Band Theory and Colors - What causes the colors of metals like gold?

Band Theory

When light strikes the surface of a metal, electrons in a lower energy level can be excited to a higher energy level. The distance between the levels represents the relative energy required to excite an electron. When four atoms combine, the outermost energy levels merge, providing four energy levels at a low energy and four energy levels at a higher energy. As the number of neighboring atoms increases, the spacing between the energy levels decreases. More overlap occurs and bands of low and high energy replace the distinct energy levels. As more atoms combine, the distance between the two bands decreases, the band gap decreases, and less energy is required for the electron to be excited from one band to the other. In metals, when very large numbers of atoms are brought close to each other, the low and high energy bands can overlap, forming a nearly continuous band of available energy levels, where electrons may move freely.

Above the Fermi level, energy levels are empty (empty at absolute zero), and can accept excited electrons. The surface of a metal can absorb all wavelengths of incident light, and excited electrons jump to a higher unoccupied energy level. This creates current, which rapidly discharges to emit a photon of light of the same wavelength. So, most of the incident light is immediately re-emitted at the surface, creating the metallic luster we see in gold, silver, copper, and other metals. This is why most metals are white or silver, and a smooth surface will be highly reflective, since it does not allow light to penetrate deeply.

Metals are colored because the absorption and re-emission of light are dependent on wavelength. Gold and copper have low reflectivity at short wavelengths, and yellow and red are preferentially reflected, as the color here suggests. Silver has good reflectivity that does not vary with wavelength, and therefore appears very close to white.

Showing the variation of density of states and the excitation seen in gold, silver and copper (actually from the 3d band to above the Fermi level)

The blue end of the spectrum is at a higher energy level than yellow and orange.

The color of metals can be explained by band theory, which assumes that overlapping energy levels form bands.

The mobility of electrons exposed to an electric field depends on the width of the energy bands, and their proximity to other electrons. In metallic substances, empty bands can overlap with bands containing electrons. The electrons of a particular atom are able to move to what would normally be a higher-level state, with little or no additional energy. The outer electrons are said to be "free," and ready to move in the presence of an electric field.

Some substances do not experience band overlap, no matter how many atoms are in close proximity. For these substances, a large gap remains between the highest band containing electrons (the valence band) and the next band, which is empty (the conduction band). As a result, valence electrons are bound to a particular atom and cannot become mobile without a significant amount of energy being made available. These substances are electrical insulators. Semiconductors are similar, except that the gap is smaller, falling between these two extremes.

The highest energy level occupied by electrons is called the Fermi energy, Fermi level, or Fermi surface.

Above the Fermi level, energy levels are empty (empty at absolute zero), and can accept excited electrons. The surface of a metal can absorb all wavelengths of incident light, and excited electrons jump to a higher unoccupied energy level. This creates current, which rapidly discharges to emit a photon of light of the same wavelength. So, most of the incident light is immediately re-emitted at the surface, creating the metallic luster we see in gold, silver, copper, and other metals. This is why most metals are white or silver, and a smooth surface will be highly reflective, since it does not allow light to penetrate deeply.

If the efficiency of absorption and re-emission is approximately equal at all optical energies, then all the different colors in white light will be reflected equally well. This leads to the silver color of polished iron and silver surfaces.

The efficiency of this emission process depends on selection rules. However, even when the energy supplied is sufficient, and an energy level transition is permitted by the selection rules, this transition may not yield appreciable absorption. This can happen because the energy level accommodates a small number of electrons.

For most metals, a single continuous band extends through to high energies. Inside this band, each energy level accommodates only so many electrons (we call this the density of states). The available electrons fill the band structure to the level of the Fermi surface and the density of states varies as energy increases (the shape is based on which energy levels broaden to form the various parts of the band).

If the efficiency decreases with increasing energy, as is the case for gold and copper, the reduced reflectivity at the blue end of the spectrum produces yellow and reddish colors.

Metals are colored because the absorption and re-emission of light are dependent on wavelength. Gold and copper have low reflectivity at short wavelengths, and yellow and red are preferentially reflected, as the color here suggests. Silver has good reflectivity that does not vary with wavelength, and therefore appears very close to white.

Silver, gold and copper have similar electron configurations, but we perceive them as having quite distinct colors. Electrons absorb energy from incident light, and are excited from lower energy levels to higher, vacant energy levels. The excited electrons can then return to the lower energies and emit the difference of energy as a photon.

If an energy level (like the 3d band) holds many more electrons (than other energy levels) then the excitation of electrons from this highly occupied level to above the Fermi level will become quite important. Gold fulfills all the requirements for an intense absorption of light with energy of 2.3 eV (from the 3d band to above the Fermi level). The color we see is yellow, as the corresponding wavelengths are re-emitted. Copper has a strong absorption at a slightly lower energy, with orange being most strongly absorbed and re-emitted. In silver, the absorption peak lies in the ultraviolet region, at about 4 eV. As a result, silver maintains high reflectivity evenly across the visible spectrum, and we see it as a pure white. The lower energies (which in this case contain energies corresponding to the entire visible spectrum of color) are equally absorbed and re-emitted.

Silver and aluminum powders appear black because the white light that has been re-emitted is absorbed by nearby grains of powder and no light reaches the eye.

Showing the variation of density of states and the excitation seen in gold, silver and copper (actually from the 3d band to above the Fermi level)

The blue end of the spectrum is at a higher energy level than yellow and orange.

Transmitted color of gold

Gold is so malleable that it can be beaten into gold leaf less than 100 nm thick, revealing a bluish-green color when light is transmitted through it. Gold reflects yellow and red, but not blue or blue-green. The direct transmission of light through a metal in the absence of reflection is observed only in rare instances.

Colored gold alloys

When two metals are dissolved in each other (as is the case with alloys), the color is often a mixture of the two. For example, copper dissolved in gold changes the color from a yellow-gold to a red-gold. Silver dissolved in gold creates a green-gold color. White gold contains palladium and silver. The color of gold jewelry can be attributed to the addition of different amounts of several metals (such as copper, silver, zinc, and so on). Some of these color changes can be explained by shifts in the energy levels relative to the Fermi level.


This platinum ring has rose gold flowers with diamond centers to either side of the central diamond, and leaves of green gold.


These 18 karat gold bands contrast the hues of white, pink and green gold.

Some alloys form intermetallics, where strong covalent bonds replace metallic bonding. Bonding is localized, so there is no sea of electrons.


The addition of aluminum to gold creates a brittle purple gold. Purple gold used in a pin, and a purple gold inlay within a yellow gold ring.

When indium or gallium is added to gold, a blue color can result. The cause of color in these intermetallics is different than that of yellow gold.

Surface colors

Many metals create the illusion of being colored. The color can be attributed to a very thin surface coating, such as a paint or dye, or thin oxide layers can create interference colors (see butterflies) similar to those in oil or soap bubbles.

Some metals like aluminum (left) and titanium (right) can be anodized to create colors. The anodizing process creates a thin oxide layer. Aluminum and titanium films produced by anodizing can form thin, transparent coatings that produce interference effects in reflected light. The colors are applied using a bath, a brush, or a sponge, with the voltage applied determining the final color. Another anodizing application, particularly in aluminum, is the formation of thick, porous coatings that can absorb dyes to produce intense colors.


Stainless steel can also be colored, the color varying with oxide thickness, but the anodizing process is not used. In Sky Church, the purple area consists of stainless steel, coated to create interference effects. The panels appearing to flutter above the path of the monorail speeding below are made from painted aluminum.


Gold can be colored by creating surface oxide layers. Because gold does not oxidize in its pure form, base metals have to be added to create blue, brown, and black gold. The "Hearts" collection, in blue gold, is by Ludwig Muller of Switzerland. Crosses of black gold may be colored in different ways, as shown above.


This antique engraved Czechoslovakian glass shows color produced by colloidal suspensions. When gold is in metallic colloidal form, as in the 10-nm-diameter particles in "ruby glass," the very complex "Mie scattering theory" has to be used to explain the unexpected red color illustrated; the yellow glass in this figure is colored by Mie scattering from metallic colloidal silver particles.

The color of nanoparticles
The color known as "Purple of Cassius" in glass and glass enamel is created by incorporating a colloidal suspension of gold nanoparticles, a technology in use since ancient times. Colloidal silver is yellow, and alloys of gold and silver create shades of purple-red and pink.

Nanoshells are a recent product from the field of nanotechnology. A dielectric core is coated with metal, and a plasmon resonance mechanism creates color, the wavelength depending on the ratio of coating thickness to core size. For gold, a purple color gives way to greens and blues as the coating shell is made thinner. In the future, jewelry applications may include other precious metals, such as platinum.


Dispersions of discrete gold nanoparticles in transparent media provide a fascinating range of colors, only recently exploited in the manufacture of paints and coatings. The shape of the particles and the viewing conditions determine the color we see. The gold particles in the test tubes on the left are shown in transmitted light, while the image on the right shows the same gold nanoparticles viewed in reflected light.

The diameter of gold nanoparticles determines the wavelengths of light absorbed. The colors in this diagram illustrate this effect.

Different sized quantum dot nanoparticles are shown above, first in ultraviolet light and then in ambient light. The length of the synthesis reaction determines particle size for CdSe, increasing from left to right. In colloidal suspension, this semiconductor behaves in the same way as a metal.

https://www.webexhibits.org/causesofcolor/9.html

Kind of makes me wonder if gold "shines" at absolute zero?

The Heat Capacity and Entropy of Gold from 15 to 300°K.1
T. H. Geballe and W. F. Giauque
Cite this: J. Am. Chem. Soc. 1952, 74, 9, 2368–2369
Publication Date:May 1, 1952
https://doi.org/10.1021/ja01129a056
American Chemical Society
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https://pubs.acs.org/doi/pdf/10.1021/ja01129a056?src=recsys
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Hydrogen bonds to Au atoms in coordinated gold clusters
Md. Abu Bakar, Mizuho Sugiuchi, Mitsuhiro Iwasaki, Yukatsu Shichibu & Katsuaki Konishi
Nature Communications volume 8, Article number: 576 (2017) Cite this article

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Matters Arising to this article was published on 09 April 2019

Abstract
It is well known that various transition elements can form M···H hydrogen bonds. However, for gold, there has been limited decisive experimental evidence of such attractive interactions. Herein we demonstrate an example of spectroscopically identified hydrogen bonding interaction of C–H units to Au atoms in divalent hexagold clusters ([Au6]2+) decorated by diphosphine ligands. X-ray crystallography reveals substantially short Au–H/Au–C distances to indicate the presence of attractive interactions involving unfunctionalized C–H moieties. Solution 1H and 13C NMR signals of the C–H units appear at considerably downfield regions, indicating the hydrogen-bond character of the interactions. The Au···H interactions are critically involved in the ligand-cluster interactions to affect the stability of the cluster framework. This work demonstrates the uniqueness and potential of partially oxidised Au cluster moieties to participate in non-covalent interaction with various organic functionalities, which would expand the scope of gold clusters.

Introduction
For several decades, interatomic forces between metal (M) and hydrogen atoms (M···H or H···M) have attracted continuing interest not only from the fundamental aspects of chemical bonding but also in relation to their involvement in some organometallic catalysts. One of the typical examples is the “agostic” bond used for 3-center-2-electron C–H···M systems1,2,3,4. On the other hand, similar but different types of interactions that cannot be categorized in the agostic family are also known1, 5,6,7,8,9. Various terms, e.g., anagostic and preagostic, have been proposed for the description of such M···H–C systems, but they are virtually electrostatic-based attractive forces and are more similar to hydrogen bonds. In this relation, numerous examples of M···H “hydrogen bonds” involving O–H/N–H donor groups have been reported for the complexes of various transition metal elements5, 10,11,12,13,14,15,16,17,18.

Among late-transition metal elements gold occupies a special position because of the strong relativistic effect19. For the interaction with hydrogen atoms, plenty of examples of close contacts with hydrogen atoms have been reported in the crystal structures of Au–, Au+, and Au3+ complexes20. However, as claimed in a recent review by Schmidbaur et al., the reported contacts are mostly due to the ligand-counterion interaction and/or crystal packing rather than the attractive interactions between Au and H atoms. Very recently, the first example of “agostic” C–H···Au interactions was reported21, but even now there have been no examples of spectroscopically identified “hydrogen-bond type” Au···H interactions22. This is contrasted with the cases of the other transition metal complexes (e.g., platinum11,12,13,14,15,16), which offer abundant examples of M···H hydrogen bonds.

Ligand-protected gold clusters have currently attracted attention as a class of molecule-like metal species residing between particles and simple complexes23,24,25,26. Recent steep advances in the experimental/theoretical structural studies have revealed the critical involvement of the residual 6 s electrons in the emergence of unique structural and optical/electronic features, which lead to the development of superatom concepts. One of the emerging topics in this research area is unique catalysis27,28,29,30. However, the mechanism behind the catalytic processes, e.g., the interaction/activation at the gold surface, is still ambiguous because of the lack of information on the nature of interaction of the gold core with organic substrates.

In this work, we provide an example of Au···H–C hydrogen bonds in diphosphine-ligated divalent Au6 clusters, which are firmly evidenced by both X-ray crystallography and solution nuclear magnetic resonance (NMR) spectroscopy, and reveal that hydrogen bonding to Au atoms is a possible interaction mode between organic moieties and an Au cluster. We also demonstrate the electronic coupling of the Au6 cluster unit with neighbouring π-systems, and possible contributions of the Au···H–C interactions to the maintenance of the cluster framework to enhance the intrinsic stability.

Results
Synthesis and crystal structures of Au6 clusters
The gold clusters we employed in this study here have a core + exo-type Au6 framework decorated by four diphosphine ligands (Fig. 1a). During the course of studies exploring new diphosphine-ligated Au clusters25, we preliminarily found that the solution colours of two Au6 clusters decorated by m-phenylene-bridged ([Au6(mPhDP)4]2+, 1) and by trimethylene-bridged diphosphines ([Au6(TMDP)4]2+, 2) (Fig. 1a, b) are significantly different. Since the electronic structure features and optical properties of molecular-sized Au clusters are essentially governed by their nuclearity and geometrical structures of the metallic units31, 32, the above significant ligand effect is puzzling, which motivated us to obtain further insights from structural aspects.

Fig. 1
figure 1
Structures of the diphosphine ligands and the hexagold clusters. a Schematic illustration of the Au6 cluster decorated by four diphosphine ligands. b Chemical structures of the mPhDP and TMDP ligands. c, d X-ray crystal structure of the cationic moieties of 1·(PF6)2 (c) and 2·(NO3)2 (d). H-2 atoms nearest neighbour to the cluster moieties highlighted in light green with the other H atoms omitted for clarity. Au, P, and C atoms are coloured in yellow, orange, and gray, respectively. e–g Partial structures of 1. e A bird view showing the Au6 unit and a diphosphine ligand moiety. f A side view highlighting the Au···H–C interaction. g A top view showing the phenylene unit and neighbouring four Au atoms

Full size image
The cluster carrying m-phenylene-bridged diphosphines (1) was synthesized in a similar manner to that reported previously for the synthesis of a trimethylene-bridged cluster (2)33, 34. Briefly, the treatment of [Au9(PPh3)8](NO3)3 with mPhDP (Fig. 1b) in dichloromethane resulted in an instant color change from yellowish brown to greenish blue. The cationic cluster generated was isolated as the PF6 salt, which was thoroughly characterized by means of mass spectrometry, elemental analysis, and single-crystal X-ray analysis. For example, electrospray ionization mass (ESI-MS) spectrum in methanol showed a sole set of signals at ~1484 in the range 1–6 kD, which was unambiguously assigned to the divalent cluster cation through comparison with the simulated isotope distribution pattern (Supplementary Fig. 1). X-ray crystallographic analysis (Fig. 1c) revealed that the geometrical structure of the Au6 unit is very similar to that of 2 (Fig. 1d), having a core + exo type structure composed of a tetrahedral Au4 core and two attached gold atoms at the exo positions. For instance, the Au–Au distances of 1 fell in the range 2.624–2.929 Å, which is close to that of 2 (2.614–2.966 Å).

The crystal structure also revealed close contacts of the gold framework to the bridging m-phenylene units. As shown in the partial structures (Fig. 1e–g), the hydrogen atom at the 2-position of an m-phenylene bridge (H-2) is located in proximity to Au2 with an apparent distance of 2.723 Å. For these results, one has to consider that the H positions were determined by the calculation based on the geometrically determined positions (riding model), giving shorter C–H bond lengths (~0.95 Å) than the “true” C–H lengths (1.08 Å)35. By simple geometrical calculation, the distance between H-2 and Au2 (Fig. 1c) was corrected to be 2.60 Å (Table 1), which is definitively shorter than the sum of the van der Waals radii (2.86 Å). Accordingly, the distance between C-2 and Au2 atoms in Fig. 1c (3.641 Å) was explicitly shorter than the Au–C distance when C, H, and Au atoms are aligned with van der Waals Au–H contact (3.95 Å). As summarized in Table 1, the other three phenylene units also showed sufficiently short Au–H and Au–C distances, which fall in the ranges of 2.60–2.65 Å (average 2.62 Å) and 3.641–3.699 Å (average 3.671 Å), respectively. Therefore, all four phenylene bridges are clipped to the Au6 unit by attractive interactions. The Au–H–C angles for the above short Au–H contacts were in the range of 162.0–171.0° (Table 1). Therefore, considering the criterion for the distinction between the agostic/anagostic interactions1, the interactions between the Au and H atoms should have hydrogen-bond characters rather than agostic.

https://www.nature.com/articles/s41467-017-00720-3