Optical properties of Ag, Au, and Cu from first principles

Emmanouil Kioupakis; Xiao Zhang

REVIEW 3 major objections 5 minor 13 references

Optical properties of Ag, Au, and Cu from first principles

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A first-principles framework reproduces the infrared-to-visible optical spectra of silver, gold, and copper.

desk verdict Solid benchmark computation that puts direct, phonon-assisted, and Drude contributions on the same footing for Ag, Au, and Cu, but the fitted Hubbard U makes the headline agreement partly postdictive. read the letter →

arxiv 2608.02968 v1 pith:R3MM2E54 submitted 2026-08-04 cond-mat.mtrl-sci

Xiao Zhang , Emmanouil Kioupakis This is my paper · ORCID

classification cond-mat.mtrl-sci PACS 78.20.Ci71.20.Gj71.15.Qe

keywords opticalpropertiesofmetalsnobleGWapproximationphonon-assistedabsorptionDrudecontributionBoltzmanntransportequationdielectricfunctionfirst-principlescalculation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the measured optical constants of silver, gold, and copper can be computed from first principles by combining DFT+GW+U electronic structure, phonons from density-functional perturbation theory, Wannier interpolation, and the Boltzmann transport equation. The central result is that the imaginary part of the dielectric function $\mathrm{Im}\,\varepsilon(\omega)$ from the infrared through the visible is reproduced only when both single-particle excitations (direct and phonon-assisted) and the collective Drude (resistive) contribution are included. Below the direct absorption onset, the phonon-assisted and resistive terms are comparable in magnitude, so omitting either one would visibly misfit the measured spectrum. The authors use the decomposition to show that gold's broad absorption onset comes from strong spin–orbit splitting of the 5d bands, while silver and copper have sharp onsets. The framework is meant to be a generally applicable tool for optoelectronic response of metallic materials.

What carries the argument

The central mechanism is a three-channel decomposition of the optical absorption spectrum computed on fine Brillouin-zone grids: direct interband transitions, phonon-assisted indirect transitions evaluated with second-order perturbation theory (regularized by a $0.1$ eV broadening parameter to control the resonant divergence), and the resistive Drude term obtained from the converged Boltzmann-transport electrical conductivity. All channels are fed by a PBEsol$+U+$GW quasiparticle band structure with spin–orbit coupling for Ag and Au, interpolated with maximally localized Wannier functions, with the Hubbard $U$ chosen to match ARPES-measured d-band positions.

What would settle it

A decisive check is a measurement of the dielectric function of a clean single-crystal silver film between $0.4$ and $3.6$ eV with uncertainty small enough to distinguish the paper's total $\mathrm{Im}\,\varepsilon(\omega)$ from its resistive-only or phonon-assisted-only partial sums; a match of the total alongside a mismatch of either partial would confirm the two-channel requirement, while a failure of the total would refute the framework. A second test is to recalculate the spectra with $U=0$: if the d-bands already match ARPES without the Hubbard term, the fitted $U$ is not load-bearing.

Watch

Extended reading notes

Core claim

The paper establishes that the total $\mathrm{Im}\,\varepsilon(\omega)$ of Ag, Au, and Cu, computed as the sum of direct interband absorption, phonon-assisted indirect absorption, and the resistive Drude term, agrees with experimental measurements across the infrared-to-visible range for all three metals. The direct and phonon-assisted contributions are obtained from first- and second-order time-dependent perturbation theory, while the resistive contribution follows from the electrical conductivity found by iteratively solving the Boltzmann transport equation. In the infrared, the phonon-assisted single-particle channel and the collective resistive channel are comparable, and both are required; above the direct onset, direct absorption dominates. The paper also reports that spin–orbit coupling is essential for gold, shifting the strong single-particle onset from about $2.2$ eV to $1.6$ eV and thereby reproducing the experimentally broad absorption edge.

Load-bearing premise

The load-bearing premise is that the Hubbard $U$ values ($1$ eV for Ag and Au, $2$ eV for Cu), fitted to ARPES-measured d-band positions rather than derived from first principles, correctly place the interband absorption onset of all three metals.

Editorial extensions

If this is right

For photon energies below the direct absorption onset, neither the phonon-assisted nor the resistive contribution alone reproduces the measured spectra; both must be computed.
The calculated spectra provide benchmark optical constants for Ag, Au, and Cu that can serve as reference data for plasmonics, photocatalysis, and nanophotonics design.
The decomposition into single-particle and collective channels yields the fraction of absorption that generates hot carriers as a function of photon energy, quantifying the regimes where interband transitions dominate.
Spin–orbit coupling is required for correct optical spectra of gold and silver; omitting it shifts gold's single-particle onset by roughly $0.6$ eV.
Because the machinery is not specific to noble metals, the same approach applies to other metallic materials whose band structures and phonons can be computed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the framework holds, empirical Drude-plus-critical-points models for noble-metal permittivity could be replaced or benchmarked against parameter-light ab initio spectra over the full IR-visible range.
The fitted Hubbard U means the method's predictive power for the absorption onset is conditional on experimental d-band knowledge; for metals without ARPES data, the onset position is the main uncertainty.
The paper notes the phonon-assisted spectrum is sensitive to the broadening parameter below 0.1 eV and above the direct onset; a treatment with phonon lifetimes or vertex corrections could extend the framework reliably into the far infrared.
The predicted strong rise of the single-particle fraction in gold below 2 eV due to spin–orbit coupling could be tested by measuring hot-electron photocurrent or plasmon-induced carrier multiplication in gold nanoparticles in the 1.5–2.5 eV window.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Worth your time if you care about computational optics of metals. The genuinely new thing is the combined treatment: direct interband, phonon-assisted indirect, and resistive Drude contributions are all computed on the same footing for the three noble metals, and the paper shows quantitatively that the phonon-assisted and Drude terms are comparable in the infrared. The decomposition into mechanisms is useful, and the agreement with multiple independent experimental datasets is visually strong. The central comparison is not circular: the optical spectra are not fitted to the optical data, and the key quantities (band structure, phonons, conductivity) are each checked against experiment separately.

The soft spot, as the stress test notes, is the Hubbard U. The U values (1 eV for Ag/Au, 2 eV for Cu) are chosen to match ARPES d-band positions, and those same d-bands set the direct absorption onset that dominates the visible spectrum. So the excellent agreement above the onset is partly a postdiction, not a parameter-free prediction. The paper is transparent about this, and the SI shows how U shifts the bands, but there is no sensitivity analysis of the optical spectra themselves to U. That is a real gap, though it does not sink the framework. The truncation of phonon-assisted absorption above the direct onset is stated and justified; it is a minor limitation, not a flaw. The lack of released code or data is mildly annoying but the methods are described well enough to reimplement. The broadening parameter eta is tested in the SI, and the conductivity convergence is shown.

Overall, the central argument holds: a standard DFT+GW+DFPT+Wannier pipeline plus second-order perturbation theory can reproduce measured optical constants across a wide range. The "first principles" label is a bit generous given the fitted U, but the paper is honest about its choices and the physics conclusions about the comparable roles of single-particle and collective excitations rest on solid ground. I would send this to a serious referee. The expected revision is to add a U-sensitivity check for the optical spectra and to soften the parameter-free language. It is a useful benchmark paper for the plasmonics and hot-carrier communities.

Referee Report

3 major / 5 minor

Summary. This manuscript presents a computational framework for the optical response of metals that combines PBEsol+U+GW quasiparticle band structures, DFPT phonons, Wannier interpolation, iteratively solved Boltzmann transport for conductivity, and first- and second-order perturbation theory for direct and phonon-assisted absorption, plus a Drude resistive term. The framework is applied to Ag, Au, and Cu. The authors report that the calculated imaginary part of the dielectric function and the complex refractive index are in excellent agreement with experimental data from the infrared through the visible, and that both single-particle (direct plus phonon-assisted) and collective (Drude) contributions are needed below the direct interband onset. They also analyze the ratio of single-particle to total absorption and the role of spin-orbit coupling.

Significance. If the results are robust, the paper provides a useful methodological benchmark: a single framework treats direct interband, phonon-assisted, and Drude contributions on equal footing and separates them spectrally, which is valuable for plasmonics and hot-carrier applications. The study is strengthened by multiple experimental comparisons, convergence tests for conductivity and optical grids, and SI sensitivity tests for broadening and spin-orbit coupling. However, the central quantitative comparison relies on Hubbard U parameters fitted to ARPES, and the phonon-assisted term is omitted above the direct onset by assumption, so the headline 'excellent agreement' is not a fully parameter-free prediction. The work is a solid contribution but requires additional sensitivity analysis and a more cautious statement of predictive content.

major comments (3)

[Section 2, Figure 4, SI Figure S1] The Hubbard U parameters (1 eV for Ag and Au, 2 eV for Cu) are fitted to ARPES-measured d-band positions, and the direct interband absorption that dominates the visible spectrum is controlled by those same d-band positions. Although SI Figure S1 documents the effect of U on the band structure, no corresponding sensitivity test is shown for the optical spectra. Since the central claim of the paper is the excellent agreement of the total Imε(ω) with experiment, the authors should quantify how Imε(ω) and the direct onset shift when U is varied (for example, U±0.5 eV) and demonstrate that the agreement is robust; otherwise the comparison is partly postdictive and the 'from first principles' characterization is too strong.
[Section 3.3, SI Section 5.2] The phonon-assisted contribution is excluded for photon energies above the calculated direct-absorption onset because direct transitions are assumed to dominate and the second-order perturbation-theory result is strongly dependent on the broadening η in that region. This is a reasonable physical assumption, but it means that the paper does not actually compute the full spectrum above the onset. The authors should explicitly acknowledge that the visible-region comparison contains only the direct contribution, and should provide a quantitative estimate or bound for the omitted phonon-assisted term, at least for one material, to justify the truncation. The direct onset that defines the truncation boundary also depends on the fitted U, which makes this assumption load-bearing for the headline agreement.
[Section 3.2, Figure 3] The calculated electrical conductivity is converged to within 10% of experiment, and the resistive contribution dominates Imε(ω) below 0.4 eV. Because the Drude term is directly proportional to the conductivity, a 10% error in conductivity translates into a 10% uncertainty in the IR part of the spectrum. The paper should state whether the observed deviations from the experimental IR data are consistent with this uncertainty, or whether they are dominated by other factors such as surface-scattering corrections in the experimental films.

minor comments (5)

[SI Figure S2 caption] The caption lists 'η=0.001,0.05,0.01,0.05 eV' for the dashed curves, which contains a duplicate 0.05 and omits the 0.1 eV value used in the main text; please correct this.
[Introduction, Section 3.3] The phrase 'negative refractive index' for metals is imprecise; the relevant property is the negative real part of the permittivity, while the refractive index is complex.
[Section 3.3] For silver the authors state that the experimental data exhibit higher variance and that their results agree particularly well with recent reports; the choice of which datasets are considered most reliable should be justified more explicitly, since the older Johnson and Christy dataset is widely used.
[Section 2] The sentence describing the choice of U values should explicitly state that the fit is to the d-band positions and should reference the optical sensitivity analysis (or its absence) to avoid the impression that the spectra themselves were fitted.
[Title and Abstract] The phrase 'from first principles' is too strong given the use of experimental lattice constants and ARPES-fitted U; consider 'first-principles-based' or clearly list the empirical inputs in the abstract.

Circularity Check

1 steps flagged · score 3.0 of 10

Direct interband onset is tuned by ARPES-fitted Hubbard U, so the visible-region agreement is partly postdictive; below-onset and resistive contributions remain independent.

fitted input called prediction [Section 2 (Computational methods), GW/U paragraph; Section 3.1 (Electronic structure and phonon dispersion)]
"The U values used are 1 eV for Au and Ag, and 2 eV for Cu. The values are chosen based on agreement between the electronic structure from angle-resolved photoemission experiments 48–51 and our calculated electronic band structure after quasiparticle corrections are taken into account. ... the combination of PBEsol, HubbardU corrections and theGWapproximation ensure good agreement of both the occupied and the empty states with experimentally measured electron energies, which is essential to correctly evaluate the onset of direct optical absorption."

Hubbard U is the empirical tuning parameter that fixes the d-band positions; the minimum direct transition—hence the interband onset in Im ε(ω) that dominates the visible spectrum—is determined by those same d-band positions. The paper selects U by fitting to ARPES-measured band energies and then presents the resulting onset agreement with optical data as a first-principles result. The onset is therefore a fitted quantity relabeled as a prediction. The phonon-assisted and resistive (Drude) contributions below the onset are not fixed by this fit, so the circularity is partial, not total.

full rationale

The central comparison is against independent experimental optical constants, and the optical spectra are not fitted to those data, so the main framework is not circular. The only substantive circularity is the Hubbard U calibration: U is adjusted to reproduce ARPES d-band positions, and those positions control the direct absorption onset that dominates the visible response. Supplemental Fig. S1 shows that varying U shifts the d-bands substantially, yet no corresponding optical-spectrum sensitivity analysis is presented, making the 'excellent agreement' above the onset partly postdictive. The below-onset phonon-assisted and Drude contributions, plus the material-specific SOC effects, are computed from the same band structure but are not directly forced by the U fit, so the central claim retains independent content. Self-citations to the authors' earlier free-carrier absorption formalism (Refs. 15, 55) are methodological and not load-bearing in a circular sense; no uniqueness theorem or ansatz is smuggled in by citation. Score 3 reflects one empirical fit that compromises the 'first principles' label for the direct interband onset without making the whole derivation equivalent to its inputs.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The framework rests on several standard domain assumptions (DFT accuracy, GW accuracy, Wannier interpolation, Boltzmann transport with phonon-only scattering) plus the ad hoc truncation of the phonon-assisted contribution above the direct onset. The main empirical inputs are the three Hubbard U values and the broadening parameter.

free parameters (4)

Hubbard U for Ag = 1 eV
Chosen to match ARPES d-band positions; affects interband absorption onset.
Hubbard U for Au = 1 eV
Chosen to match ARPES d-band positions; affects interband absorption onset.
Hubbard U for Cu = 2 eV
Chosen to match ARPES d-band positions; affects interband absorption onset.
Imaginary broadening eta = 0.1 eV
Hand-chosen to regularize the second-order perturbation divergence; demonstrated to be insensitive in the spectral region of interest (below direct onset), but still a free parameter.

assumptions (7)

domain assumption DFT with PBEsol and the plane-wave cutoff provides accurate ground-state wavefunctions and charge densities for Ag, Au, Cu.
Standard DFT accuracy; not independently verified in this paper.
domain assumption The GW approximation with the generalized plasmon pole model gives accurate quasiparticle energies for the three metals.
Standard MBPT approach; accuracy depends on the approximations, and U is additionally fitted.
domain assumption Wannier interpolation accurately reproduces quasiparticle energies, velocity matrix elements, and electron-phonon matrix elements on fine grids.
Standard method; convergence is tested for conductivity, not explicitly for optical spectra.
domain assumption The iterative Boltzmann transport equation with only electron-phonon scattering (no impurities) describes the DC conductivity of the metals at the temperatures of interest.
The authors compare to experiment within 10%, so this seems reasonable; residual impurity/defect scattering is neglected.
domain assumption Second-order time-dependent perturbation theory with an imaginary broadening is valid for phonon-assisted absorption, and the results are independent of the broadening in the region of interest.
The divergence is regularized; the paper demonstrates insensitivity below the direct onset.
ad hoc to paper Direct transitions dominate above the calculated direct onset, so the phonon-assisted contribution can be omitted there.
This is a truncation of the computed spectrum justified by the expectation that direct transitions dominate, but it removes a computed contribution in that range.
domain assumption Experimental lattice constants and the choice of LDA (not PBEsol) phonons for Cu are appropriate inputs.
Using experimental lattice constants is standard; the LDA phonon choice is ad hoc, made to better match the measured phonon dispersion.

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Cite this review

Pith. "Pith review of Optical properties of Ag, Au, and Cu from first principles." pith.science (2026). https://pith.science/paper/R3MM2E54

@misc{pith2026260802968,
  author       = {Pith},
  title        = {Pith review of: Optical properties of Ag, Au, and Cu from first principles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R3MM2E54}},
  note         = {Machine review of arXiv:2608.02968}
}

read the original abstract

We present a comprehensive framework for investigating the optical response of metals from first principles that combines density functional theory, many-body perturbation theory, and efficient interpolation techniques based on maximally localized Wannier functions, and apply it to analyze the optical properties of silver (Ag), gold (Au), and copper (Cu). We evaluate the optical properties of these metallic materials considering both single-particle direct and phonon-assisted excitations, as well as the resistive Drude contribution. We find an overall excellent agreement with experimental optical measurements for these materials, and show that both single-particle and collective excitations are important in capturing their optical response in the infrared. Our methodology provides fundamental understanding of the optical response of metals and is generally applicable to investigate the optoelectronic properties of emerging metallic materials.

Figures

Figures reproduced from arXiv: 2608.02968 by the authors.

**Figure 2.** Phonon dispersion relationship calculated with Quantum Espresso using DFPT for [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Convergence of electrical conductivity calculated with Wannier interpolation for [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Imaginary part of the dielectric function from phonon-assisted contribution (red), [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Complex refractive index (black curves) evaluated for (a) Ag, (b) Au, and (c) [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Ratio of single-particle absorption contribution to the total absorption character [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

Searching for better plasmonic materials.Laser & Photon

(1) West, P.; Ishii, S.; Naik, G.; Emani, N.; Shalaev, V.; Boltasseva, A. Searching for better plasmonic materials.Laser & Photon. Rev.2010,4, 795–808. (2) Novotny, L.; Hecht, B.Principles of Nano-Optics, 2nd ed.; Cambridge University Press: Cambridge,

work page 2010
[54]

A.; Jain, M.; Cohen, M

(44) Deslippe, J.; Samsonidze, G.; Strubbe, D. A.; Jain, M.; Cohen, M. L.; Louie, S. G. BerkeleyGW: A massively parallel computer package for the calculation of the quasipar- ticle and optical properties of materials and nanostructures.Comput. Phys. Commun 2012,183, 1269 –

work page 2012
[129]

(24) Stahrenberg, K.; Herrmann, T.; Wilmers, K.; Esser, N.; Richter, W.; Lee, M. J. G. Optical properties of copper and silver in the energy range 2.5–9.0 eV.Phys. Rev. B 2001,64, 115111. (25) Marini, A.; Del Sole, R. Dynamical Excitonic Effects in Metals and Semiconductors. Physical Review Letters2003,91. (26) Brown, A. M.; Sundararaman, R.; Narang, P.; ...

work page 2001
[156]

G.; Louie, S

(55) Noffsinger, J.; Kioupakis, E.; Van de Walle, C. G.; Louie, S. G.; Cohen, M. L. Phonon- Assisted Optical Absorption in Silicon from First Principles.Phys. Rev. Lett.2012, 108, 167402. (56) Kamitakahara, W.; Brockhouse, B. Crystal dynamics of silver.Physics Letters A1969, 29, 639–640. 26 (57) Lynn, J. W.; Smith, H. G.; Nicklow, R. M. Lattice Dynamics o...

work page 2012
[222]

L.; Ratner, M

(75) Gieseking, R. L.; Ratner, M. A.; Schatz, G. C.Frontiers of Plasmon Enhanced Spec- troscopy Volume 1; ACS Symposium Series 1245; American Chemical Society, 2016; Vol. 1245; pp 1–22, Section:

work page 2016
[435]

Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.J

(68) Hagemann, H.-J.; Gudat, W.; Kunz, C. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.J. Opt. Soc. Am.1975,65, 742–744. (69) Ferrera, M.; Magnozzi, M.; Bisio, F.; Canepa, M. Temperature-dependent permittivity of silver and implications for thermoplasmonics.Phys. Rev. Mater.2019,3, 105201. (70) Jiang, Y...

work page 1975
[562]

A.; Yates, J

(34) Marzari, N.; Mostofi, A. A.; Yates, J. R.; Souza, I.; Vanderbilt, D. Maximally localized Wannier functions: Theory and applications.Rev. Mod. Phys.2012,84, 1419–1475. (35) Davey, W. P. Precision Measurements of the Lattice Constants of Twelve Common Metals.Phys. Rev.1925,25, 753–761. (36) Maeland, A.; Flanagan, T. B. LATTICE SPACINGS OF GOLD–PALLADIU...

work page 2012
[683]

OPTISCHE EIGENSCHAFTEN VON EDELMETALLEN UBER- GANGSMETALLEN UND DEREN LEGIERUNGEN IM INFRAROT.1965,22,

27 (67) Dold, B.; Mecke, R. OPTISCHE EIGENSCHAFTEN VON EDELMETALLEN UBER- GANGSMETALLEN UND DEREN LEGIERUNGEN IM INFRAROT.1965,22,

work page 1965

Show all 13 references

[693]

M.; Jayanti, S

(61) McPeak, K. M.; Jayanti, S. V.; Kress, S. J. P.; Meyer, S.; Iotti, S.; Rossinelli, A.; Norris, D. J. Plasmonic Films Can Easily Be Better: Rules and Recipes.ACS Photonics 2015,2, 326–333. (62) Wu, Y.; Zhang, C.; Estakhri, N. M.; Zhao, Y.; Kim, J.; Zhang, M.; Liu, X.-X.; Pr...

2015
[2012]

J.; Nicolet, A

(3) Kolesov, R.; Grotz, B.; Balasubramanian, G.; St¨ ohr, R. J.; Nicolet, A. A. L.; Hem- mer, P. R.; Jelezko, F.; Wrachtrup, J. Wave–particle duality of single surface plasmon polaritons.Nature Phys2009,5, 470–474. (4) Ozbay, E. Plasmonics: Merging Photonics and Electronics at...

2001
[5271]

L.; Slovick, B.; Johnson, T

(65) Olmon, R. L.; Slovick, B.; Johnson, T. W.; Shelton, D.; Oh, S.-H.; Boreman, G. D.; Raschke, M. B. Optical dielectric function of gold.Phys. Rev. B2012,86, 235147. (66) Lenham, A. P.; Treherne, D. M. Applicability of the Anomalous Skin-Effect Theory to the Optical Constant...

1966
[5390]

I.; Anisimov, V

(47) Liechtenstein, A. I.; Anisimov, V. I.; Zaanen, J. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators.Phys. Rev. B1995,52, R5467–R5470. 25 (48) Wehner, P. S.; Williams, R. S.; Kevan, S. D.; Denley, D.; Shirley, D. A. Valence-band...

1983
[5788]

(42) Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials.Phys. Rev. B 2013,88, 085117. (43) van Setten, M.; Giantomassi, M.; Bousquet, E.; Verstraete, M.; Hamann, D.; Gonze, X.; Rignanese, G.-M. The PseudoDojo: Training and grading a 85 element optimized norm- ...

2013

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

Searching for better plasmonic materials.Laser & Photon

(1) West, P.; Ishii, S.; Naik, G.; Emani, N.; Shalaev, V.; Boltasseva, A. Searching for better plasmonic materials.Laser & Photon. Rev.2010,4, 795–808. (2) Novotny, L.; Hecht, B.Principles of Nano-Optics, 2nd ed.; Cambridge University Press: Cambridge,

work page 2010

[2] [54]

A.; Jain, M.; Cohen, M

(44) Deslippe, J.; Samsonidze, G.; Strubbe, D. A.; Jain, M.; Cohen, M. L.; Louie, S. G. BerkeleyGW: A massively parallel computer package for the calculation of the quasipar- ticle and optical properties of materials and nanostructures.Comput. Phys. Commun 2012,183, 1269 –

work page 2012

[3] [129]

(24) Stahrenberg, K.; Herrmann, T.; Wilmers, K.; Esser, N.; Richter, W.; Lee, M. J. G. Optical properties of copper and silver in the energy range 2.5–9.0 eV.Phys. Rev. B 2001,64, 115111. (25) Marini, A.; Del Sole, R. Dynamical Excitonic Effects in Metals and Semiconductors. Physical Review Letters2003,91. (26) Brown, A. M.; Sundararaman, R.; Narang, P.; ...

work page 2001

[4] [156]

G.; Louie, S

(55) Noffsinger, J.; Kioupakis, E.; Van de Walle, C. G.; Louie, S. G.; Cohen, M. L. Phonon- Assisted Optical Absorption in Silicon from First Principles.Phys. Rev. Lett.2012, 108, 167402. (56) Kamitakahara, W.; Brockhouse, B. Crystal dynamics of silver.Physics Letters A1969, 29, 639–640. 26 (57) Lynn, J. W.; Smith, H. G.; Nicklow, R. M. Lattice Dynamics o...

work page 2012

[5] [222]

L.; Ratner, M

(75) Gieseking, R. L.; Ratner, M. A.; Schatz, G. C.Frontiers of Plasmon Enhanced Spec- troscopy Volume 1; ACS Symposium Series 1245; American Chemical Society, 2016; Vol. 1245; pp 1–22, Section:

work page 2016

[6] [435]

Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.J

(68) Hagemann, H.-J.; Gudat, W.; Kunz, C. Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3.J. Opt. Soc. Am.1975,65, 742–744. (69) Ferrera, M.; Magnozzi, M.; Bisio, F.; Canepa, M. Temperature-dependent permittivity of silver and implications for thermoplasmonics.Phys. Rev. Mater.2019,3, 105201. (70) Jiang, Y...

work page 1975

[7] [562]

A.; Yates, J

(34) Marzari, N.; Mostofi, A. A.; Yates, J. R.; Souza, I.; Vanderbilt, D. Maximally localized Wannier functions: Theory and applications.Rev. Mod. Phys.2012,84, 1419–1475. (35) Davey, W. P. Precision Measurements of the Lattice Constants of Twelve Common Metals.Phys. Rev.1925,25, 753–761. (36) Maeland, A.; Flanagan, T. B. LATTICE SPACINGS OF GOLD–PALLADIU...

work page 2012

[8] [683]

OPTISCHE EIGENSCHAFTEN VON EDELMETALLEN UBER- GANGSMETALLEN UND DEREN LEGIERUNGEN IM INFRAROT.1965,22,

27 (67) Dold, B.; Mecke, R. OPTISCHE EIGENSCHAFTEN VON EDELMETALLEN UBER- GANGSMETALLEN UND DEREN LEGIERUNGEN IM INFRAROT.1965,22,

work page 1965