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C: Spectroscopy and Dynamics of Nano, Hybrid, and Low-Dimensional MaterialsJanuary 29, 2021

Dielectric Engineering of Hot-Carrier Generation by Quantized Plasmons in Embedded Silver Nanoparticles
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Lara Román Castellanos
Lara Román Castellanos
Department of Physics, Imperial College London, London SW7 2AZ, U.K.
More by Lara Román Castellanos
Ortwin Hess*
Ortwin Hess
Department of Physics, Imperial College London, London SW7 2AZ, U.K.
The Thomas Young Centre for Theory and Simulation of Materials, London E1 4NS, U.K.
School of Physics and CRANN Institute, Trinity College Dublin, Dublin 2, Ireland
*Email: [email protected]
More by Ortwin Hess
http://orcid.org/0000-0002-6024-0677
Johannes Lischner*
Johannes Lischner
Department of Physics and Materials, Imperial College London, London SW7 2AZ, U.K.
The Thomas Young Centre for Theory and Simulation of Materials, London E1 4NS, U.K.
*Email: [email protected]
More by Johannes Lischner
http://orcid.org/0000-0002-9601-7821

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The Journal of Physical Chemistry C

Cite this: J. Phys. Chem. C 2021, 125, 5, 3081–3087

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https://doi.org/10.1021/acs.jpcc.0c07617

Published January 29, 2021

Abstract

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Understanding and controlling properties of plasmon-induced hot carriers is a key step toward next-generation photovoltaic and photocatalytic devices. Here, we uncover a route to engineering hot-carrier generation rates of silver nanoparticles by designed embedding in dielectric host materials. Extending our recently established quantum-mechanical approach to describe the decay of quantized plasmons into hot carriers we capture both external screening by the nanoparticle environment and internal screening by silver d-electrons through an effective electron–electron interaction. We find that hot-carrier generation can be maximized by engineering the dielectric host material such that the energy of the localized surface plasmon coincides with the highest value of the nanoparticle joint density of states. This allows us to uncover a path to control the energy of the carriers and the amount produced, for example, a large number of relatively low-energy carriers are obtained by embedding in strongly screening environments.

Subjects

Introduction

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Understanding and controlling light–matter interactions at the nanoscale is important for increasing the efficiency of photovoltaic and photocatalytic devices. (1−3) In this context, localized surface plasmons (LSP) in metallic nanoparticles provide a unique platform because the LSP decay generates energetic or “hot” carriers that can be harnessed to induce chemical reactions (4) or overcome interfacial barriers. (5) Other applications of hot carriers include biochemical sensing, (6) spectroscopy, (7) nanophotonic lasers, (8) and quantum information devices. (9) These applications usually require a generation of a large number of energetic carriers, but in many current devices, the hot-carrier generation rates are relatively small. (10)

To improve the performance of hot-carrier devices, significant efforts have been made to understand the dependence of hot-carrier properties on the nanoparticle material and its geometry. (11−13) However, in real devices, the nanoparticles are often embedded in insulating host materials or placed on top of their surfaces (14−17) and therefore the influence of the nanoparticle environment on hot carriers must also be considered. It is well known that the dielectric properties of the nanoparticle environment modify the LSP frequency, (18) influence interfacial transport barriers, and protect the nanoparticle from oxidation, (19) but not much is known about their effect on hot-carrier generation rates.

Microscopically, the dielectric environment modifies the effective interaction between conduction electrons in the nanoparticle. To approximate this screened interaction, several groups have modeled the environment as a linear polarizable medium, solved the corresponding Maxwell equations for a point charge in this system, and used the result to study the changes in the photoabsorption behavior of the nanoparticle induced by the environment. (14,20,21) By treating the nanoparticle itself as a polarizable medium, this approach can easily be extended to also capture the dielectric screening by bound charges in the material, such as d-band electrons in silver.

In this paper, we present a quantum-mechanical approach for calculating the effect of a dielectric environment on hot-carrier properties in embedded silver nanoparticles. In particular, we combine a recently developed method for describing hot-carrier generation by quantized plasmons (22) with a screened interaction between conduction electrons that takes the dielectric response of the environment and also of the polarizable d-band electrons into account. We present results for four different host materials (silicon dioxide, titanium dioxide, silicon nitride, and gallium phosphide) and compare them to results obtained for nanoparticles in air. We also study the dependence of hot-carrier properties on the size of the embedded nanoparticle. Our calculations reveal that hot-carrier rates in these systems depend sensitively on the dielectric properties of the environment. In particular, the environmental screening reduces the LSP energy and thereby changes the accessible LSP decay channels. Moreover, screening reduces the electron–plasmon coupling, but this effect can be compensated by the increase of the coupling due to the reduced LSP energy. These results pave the way toward a detailed understanding of hot-carrier generation in embedded nanoparticles and open up the possibility of dielectric engineering of hot-carrier properties.

Methods

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We review here the solution of the Poisson equation for a sphere of radius R with dielectric constant ϵ_d embedded in a material with dielectric constant ϵ₁. (23−25) As the charge density of a jellium nanoparticle can spill beyond the positive charge background representing the ions, three scenarios are considered: (i) the potential inside the nanoparticle generated by a charge inside the nanoparticle (denoted V_in-in), (ii) the potential outside the nanoparticle generated by a charge inside (denoted V_in-out), and (iii) the potential outside the nanoparticle generated by a charge outside the nanoparticle (denoted V_out-out). Note that the potential inside the nanoparticle generated by a charge outside is also described by V_in-out. We carry out linear response TDDFT calculations where the Coulomb interaction is described via these potentials which are given by

(1)

(2)

(3)

where P_l denotes the Legendre polynomial of order l. In principle, the radius of the dielectric sphere is an adjustable parameter. (21) In our work, we set the radius of the dielectric sphere equal to the radius of the sphere of positive background charge of the jellium nanoparticles. It is also worth noting that the dielectric properties of real materials are frequency-dependent. Here, we neglect this frequency dependence (as this would drastically increase the cost of solving the Casida equation) and use the static electronic dielectric constants of the dielectric sphere and the environment in the effective interaction. The Coulomb integrals were computed using the LIBERI library. (26) The TDDFT calculations were carefully converged with respect to the number of empty states. Note that our framework includes a quantized treatment of the plasmon, relevant to describe quantum effects present in small nanoparticles and/or when a low density of plasmons are excited as introduced in ref (22).

Results and Discussion

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Description of the Model

We have studied hot-carrier properties of embedded spherical silver nanoparticles consisting of between 68 and 254 atoms corresponding to diameters between 1.08 and 2.10 nm. To calculate hot-carrier distributions in these systems, we extended the approach developed in ref (22) for alkali metal nanoparticles. Following this approach, the decay of the localized surface plasmon (LSP) into a single electron-pair is considered. (27,28) The corresponding generation rate N(E) of hot electrons with energy E created by the decay of a single LSP quantum is obtained from Fermi’s golden rule according to

(4)

where ε_c and ε_v denote the quasiparticle energies of occupied and empty states and ω_P is the LSP frequency. To determine these quantities, we first carry out density functional theory (DFT) calculations on jellium spheres with a Wigner–Seitz radius of r_s = 3.0 Bohr (corresponding to the density of conduction electrons in the Ag sp-band) using the local density approximation. (29,30) Next, we use the Δ-SCF approach to calculate the ionization potential of the nanoparticles. (22) The quasiparticle energies are then obtained by shifting the Kohn–Sham (KS) energies by the difference between the ionization potential and the KS energy of the highest occupied orbital. Finally, the LSP frequency is obtained from time-dependent density functional theory (TDDFT) calculations in the random-phase approximation.

In eq 4, the electron–plasmon coupling g_vc is given by

(5)

where ϕ_v(r) [ϕ_c(r)] denotes the quasiparticle wavefunction of an occupied (empty) state, ρ_P(r) is the LSP transition density, and V(r, r^′) denotes the screened interaction between electrons.

To describe the screening by the Ag d-electrons and by the nanoparticle environment, we calculate the potential created by a point charge in a sphere with dielectric constant ϵ_d surrounded by an environment with dielectric constant ϵ₁. Solving the corresponding Poisson equation yields the effective interaction given in eqs 1–3. (20,21) Besides eq 5, we also use this screened interaction to calculate the TDDFT interaction matrix elements and thereby capture the screening-induced changes to the LSP energy and transition density. For the internal screening by the d-band electrons, we use ϵ_d = 3.3 (31) (in the Supporting Information, we verify that our results do not qualitatively depend on the precise value of this parameter). Note that the frequency-dependent screening of the conduction electrons is captured through the explicit solution of the Casida equation, which yields the frequency-dependent susceptibility of the nanoparticle.

We expect that this approach for calculating hot-carrier properties in embedded silver nanoparticles gives accurate results as long as the LSP energy is smaller than the separation between the d-bands and the Fermi level, which is approximately 4 eV. (32) If this condition is not fulfilled, the LSP decay can lead to the creation of hot holes in the d-bands and band structure methods beyond the jellium model are needed. (22) In practice, we find that LSP energies in Ag nanoparticles are in fact smaller than 4 eV as long as internal screening by d-band electrons is taken into account.

Note that, in the above equations, ℏ denotes the reduced Planck constant and e is the electron charge. Also, we replace the two delta-functions in eq 4 by Gaussians in our numerical calculations. The standard deviation of the first Gaussian is 0.12 eV, reflecting the lifetime of the LSP, (33) while the standard deviation of the second Gaussian is 0.05 eV, reflecting the quasiparticle lifetime in Ag. (34,35)

Finally, it is worth pointing out that eq 4 assumes ground-state occupancies, i.e., all states below the Fermi level are fully occupied and all states above the Fermi level are completely empty. Of course, different occupancies must be used if the nanoparticle contains an excited population of hot carriers, which can result in the Pauli blocking of certain transitions. This can happen, for example, when the system is illuminated continuously by a strong light source or when electron–phonon coupling leads to a significant increase in the nanoparticle temperature. (36)

Optical Properties of Silver Nanoparticles

We first study the optical properties of Ag nanoparticles in air (ϵ₁ = 1) and consider the effect of internal screening by the d-electrons. The left column of Figure 1 shows the optical absorption cross section σ of different Ag nanoparticles calculated with and without d-electron screening (see the Methods section for details). For all nanoparticles, the spectrum is dominated by a single LSP peak. Inclusion of d-electron screening redshifts the LSP frequency compared to its unscreened value because screening weakens the interaction between conduction electrons, facilitating the excitation of a collective oscillation. Interestingly, the size of the redshift depends sensitively on the nanoparticle radius, see Table 1. For example, a redshift of 2.1 eV is found for Ag₉₂, but for Ag₁₃₈, it is only 0.1 eV. As the nanoparticle size increases, the plasmon energy decreases non-monotonically.

Figure 1. Left: Absorption spectra of Ag nanoparticles in air with (purple curves) and without (green curves) d-electron screening as function of photon energy: (a) Ag₂₅₄, (b) Ag₁₃₈, (c) Ag₉₂, and (d) Ag₆₈. Right: Plasmon-induced hot carrier distributions (HCD) of Ag nanoparticles in air with and without d-electron screening as function of hot-carrier energy: (e) Ag₂₅₄, (f) Ag₁₃₈, (g) Ag₉₂, and (h) Ag₆₈. Note that the screened results have been rescaled by the indicated factors, and the dotted vertical lines denote the Fermi level.

Table 1. Effect of d-Electron Screening on the Energy ℏω_P of the Localized Surface Plasmon in Ag Nanoparticles in Air (All Energies in eV)

	with d-electron screening	without d-electron screening	redshift
Ag₂₅₄	3.4	4.6	1.2
Ag₁₃₈	3.1	3.2	0.1
Ag₉₂	3.6	5.5	2.1
Ag₆₈	3.8	5.2	1.4

For Ag₉₂, the LSP peak breaks into multiple peaks when d-electron screening is included. This Landau fragmentation is caused by the coupling of the collective LSP excitation to electron–hole pair excitations that have a similar energy. (37,38)

Next, we study the effect of embedding Ag nanoparticles in insulating host materials. In particular, we consider the following hosts: silicon dioxide (SiO₂), silicon nitride (SiN), titanium dioxide (TiO₂), and gallium phosphide (GaP). These materials are often used in experiments (4,14,21,41) and cover a wide range of dielectric constants, see caption of Figure 2. Figure 2 compares the optical absorption spectra of embedded Ag nanoparticles with those obtained in air. Internal screening by d-electrons is included in all calculations.

Figure 2. Absorption spectra of (a) Ag₂₅₄, (b) Ag₁₃₈, (c) Ag₉₂, and (d) Ag₆₈ embedded in SiO₂ (ϵ₁ = 2.16 from ref (21), SiN (ϵ₁ = 3.2 from ref (14), TiO₂ (ϵ₁ = 8.2 from ref (39), and GaP (ϵ₁ = 20.2 from ref (40).

We observe that the LSP frequency of embedded nanoparticles is redshifted compared to the result in air. This is again a consequence of enhanced screening due to the presence of the dielectric environment, which further weakens the effective interaction between conduction electrons in the nanoparticle. Unsurprisingly, the redshift increases with the value of the environment dielectric constant ϕ₁, see Figure 3. In some cases, the LSP peak splits into multiple peaks upon embedding. This fragmentation occurs for Ag₁₃₈ in TiO₂ and GaP and Ag₆₈ in SiO₂.

Figure 3. Localized surface plasmon energy of silver nanoparticles embedded in SiO₂ (ϵ₁ = 2.16 from ref (21), SiN (ϵ₁ = 3.2 from ref (14), TiO₂ (ϵ₁ = 8.2 from ref (39), and GaP (ϵ₁ = 20.2 from ref (40).

Next, we compare our findings to previous theoretical and experimental studies of small Ag nanoparticles. Scholl and co-workers (42) measured LSP energies for a range of nanoparticle sizes using electron energy loss spectroscopy. In their experiments, the Ag nanoparticles are deposited on either carbon films or SiO₂ substrates. For the smallest systems (with diameters of about 2 nm), they observe LSP energies that are blueshifted by about 0.5 eV from the classical LSP energy found in large nanoparticles. Specifically, LSP energies in the range of 3.6–3.8 eV are observed for the smallest nanoparticles. These LSP energies are consistent with our calculations when d-electron screening is included. Interestingly, Scholl et al. also find that the LSP energies do not approach the large nanoparticle limit in a monotonic fashion. Instead, there is significant scatter on the order of several tenths of an electronvolt. Again, this is similar to the non-monotonic behavior in our calculations.

To explain their findings, Scholl et al. (42) use a theoretical model developed by Genzel, Martin, and Kreibig. (43) In this semiclassical approach, the frequency-dependent bulk dielectric function of silver is replaced by an expression that includes transitions between nanoparticle states as additional Lorentz oscillator terms. In the work of Scholl et al., these transitions are obtained from an infinite spherical well model. The resulting dielectric function is then used in a classical expression for the nanoparticle absorption spectrum. The resulting LSP energies are in good agreement with the measured ones. In particular, the blueshift at small particle sizes and the non-monotonic behavior are correctly reproduced. Scholl et al. interpret the non-monotonic behavior as a consequence of transitions from occupied states with high binding energies to unoccupied states near the Fermi level. These transitions play a more dominant role in small nanoparticles: at specific radii, these transitions can strongly influence the dipolar resonance condition and therefore result in significant shifts of the LSP energy. The same theoretical approach was also recently used by Saavedra and co-workers. (1) The good agreement between the semiclassical model and the experimental measurement shows that a detailed description of nanoparticle transitions is needed to describe optical absorption of small Ag nanoparticles. Of course, these transitions are also captured by our fully quantum-mechanical approach. Importantly, we do not make an infinite spherical well approximation but instead use a more accurate jellium model, which allows spill-out of the electron density.

A non-monotonic behavior of the LSP energy was also observed by Lünskens and co-workers, (44) who used surface second harmonic generation spectroscopy to study Ag clusters consisting of 55 atoms or less. In general, they find a blueshift of several tenths of an electronvolt as the cluster size is reduced.

Yu and co-workers (45) measured the optical spectra of Ag clusters with up to 120 atoms. They find that the spectra are dominated by a single LSP peak if the cluster contains more than 20 atoms. They also observe a non-monotonic behavior of the LSP energy as a function of cluster size. Overall, the LSP energies of small clusters are blueshifted from the large nanoparticle result by several tenths of an electronvolt. The LSP energies that are observed for these nanoparticles lie between 3.7 and 3.9 eV.

Tiggesbäumker and co-workers (46) used photodepletion spectroscopy to study the LSP energy of ionic Ag clusters with up to 70 atoms. They also report a blueshift as the cluster size is decreased with some non-monotonic behavior. For the largest cluster, Ag₇₀⁺, they find an LSP energy of 3.77 eV, which is in good quantitative agreement with our result for Ag₆₈. Similar results were obtained by Charlé and co-workers. (47)

Tunability of LSP energies by nanoparticle size and also through environmental screening was demonstrated by Jensen and co-workers. (48) By systematically increasing the thickness of the SiO_x encapsulation, they could control the redshift of the LSP energy. This is consistent with our finding that the environmental screening reduces the LSP energy. Similar results were obtained by Hilger and co-workers. (49)

Hot-Carrier Properties of Silver Nanoparticles

The right column of Figure 1 shows the energy distribution of hot carriers that are generated per unit time from the LSP decay in Ag nanoparticles of different sizes in air (obtained by evaluating eq 4). Results from calculations with and without d-electron screening are compared. The hot-carrier distributions exhibit sharp peaks reflecting the discreteness of the energy level spectrum of the small nanoparticles under consideration. Energy conservation requires that peaks in the hot hole and hot electron distributions that originate from the same decay process are separated by the LSP energy (which itself depends on the nanoparticle size and inclusion of d-electron screening as discussed above).

For applications, it is often important to know how the LSP energy is distributed among the hot electron and the hot hole. We find that this depends sensitively on the inclusion of d-electron screening: when d-electron screening is neglected, energetic holes and less energetic electrons are produced (except in Ag₁₃₈), while inclusion of d-electron screening favors the generation of hot electrons (and somewhat less energetic holes). Inclusion of d-electron screening also results in drastic changes in the magnitude of hot-carrier rates. In particular, the screened hot-carrier rates in Ag₆₈ and Ag₁₃₈ are more than one order of magnitude smaller than the unscreened ones, while they are one order of magnitude larger in Ag₉₂.

Figure 4 shows the hot-carrier distributions of embedded Ag nanoparticles (including internal screening by d-electrons). These distributions exhibit a large number of peaks for large nanoparticles in weakly screening environments (see, for example, Ag₂₅₄ and Ag₁₃₈ in air or SiO₂), while only a few peaks are found for nanoparticles in GaP. In most systems, the generation of energetic electrons is favored compared to energetic holes and the energy of hot carriers (measured with respect to the Fermi level) is generally larger in weakly screening environments.

Figure 4. Plasmon-induced hot-carrier distributions of silver nanoparticles embedded in different host materials.

We have also calculated the hot carrier distributions using a semiclassical approach (see the Supporting Information). The semiclassical hot carrier rates have a similar shape as the fully quantum-mechanical ones but a significantly larger magnitude. This is caused by (i) the actual transition dipole moments of LSPs in small nanoparticles being smaller than the classical result and (ii) the spectral weight of the LSP being reduced due to coupling to electron–hole pair excitations (see detailed discussion in ref (22).

Figure 5 shows the total number of hot carriers produced per unit time in embedded Ag nanoparticles. Large hot-carrier rates are generally obtained in environments with large dielectric constants (in particular, GaP and TiO₂), but for Ag₉₂ and Ag₂₅₄, the maximum rate is actually obtained in air.

Figure 5. Total hot-carrier generation rates of embedded Ag nanoparticles. The crosses indicate the environment where the highest hot-carrier rates are expected based on the analysis of the nanoparticle joint density of states, see Figure 6a,b.

To understand the observed trends, we separately analyze the two ingredients that determine hot-carrier rates according to Fermi’s golden rule, see eq 4: the number of available energy-conserving transitions, which is described by the joint density of states and the electron–plasmon coupling. For most hot-carrier applications, only hot electrons in bound states are relevant and we therefore restrict ourselves to the joint density of bound states (JDOBS). Figure 6a and Figure 6b show the JDOBS of Ag₆₈ and Ag₂₅₄ as function of the excitation energy, respectively. Because of the discreteness of the electronic energy levels, the JDOBS curves are oscillatory, but they exhibit an overall maximum near 3 eV. Therefore, the number of energy-conserving transitions is maximized when the LSP energy (denoted by vertical lines in the figure) coincides with the maximum of the JDOBS. For Ag₆₈, this is achieved when the nanoparticle is embedded in TiO₂, while for Ag₂₅₄, embedding in SiN is required. The environments that maximize the number of available transitions are denoted by crosses in Figure 5, and we observe that these environments indeed yield very large hot-carrier rates. The oscillatory nature of the JDOBS also explains why small changes in the environmental screening (and therefore in the LSP energy) can lead to large changes in hot-carrier rates.

Figure 6. Top: Joint density of bound states of (a) Ag₆₈ and (b) Ag₂₅₄. The vertical lines denote the localized surface plasmon energy of the nanoparticles embedded in different host materials (from left to right: air, SiN, SiO₂, TiO₂, and GaP). Bottom: Electron–plasmon coupling in (c) Ag₆₈ and (d) Ag₂₅₄ in different host materials as a function of transition energy.

Considering next the electron–plasmon coupling, one would naively expect that increased screening would reduce g_vc as the effective electron–electron interaction in eq 5 is weakened. Figure 6c and Figure 6d show that this trend is indeed followed in Ag₆₈ and Ag₂₅₄, respectively. However, this reduction in g_vc is not directly relevant to hot-carrier rates because the concomitant reduction of the LSP frequency leads to the excitation of different vc transitions with smaller energies. As the excitation energy decreases, the electron–plasmon coupling increases, see Figure 6c,d, and this explains the observed large hot-carrier rates in GaP in Figure 5.

Conclusions

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We have developed a quantum-mechanical approach for describing hot carriers resulting from the decay of localized surface plasmons in small silver nanoparticles that are embedded in dielectric media. Dielectric screening by the nanoparticle environment and by Ag d-electrons is taken into account by means of an effective electron–electron interaction, which is used to calculate electron–electron interaction matrix elements and electron–plasmon couplings. We find that hot-carrier generation rates depend sensitively on the environmental and internal screening. We demonstrate that hot-carrier production can be maximized by choosing the host material such that the LSP energy of the embedded nanoparticle coincides with the maximum of its joint density of states. Moreover, high hot-carrier generation rates are achieved in host materials with very large dielectric constants as the concomitant small LSP energies result in large electron–plasmon couplings. In this case, however, the hot carriers are less energetic. These insights can be used as design rules for creating efficient hot-carrier devices and open up the possibility of tailoring hot-carrier properties by dielectric engineering.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.0c07617.

Dependence of the absorption spectrum on ϵ_d and semiclassical hot carrier distributions (PDF)

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Author Information

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Corresponding Authors
- Ortwin Hess - Department of Physics, Imperial College London, London SW7 2AZ, U.K.; The Thomas Young Centre for Theory and Simulation of Materials, London E1 4NS, U.K.; School of Physics and CRANN Institute, Trinity College Dublin, Dublin 2, Ireland; http://orcid.org/0000-0002-6024-0677; Email: [email protected]
- Johannes Lischner - Department of Physics and Materials, Imperial College London, London SW7 2AZ, U.K.; The Thomas Young Centre for Theory and Simulation of Materials, London E1 4NS, U.K.; http://orcid.org/0000-0002-9601-7821; Email: [email protected]
Author
- Lara Román Castellanos - Department of Physics, Imperial College London, London SW7 2AZ, U.K.
Notes
The authors declare no competing financial interest.

Acknowledgments

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The authors acknowledge support from the Thomas Young Centre under grant no. TYC-101. This work was supported through a studentship in the Centre for Doctoral Training on Theory and Simulation of Materials at Imperial College London funded by the EPSRC (EP/L015579/1) and through EPSRC projects EP/L024926/1 and EP/L027151/1. Support by the Science Foundation Ireland (SFI) under grant 18/RP/6236 is gratefully acknowledged.

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Photocatalytic decompn. of a typical emerging pollutant perfluorooctanoic acid (PFOA) in aq. soln. by using noble metallic nanoparticles modified TiO2 (M-TiO2, M = Pt, Pd, Ag) were investigated. The M-TiO2 photocatalysts were obtained by chem. redn. method and were characterized by field emission scanning electron microscope with energy dispersive spectrometer, transmission electron microscopy, X-ray diffractometer system and UV-vis diffuse reflectance spectroscopy. Compared with pure TiO2, M-TiO2 exhibited higher activities for PFOA decompn. The rate consts. of pseudo-first-order kinetics for Pt, Pd, Ag modified TiO2 were 0.7267, 0.4369 and 0.1257 h-1, which were 12.5, 7.5 and 2.2 times higher than that for TiO2 resp. Shorter chain perfluorinated carboxylic acids were identified as main products. The great photo-activities of M-TiO2 were attributed to the noble metal nanoparticles, acting as electron sinks to store the excess electrons in conduction band when the holes in valence band were utilized in PFOA decompn. Noble metal with larger work function such as Pt and Pd were more effective to capture the electrons, thereby Pt-TiO2 and Pd-TiO2 showed higher photo-activities.
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Clavero, C. Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices. Nat. Photonics 2014, 8, 95– 103, DOI: 10.1038/nphoton.2013.238
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Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices
Clavero, Cesar
Nature Photonics (2014), 8 (2), 95-103CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
A review. Finding higher efficiency schemes for electron-hole sepn. is of paramount importance for realizing more efficient conversion of solar energy in photovoltaic and photocatalytic devices. Plasmonic energy conversion has been proposed as a promising alternative to conventional electron-hole sepn. in semiconductor devices. This emerging method is based on the generation of hot electrons in plasmonic nanostructures through electromagnetic decay of surface plasmons. Here, the fundamentals of hot-electron generation, injection and regeneration are reviewed, with special attention paid to recent progress towards photovoltaic devices. This new energy-conversion method potentially offers high conversion efficiencies, while keeping fabrication costs low. However, several considerations regarding the materials, architectures and fabrication methods used need to be carefully evaluated to advance this field.
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Anker, J. N.; Hall, W. P.; Lyandres, O.; Shah, N. C.; Zhao, J.; Van Duyne, R. P. Biosensing with plasmonic nanosensors. Nat. Mater. 2008, 7, 442– 453, DOI: 10.1038/nmat2162
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Biosensing with plasmonic nanosensors
Anker, Jeffrey N.; Hall, W. Paige; Lyandres, Olga; Shah, Nilam C.; Zhao, Jing; Van Duyne, Richard P.
Nature Materials (2008), 7 (6), 442-453CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
A review. Light incident on metallic nanoparticles can induce a collective motion of electrons that can lead to a strong amplification of the local electromagnetic field. As reviewed here, these plasmonic resonances have important applications in biosensing where they push resoln. and sensitivity towards the single-mol. detection limit. Recent developments have greatly improved the sensitivity of optical sensors based on metal nanoparticle arrays and single nanoparticles. The authors introduce the localized surface plasmon resonance (LSPR) sensor and describe how its exquisite sensitivity to size, shape and environment can be harnessed to detect mol. binding events and changes in mol. conformation. The authors then describe recent progress in three areas representing the most significant challenges: pushing sensitivity towards the single-mol. detection limit, combining LSPR with complementary mol. identification techniques such as surface-enhanced Raman spectroscopy, and practical development of sensors and instrumentation for routine use and high-throughput detection. This review highlights several exceptionally promising research directions and discusses how diverse applications of plasmonic nanoparticles can be integrated in the near future.
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Halas, N. J.; Lal, S.; Chang, W. S.; Link, S.; Nordlander, P. Plasmons in strongly coupled metallic nanostructures. Chem. Rev. 2011, 111, 3913– 3961, DOI: 10.1021/cr200061k
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Plasmons in Strongly Coupled Metallic Nanostructures
Halas, Naomi J.; Lal, Surbhi; Chang, Wei-Shun; Link, Stephan; Nordlander, Peter
Chemical Reviews (Washington, DC, United States) (2011), 111 (6), 3913-3961CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review examines the unique light-focusing properties of strongly coupled plasmonic systems, properties that resulted in an extraordinary increase in interest in these systems within the chem. community. It describes the concept of plasmon hybridization that takes advantage of the analogy between plasmons and the wave functions of simple quantum systems to provide a simple, intuitive explanation of the properties of complex plasmonic systems. It discusses coupled plasmonic systems where the classical electromagnetic description of coupled plasmons is no longer adequate and a quantum mech. description is necessary to understand their behavior.
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Wang, D.; Bourgeois, M. R.; Lee, W.-K.; Li, R.; Trivedi, D.; Knudson, M. P.; Wang, W.; Schatz, G. C.; Odom, T. W. Stretchable Nanolasing from Hybrid Quadrupole Plasmons. Nano Lett. 2018, 18, 4549– 4555, DOI: 10.1021/acs.nanolett.8b01774
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Stretchable Nanolasing from Hybrid Quadrupole Plasmons
Wang, Danqing; Bourgeois, Marc R.; Lee, Won-Kyu; Li, Ran; Trivedi, Dhara; Knudson, Michael P.; Wang, Weijia; Schatz, George C.; Odom, Teri W.
Nano Letters (2018), 18 (7), 4549-4555CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
A robust and stretchable nanolaser platform that can preserve its high mode quality by exploiting hybrid quadrupole plasmons as an optical feedback mechanism is reported. Increasing the size of metal nanoparticles in an array can introduce ultrasharp lattice plasmon resonances with out-of-plane charge oscillations that are tolerant to lateral strain. By patterning these nanoparticles onto an elastomeric slab surrounded by liq. gain, the authors realized reversible, tunable nanolasing with high strain sensitivity and no hysteresis. The semiquantum modeling demonstrates that lasing build-up occurs at the hybrid quadrupole electromagnetic hot spots, which provides a route toward mech. modulation of light-matter interactions on the nanoscale.
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Kolwas, K. Decay Dynamics of Localized Surface Plasmons: Damping of Coherences and Populations of the Oscillatory Plasmon Modes. Plasmonics 2019, 1629, DOI: 10.1007/s11468-019-00958-1
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Liu, T.; Besteiro, L. V.; Wang, Z.; Govorov, A. O. Generation of hot electrons in nanostructures incorporating conventional and unconventional plasmonic materials. Faraday Discuss. 2019, 214, 199– 213, DOI: 10.1039/C8FD00145F
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Generation of hot electrons in nanostructures incorporating conventional and unconventional plasmonic materials
Liu, Tianji; Besteiro, Lucas V.; Wang, Zhiming; Govorov, Alexander O.
Faraday Discussions (2019), 214 (Hot-Electron Science and Microscopic Processes in Plasmonics and Catalysis), 199-213CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
The generation of energetic electrons is an effect occurring in any plasmonic nanostructure. However, the no. of electrons with high energies generated optically in a plasmonic nanostructure can be relatively small. This is an intrinsic property of the collective plasmon excitations in a Fermi gas of electrons. But the choices of material and geometry have a great impact on the generation rate, and are therefore crucial for designing a nanostructure with a large rate of generation of energetic (hot) electrons. Here we test different plasmonic materials from the point of view of the generation of hot electrons (HEs). Our choice of materials includes both strongly-plasmonic materials (Au, Ag, Cu and Al) and crystals with strongly broadened plasmonic resonances (Pt, TiN and ZrN). Regarding the choice of geometry, we consider two types of nanostructures, single nanocrystals deposited over a dielec. substrate and metastructure absorbers, observing interesting opto-electronic properties. For single nanocrystals, the rate of HE generation is strongly material-dependent since the HE generation rate strongly depends on several phys. parameters such as plasmonic enhancement, plasmonic resonance wavelength, Fermi energy, etc. Interestingly, the plasmonic meta-absorbers exhibit a different behavior. The strongly-plasmonic metals, such as Au, Ag, Cu or Al, show very similar performances, while the materials with damped plasmon resonances demonstrate diverse and reduced rates of HE generation. The phys. reason for these different behaviors lies in the dielec. functions of these materials. In the metastructures, plasmonic resonances are in the IR region and the strongly-plasmonic materials behave as an almost ideal metal, whereas the second group of materials exhibits strong dissipation. This makes the responses from the metastructures made of crystals with damped plasmons strongly dependent on the choice of material. The phys. principles described in our study can be useful for designing metastructures and nanodevices based on HEs, which can be used in photo-chem. and opto-electronics.
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Besteiro, L. V.; Kong, X.-T.; Wang, Z.; Hartland, G.; Govorov, A. O. Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms. ACS Photonics 2017, 4, 2759– 2781, DOI: 10.1021/acsphotonics.7b00751
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Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms
Besteiro, Lucas V.; Kong, Xiang-Tian; Wang, Zhiming; Hartland, Gregory; Govorov, Alexander O.
ACS Photonics (2017), 4 (11), 2759-2781CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
Generation of energetic (hot) electrons is an intrinsic property of any plasmonic nanostructure under illumination. Simultaneously, a striking advantage of metal nanocrystals over semiconductors lies in their very large absorption cross sections. Therefore, metal nanostructures with strong and tailored plasmonic resonances are very attractive for photocatalytic applications in which excited electrons play an important role. However, the central questions in the problem of plasmonic hot electrons are the no. of optically-excited energetic electrons in a nanocrystal and how to ext. such electrons. Here we develop a theory describing the generation rates and the energy-distributions of hot electrons in nanocrystals with various geometries. In our theory, hot electrons are generated owing to surfaces and hot spots. As expected, the formalism predicts that large optically-excited nanocrystals show the excitation of mostly low-energy Drude electrons, whereas plasmons in small nanocrystals involve mostly high-energy (hot) electrons. We obtain anal. expressions for the distribution functions of excited carriers for simple shapes. For complex shapes and for small quantum nanocrystals, our results are computational. By looking at the energy distributions of electrons in an optically-excited nanocrystal, we see how the quantum many-body state in small particles evolves towards the classical state described by the Drude model when increasing nanocrystal size. We show that the rate of surface decay of plasmons in nanocrystals is directly related to the rate of generation of hot electrons. Based on a detailed many-body theory involving kinetic coeffs., we formulate a simple scheme describing how the plasmon in a nanocrystal dephases over time. In most nanocrystals, the main decay mechanism of a plasmon is the Drude friction-like process and the secondary path comes from generation of hot electrons due to surfaces and electromagnetic hot spots. The hot-electron path strongly depends on the material system and on its shape. Correspondingly, the efficiency of hot-electron prodn. in a nanocrystal strongly varies with size, shape and material. The results in the paper can be used to guide the design of plasmonic nanomaterials for photochem. and photodetectors.
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Naldoni, A.; Guler, U.; Wang, Z.; Marelli, M.; Malara, F.; Meng, X.; Besteiro, L. V.; Govorov, A. O.; Kildishev, A. V.; Boltasseva, A.; Shalaev, V. M. Broadband Hot-Electron Collection for Solar Water Splitting with Plasmonic Titanium Nitride. Adv. Opt. Mater. 2017, 5, 1601031, DOI: 10.1002/adom.201601031
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There is no corresponding record for this reference.
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Brown, A. M.; Sundararaman, R.; Narang, P.; Goddard, W. A., III; Atwater, H. A. Non-Radiative Plasmon Decay and Hot Carrier Dynamics: Effects of Phonons, Surfaces and Geometry. ACS Nano 2016, 10, 957, DOI: 10.1021/acsnano.5b06199
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Nonradiative Plasmon Decay and Hot Carrier Dynamics: Effects of Phonons, Surfaces, and Geometry
Brown, Ana M.; Sundararaman, Ravishankar; Narang, Prineha; Goddard, William A.; Atwater, Harry A.
ACS Nano (2016), 10 (1), 957-966CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
The behavior of metals across a broad frequency range from microwave to UV frequencies is of interest in plasmonics, nanophotonics, and metamaterials. Depending on the frequency, losses of collective excitations in metals can be predominantly classical resistive effects or Landau damping. In this context, we present first-principles calcns. that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. Specifically, we include ab initio predictions of phonon-assisted optical excitations in metals, which are crit. to bridging the frequency range between resistive losses at low frequencies and direct interband transitions at high frequencies. In the commonly used plasmonic materials, gold, silver, copper, and aluminum, we find that resistive losses compete with phonon-assisted carrier generation below the interband threshold, but hot carrier generation via direct transitions dominates above threshold. Finally, we predict energy-dependent lifetimes and mean free paths of hot carriers, accounting for electron-electron and electron-phonon scattering, to provide insight toward transport of plasmonically generated carriers at the nanoscale.
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Raza, S.; Kadkhodazadeh, S.; Christensen, T.; Di Vece, M.; Wubs, M.; Mortensen, N. A.; Stenger, N. Multipole plasmons and their disappearance in few-nanometre silver nanoparticles. Nat. Commun. 2015, 6, 8788, DOI: 10.1038/ncomms9788
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Multipole plasmons and their disappearance in few-nanometer silver nanoparticles
Raza, Soeren; Kadkhodazadeh, Shima; Christensen, Thomas; Di Vece, Marcel; Wubs, Martijn; Mortensen, N. Asger; Stenger, Nicolas
Nature Communications (2015), 6 (), 8788CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
Electron energy-loss spectroscopy can be used for detailed spatial and spectral characterization of optical excitations in metal nanoparticles. In previous electron energy-loss expts. on silver nanoparticles with radii smaller than 20 nm, only the dipolar surface plasmon resonance was assumed to play a role. Here, applying electron energy-loss spectroscopy to individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an addnl. surface plasmon resonance corresponding to higher angular momenta for nanoparticle radii as small as 4 nm. We study the radius and electron beam impact position dependence of both resonances sep. For particles smaller than 4 nm in radius the higher-order surface plasmon mode disappears, in agreement with generalized non-local optical response theory, while the dipole resonance blue shift exceeds our theor. predictions. Unlike in optical spectra, multipole surface plasmons are important in electron energy-loss spectra even of ultrasmall metallic nanoparticles.
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Mittal, R.; Glenn, R.; Saytashev, I.; Lozovoy, V. V.; Dantus, M. Femtosecond nanoplasmonic dephasing of individual silver nanoparticles and small clusters. J. Phys. Chem. Lett. 2015, 6, 1638– 1644, DOI: 10.1021/acs.jpclett.5b00264
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Femtosecond Nanoplasmonic Dephasing of Individual Silver Nanoparticles and Small Clusters
Mittal, Richa; Glenn, Rachel; Saytashev, Ilyas; Lozovoy, Vadim V.; Dantus, Marcos
Journal of Physical Chemistry Letters (2015), 6 (9), 1638-1644CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
The authors present exptl. measurements of localized surface plasmon emission from individual Ag nanoparticles and small clusters via accurately delayed femtosecond laser pulses. Fourier transform anal. of the nanoplasmonic coherence oscillations reveals different frequency components and dephasing rates for each nanoparticle. Three different types of behavior: single exponential decay, beating between 2 frequencies, and beating among ≥3 frequencies were found. Results provide insight into inhomogeneous and homogeneous broadening mechanisms in nanoplasmonic spectroscopy that depend on morphol. and nearby neighbors. The optical response of certain pairs of nanoparticles to be at least an order of magnitude more intense than the response of single particles were found.
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Crut, A.; Maioli, P.; Del Fatti, N.; Vallée, F. Optical absorption and scattering spectroscopies of single nano-objects. Chem. Soc. Rev. 2014, 43, 3921– 3956, DOI: 10.1039/c3cs60367a
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Optical absorption and scattering spectroscopies of single nano-objects
Crut, Aurelien; Maioli, Paolo; Del Fatti, Natalia; Vallee, Fabrice
Chemical Society Reviews (2014), 43 (11), 3921-3956CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
A review. Developments of optical detection and spectroscopy methods for single nano-objects are key advances for applications and fundamental understanding of the novel properties exhibited by nanosize systems. These methods are reviewed, focusing on far-field optical approaches based on light absorption and elastic scattering. The principles of the main linear and nonlinear methods are described and exptl. results are illustrated in the case of metal nanoparticles, stressing the key role played by the object environment, such as the presence of a substrate, bound surface mols. or other nano-objects. Special attention is devoted to quant. methods and correlation of the measured optical spectra of a nano-object with its morphol., characterized either optically or by electron microscopy, as this permits precise comparison with theor. models. Application of these methods to optical detection and spectroscopy for single semiconductor nanowires and carbon nanotubes is also presented. Extension to ultrafast nonlinear extinction or scattering spectroscopies of single nano-objects is finally discussed in the context of investigation of their nonlinear optical response and their electronic, acoustic and thermal properties.
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Codrington, J.; Eldabagh, N.; Fernando, K.; Foley, J. J., IV Unique hot carrier distributions from scattering-mediated absorption. ACS Photonics 2017, 4, 552– 559, DOI: 10.1021/acsphotonics.6b00773
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Unique Hot Carrier Distributions from Scattering-Mediated Absorption
Codrington, Jason; Eldabagh, Noor; Fernando, Kimberly; Foley, Jonathan J.
ACS Photonics (2017), 4 (3), 552-559CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
Light-initiated generation of energetic carriers has attracted considerable attention as a paradigm for photocatalysis and solar energy conversion, and the use of noble metal nanoparticles that support localized surface plasmon resonances has been widely explored as a medium for realizing this paradigm. It was recently shown that composite nanostructures enabling the interplay between dielec. scattering resonances and broadband absorption in small metal nanostructures, a phenomenon termed scattering-mediated absorption, can be used to mediate energetic carrier transfer and selective photochem. with low-intensity light while completely circumventing plasmon resonance. In this work, we develop a multiscale modeling approach for elucidating the hot carrier dynamics initiated by scattering-mediated absorption. Our calcns. reveal that unique hot carrier distributions and dynamics arise from scattering-mediated absorption as compared to plasmon excitation and also suggest that in a variety of circumstances scattering-mediated absorption may lead to more efficient hot carrier generation compared to plasmon resonance under the same external illumination conditions. These results are an important first step in understanding the phenomena of scattering-mediated hot carrier generation, which has potential for expanding the palette of materials that can be utilized for hot carrier mediated photochem. beyond plasmonic metals and for enabling unique pathways for photocatalytic transformations.
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Kreibig, U.; Schmitz, B.; Breuer, H. D. Separation of plasmon-polariton modes of small metal particles. Phys. Rev. B 1987, 36, 5027– 5030, DOI: 10.1103/PhysRevB.36.5027
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Separation of plasmon-polariton modes of small metal particles
Kreibig; Schmitz; Breuer
Physical review. B, Condensed matter (1987), 36 (9), 5027-5030 ISSN:0163-1829.
There is no expanded citation for this reference.
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Zong, R.-L.; Zhou, J.; Li, B.; Fu, M.; Shi, S.-K.; Li, L.-T. Optical properties of transparent copper nanorod and nanowire arrays embedded in anodic alumina oxide. J. Chem. Phys. 2005, 123, 094710 DOI: 10.1063/1.2018642
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Optical properties of transparent copper nanorod and nanowire arrays embedded in anodic alumina oxide
Zong, Rui-Long; Zhou, Ji; Li, Bo; Fu, Ming; Shi, Shi-Kao; Li, Long-Tu
Journal of Chemical Physics (2005), 123 (9), 094710/1-094710/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Transparent Cu nanorod/nanowire arrays and anodic alumina oxide composite films were prepd. by a.c. electrodeposition, and their linear optical properties were systematically characterized by absorption spectra. In the exptl. spectra, there exist transverse and longitudinal resonance peaks, which are caused by the surface-plasmon resonance along the diam. and the length of the Cu nanorods, resp. The transverse resonance peak is affected by the diam. and aspect ratio of the nanorod. The longitudinal resonance peak appears at longer wavelength when a polarized light illuminates the film with an angle of incidence of ∼70°, where the angle is defined with respect to the surface normal. Also, the longitudinal resonance mode is sensitive to the polarization direction when compared with the transverse resonance mode.
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Rubio, A.; Serra, L. Dielectric screening effects on the photoabsorption cross section of embedded metallic clusters. Phys. Rev. B 1993, 48, 18222– 18229, DOI: 10.1103/PhysRevB.48.18222
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Dielectric screening effects on the photoabsorption cross section of embedded metallic clusters
Rubio, Angel; Serra, Llorenc
Physical Review B: Condensed Matter and Materials Physics (1993), 48 (24), 18222-9CODEN: PRBMDO; ISSN:0163-1829.
The surface plasmon resonance of alkali-metal (potassium) and noble-metal (silver) clusters embedded in different dielec. matrixes is studied within the time-dependent d.-functional formalism and the jellium model, including dielec. screening for the electron-electron interaction. The calcd. red shift of the plasma frequency as the dielec. const. (ε) of the matrix increases is in good agreement with the available exptl. data for both potassium and silver clusters. In the case of potassium, the shifts induced by rare-gas matrixes are predicted. A tendency to satn. in the polarizability and surface plasmon resonance when ε increases is obtained and is due to the screening of the Coulomb interaction by the dielec. surrounding the cluster. It was concluded that the basic effect of the dielec. matrix comes from the direct screening of the electron-electron interaction and not from the modification of the cluster ground state.
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Campos, A.; Troc, N.; Cottancin, E.; Pellarin, M.; Weissker, H. C.; Lermé, J.; Kociak, M.; Hillenkamp, M. Plasmonic quantum size effects in silver nanoparticles are dominated by interfaces and local environments. Nat. Phys. 2019, 15, 275– 280, DOI: 10.1038/s41567-018-0345-z
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Plasmonic quantum size effects in silver nanoparticles are dominated by interfaces and local environments
Campos, Alfredo; Troc, Nicolas; Cottancin, Emmanuel; Pellarin, Michel; Weissker, Hans-Christian; Lerme, Jean; Kociak, Mathieu; Hillenkamp, Matthias
Nature Physics (2019), 15 (3), 275-280CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)
The phys. properties of metals change when their dimensions are reduced to the nano-scale and new phenomena such as the localized surface-plasmon resonance (LSPR) appear. This collective electronic excitation can be tuned over a large spectral range by adapting the material, size and shape. The existing literature is as rich as it is controversial-for example, size-dependent spectral shifts of the LSPR in small metal nanoparticles, induced by quantum effects, are reported to the red, to the blue or entirely absent. Here we report how complementary expts. on size-selected small silver nanoparticles embedded in silica can yield inconsistent results on the same system: whereas optical absorption shows no size effect in the range between only a few atoms and ~ 10 nm, a clear spectral shift is obsd. in single-particle electron spectroscopy. Our quant. interpretation, based on a mixed classical/quantum model, resolves the apparent contradictions, not only within our exptl. data, but also in the literature. Our comprehensive model describes how the local environment is the crucial parameter controlling the manifestation or absence of quantum size effects.
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Román Castellanos, L.; Hess, O.; Lischner, J. Single plasmon hot carrier generation in metallic nanoparticles. Commun. Phys. 2019, 2, 47, DOI: 10.1038/s42005-019-0148-2
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Deng, S. Electrostatic potential of point charges inside dielectric oblate spheroids. J. Electrost. 2009, 67, 807– 814, DOI: 10.1016/j.elstat.2009.06.007
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Electrostatic potential of point charges inside dielectric oblate spheroids
Deng Shaozhong
Journal of electrostatics (2009), 67 (5), 807-814 ISSN:0304-3886.
As a sequel to a previous paper on electrostatic potential of point charges inside dielectric prolate spheroids [J. Electrostatics 66 (2008) 549-560], this note further presents the exact solution to the electrostatic problem of finding the electric potential of point charges inside a dielectric oblate spheroid that is embedded in a dissimilar dielectric medium. Numerical experiments have demonstrated the convergence of the proposed series solutions.
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Kirkwood, J. G. Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J. Chem. Phys. 1934, 2, 351– 361, DOI: 10.1063/1.1749489
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Theory of solutions of molecules containing widely separated charges with special application to amphoteric ions
Kirkwood, John G.
Journal of Chemical Physics (1934), 2 (), 351-61CODEN: JCPSA6; ISSN:0021-9606.
The elec. contribution to the chem. potential of an ion having an arbitrary charge distribution is calcd. from the Debye-H.ovrddot.uckel theory, and the Born relation between the free energy of solvation of a spherical ion and the dielec. const. of the solvent is generalized to include ions of arbitrary charge distribution. The theory gives an approx. account of the soly. of glycine in EtOHH2O mixts., both in the presence and absence of salts, as long as the glycine concn. is small, and gives reasonable values for the dipole moment and size of the amphoteric ion.
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Serra, L.; Rubio, A. Core polarization in the optical response of metal clusters: Generalized time-dependent density-functional theory. Phys. Rev. Lett. 1997, 78, 1428– 1431, DOI: 10.1103/PhysRevLett.78.1428
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Core polarization in the optical response of metal clusters: generalized time-dependent density-functional theory
Serra, Llorenc; Rubio, Angel
Physical Review Letters (1997), 78 (8), 1428-1431CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
The authors present a generalized time-dependent d.-functional theory (TDDFT) for the optical response of metal clusters where both core polarization and valence responses are treated microscopically. The valence electrons response is described by an effective external field and residual interaction that are those of the std. TDDFT modified by the self-consistent contributions of the array of polarizable ionic cores. As an application the equations are solved within the adiabatic local-d. approxn. for Ag clusters, where core 4d electrons greatly influence the optical response. The exptl. data are well reproduced by the present theory.
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Toyoda, M.; Ozaki, T. LIBERI: Library for numerical evaluation of electron-repulsion integrals. Comput. Phys. Commun. 2010, 181, 1455– 1463, DOI: 10.1016/j.cpc.2010.03.019
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LIBERI: library for numerical evaluation of electron-repulsion integrals
Toyoda, Masayuki; Ozaki, Taisuke
Computer Physics Communications (2010), 181 (8), 1455-1463CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
We provide a C library, called LIBERI, for numerical evaluation of four-center electron repulsion integrals, based on successive redn. of integral dimension by using Fourier transforms. LIBERI enables us to compute the integrals for numerically defined basis functions within 10-5 Hartree accuracy as well as their derivs. with respect to the at. nuclear positions. Damping of the Coulomb interaction can also be imposed to take account of screening effect.
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Khurgin, J. B.; Levy, U. Generating Hot Carriers in Plasmonic Nanoparticles: When Quantization Does Matter?. ACS Photonics 2020, 547– 553, DOI: 10.1021/acsphotonics.9b01774
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Generating Hot Carriers in Plasmonic Nanoparticles: When Quantization Does Matter?
Khurgin, Jacob B.; Levy, Uriel
ACS Photonics (2020), 7 (3), 547-553CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
Plasmon-assisted hot carrier processes in metal nanoparticles can be described either classically or using the full strength of quantum mechanics. We reconfirm that from the practical applications point of view, when it comes to description of the decay of plasmons in nanoparticles, classical description is sufficiently adequate for all but the smallest of the nanoparticles. At the same time, the electron temp. rise in nanoparticles is discrete (quantized), and neglecting this fact can lead to significant underestimating of hot carrier assisted effects such as photocatalysis.
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Bernardi, M.; Mustafa, J.; Neaton, J. B.; Louie, S. G. Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals. Nat. Commun. 2015, 6, 7044, DOI: 10.1038/ncomms8044
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Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals
Bernardi, Marco; Mustafa, Jamal; Neaton, Jeffrey B.; Louie, Steven G.
Nature Communications (2015), 6 (), 7044CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
Hot carriers (HC) generated by surface plasmon polaritons (SPPs) in noble metals are promising for application in optoelectronics, plasmonics and renewable energy. However, existing models fail to explain key quant. details of SPP-to-HC conversion expts. Here we develop a quantum mech. framework and apply first-principles calcns. to study the energy distribution and scattering processes of HCs generated by SPPs in Au and Ag. We find that the relative positions of the s and d bands of noble metals regulate the energy distribution and mean free path of the HCs, and that the electron-phonon interaction controls HC energy loss and transport. Our results prescribe optimal conditions for HC generation and extn., and invalidate previously employed free-electron-like models. Our work combines d. functional theory, GW and electron-phonon calcns. to provide microscopic insight into HC generation and ultrafast dynamics in noble metals.
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Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133– A1138, DOI: 10.1103/PhysRev.140.A1133
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Perdew, J. P.; Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 1981, 23, 5048– 5079, DOI: 10.1103/PhysRevB.23.5048
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Perdew, J. P.; Zunger, Alex
Physical Review B: Condensed Matter and Materials Physics (1981), 23 (10), 5048-79CODEN: PRBMDO; ISSN:0163-1829.
The exact d. functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approxns. to it, including the local-spin-d. (LSD) approxn. for exchange and correlation, are not. Two related methods are given for the self-interaction correction (SIC) of any d. functional for the energy; correction of the self-consistent one-electron potential follows naturally from the variational principle. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. The 1st method was applied to LSD, it properly conserves the no. content of the exchange-correlation hole, while substantially improving the description of its shape. The LSD spin splitting in at. Ni and s-d interconfigurational energies of transition elements are almost unchanged by SIC.
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Time-dependent current-density-functional theory for the metallic response of solids
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Physical Review B: Condensed Matter and Materials Physics (2005), 71 (15), 155108/1-155108/17CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We extend the formulation of time-dependent current-d.-functional theory for the linear response properties of dielec. and semimetallic solids [Kootstra et al., J. Chem. Phys. 112, 6517 (2000)] to treat metals as well. To achieve this, the Kohn-Sham response functions have to include both interband and intraband transitions with an accurate treatment of the Fermi surface in the Brillouin-zone integrations. The intraband contributions in particular have to be evaluated using a wave-vector-dependent description. To test the method we calc. the optical properties of the two noble metals Cu and Ag. The dielec. and energy loss functions are compared with expts. and with the classical Drude theory. In general we find a good agreement with the expts. for the calcd. results obtained within the adiabatic local d. approxn. In order to describe the Drude-like absorption below the interband onset and the sharp plasma feature in silver exchange-correlation, effects beyond the adiabatic local d. approxn. are needed, which may be included in a natural way in the present current-d.-functional approach.
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Physical Review B: Condensed Matter and Materials Physics (2000), 61 (12), 8033-8042CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The delicate interplay between plasmonic excitations and interband transitions in noble metals is described by ab initio calcns. and a simple model in which the conduction electron plasmon is coupled to the continuum of electron-hole pairs. Band-structure effects, esp. the energy at which the excitation of the d-like bands takes place, det. the existence of a threshold plasmonic mode, which manifests itself in Ag as a sharp resonance exptl. obsd. at 3.8 eV. However, such a resonance does not appear in the spectra of the other noble metals. Here this different behavior is also analyzed, and an explanation is provided.
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Journal of Chemical Theory and Computation (2017), 13 (10), 4779-4790CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Electronic excitations can be efficiently analyzed in terms of the underlying Kohn-Sham (KS) electron-hole transitions. While such a decompn. is readily available in the linear-response time-dependent d.-functional theory (TDDFT) approaches based on the Casida equations, a comparable anal. is less commonly conducted within the real-time-propagation TDDFT (RT-TDDFT). To improve this situation, we present here an implementation of a KS decompn. tool within the local-basis-set RT-TDDFT code in the free GPAW package. Our implementation is based on postprocessing of data that is readily available during time propagation, which is important for retaining the efficiency of the underlying RT-TDDFT to large systems. After benchmarking our implementation on small benzene derivs. by explicitly reconstructing the Casida eigenvectors from RT-TDDFT, we demonstrate the performance of the method by analyzing the plasmon resonances of icosahedral silver nanoparticles up to Ag561. The method provides a clear description of the splitting of the plasmon in small nanoparticles due to individual single-electron transitions as well as the formation of a distinct d-electron-screened plasmon resonance in larger nanoparticles.
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Understanding the interplay between illumination and the electron distribution in metallic nanostructures is a crucial step towards developing applications such as plasmonic photocatalysis for green fuels, nanoscale photodetection and more. Elucidating this interplay is challenging, as it requires taking into account all channels of energy flow in the electronic system. Here, we develop such a theory, which is based on a coupled Boltzmann-heat equations and requires only energy conservation and basic thermodynamics, where the electron distribution, and the electron and phonon (lattice) temperatures are determined uniquely. Applying this theory to realistic illuminated nanoparticle systems, we find that the electron and phonon temperatures are similar, thus justifying the (classical) single-temperature models. We show that while the fraction of high-energy "hot" carriers compared to thermalized carriers grows substantially with illumination intensity, it remains extremely small (on the order of 10(-8)). Importantly, most of the absorbed illumination power goes into heating rather than generating hot carriers, thus rendering plasmonic hot carrier generation extremely inefficient. Our formulation allows for the first time a unique quantitative comparison of theory and measurements of steady-state electron distributions in metallic nanostructures.
37
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The optical response of free and matrix-embedded Au metal clusters AuN was studied in the framework of the time-dependent local-d.-approxn. (TDLDA). The characteristics of the surface plasmon resonance are carefully analyzed as a function of the model parameters and the particle radius. The strong influence of the frequency-dependence of the 5d core-electron dielec. function in the vicinity of the interband threshold is emphasized. The size evolution of the Mie-frequency in free Au clusters exhibits a noticeable blue-shift trend as the particle size decreases, much stronger than in Ag clusters. The width and shape of the resonance, essentially ruled by the decay via the interband transitions, are found closely correlated to the imaginary component of the core-electron dielec. function. In presence of a surrounding matrix the blue-shift trend is largely rubbed out. Agreement with recent exptl. results on size-selected Au clusters embedded in an alumina matrix may be achieved by taking into account the porosity effects at the metal/matrix interface. The comparison with the predictions of classical models is also provided.
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The evolution toward the bulk values of the energy centroid and of the width characterizing the surface-plasmon resonance in spherical neutral sodium clusters is studied. For this purpose, the photoabsorption spectrum of clusters comprising from 8 to 338 atoms is calcd. microscopically making use of the jellium shell model to describe the motion of delocalized electrons and of the matrix RPA to det. the collective response of the system to electromagnetic radiation. The Coulomb force is treated in the local-d. approxn. The case of large potassium clusters having approx. 500 and 900 atoms is also considered.
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Nano Letters (2013), 13 (1), 240-247CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
Heterogeneous catalysis is of paramount importance in chem. and energy applications. Catalysts that couple light energy into chem. reactions in a directed, orbital-specific manner would greatly reduce the energy input requirements of chem. transformations, revolutionizing catalysis-driven chem. Here we report the room temp. dissocn. of H2 on gold nanoparticles using visible light. Surface plasmons excited in the Au nanoparticle decay into hot electrons with energies between the vacuum level and the work function of the metal. In this transient state, hot electrons can transfer into a Feshbach resonance of an H2 mol. adsorbed on the Au nanoparticle surface, triggering dissocn. We probe this process by detecting the formation of HD mols. from the dissocns. of H2 and D2 and investigate the effect of Au nanoparticle size and wavelength of incident light on the rate of HD formation. This work opens a new pathway for controlling chem. reactions on metallic catalysts.
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The plasmon resonances of metallic nanoparticles have received considerable attention for their applications in nanophotonics, biol., sensing, spectroscopy and solar energy harvesting. Although thoroughly characterized for spheres larger than 10 nm in diam., the plasmonic properties of particles in the quantum size regime were historically difficult to describe owing to weak optical scattering, metal-ligand interactions, and inhomogeneity in ensemble measurements. Such difficulties have precluded probing and controlling the plasmonic properties of quantum-sized particles in many natural and engineered processes, notably catalysis. The plasmon resonances of individual ligand-free Ag nanoparticles was studied using aberration-cor. TEM imaging and monochromated scanning TEM EELS. This technique allows direct correlation between a particle's geometry and its plasmon resonance. As the nanoparticle diam. decreases from 20 to <2 nm, the plasmon resonance shifts to higher energy by 0.5 eV, a substantial deviation from classical predictions. An anal. quantum mech. model that describes this shift due to a change in particle permittivity is presented. The results highlight the quantum plasmonic properties of small metallic nanospheres, with direct application to understanding and exploiting catalytically active and biol. relevant nanoparticles.
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The authors present novel exptl. results about influences of surrounding foreign materials on optical properties of small Ag clusters. The authors show spectra of free cluster beams produced with different seeding gases Ar, Kr, Xe. The authors est., from measured spectra, the cluster deformations and contact areas after deposition on different substrates (Cr2O3 and MgF2) at room temp. and on SiO2 at 110 K and at 160 - 300 K. The authors present and compare the static and dynamic charge transfer after embedding the clusters in various fluorides and compare with previous results on oxides.

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Abstract
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Figure 1
Figure 1. Left: Absorption spectra of Ag nanoparticles in air with (purple curves) and without (green curves) d-electron screening as function of photon energy: (a) Ag₂₅₄, (b) Ag₁₃₈, (c) Ag₉₂, and (d) Ag₆₈. Right: Plasmon-induced hot carrier distributions (HCD) of Ag nanoparticles in air with and without d-electron screening as function of hot-carrier energy: (e) Ag₂₅₄, (f) Ag₁₃₈, (g) Ag₉₂, and (h) Ag₆₈. Note that the screened results have been rescaled by the indicated factors, and the dotted vertical lines denote the Fermi level.
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Figure 2
Figure 2. Absorption spectra of (a) Ag₂₅₄, (b) Ag₁₃₈, (c) Ag₉₂, and (d) Ag₆₈ embedded in SiO₂ (ϵ₁ = 2.16 from ref (21), SiN (ϵ₁ = 3.2 from ref (14), TiO₂ (ϵ₁ = 8.2 from ref (39), and GaP (ϵ₁ = 20.2 from ref (40).
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Figure 3
Figure 3. Localized surface plasmon energy of silver nanoparticles embedded in SiO₂ (ϵ₁ = 2.16 from ref (21), SiN (ϵ₁ = 3.2 from ref (14), TiO₂ (ϵ₁ = 8.2 from ref (39), and GaP (ϵ₁ = 20.2 from ref (40).
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Figure 4
Figure 4. Plasmon-induced hot-carrier distributions of silver nanoparticles embedded in different host materials.
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Figure 5
Figure 5. Total hot-carrier generation rates of embedded Ag nanoparticles. The crosses indicate the environment where the highest hot-carrier rates are expected based on the analysis of the nanoparticle joint density of states, see Figure 6a,b.
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Figure 6
Figure 6. Top: Joint density of bound states of (a) Ag₆₈ and (b) Ag₂₅₄. The vertical lines denote the localized surface plasmon energy of the nanoparticles embedded in different host materials (from left to right: air, SiN, SiO₂, TiO₂, and GaP). Bottom: Electron–plasmon coupling in (c) Ag₆₈ and (d) Ag₂₅₄ in different host materials as a function of transition energy.
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References
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  Saavedra, J. R. M.; Asenjo-Garcia, A.; de Abajo, F. J. G. Hot-Electron Dynamics and Thermalization in Small Metallic Nanoparticles. ACS Photonics 2016, 3, 1637– 1646, DOI: 10.1021/acsphotonics.6b00217
  1
  Hot-Electron Dynamics and Thermalization in Small Metallic Nanoparticles
  Saavedra, J. R. M.; Asenjo-Garcia, Ana; Garcia de Abajo, F. Javier
  ACS Photonics (2016), 3 (9), 1637-1646CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
  The important role played by hot electrons in photocatalysis and light harvesting has attracted great interest in their dynamics and mechanisms of generation. Here, we theor. study the temporal evolution of optically excited conduction electrons in small plasmon-supporting gold and silver nanoparticles. We describe the electron dynamics through a master equation incorporating transition rates for optical excitations and electron-electron collisions that are calcd. using the screened interaction within an independent-electron picture. Upon optical excitation of the particle by a light pulse, a nonthermal electron distribution is produced, which takes 10s fs to thermalize at an elevated electron temp. due to electron-electron collisions and eventually relaxes back to ambient temp. via coupling to phonons and thermal diffusion. Phonons and diffusion are introduced through a phenomenol. inelastic attenuation rate. We find the temporal evolution of the electron energy distribution to strongly depend on the total absorbed energy, which is in turn detd. by particle size, pulse fluence, and photon energy. Our results provide detailed insight into hot-electron dynamics that can be beneficial for the design of improved photocatalysis and photodetection devices.
2. 2
  Zhang, R.; Bursi, L.; Cox, J. D.; Cui, Y.; Krauter, C. M.; Alabastri, A.; Manjavacas, A.; Calzolari, A.; Corni, S.; Molinari, E.; Carter, E. A.; de Abajo, F. J. G.; Zhang, H.; Nordlander, P. How To Identify Plasmons from the Optical Response of Nanostructures. ACS Nano 2017, 11, 7321– 7335, DOI: 10.1021/acsnano.7b03421
  2
  How To Identify Plasmons from the Optical Response of Nanostructures
  Zhang, Runmin; Bursi, Luca; Cox, Joel D.; Cui, Yao; Krauter, Caroline M.; Alabastri, Alessandro; Manjavacas, Alejandro; Calzolari, Arrigo; Corni, Stefano; Molinari, Elisa; Carter, Emily A.; Garcia de Abajo, F. Javier; Zhang, Hui; Nordlander, Peter
  ACS Nano (2017), 11 (7), 7321-7335CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
  A promising trend in plasmonics involves shrinking the size of plasmon-supporting structures down to a few nanometers, thus enabling control over light-matter interaction at extreme-subwavelength scales. In this limit, quantum mech. effects, such as nonlocal screening and size quantization, strongly affect the plasmonic response, rendering it substantially different from classical predictions. For very small clusters and mols., collective plasmonic modes are hard to distinguish from other excitations such as single-electron transitions. Using rigorous quantum mech. computational techniques for a wide variety of phys. systems, we describe how an optical resonance of a nanostructure can be classified as either plasmonic or nonplasmonic. More precisely, we define a universal metric for such classification, the generalized plasmonicity index (GPI), which can be straightforwardly implemented in any computational electronic-structure method or classical electromagnetic approach to discriminate plasmons from single-particle excitations and photonic modes. Using the GPI, we investigate the plasmonicity of optical resonances in a wide range of systems including: the emergence of plasmonic behavior in small jellium spheres as the size and the no. of electrons increase; at.-scale metallic clusters as a function of the no. of atoms; and nanostructured graphene as a function of size and doping down to the mol. plasmons in polycyclic arom. hydrocarbons. Our study provides a rigorous foundation for the further development of ultrasmall nanostructures based on mol. plasmonics.
3. 3
  Hartland, G. V.; Besteiro, L. V.; Johns, P.; Govorov, A. O. What’s so Hot about Electrons in Metal Nanoparticles?. ACS Energy Lett. 2017, 2, 1641– 1653, DOI: 10.1021/acsenergylett.7b00333
  3
  What's so Hot about Electrons in Metal Nanoparticles?
  Hartland, Gregory V.; Besteiro, Lucas V.; Johns, Paul; Govorov, Alexander O.
  ACS Energy Letters (2017), 2 (7), 1641-1653CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
  A review. Metal nanoparticles are excellent light absorbers. The absorption processes create highly excited electron-hole pairs, and recently there has been interest in harnessing these hot charge carriers for photocatalysis and solar energy conversion applications. The goal of this Perspective is to describe the dynamics and energy distribution of the charge carriers produced by photon absorption and the implications for the photocatalysis mechanism. The authors will also discuss how spectroscopy can be used to provide insight into the coupling between plasmons and mol. resonances. In particular, the anal. shows that the choice of material and shape of the nanocrystal can play a crucial role in hot electron generation and coupling between plasmons and mol. transitions. The detection and even calcn. of many-body hot-electron processes in the plasmonic systems with continuous spectra of electrons and short lifetimes are challenging, but at the same time they are very interesting from the points of view of both potential applications and fundamental science. The authors propose that developing an understanding of these processes will provide a pathway for improving the efficiency of plasmon-induced photocatalysis.
4. 4
  Li, M.; Yu, Z.; Liu, Q.; Sun, L.; Huang, W. Photocatalytic decomposition of perfluorooctanoic acid by noble metallic nanoparticles modified TiO₂. Chem. Eng. J. 2016, 286, 232– 238, DOI: 10.1016/j.cej.2015.10.037
  4
  Photocatalytic decomposition of perfluorooctanoic acid by noble metallic nanoparticles modified TiO2
  Li, Mingjie; Yu, Zebin; Liu, Qing; Sun, Lei; Huang, Wenyu
  Chemical Engineering Journal (Amsterdam, Netherlands) (2016), 286 (), 232-238CODEN: CMEJAJ; ISSN:1385-8947. (Elsevier B.V.)
  Photocatalytic decompn. of a typical emerging pollutant perfluorooctanoic acid (PFOA) in aq. soln. by using noble metallic nanoparticles modified TiO2 (M-TiO2, M = Pt, Pd, Ag) were investigated. The M-TiO2 photocatalysts were obtained by chem. redn. method and were characterized by field emission scanning electron microscope with energy dispersive spectrometer, transmission electron microscopy, X-ray diffractometer system and UV-vis diffuse reflectance spectroscopy. Compared with pure TiO2, M-TiO2 exhibited higher activities for PFOA decompn. The rate consts. of pseudo-first-order kinetics for Pt, Pd, Ag modified TiO2 were 0.7267, 0.4369 and 0.1257 h-1, which were 12.5, 7.5 and 2.2 times higher than that for TiO2 resp. Shorter chain perfluorinated carboxylic acids were identified as main products. The great photo-activities of M-TiO2 were attributed to the noble metal nanoparticles, acting as electron sinks to store the excess electrons in conduction band when the holes in valence band were utilized in PFOA decompn. Noble metal with larger work function such as Pt and Pd were more effective to capture the electrons, thereby Pt-TiO2 and Pd-TiO2 showed higher photo-activities.
5. 5
  Clavero, C. Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices. Nat. Photonics 2014, 8, 95– 103, DOI: 10.1038/nphoton.2013.238
  5
  Plasmon-induced hot-electron generation at nanoparticle/metal-oxide interfaces for photovoltaic and photocatalytic devices
  Clavero, Cesar
  Nature Photonics (2014), 8 (2), 95-103CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
  A review. Finding higher efficiency schemes for electron-hole sepn. is of paramount importance for realizing more efficient conversion of solar energy in photovoltaic and photocatalytic devices. Plasmonic energy conversion has been proposed as a promising alternative to conventional electron-hole sepn. in semiconductor devices. This emerging method is based on the generation of hot electrons in plasmonic nanostructures through electromagnetic decay of surface plasmons. Here, the fundamentals of hot-electron generation, injection and regeneration are reviewed, with special attention paid to recent progress towards photovoltaic devices. This new energy-conversion method potentially offers high conversion efficiencies, while keeping fabrication costs low. However, several considerations regarding the materials, architectures and fabrication methods used need to be carefully evaluated to advance this field.
6. 6
  Anker, J. N.; Hall, W. P.; Lyandres, O.; Shah, N. C.; Zhao, J.; Van Duyne, R. P. Biosensing with plasmonic nanosensors. Nat. Mater. 2008, 7, 442– 453, DOI: 10.1038/nmat2162
  6
  Biosensing with plasmonic nanosensors
  Anker, Jeffrey N.; Hall, W. Paige; Lyandres, Olga; Shah, Nilam C.; Zhao, Jing; Van Duyne, Richard P.
  Nature Materials (2008), 7 (6), 442-453CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
  A review. Light incident on metallic nanoparticles can induce a collective motion of electrons that can lead to a strong amplification of the local electromagnetic field. As reviewed here, these plasmonic resonances have important applications in biosensing where they push resoln. and sensitivity towards the single-mol. detection limit. Recent developments have greatly improved the sensitivity of optical sensors based on metal nanoparticle arrays and single nanoparticles. The authors introduce the localized surface plasmon resonance (LSPR) sensor and describe how its exquisite sensitivity to size, shape and environment can be harnessed to detect mol. binding events and changes in mol. conformation. The authors then describe recent progress in three areas representing the most significant challenges: pushing sensitivity towards the single-mol. detection limit, combining LSPR with complementary mol. identification techniques such as surface-enhanced Raman spectroscopy, and practical development of sensors and instrumentation for routine use and high-throughput detection. This review highlights several exceptionally promising research directions and discusses how diverse applications of plasmonic nanoparticles can be integrated in the near future.
7. 7
  Halas, N. J.; Lal, S.; Chang, W. S.; Link, S.; Nordlander, P. Plasmons in strongly coupled metallic nanostructures. Chem. Rev. 2011, 111, 3913– 3961, DOI: 10.1021/cr200061k
  7
  Plasmons in Strongly Coupled Metallic Nanostructures
  Halas, Naomi J.; Lal, Surbhi; Chang, Wei-Shun; Link, Stephan; Nordlander, Peter
  Chemical Reviews (Washington, DC, United States) (2011), 111 (6), 3913-3961CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review examines the unique light-focusing properties of strongly coupled plasmonic systems, properties that resulted in an extraordinary increase in interest in these systems within the chem. community. It describes the concept of plasmon hybridization that takes advantage of the analogy between plasmons and the wave functions of simple quantum systems to provide a simple, intuitive explanation of the properties of complex plasmonic systems. It discusses coupled plasmonic systems where the classical electromagnetic description of coupled plasmons is no longer adequate and a quantum mech. description is necessary to understand their behavior.
8. 8
  Wang, D.; Bourgeois, M. R.; Lee, W.-K.; Li, R.; Trivedi, D.; Knudson, M. P.; Wang, W.; Schatz, G. C.; Odom, T. W. Stretchable Nanolasing from Hybrid Quadrupole Plasmons. Nano Lett. 2018, 18, 4549– 4555, DOI: 10.1021/acs.nanolett.8b01774
  8
  Stretchable Nanolasing from Hybrid Quadrupole Plasmons
  Wang, Danqing; Bourgeois, Marc R.; Lee, Won-Kyu; Li, Ran; Trivedi, Dhara; Knudson, Michael P.; Wang, Weijia; Schatz, George C.; Odom, Teri W.
  Nano Letters (2018), 18 (7), 4549-4555CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  A robust and stretchable nanolaser platform that can preserve its high mode quality by exploiting hybrid quadrupole plasmons as an optical feedback mechanism is reported. Increasing the size of metal nanoparticles in an array can introduce ultrasharp lattice plasmon resonances with out-of-plane charge oscillations that are tolerant to lateral strain. By patterning these nanoparticles onto an elastomeric slab surrounded by liq. gain, the authors realized reversible, tunable nanolasing with high strain sensitivity and no hysteresis. The semiquantum modeling demonstrates that lasing build-up occurs at the hybrid quadrupole electromagnetic hot spots, which provides a route toward mech. modulation of light-matter interactions on the nanoscale.
9. 9
  Kolwas, K. Decay Dynamics of Localized Surface Plasmons: Damping of Coherences and Populations of the Oscillatory Plasmon Modes. Plasmonics 2019, 1629, DOI: 10.1007/s11468-019-00958-1
  There is no corresponding record for this reference.
10. 10
  Liu, T.; Besteiro, L. V.; Wang, Z.; Govorov, A. O. Generation of hot electrons in nanostructures incorporating conventional and unconventional plasmonic materials. Faraday Discuss. 2019, 214, 199– 213, DOI: 10.1039/C8FD00145F
  10
  Generation of hot electrons in nanostructures incorporating conventional and unconventional plasmonic materials
  Liu, Tianji; Besteiro, Lucas V.; Wang, Zhiming; Govorov, Alexander O.
  Faraday Discussions (2019), 214 (Hot-Electron Science and Microscopic Processes in Plasmonics and Catalysis), 199-213CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
  The generation of energetic electrons is an effect occurring in any plasmonic nanostructure. However, the no. of electrons with high energies generated optically in a plasmonic nanostructure can be relatively small. This is an intrinsic property of the collective plasmon excitations in a Fermi gas of electrons. But the choices of material and geometry have a great impact on the generation rate, and are therefore crucial for designing a nanostructure with a large rate of generation of energetic (hot) electrons. Here we test different plasmonic materials from the point of view of the generation of hot electrons (HEs). Our choice of materials includes both strongly-plasmonic materials (Au, Ag, Cu and Al) and crystals with strongly broadened plasmonic resonances (Pt, TiN and ZrN). Regarding the choice of geometry, we consider two types of nanostructures, single nanocrystals deposited over a dielec. substrate and metastructure absorbers, observing interesting opto-electronic properties. For single nanocrystals, the rate of HE generation is strongly material-dependent since the HE generation rate strongly depends on several phys. parameters such as plasmonic enhancement, plasmonic resonance wavelength, Fermi energy, etc. Interestingly, the plasmonic meta-absorbers exhibit a different behavior. The strongly-plasmonic metals, such as Au, Ag, Cu or Al, show very similar performances, while the materials with damped plasmon resonances demonstrate diverse and reduced rates of HE generation. The phys. reason for these different behaviors lies in the dielec. functions of these materials. In the metastructures, plasmonic resonances are in the IR region and the strongly-plasmonic materials behave as an almost ideal metal, whereas the second group of materials exhibits strong dissipation. This makes the responses from the metastructures made of crystals with damped plasmons strongly dependent on the choice of material. The phys. principles described in our study can be useful for designing metastructures and nanodevices based on HEs, which can be used in photo-chem. and opto-electronics.
11. 11
  Besteiro, L. V.; Kong, X.-T.; Wang, Z.; Hartland, G.; Govorov, A. O. Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms. ACS Photonics 2017, 4, 2759– 2781, DOI: 10.1021/acsphotonics.7b00751
  11
  Understanding Hot-Electron Generation and Plasmon Relaxation in Metal Nanocrystals: Quantum and Classical Mechanisms
  Besteiro, Lucas V.; Kong, Xiang-Tian; Wang, Zhiming; Hartland, Gregory; Govorov, Alexander O.
  ACS Photonics (2017), 4 (11), 2759-2781CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
  Generation of energetic (hot) electrons is an intrinsic property of any plasmonic nanostructure under illumination. Simultaneously, a striking advantage of metal nanocrystals over semiconductors lies in their very large absorption cross sections. Therefore, metal nanostructures with strong and tailored plasmonic resonances are very attractive for photocatalytic applications in which excited electrons play an important role. However, the central questions in the problem of plasmonic hot electrons are the no. of optically-excited energetic electrons in a nanocrystal and how to ext. such electrons. Here we develop a theory describing the generation rates and the energy-distributions of hot electrons in nanocrystals with various geometries. In our theory, hot electrons are generated owing to surfaces and hot spots. As expected, the formalism predicts that large optically-excited nanocrystals show the excitation of mostly low-energy Drude electrons, whereas plasmons in small nanocrystals involve mostly high-energy (hot) electrons. We obtain anal. expressions for the distribution functions of excited carriers for simple shapes. For complex shapes and for small quantum nanocrystals, our results are computational. By looking at the energy distributions of electrons in an optically-excited nanocrystal, we see how the quantum many-body state in small particles evolves towards the classical state described by the Drude model when increasing nanocrystal size. We show that the rate of surface decay of plasmons in nanocrystals is directly related to the rate of generation of hot electrons. Based on a detailed many-body theory involving kinetic coeffs., we formulate a simple scheme describing how the plasmon in a nanocrystal dephases over time. In most nanocrystals, the main decay mechanism of a plasmon is the Drude friction-like process and the secondary path comes from generation of hot electrons due to surfaces and electromagnetic hot spots. The hot-electron path strongly depends on the material system and on its shape. Correspondingly, the efficiency of hot-electron prodn. in a nanocrystal strongly varies with size, shape and material. The results in the paper can be used to guide the design of plasmonic nanomaterials for photochem. and photodetectors.
12. 12
  Naldoni, A.; Guler, U.; Wang, Z.; Marelli, M.; Malara, F.; Meng, X.; Besteiro, L. V.; Govorov, A. O.; Kildishev, A. V.; Boltasseva, A.; Shalaev, V. M. Broadband Hot-Electron Collection for Solar Water Splitting with Plasmonic Titanium Nitride. Adv. Opt. Mater. 2017, 5, 1601031, DOI: 10.1002/adom.201601031
  There is no corresponding record for this reference.
13. 13
  Brown, A. M.; Sundararaman, R.; Narang, P.; Goddard, W. A., III; Atwater, H. A. Non-Radiative Plasmon Decay and Hot Carrier Dynamics: Effects of Phonons, Surfaces and Geometry. ACS Nano 2016, 10, 957, DOI: 10.1021/acsnano.5b06199
  13
  Nonradiative Plasmon Decay and Hot Carrier Dynamics: Effects of Phonons, Surfaces, and Geometry
  Brown, Ana M.; Sundararaman, Ravishankar; Narang, Prineha; Goddard, William A.; Atwater, Harry A.
  ACS Nano (2016), 10 (1), 957-966CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
  The behavior of metals across a broad frequency range from microwave to UV frequencies is of interest in plasmonics, nanophotonics, and metamaterials. Depending on the frequency, losses of collective excitations in metals can be predominantly classical resistive effects or Landau damping. In this context, we present first-principles calcns. that capture all of the significant microscopic mechanisms underlying surface plasmon decay and predict the initial excited carrier distributions so generated. Specifically, we include ab initio predictions of phonon-assisted optical excitations in metals, which are crit. to bridging the frequency range between resistive losses at low frequencies and direct interband transitions at high frequencies. In the commonly used plasmonic materials, gold, silver, copper, and aluminum, we find that resistive losses compete with phonon-assisted carrier generation below the interband threshold, but hot carrier generation via direct transitions dominates above threshold. Finally, we predict energy-dependent lifetimes and mean free paths of hot carriers, accounting for electron-electron and electron-phonon scattering, to provide insight toward transport of plasmonically generated carriers at the nanoscale.
14. 14
  Raza, S.; Kadkhodazadeh, S.; Christensen, T.; Di Vece, M.; Wubs, M.; Mortensen, N. A.; Stenger, N. Multipole plasmons and their disappearance in few-nanometre silver nanoparticles. Nat. Commun. 2015, 6, 8788, DOI: 10.1038/ncomms9788
  14
  Multipole plasmons and their disappearance in few-nanometer silver nanoparticles
  Raza, Soeren; Kadkhodazadeh, Shima; Christensen, Thomas; Di Vece, Marcel; Wubs, Martijn; Mortensen, N. Asger; Stenger, Nicolas
  Nature Communications (2015), 6 (), 8788CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
  Electron energy-loss spectroscopy can be used for detailed spatial and spectral characterization of optical excitations in metal nanoparticles. In previous electron energy-loss expts. on silver nanoparticles with radii smaller than 20 nm, only the dipolar surface plasmon resonance was assumed to play a role. Here, applying electron energy-loss spectroscopy to individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an addnl. surface plasmon resonance corresponding to higher angular momenta for nanoparticle radii as small as 4 nm. We study the radius and electron beam impact position dependence of both resonances sep. For particles smaller than 4 nm in radius the higher-order surface plasmon mode disappears, in agreement with generalized non-local optical response theory, while the dipole resonance blue shift exceeds our theor. predictions. Unlike in optical spectra, multipole surface plasmons are important in electron energy-loss spectra even of ultrasmall metallic nanoparticles.
15. 15
  Mittal, R.; Glenn, R.; Saytashev, I.; Lozovoy, V. V.; Dantus, M. Femtosecond nanoplasmonic dephasing of individual silver nanoparticles and small clusters. J. Phys. Chem. Lett. 2015, 6, 1638– 1644, DOI: 10.1021/acs.jpclett.5b00264
  15
  Femtosecond Nanoplasmonic Dephasing of Individual Silver Nanoparticles and Small Clusters
  Mittal, Richa; Glenn, Rachel; Saytashev, Ilyas; Lozovoy, Vadim V.; Dantus, Marcos
  Journal of Physical Chemistry Letters (2015), 6 (9), 1638-1644CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The authors present exptl. measurements of localized surface plasmon emission from individual Ag nanoparticles and small clusters via accurately delayed femtosecond laser pulses. Fourier transform anal. of the nanoplasmonic coherence oscillations reveals different frequency components and dephasing rates for each nanoparticle. Three different types of behavior: single exponential decay, beating between 2 frequencies, and beating among ≥3 frequencies were found. Results provide insight into inhomogeneous and homogeneous broadening mechanisms in nanoplasmonic spectroscopy that depend on morphol. and nearby neighbors. The optical response of certain pairs of nanoparticles to be at least an order of magnitude more intense than the response of single particles were found.
16. 16
  Crut, A.; Maioli, P.; Del Fatti, N.; Vallée, F. Optical absorption and scattering spectroscopies of single nano-objects. Chem. Soc. Rev. 2014, 43, 3921– 3956, DOI: 10.1039/c3cs60367a
  16
  Optical absorption and scattering spectroscopies of single nano-objects
  Crut, Aurelien; Maioli, Paolo; Del Fatti, Natalia; Vallee, Fabrice
  Chemical Society Reviews (2014), 43 (11), 3921-3956CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
  A review. Developments of optical detection and spectroscopy methods for single nano-objects are key advances for applications and fundamental understanding of the novel properties exhibited by nanosize systems. These methods are reviewed, focusing on far-field optical approaches based on light absorption and elastic scattering. The principles of the main linear and nonlinear methods are described and exptl. results are illustrated in the case of metal nanoparticles, stressing the key role played by the object environment, such as the presence of a substrate, bound surface mols. or other nano-objects. Special attention is devoted to quant. methods and correlation of the measured optical spectra of a nano-object with its morphol., characterized either optically or by electron microscopy, as this permits precise comparison with theor. models. Application of these methods to optical detection and spectroscopy for single semiconductor nanowires and carbon nanotubes is also presented. Extension to ultrafast nonlinear extinction or scattering spectroscopies of single nano-objects is finally discussed in the context of investigation of their nonlinear optical response and their electronic, acoustic and thermal properties.
17. 17
  Codrington, J.; Eldabagh, N.; Fernando, K.; Foley, J. J., IV Unique hot carrier distributions from scattering-mediated absorption. ACS Photonics 2017, 4, 552– 559, DOI: 10.1021/acsphotonics.6b00773
  17
  Unique Hot Carrier Distributions from Scattering-Mediated Absorption
  Codrington, Jason; Eldabagh, Noor; Fernando, Kimberly; Foley, Jonathan J.
  ACS Photonics (2017), 4 (3), 552-559CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
  Light-initiated generation of energetic carriers has attracted considerable attention as a paradigm for photocatalysis and solar energy conversion, and the use of noble metal nanoparticles that support localized surface plasmon resonances has been widely explored as a medium for realizing this paradigm. It was recently shown that composite nanostructures enabling the interplay between dielec. scattering resonances and broadband absorption in small metal nanostructures, a phenomenon termed scattering-mediated absorption, can be used to mediate energetic carrier transfer and selective photochem. with low-intensity light while completely circumventing plasmon resonance. In this work, we develop a multiscale modeling approach for elucidating the hot carrier dynamics initiated by scattering-mediated absorption. Our calcns. reveal that unique hot carrier distributions and dynamics arise from scattering-mediated absorption as compared to plasmon excitation and also suggest that in a variety of circumstances scattering-mediated absorption may lead to more efficient hot carrier generation compared to plasmon resonance under the same external illumination conditions. These results are an important first step in understanding the phenomena of scattering-mediated hot carrier generation, which has potential for expanding the palette of materials that can be utilized for hot carrier mediated photochem. beyond plasmonic metals and for enabling unique pathways for photocatalytic transformations.
18. 18
  Kreibig, U.; Schmitz, B.; Breuer, H. D. Separation of plasmon-polariton modes of small metal particles. Phys. Rev. B 1987, 36, 5027– 5030, DOI: 10.1103/PhysRevB.36.5027
  18
  Separation of plasmon-polariton modes of small metal particles
  Kreibig; Schmitz; Breuer
  Physical review. B, Condensed matter (1987), 36 (9), 5027-5030 ISSN:0163-1829.
  There is no expanded citation for this reference.
19. 19
  Zong, R.-L.; Zhou, J.; Li, B.; Fu, M.; Shi, S.-K.; Li, L.-T. Optical properties of transparent copper nanorod and nanowire arrays embedded in anodic alumina oxide. J. Chem. Phys. 2005, 123, 094710 DOI: 10.1063/1.2018642
  19
  Optical properties of transparent copper nanorod and nanowire arrays embedded in anodic alumina oxide
  Zong, Rui-Long; Zhou, Ji; Li, Bo; Fu, Ming; Shi, Shi-Kao; Li, Long-Tu
  Journal of Chemical Physics (2005), 123 (9), 094710/1-094710/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Transparent Cu nanorod/nanowire arrays and anodic alumina oxide composite films were prepd. by a.c. electrodeposition, and their linear optical properties were systematically characterized by absorption spectra. In the exptl. spectra, there exist transverse and longitudinal resonance peaks, which are caused by the surface-plasmon resonance along the diam. and the length of the Cu nanorods, resp. The transverse resonance peak is affected by the diam. and aspect ratio of the nanorod. The longitudinal resonance peak appears at longer wavelength when a polarized light illuminates the film with an angle of incidence of ∼70°, where the angle is defined with respect to the surface normal. Also, the longitudinal resonance mode is sensitive to the polarization direction when compared with the transverse resonance mode.
20. 20
  Rubio, A.; Serra, L. Dielectric screening effects on the photoabsorption cross section of embedded metallic clusters. Phys. Rev. B 1993, 48, 18222– 18229, DOI: 10.1103/PhysRevB.48.18222
  20
  Dielectric screening effects on the photoabsorption cross section of embedded metallic clusters
  Rubio, Angel; Serra, Llorenc
  Physical Review B: Condensed Matter and Materials Physics (1993), 48 (24), 18222-9CODEN: PRBMDO; ISSN:0163-1829.
  The surface plasmon resonance of alkali-metal (potassium) and noble-metal (silver) clusters embedded in different dielec. matrixes is studied within the time-dependent d.-functional formalism and the jellium model, including dielec. screening for the electron-electron interaction. The calcd. red shift of the plasma frequency as the dielec. const. (ε) of the matrix increases is in good agreement with the available exptl. data for both potassium and silver clusters. In the case of potassium, the shifts induced by rare-gas matrixes are predicted. A tendency to satn. in the polarizability and surface plasmon resonance when ε increases is obtained and is due to the screening of the Coulomb interaction by the dielec. surrounding the cluster. It was concluded that the basic effect of the dielec. matrix comes from the direct screening of the electron-electron interaction and not from the modification of the cluster ground state.
21. 21
  Campos, A.; Troc, N.; Cottancin, E.; Pellarin, M.; Weissker, H. C.; Lermé, J.; Kociak, M.; Hillenkamp, M. Plasmonic quantum size effects in silver nanoparticles are dominated by interfaces and local environments. Nat. Phys. 2019, 15, 275– 280, DOI: 10.1038/s41567-018-0345-z
  21
  Plasmonic quantum size effects in silver nanoparticles are dominated by interfaces and local environments
  Campos, Alfredo; Troc, Nicolas; Cottancin, Emmanuel; Pellarin, Michel; Weissker, Hans-Christian; Lerme, Jean; Kociak, Mathieu; Hillenkamp, Matthias
  Nature Physics (2019), 15 (3), 275-280CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)
  The phys. properties of metals change when their dimensions are reduced to the nano-scale and new phenomena such as the localized surface-plasmon resonance (LSPR) appear. This collective electronic excitation can be tuned over a large spectral range by adapting the material, size and shape. The existing literature is as rich as it is controversial-for example, size-dependent spectral shifts of the LSPR in small metal nanoparticles, induced by quantum effects, are reported to the red, to the blue or entirely absent. Here we report how complementary expts. on size-selected small silver nanoparticles embedded in silica can yield inconsistent results on the same system: whereas optical absorption shows no size effect in the range between only a few atoms and ~ 10 nm, a clear spectral shift is obsd. in single-particle electron spectroscopy. Our quant. interpretation, based on a mixed classical/quantum model, resolves the apparent contradictions, not only within our exptl. data, but also in the literature. Our comprehensive model describes how the local environment is the crucial parameter controlling the manifestation or absence of quantum size effects.
22. 22
  Román Castellanos, L.; Hess, O.; Lischner, J. Single plasmon hot carrier generation in metallic nanoparticles. Commun. Phys. 2019, 2, 47, DOI: 10.1038/s42005-019-0148-2
  There is no corresponding record for this reference.
23. 23
  Deng, S. Electrostatic potential of point charges inside dielectric oblate spheroids. J. Electrost. 2009, 67, 807– 814, DOI: 10.1016/j.elstat.2009.06.007
  23
  Electrostatic potential of point charges inside dielectric oblate spheroids
  Deng Shaozhong
  Journal of electrostatics (2009), 67 (5), 807-814 ISSN:0304-3886.
  As a sequel to a previous paper on electrostatic potential of point charges inside dielectric prolate spheroids [J. Electrostatics 66 (2008) 549-560], this note further presents the exact solution to the electrostatic problem of finding the electric potential of point charges inside a dielectric oblate spheroid that is embedded in a dissimilar dielectric medium. Numerical experiments have demonstrated the convergence of the proposed series solutions.
24. 24
  Kirkwood, J. G. Theory of solutions of molecules containing widely separated charges with special application to zwitterions. J. Chem. Phys. 1934, 2, 351– 361, DOI: 10.1063/1.1749489
  24
  Theory of solutions of molecules containing widely separated charges with special application to amphoteric ions
  Kirkwood, John G.
  Journal of Chemical Physics (1934), 2 (), 351-61CODEN: JCPSA6; ISSN:0021-9606.
  The elec. contribution to the chem. potential of an ion having an arbitrary charge distribution is calcd. from the Debye-H.ovrddot.uckel theory, and the Born relation between the free energy of solvation of a spherical ion and the dielec. const. of the solvent is generalized to include ions of arbitrary charge distribution. The theory gives an approx. account of the soly. of glycine in EtOHH2O mixts., both in the presence and absence of salts, as long as the glycine concn. is small, and gives reasonable values for the dipole moment and size of the amphoteric ion.
25. 25
  Serra, L.; Rubio, A. Core polarization in the optical response of metal clusters: Generalized time-dependent density-functional theory. Phys. Rev. Lett. 1997, 78, 1428– 1431, DOI: 10.1103/PhysRevLett.78.1428
  25
  Core polarization in the optical response of metal clusters: generalized time-dependent density-functional theory
  Serra, Llorenc; Rubio, Angel
  Physical Review Letters (1997), 78 (8), 1428-1431CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  The authors present a generalized time-dependent d.-functional theory (TDDFT) for the optical response of metal clusters where both core polarization and valence responses are treated microscopically. The valence electrons response is described by an effective external field and residual interaction that are those of the std. TDDFT modified by the self-consistent contributions of the array of polarizable ionic cores. As an application the equations are solved within the adiabatic local-d. approxn. for Ag clusters, where core 4d electrons greatly influence the optical response. The exptl. data are well reproduced by the present theory.
26. 26
  Toyoda, M.; Ozaki, T. LIBERI: Library for numerical evaluation of electron-repulsion integrals. Comput. Phys. Commun. 2010, 181, 1455– 1463, DOI: 10.1016/j.cpc.2010.03.019
  26
  LIBERI: library for numerical evaluation of electron-repulsion integrals
  Toyoda, Masayuki; Ozaki, Taisuke
  Computer Physics Communications (2010), 181 (8), 1455-1463CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
  We provide a C library, called LIBERI, for numerical evaluation of four-center electron repulsion integrals, based on successive redn. of integral dimension by using Fourier transforms. LIBERI enables us to compute the integrals for numerically defined basis functions within 10-5 Hartree accuracy as well as their derivs. with respect to the at. nuclear positions. Damping of the Coulomb interaction can also be imposed to take account of screening effect.
27. 27
  Khurgin, J. B.; Levy, U. Generating Hot Carriers in Plasmonic Nanoparticles: When Quantization Does Matter?. ACS Photonics 2020, 547– 553, DOI: 10.1021/acsphotonics.9b01774
  27
  Generating Hot Carriers in Plasmonic Nanoparticles: When Quantization Does Matter?
  Khurgin, Jacob B.; Levy, Uriel
  ACS Photonics (2020), 7 (3), 547-553CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
  Plasmon-assisted hot carrier processes in metal nanoparticles can be described either classically or using the full strength of quantum mechanics. We reconfirm that from the practical applications point of view, when it comes to description of the decay of plasmons in nanoparticles, classical description is sufficiently adequate for all but the smallest of the nanoparticles. At the same time, the electron temp. rise in nanoparticles is discrete (quantized), and neglecting this fact can lead to significant underestimating of hot carrier assisted effects such as photocatalysis.
28. 28
  Bernardi, M.; Mustafa, J.; Neaton, J. B.; Louie, S. G. Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals. Nat. Commun. 2015, 6, 7044, DOI: 10.1038/ncomms8044
  28
  Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals
  Bernardi, Marco; Mustafa, Jamal; Neaton, Jeffrey B.; Louie, Steven G.
  Nature Communications (2015), 6 (), 7044CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
  Hot carriers (HC) generated by surface plasmon polaritons (SPPs) in noble metals are promising for application in optoelectronics, plasmonics and renewable energy. However, existing models fail to explain key quant. details of SPP-to-HC conversion expts. Here we develop a quantum mech. framework and apply first-principles calcns. to study the energy distribution and scattering processes of HCs generated by SPPs in Au and Ag. We find that the relative positions of the s and d bands of noble metals regulate the energy distribution and mean free path of the HCs, and that the electron-phonon interaction controls HC energy loss and transport. Our results prescribe optimal conditions for HC generation and extn., and invalidate previously employed free-electron-like models. Our work combines d. functional theory, GW and electron-phonon calcns. to provide microscopic insight into HC generation and ultrafast dynamics in noble metals.
29. 29
  Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133– A1138, DOI: 10.1103/PhysRev.140.A1133
  There is no corresponding record for this reference.
30. 30
  Perdew, J. P.; Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 1981, 23, 5048– 5079, DOI: 10.1103/PhysRevB.23.5048
  30
  Self-interaction correction to density-functional approximations for many-electron systems
  Perdew, J. P.; Zunger, Alex
  Physical Review B: Condensed Matter and Materials Physics (1981), 23 (10), 5048-79CODEN: PRBMDO; ISSN:0163-1829.
  The exact d. functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approxns. to it, including the local-spin-d. (LSD) approxn. for exchange and correlation, are not. Two related methods are given for the self-interaction correction (SIC) of any d. functional for the energy; correction of the self-consistent one-electron potential follows naturally from the variational principle. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. The 1st method was applied to LSD, it properly conserves the no. content of the exchange-correlation hole, while substantially improving the description of its shape. The LSD spin splitting in at. Ni and s-d interconfigurational energies of transition elements are almost unchanged by SIC.
31. 31
  Romaniello, P.; De Boeij, P. L. Time-dependent current-density-functional theory for the metallic response of solids. Phys. Rev. B 2005, 71, 155108, DOI: 10.1103/PhysRevB.71.155108
  31
  Time-dependent current-density-functional theory for the metallic response of solids
  Romaniello, P.; de Boeij, P. L.
  Physical Review B: Condensed Matter and Materials Physics (2005), 71 (15), 155108/1-155108/17CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We extend the formulation of time-dependent current-d.-functional theory for the linear response properties of dielec. and semimetallic solids [Kootstra et al., J. Chem. Phys. 112, 6517 (2000)] to treat metals as well. To achieve this, the Kohn-Sham response functions have to include both interband and intraband transitions with an accurate treatment of the Fermi surface in the Brillouin-zone integrations. The intraband contributions in particular have to be evaluated using a wave-vector-dependent description. To test the method we calc. the optical properties of the two noble metals Cu and Ag. The dielec. and energy loss functions are compared with expts. and with the classical Drude theory. In general we find a good agreement with the expts. for the calcd. results obtained within the adiabatic local d. approxn. In order to describe the Drude-like absorption below the interband onset and the sharp plasma feature in silver exchange-correlation, effects beyond the adiabatic local d. approxn. are needed, which may be included in a natural way in the present current-d.-functional approach.
32. 32
  Cazalilla, M. A.; Dolado, J. S.; Rubio, A.; Echenique, P. M. Plasmonic excitations in noble metals: The case of Ag. Phys. Rev. B 2000, 61, 8033– 8042, DOI: 10.1103/PhysRevB.61.8033
  32
  Plasmonic excitations in noble metals: The case of Ag
  Cazalilla, M. A.; Dolado, J. S.; Rubio, A.; Echenique, P. M.
  Physical Review B: Condensed Matter and Materials Physics (2000), 61 (12), 8033-8042CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The delicate interplay between plasmonic excitations and interband transitions in noble metals is described by ab initio calcns. and a simple model in which the conduction electron plasmon is coupled to the continuum of electron-hole pairs. Band-structure effects, esp. the energy at which the excitation of the d-like bands takes place, det. the existence of a threshold plasmonic mode, which manifests itself in Ag as a sharp resonance exptl. obsd. at 3.8 eV. However, such a resonance does not appear in the spectra of the other noble metals. Here this different behavior is also analyzed, and an explanation is provided.
33. 33
  Sönnichsen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J. Plasmon resonances in large noble-metal clusters. New J. Phys. 2002, 4, 93, DOI: 10.1088/1367-2630/4/1/393
  There is no corresponding record for this reference.
34. 34
  Aeschlimann, M.; Bauer, M.; Pawlik, S. Competing nonradiative channels for hot electron induced surface photochemistry. Chem. Phys. 1996, 205, 127– 141, DOI: 10.1016/0301-0104(95)00372-X
  34
  Competing nonradiative channels for hot electron induced surface photochemistry
  Aeschlimann, M.; Bauer, M.; Pawlik, S.
  Chemical Physics (1996), 205 (1,2), 127-41CODEN: CMPHC2; ISSN:0301-0104. (Elsevier)
  We report expts. in which we investigated the ultrafast dynamics of competing nonradiative channels for hot electron mechanisms in various polycryst. metal samples. Time resolved two-photon photoemission, based on the equal pulse correlation technique, is used to measure the energy relaxation and the transport of the photoexcited carriers. In these studies the role of coherent effects in auto- and cross-correlation expts. has been considered. While the inelastic lifetime of Ag is in qual. and quant. agreement with the Fermi liq. theory, the result obtained for Au is very different. The measured inelastic relaxation time for transition metals with unoccupied d orbitals is shorter as compared to the noble metals. The results demonstrate the feasibility of studying electron relaxation in noble and transition metals directly in the time domain and provide a framework for understanding the dynamics of hot electron transfer from a metal surface to the adsorbate.
35. 35
  Rossi, T. P.; Kuisma, M.; Puska, M. J.; Nieminen, R. M.; Erhart, P. Kohn-Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory: An Efficient Tool for Analyzing Plasmonic Excitations. J. Chem. Theory Comput. 2017, 13, 4779– 4790, DOI: 10.1021/acs.jctc.7b00589
  35
  Kohn-Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory: An Efficient Tool for Analyzing Plasmonic Excitations
  Rossi, Tuomas P.; Kuisma, Mikael; Puska, Martti J.; Nieminen, Risto M.; Erhart, Paul
  Journal of Chemical Theory and Computation (2017), 13 (10), 4779-4790CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Electronic excitations can be efficiently analyzed in terms of the underlying Kohn-Sham (KS) electron-hole transitions. While such a decompn. is readily available in the linear-response time-dependent d.-functional theory (TDDFT) approaches based on the Casida equations, a comparable anal. is less commonly conducted within the real-time-propagation TDDFT (RT-TDDFT). To improve this situation, we present here an implementation of a KS decompn. tool within the local-basis-set RT-TDDFT code in the free GPAW package. Our implementation is based on postprocessing of data that is readily available during time propagation, which is important for retaining the efficiency of the underlying RT-TDDFT to large systems. After benchmarking our implementation on small benzene derivs. by explicitly reconstructing the Casida eigenvectors from RT-TDDFT, we demonstrate the performance of the method by analyzing the plasmon resonances of icosahedral silver nanoparticles up to Ag561. The method provides a clear description of the splitting of the plasmon in small nanoparticles due to individual single-electron transitions as well as the formation of a distinct d-electron-screened plasmon resonance in larger nanoparticles.
36. 36
  Dubi, Y.; Sivan, Y. Hot electrons in metallic nanostructures—non-thermal carriers or heating?. Light: Sci. Appl. 2019, 8, 89, DOI: 10.1038/s41377-019-0199-x
  36
  "Hot" electrons in metallic nanostructures-non-thermal carriers or heating?
  Dubi Yonatan; Sivan Yonatan
  Light, science & applications (2019), 8 (), 89 ISSN:.
  Understanding the interplay between illumination and the electron distribution in metallic nanostructures is a crucial step towards developing applications such as plasmonic photocatalysis for green fuels, nanoscale photodetection and more. Elucidating this interplay is challenging, as it requires taking into account all channels of energy flow in the electronic system. Here, we develop such a theory, which is based on a coupled Boltzmann-heat equations and requires only energy conservation and basic thermodynamics, where the electron distribution, and the electron and phonon (lattice) temperatures are determined uniquely. Applying this theory to realistic illuminated nanoparticle systems, we find that the electron and phonon temperatures are similar, thus justifying the (classical) single-temperature models. We show that while the fraction of high-energy "hot" carriers compared to thermalized carriers grows substantially with illumination intensity, it remains extremely small (on the order of 10(-8)). Importantly, most of the absorbed illumination power goes into heating rather than generating hot carriers, thus rendering plasmonic hot carrier generation extremely inefficient. Our formulation allows for the first time a unique quantitative comparison of theory and measurements of steady-state electron distributions in metallic nanostructures.
37. 37
  Lermé, J.; Palpant, B.; Prével, B.; Cottancin, E.; Pellarin, M.; Treilleux, M.; Vialle, J. L.; Perez, A.; Broyer, M. Optical properties of gold metal clusters: A time-dependent local-density-approximation investigation. Eur. Phys. J. D 1998, 4, 95– 108, DOI: 10.1007/s100530050189
  37
  Optical properties of gold metal clusters: a time-dependent local-density-approximation investigation
  Lerme, J.; Palpant, B.; Prevel, B.; Cottancin, E.; Pellarin, M.; Treilleux, M.; Vialle, J. L.; Perez, A.; Broyer, M.
  European Physical Journal D: Atomic, Molecular and Optical Physics (1998), 4 (1), 95-108CODEN: EPJDF6; ISSN:1434-6060. (Springer-Verlag)
  The optical response of free and matrix-embedded Au metal clusters AuN was studied in the framework of the time-dependent local-d.-approxn. (TDLDA). The characteristics of the surface plasmon resonance are carefully analyzed as a function of the model parameters and the particle radius. The strong influence of the frequency-dependence of the 5d core-electron dielec. function in the vicinity of the interband threshold is emphasized. The size evolution of the Mie-frequency in free Au clusters exhibits a noticeable blue-shift trend as the particle size decreases, much stronger than in Ag clusters. The width and shape of the resonance, essentially ruled by the decay via the interband transitions, are found closely correlated to the imaginary component of the core-electron dielec. function. In presence of a surrounding matrix the blue-shift trend is largely rubbed out. Agreement with recent exptl. results on size-selected Au clusters embedded in an alumina matrix may be achieved by taking into account the porosity effects at the metal/matrix interface. The comparison with the predictions of classical models is also provided.
38. 38
  Yannouleas, C.; Vigezzi, E.; Broglia, R. A. Evolution of the optical properties of alkali-metal microclusters towards the bulk: The matrix random-phase-approximation description. Phys. Rev. B 1993, 47, 9849– 9861, DOI: 10.1103/PhysRevB.47.9849
  38
  Evolution of the optical properties of alkali-metal microclusters towards the bulk: the matrix random-phase approximation description
  Yannouleas, C.; Vigezzi, E.; Broglia, R. A.
  Physical Review B: Condensed Matter and Materials Physics (1993), 47 (15), 9849-61CODEN: PRBMDO; ISSN:0163-1829.
  The evolution toward the bulk values of the energy centroid and of the width characterizing the surface-plasmon resonance in spherical neutral sodium clusters is studied. For this purpose, the photoabsorption spectrum of clusters comprising from 8 to 338 atoms is calcd. microscopically making use of the jellium shell model to describe the motion of delocalized electrons and of the matrix RPA to det. the collective response of the system to electromagnetic radiation. The Coulomb force is treated in the local-d. approxn. The case of large potassium clusters having approx. 500 and 900 atoms is also considered.
39. 39
  DeVore, J. R. Refractive Indices of Rutile and Sphalerite. J. Opt. Soc. Am. 1951, 41, 416– 419, DOI: 10.1364/JOSA.41.000416
  39
  Refractive indexes of rutile and sphalerite
  DeVore, J. R.
  Journal of the Optical Society of America (1951), 41 (), 416-19CODEN: JOSAAH; ISSN:0030-3941.
  Prisms were made from single crystals of rutile and sphalerite and used in measuring the ns of these materials. The measurements were made through the visible spectrum and extended to 1.5 microns in the infrared by the use of an infrared-sensitive screen. The dispersion curves and the equations for the curves were detd. Values taken from the curves agree moderately well with published values. The results demonstrate the high dispersion and the large birefringence of rutile. The exptl. results also demonstrate the strong absorption of rutile in the violet end of the visible spectrum, which accounts for the slight yellow color of rutile.
40. 40
  Jellison, G. E., Jr. Optical functions of GaAs, GaP, and Ge determined by two-channel polarization modulation ellipsometry. Opt. Mater. 1992, 1, 151– 160, DOI: 10.1016/0925-3467(92)90022-F
  40
  Optical functions of gallium arsenide, gallium phosphide and germanium determined by two-channel polarization modulation ellipsometry
  Jellison, G. E., Jr.
  Optical Materials (Amsterdam, Netherlands) (1992), 1 (3), 151-60CODEN: OMATET; ISSN:0925-3467.
  The optical functions of (100) and (111) GaAs, (100) GaP, and (100) Ge were detd. 234-840 nm (5.30 to 1.48 eV) at room temp. using 2-channel spectroscopic polarization modulation ellipsometry. The results are cor. for oxide overlayers, where the layer thickness is measured using nulling ellipsometry at 1152 nm. The results are tabulated in terms of the refractive index n and extinction coeff. k, including the propagated errors, and are compared with some recent measurements.
41. 41
  Mukherjee, S.; Libisch, F.; Large, N.; Neumann, O.; Brown, L. V.; Cheng, J.; Lassiter, J. B.; Carter, E. A.; Nordlander, P.; Halas, N. J. Hot electrons do the impossible: Plasmon-induced dissociation of H₂ on Au. Nano Lett. 2013, 13, 240– 247, DOI: 10.1021/nl303940z
  41
  Hot Electrons Do the Impossible: Plasmon-Induced Dissociation of H2 on Au
  Mukherjee, Shaunak; Libisch, Florian; Large, Nicolas; Neumann, Oara; Brown, Lisa V.; Cheng, Jin; Lassiter, J. Britt; Carter, Emily A.; Nordlander, Peter; Halas, Naomi J.
  Nano Letters (2013), 13 (1), 240-247CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  Heterogeneous catalysis is of paramount importance in chem. and energy applications. Catalysts that couple light energy into chem. reactions in a directed, orbital-specific manner would greatly reduce the energy input requirements of chem. transformations, revolutionizing catalysis-driven chem. Here we report the room temp. dissocn. of H2 on gold nanoparticles using visible light. Surface plasmons excited in the Au nanoparticle decay into hot electrons with energies between the vacuum level and the work function of the metal. In this transient state, hot electrons can transfer into a Feshbach resonance of an H2 mol. adsorbed on the Au nanoparticle surface, triggering dissocn. We probe this process by detecting the formation of HD mols. from the dissocns. of H2 and D2 and investigate the effect of Au nanoparticle size and wavelength of incident light on the rate of HD formation. This work opens a new pathway for controlling chem. reactions on metallic catalysts.
42. 42
  Scholl, J. A.; Koh, A. L.; Dionne, J. A. Quantum plasmon resonances of individual metallic nanoparticles. Nature 2012, 483, 421– 427, DOI: 10.1038/nature10904
  42
  Quantum plasmon resonances of individual metallic nanoparticles
  Scholl, Jonathan A.; Koh, Ai Leen; Dionne, Jennifer A.
  Nature (London, United Kingdom) (2012), 483 (7390), 421-427CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  The plasmon resonances of metallic nanoparticles have received considerable attention for their applications in nanophotonics, biol., sensing, spectroscopy and solar energy harvesting. Although thoroughly characterized for spheres larger than 10 nm in diam., the plasmonic properties of particles in the quantum size regime were historically difficult to describe owing to weak optical scattering, metal-ligand interactions, and inhomogeneity in ensemble measurements. Such difficulties have precluded probing and controlling the plasmonic properties of quantum-sized particles in many natural and engineered processes, notably catalysis. The plasmon resonances of individual ligand-free Ag nanoparticles was studied using aberration-cor. TEM imaging and monochromated scanning TEM EELS. This technique allows direct correlation between a particle's geometry and its plasmon resonance. As the nanoparticle diam. decreases from 20 to <2 nm, the plasmon resonance shifts to higher energy by 0.5 eV, a substantial deviation from classical predictions. An anal. quantum mech. model that describes this shift due to a change in particle permittivity is presented. The results highlight the quantum plasmonic properties of small metallic nanospheres, with direct application to understanding and exploiting catalytically active and biol. relevant nanoparticles.
43. 43
  Genzel, L.; Martin, T. P.; Kreibig, U. Dielectric function and plasma resonances of small metal particles. Z. Phys. B 1975, 21, 339– 346, DOI: 10.1007/BF01325393
  43
  Dielectric function and plasma resonances of small metal particles
  Genzel, L.; Martin, T. P.; Kreibig, U.
  Zeitschrift fuer Physik [Sektion] B: Condensed Matter and Quanta (1975), 21 (4), 339-46CODEN: ZPBBDJ; ISSN:0340-224X.
  By using the simple model of electrons in a box, a dielec. function is derived which should be appropriate for small metal particles. This dielec. function is used to examine quantum size effects in the optical absorption spectra. For very small particles of uniform size and shape, the plasma resonance absorption should shift and broaden and should show fine structure corresponding to transitions between discrete conduction band energy levels. The size dependence of the shift and broadening was measured and found to be in quant. agreement with theory.
44. 44
  Lünskens, T.; Heister, P.; Thämer, M.; Walenta, C. A.; Kartouzian, A.; Heiz, U. Plasmons in supported size-selected silver nanoclusters. Phys. Chem. Chem. Phys. 2015, 17, 17541– 17544, DOI: 10.1039/C5CP01582K
  44
  Plasmons in supported size-selected silver nanoclusters
  Luenskens, Tobias; Heister, Philipp; Thaemer, Martin; Walenta, Constantin A.; Kartouzian, Aras; Heiz, Ulrich
  Physical Chemistry Chemical Physics (2015), 17 (27), 17541-17544CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  The plasmonic behavior of size-selected supported Ag clusters is studied by surface 2nd harmonic generation spectroscopy. A blue shift of ∼0.2 eV in the plasmon resonance is obsd. with decreasing cluster size from Ag55 to Ag9. In addn. to the general blue shift, a nonscalable size-dependence is obsd. in plasmonic behavior of Ag nanoclusters, which is attributed to varying structural properties of the clusters. The results are in quant. agreement with a hybrid theor. model based on Mie theory and the existing DFT calcns.
45. 45
  Yu, C.; Schira, R.; Brune, H.; von Issendorff, B.; Rabilloud, F.; Harbich, W. Optical properties of size selected neutral Ag clusters: electronic shell structures and the surface plasmon resonance. Nanoscale 2018, 10, 20821– 20827, DOI: 10.1039/C8NR04861D
  45
  Optical properties of size selected neutral Ag clusters: electronic shell structures and the surface plasmon resonance
  Yu, Chongqi; Schira, Romain; Brune, Harald; von Issendorff, Bernd; Rabilloud, Franck; Harbich, Wolfgang
  Nanoscale (2018), 10 (44), 20821-20827CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
  We present optical absorption spectra from the UV to the visible for size selected neutral Agn clusters (n = 5-120) embedded in solid Ne. We compare the spectra to time-dependent d. functional calcns. (TDDFT) that address the influence of the Ne matrix. With increasing size, several highly correlated electron excitations gradually develop into a single surface plasmon. Its energy is situated between 3.9 and 4.1 eV and varies with size according to the spherical electronic shell model. The plasmon energy is highest for clusters with atom nos. fully filling states with the lowest radial quantum no. (e.g. 1s, 1p, 1d,...). TDDFT calcns. for clusters with several candidate geometrical structures embedded in Ne show excellent agreement with the exptl. data, demonstrating that the absorption bands depend only weakly on the exact structure of the cluster.
46. 46
  Tiggesbäumker, J.; Köller, L.; Meiwes-Broer, K.-H.; Liebsch, A. Blue shift of the Mie plasma frequency in Ag clusters and particles. Phys. Rev. A 1993, 48, R1749, DOI: 10.1103/PhysRevA.48.R1749
  There is no corresponding record for this reference.
47. 47
  Charlé, K.-P.; Schulze, W.; Winter, B. The size dependent shift of the surface plasmon absorption band of small spherical metal particles. Z. Phys. D 1989, 12, 471– 475, DOI: 10.1007/BF01427000
  47
  The size dependent shift of the surface plasmon absorption band of small spherical metal particles
  Charle, K. P.; Schulze, W.; Winter, B.
  Zeitschrift fuer Physik D: Atoms, Molecules and Clusters (1989), 12 (1-4), 471-5CODEN: ZDACE2; ISSN:0178-7683.
  The surface plasmon of small spherical particles, which are embedded in a noble gas matrix, shifts to higher energies (blue shift) as the mean diam. D of the particles decreases (100 > D > 20 Å). This blue shift was found for supported Ag particles, and recently it was obsd. by elastic light scattering in the gas phase. This latter expt. proves that the blue shift in small Ag particles is not induced by interactions with the environment, the presence of which is recognized in less inert matrixes such as O2 or CO. From self-consistent calcns. of the surface response of planar jellium surfaces, one would expect a red shift, which is directly confirmed by a few calcns. for selected jellium spheres. The concn. between the obsd. blue shift for small particles and the predicted red shift for jellium spheres disappears, if one accounts for the d-electrons of Ag in a simple approxn.
48. 48
  Jensen, T. R.; Malinsky, M. D.; Haynes, C. L.; Van Duyne, R. P. Nanosphere lithography: tunable localized surface plasmon resonance spectra of silver nanoparticles. J. Phys. Chem. B 2000, 104, 10549– 10556, DOI: 10.1021/jp002435e
  48
  Nanosphere Lithography: Tunable Localized Surface Plasmon Resonance Spectra of Silver Nanoparticles
  Jensen, Traci R.; Malinsky, Michelle Duval; Haynes, Christy L.; van Duyne, Richard P.
  Journal of Physical Chemistry B (2000), 104 (45), 10549-10556CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
  The wavelength corresponding to the extinction max., λmax, of the localized surface plasmon resonance (LSPR) of silver nanoparticle arrays fabricated by nanosphere lithog. (NSL) can be systematically tuned from ∼400 nm to 6000 nm. Such spectral manipulation was achieved by using (1) precise lithog. control of nanoparticle size, height, and shape, and (2) dielec. encapsulation of the nanoparticles in SiOx. These results demonstrate an unprecedented level of wavelength agility in nanoparticle optical response throughout the visible, near-IR, and mid-IR regions of the electromagnetic spectrum. It will also be shown that this level of wavelength tunability is accompanied with the preservation of narrow LSPR bandwidths (fwhm), Γ. Addnl., two other surprising LSPR optical properties were discovered: (1) the extinction max. shifts by 2-6 nm per 1 nm variation in nanoparticle width or height, and (2) the LSPR oscillator strength is equiv. to that of at. silver in gas or liq. phases. Furthermore, it will be shown that encapsulation of the nanoparticles in thin films of SiOx causes the LSPR λmax to red shift by 4 nm per nm of SiOx film thickness. The size, shape, and dielec.-dependent nanoparticle optical properties reported here are likely to have significant impact in several applications including but not limited to the following: surface-enhanced spectroscopy, single-mol. spectroscopy, near-field optical microscopy, nanoscopic object manipulation, chem./biol. sensing, information processing, data storage, and energy transport in integrated optical devices.
49. 49
  Hilger, A.; Cüppers, N.; Tenfelde, M.; Kreibig, U. Surface and interface effects in the optical properties of silver nanoparticles. Eur. Phys. J. D 2000, 10, 115– 118, DOI: 10.1007/s100530050531
  49
  Surface and interface effects in the optical properties of silver nanoparticles
  Hilger, A.; Cuppers, N.; Tenfelde, M.; Kreibig, U.
  European Physical Journal D: Atomic, Molecular and Optical Physics (2000), 10 (1), 115-118CODEN: EPJDF6; ISSN:1434-6060. (Springer-Verlag)
  The authors present novel exptl. results about influences of surrounding foreign materials on optical properties of small Ag clusters. The authors show spectra of free cluster beams produced with different seeding gases Ar, Kr, Xe. The authors est., from measured spectra, the cluster deformations and contact areas after deposition on different substrates (Cr2O3 and MgF2) at room temp. and on SiO2 at 110 K and at 160 - 300 K. The authors present and compare the static and dynamic charge transfer after embedding the clusters in various fluorides and compare with previous results on oxides.
Supporting Information
Supporting Information
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- Dependence of the absorption spectrum on ϵ_d and semiclassical hot carrier distributions (PDF)
- jp0c07617_si_001.pdf (249.57 kb)
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Dielectric Engineering of Hot-Carrier Generation by Quantized Plasmons in Embedded Silver NanoparticlesClick to copy article linkArticle link copied!

The Journal of Physical Chemistry C

Abstract

Introduction

Methods

Results and Discussion

Description of the Model

Optical Properties of Silver Nanoparticles

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Hot-Carrier Properties of Silver Nanoparticles

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Conclusions

Supporting Information

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Author Information

Acknowledgments

References

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The Journal of Physical Chemistry C

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Abstract

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Supporting Information

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Dielectric Engineering of Hot-Carrier Generation by Quantized Plasmons in Embedded Silver Nanoparticles
Click to copy article linkArticle link copied!