUMO) 13a1g (LUMO) 13e1g (LUMO) 12e2g (LUMO) 13a1g (LUMO) 13e1g (LUMO) 13e1g (LUMO) 12e2g (LUMO) 14a1g (LUMO+1) 13a1g (LUMO) 13e1g (LUMO) 14a1g (LUMO+1) 13e1g (LUMO) 12e2g (LUMO) 14a1g (LUMO+1) 14a1g (LUMO+1)


18

Page 19 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4. Calculated HOMO-LUMO Gaps of Gold Nanoparticles using the LB94 Functional shape cluster ∆E (eV) octahedra Au6-2 1.62 Au6+4 2.28 Au19-1 0.32 0.52 Au19+1 Au44-2 0.36 Au44+4 0.33 -1 Au85 0.14 Au85-5 0.02 Au85+5 0.10 -1 0.70 truncated octahedra Au13 Au13-5 0.33 Au13+5 1.79 Au38-2 0.17 Au38+4 1.15 Au55-3 0.41 Au55-1 0.32 Au55+5 0.40 -7 Au79 0.08 Au79+5 0.31 icosahedra Au13-1 0.11 Au13-5 0.69 +5 Au13 2.17 Au43-1 0.12 Au43+3 0.18 Au55-3 0.79 Au55+1 0.16


19


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 37

Figure 1. LB94/DZ.4f Kohn-Sham orbitals of the octahedral Au6-2 cluster. The orbital symmetry is provided for both the Oh point group and the closest spherical representation.


20

Page 21 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Optical absorption spectra for octahedral Au6 clusters. The absorption spectra arise from sp←sp intraband and p←sp interband transitions in the Au6-2 cluster and sp←s(d) and sp←d interband transitions in the Au6+4 cluster.


21


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 37

Figure 3. Optical absorption spectra for octahedral Au19 clusters.


22

Page 23 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




23


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 37



24

Page 25 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. Optical absorption spectra for truncated octahedral Au13 clusters.


25


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 37



26

Page 27 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 37



28

Page 29 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 10. Optical absorption spectra for icosahedral Au13 clusters.


29


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 37



30

Page 31 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60




31


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 37

Figure 13. Size comparisons of optical absorption spectra for octahedral (a), truncated octahedral (b) and icosahedral (c) gold nanoparticles using the LB94 functional


32

Page 33 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 14. Shape comparisons of optical absorption spectra for truncated octahedra and icosahedra.


33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 37

References 1. Daniel, M. C.; Astruc, D., Gold Nanoparticles: Assembly, Supramolecular Chemistry, Quantum-Size-Related Properties, and Applications toward Biology, Catalysis, and Nanotechnology. Chem. Rev. 2004, 104, 293-346. 2. Rosi, N. L.; Mirkin, C. A., Nanostructures in Biodiagnostics. Chem. Rev. 2005, 105, 1547-1562. 3. Rashid, M. H.; Bhattacharjee, R. R.; Kotal, A.; Mandal, T. K., Synthesis of Spongy Gold Nanocrystals with Pronounced Catalytic Activities. Langmuir 2006, 22, 7141-7143. 4. Melancon, M. P.; Lu, W.; Yang, Z.; Zhang, R.; Cheng, Z.; Elliot, A. M.; Stafford, J.; Olson, T.; Zhang, J. Z.; Li, C., In Vitro and in Vivo Targeting of Hollow Gold Nanoshells Directed at Epidermal Growth Factor Receptor for Photothermal Ablation Therapy. Molecular Cancer Therapeutics 2008, 7, 1730-1739. 5. Moores, A.; Goettmann, F., The Plasmon Band in Noble Metal Nanoparticles: An Introduction to Theory and Applications. New Journal of Chemistry 2006, 30, 1121-1132. 6. Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A., Chemistry and Properties of Nanocrystals of Different Shapes. Chem. Rev. 2005, 105, 1025-1102. 7. Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C., The Optical Properties of Metal Nanoparticles:The Influence of Size, Shape, and Dielectric Environment. J. Phys. Chem. B 2003, 107, 668-677. 8. Liz-Marzan, L. M., Tailoring Surface Plasmons through the Morphology and Assembly of Metal Nanoparticles. Langmuir 2006, 22, 32-41. 9. Schwartzberg, A. M.; Olson, T. Y.; Talley, C. E.; Zhang, J. Z., Synthesis, Characterization, and Tunable Optical Properties of Hollow Gold Nanospheres. J. Phys. Chem. B 2006, 110, 19935-19944. 10. Noguez, C., Surface Plasmons on Metal Nanoparticles: The Influence of Shape and Physical Environment. J. Phys. Chem. C 2007, 111, 3806-3819. 11. Kim, F.; Connor, S.; Song, H.; Kuykendall, T.; Yang, P., Platonic Gold Nanocrystals. Angew. Chem. Int. Ed. 2004, 43, 3673-3677. 12. Eguchi, M.; Mitsui, D.; Wu, H.-L.; Sato, R.; Teranishi, T., Simple Reductant Concentration-Dependent Shape Control of Polyhedral Gold Nanoparticles and Their Plasmonic Properties. Langmuir 2012, 28, 9021-9026. 13. Sun, Y.; Xia, Y., Shape-Controlled Synthesis of Gold and Silver Nanoparticles. Science 2002, 298, 2176-2179. 14. Seo, D.; Park, J. C.; Song, H., Polyhedral Gold Nanocrystals with Oh Symmetry: From Octahedra to Cubes. J. Am. Chem. Soc. 2006, 128, 14863-14870. 15. Im, S. H.; Lee, Y. T.; Wiley, B.; Xia, Y. N., Large-Scale Synthesis of Silver Nanocubes: The Role of Hcl in Promoting Cube Perfection and Monodispersity. Angew Chem. Int. Ed. 2005, 44, 2154-2157. 16. Wiley, B. J.; Xiong, Y. J.; Li, Z. Y.; Yin, Y. D.; Xia, Y. N., Right Bipyramids of Silver: A New Shape Derived from Single Twinned Seeds. Nano Lett. 2006, 6, 765-768. 17. Tao, A.; Sinsermsuksakul, P.; Yang, P., Polyhedral Silver Nanocrystals with Distinct Scattering Signatures. Angew. Chem., Int. Ed. 2006, 45, 4597-4601. 18. Sánchez-Iglesias, A.; Pastoriza-Santos, I.; Pérez-Juste, J.; Roríguez-González, B.; Abajo, F. J. G.; Liz-Marzán, L. M., Synthesis and Optical Properties of Gold Nanodecahedra with Size Control. Adv. Mater. 2006, 18, 2529-2534. 19. Li, C. C.; Shuford, K. L.; Park, Q. H.; Cai, W. P.; Li, Y.; Lee, E. J.; Cho, S. O., HighYield Synthesis of Single-Crystalline Gold Nano-Octahedra. Angew. Chem., Int. Ed. 2007, 46, 3264-3268.


34

Page 35 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20. Wei, H.; Hao, F.; Huang, Y.; Wang, W.; Nordlander, P.; Xu, H., Polarization Dependence of Surface-Enhanced Raman Scattering in Gold Nanoparticle−Nanowire Systems. Nano Letters 2008, 8, 2497-2502. 21. Sun, Y. G.; Gates, B.; Mayers, B.; Xia, Y. N., Crystalline Silver Nanowires by Soft Solution Processing. Nano Lett. 2002, 2, 165-168. 22. Wiley, B. J.; Chen, Y.; McLellan, J. M.; Xiong, Y.; Li, Z. Y.; Ginger, D.; Xia, Y. N., Synthesis and Optical Properties of Silver Nanobars and Nanorice. Nano Lett. 2007, 7, 10321036. 23. Xiong, Y.; Cai, H.; Wiley, B. J.; Wang, J.; Kim, M. J.; Xia, Y., Synthesis and Mechanistic Study of Palladium Nanobars and Nanorods. J. Am. Chem. Soc. 2007, 129, 3665-3675. 24. Tsuji, M.; Hashimoto, M.; Nishizawa, Y.; Kubobawa, M.; Tsuji, T., MicrowaveAssisted Synthesis of Metallic Nanostructures in Solution. Chem.-Eur. J. 2005, 11, 440-452. 25. Li, C. C.; Cai, W. P.; Cao, B. Q.; Sun, F. Q.; Li, Y.; Kan, C. X.; Zhang, L. D., Mass Synthesis of Large, Single-Crystal Au Nanosheets Based on a Polyol Process. Adv. Funct. Mater. 2006, 16, 83-90. 26. Mie, G., Beiträge Zur Optik Trüber Medien. Ann. Phys. (Leipzig) 1908, 25, 377-445. 27. González, A. L.; Noguez, C., Influence of Morphology on the Optical Properties of Metal Nanoparticles. J. Comp. Theor. Nanosci. 2007, 4, 231-238. 28. Sosa, I. O.; Noguez, C.; Barrera, R. G., Optical Properties of Metal Nanoparticles with Arbitrary Shapes. J. Phys. Chem. B 2003, 107, 6269-6275. 29. Hao, E.; Li, S.; Bailey, R. C.; Zou, S.; Schatz, G. C.; Hupp, J. T., Optical Properties of Metal Nanoshells. J. Phys. Chem. B 2004, 108, 1224-1229. 30. Payne, E. K.; Shuford, K. L.; Park, S.; Schatz, G. C.; Mirkin, C. A., Multipole Plasmon Resonances in Gold Nanorods. J. Phys. Chem. B 2006, 110, 2150-2154. 31. Fuchs, R., Theory of the Optical Properties of Ionic Crystal Cubes. Phys. Rev. B 1975, 11, 1732-1740. 32. Bae, G.-T.; Aikens, C. M., Time-Dependent Density Functional Theory Studies of Optical Properties of Ag Nanoparticles: Octahedra, Truncated Octahedra, and Icosahedra. J. Phys. Chem. C 2012, 116, 10356-10367. 33. Stener, M.; Nardelli, A.; De Francesco, R.; Fronzoni, G., Optical Excitations of Gold Nanoparticles: A Quantum Chemical Scalar Relativistic Time Dependent Density Functional Study. J. Phys. Chem. C 2007, 111, 11862-11871. 34. Barcaro, G.; Broyer, M.; Durante, N.; Fortunelli, A.; Stener, M., Alloying Effects on the Optical Properties of Ag-Au Nanoclusters from Tddft Calculations. J. Phys. Chem. C 2011, 115, 24085-24091. 35. Durante, N.; Fortunelli, A.; Broyer, M.; Stener, M., Optical Properties of Au Nanoclusters from Td-Dft Calculations. J. Phys. Chem. C 2011, 115, 6277-6282. 36. Weissker, H. C.; Mottet, C., Optical Properties of Pure and Core-Shell Noble-Metal Nanoclusters from Tddft: The Influence of the Atomic Structure. Physical Review B 2011, 84, 165443. 37. López-Lozano, X.; Barron, H.; Mottet, C.; Weissker, H.-C., Aspect-Ratio- and SizeDependent Emergence of the Surface-Plasmon Resonance in Gold Nanorods - an Ab Initio Tddft Study. Physical Chemistry Chemical Physics 2014, 16, 1820-1823. 38. Liao, M.-S.; Bonifassi, P.; Leszczynski, J.; Ray, P. C.; Huang, M.-J.; Watts, J. D., Structure, Bonding, and Linear Optical Properties of a Series of Silver and Gold Nanorod Clusters: Dft/Tddft Studies. J. Phys. Chem. A 2010, 114, 12701-12708. 39. Nobusada, K., Electronic Structure and Photochemical Properties of a MonolayerProtected Gold Cluster. J. Phys. Chem. B 2004, 108, 11904-11908.


35


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 37

40. Häkkinen, H.; Walter, M.; Grönbeck, H., Divide and Protect: Capping Gold Nanoclusters with Molecular Gold-Thiolate Rings. J. Phys. Chem. B 2006, 110, 9927-9931. 41. Iwasa, T.; Nobusada, K., Theoretical Investigation of Optimized Structures of Thiolated Gold Cluster [Au25(Sch3)18]+. J. Phys. Chem. C 2007, 111, 45-49. 42. Aikens, C. M., Effects of Core Distances, Solvent, Ligand, and Level of Theory on the Tddft Optical Absorption Spectrum of the Thiolate-Protected Au25 Nanoparticle. J. Phys. Chem. A 2009, 113, 10811-10817. 43. Lopez-Acevedo, O.; Tsunoyama, H.; Tsukuda, T.; Häkkinen, H.; Aikens, C. M., Chirality and Electronic Structure of the Thiolate-Protected Au38 Nanocluster. J. Am. Chem. Soc. 2010, 132, 8210-8218. 44. Aikens, C. M., Geometric and Electronic Structure of Au25(Sphx)18-(X = H, F, Cl, Br, Ch3, and Och3). J. Phys. Chem. Lett. 2010, 1, 2594-2599. 45. Zeng, C.; Li, T.; Das, A.; Rosi, N. L.; Jin, R., Chiral Structure of Thiolate-Protected 28-Gold-Atom Nanocluster Determined by X-Ray Crystallography. J. Am. Chem. Soc. 2013, 135, 10011-10013. 46. Li, G.; Jin, R., Atomically Precise Gold Nanoclusters as New Model Catalysts. Acc. Chem. Res. 2013, 46, 1749-1758. 47. Negishi, Y.; Nakazaki, T.; Malola, S.; Takano, S.; Niihori, Y.; Kurashige, W.; Yamazoe, S.; Tsukuda, T.; Häkkinen, H., A Critical Size for Emergence of Nonbulk Electronic and Geometric Structures in Dodecanethiolate-Protected Au Clusters. J. Am. Chem. Soc. 2015, 137, 1206-1212. 48. Burgess, R. W.; Keast, V. J., Tddft Study of the Optical Absorption Spectra of Bare Gold Clusters. J. Phys. Chem. C 2014, 118, 3194-3201. 49. Iida, K.; Noda, M.; Ishimura, K.; Nobusada, K., First-Principles Computational Visualization of Localized Surface Plasmon Resonance in Gold Nanoclusters. J. Phys. Chem. A 2014, 118, 11317-11322. 50. te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T., Chemistry with Adf. J. Comp. Chem. 2001, 22, 931-967. 51. Häberlen, O. D.; Chung, S.-C.; Stener, M.; Rösch, N., From Clusters to Bulk: A Relativistic Density Functional Investigation on a Series of Gold Clusters Aun, N=6,...,147. J. Chem. Phys. 1997, 106, 5189-5201. 52. van Leeuwen, R.; Baerends, E. J., Phys. Rev. A 1994, 49, 2421-2431. 53. Aikens, C. M.; Li, S.; Schatz, G. C., From Discrete Electronic States to Plasmons: Tddft Optical Absorption Properties of Agn (N = 10, 20, 35, 56, 84, 120) Tetrahedral Clusters. J. Phys. Chem. C 2008, 112, 11272-11279. 54. Li, C.; Shuford, K. L.; Chen, M.; Lee, E. J.; Cho, S. O., A Facile Polyol Route to Uniform Gold Octahedra with Tailorable Size and Their Optical Properties. ACS Nano 2008, 2, 1760-1769. 55. Kwon, K.; Lee, K. Y.; Lee, Y. W.; Kim, M.; Heo, J.; Ahn, S. J.; Han, S. W., Controlled Synthesis of Icosahedral Gold Nanoparticles and Their Surface-Enhanced Raman Scattering Property. J. Phys. Chem. C 2006, 111, 1161-1165.


36

Page 37 of 37

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For Table of Contents Only


37

Time-Dependent Density Functional Theory ... - ACS Publications

Recommend Documents