• We assume that all the atoms in metallic bonds are alike, in that they all have diffuse electron densities. They would be the cations in ionic bonds.
• Like the cation in ionic crystals, these atoms give up their valence electrons, but instead of giving the electrons to some other specific atom, they are redistributed to all, and are shared by all. The model is called "electron gas".
• Eg. Na metal. 1s²2s²2p⁶3s¹. Each Na atom gives up its 3s¹ electrons. We end up with an array of positive ions in a sea or gas of negative charged space.
• The electron gas behaves like the glue.
• Each of the valence electrons has about the same energy and since they are so diffuse to begin with, they are free to move around from atom to atom, or even place to place, within the crystal with no serious energy restrictions.

• Since we assume that all the valence electrons have been given to the electron gas, then the atoms are closed shell and assumed to be spherical, just as in the ionic model.
• Electron density of copper. Compare this with the electron density of NaCl. Note that every nearest neighbor atom has a bond in Cu, but not in NaCl.

Electron density map of copper

Electron density map of NaCl

• Properties:

• Metallic shiny luster
Eg Li metal, 1s²2s¹: Each atom has 8 nearest neighbor atoms, 6 2^nd nearest neighbors, spherical symmetry on 2s electronic orbitals. All these 2s orbitals interpenetrate to give de-localized or multi-centered orbitals throughout the whole crystal. This produces a spectrum of energies, or a "band" of energies, with only a small energy gap between the ground state and the excited state. There are a large number of these low-lying excited states, all with energy differences in the visible light range. Therefore, after striking a metallic object, light is immediately absorbed and an electron jumps up a quantum level into an excited state. This is why metals are opaque, all photons are captured at the surface. In addition, the electron quickly drops back to the ground state, thereby emitting a photon, (l change between incident wavelength and emmitted wavelength is small because l (wavelength) of incoming photon matched the DE of the electron transfer so well) and we observe reflection.
• Malleable
Because the metal is made of spherical atoms in a sea of electrons the atoms tend to pack like marbles in a box, with non-directional bonding. If you hit a metal, say with a hammer, then the metal tends to deform rather than break like an ionic crystal. This is related to the way that the atoms are packed, along with the non-directional bonding, you can glide or roll them easily over each other. The motion is actually related to defects in the crystal structure that are known as dislocations. If a metal is hammered enough, then it hardens (called cold working). This is because the large number of defects stops the gliding process.
• Electrical conductivity
The electrons are not strongly bonded to any individual atom, so they are free to travel.
• Alloys
Because the atoms are considered to be positive spheres in a sea of electrons then any similar sized sphere can fit right in without too much trouble. Even dissimilar sized (eg small H) can fit into the interstices.
• Dense
Since the atoms are packed together like marbles, you can put a lot of them into a given volume.
• At high pressures most elements become metallic.

Covalent Bonding

• A type of bond that is intermediate between ionic and metallic is the covalent bond where atoms in groups (or molecules) of 2 or more share electrons.

• Eg H₂, N₂, O₂.
• H:H where the resulting electronic configuration mimics the closed shell around each H atom simultaneously.
• These groups of atoms are quite stable and do not react easily.
• The most important covalent bond is formed with carbon. We could think of some C giving up 4 e^- and others accepting 4 e^-, or all the carbons give up 4 e^- into a sea to form a metal, but this just does not happen. Instead, the electrons are shared along individual bonds.
• Organic chemistry is the study of the carbon bond.
• The first thing that we notice is that if the atoms are sharing the e^- then the e^- must be located in between the atoms. Therefore the atoms do not have spherical shapes.
• Lewis dot diagrams.
Eg Cl₂, 1s²2s²2p⁶3s² 3p⁵=Ne3s²3p⁵ to form molecules (0 dimensional) crystal structure
Eg S, Ne3s²3p⁴ forming polymers (1 dimensional) crystal structure
Eg P, Ne3s²3p³ forming sheets (2 dimensional) crystal structure
Eg Si, Ne3s²3p² forming tetrahedral framework (3 dimensional) crystal structure
• The angular relationship between bonds is largely a function of the number of electron pairs.
Eg 2 pairs, linear, eg CO₂
Eg 3 pairs, triangular, CO₃
Eg 4 pairs, tetrahedral, SiO₄

The electron density model of bonding
• Recent work centered on the analysis of the electron density around bonded pairs of atoms show that the models discussed above for ionic, metallic and covalent are over simplified.
• The electrons around an atom do not really deform all that much in order to form a bond. The atoms really are quite spherical.

• Ionic bonds typically form between pairs of atoms where one atom has diffuse electron density and the electron density of the other falls off rapidly.
• Metallic bonds typically form between atoms where both have diffuse electron density.
• Covalent bonds typically form between atoms where both have electron densities that fall off rapidly.
• Nature does not put names on the bonds, they simply form between pairs of atoms. Every bond is unique, i.e. the MgO bond is different from the SiO bond, which is different from the CH bond, and so on.

Polarized Bonds
• Links neutral molecules together if the molecules display some sort of dipole behavior. Eg. The crystal structure of ice is stabilized by the polarized bonds formed between oriented water molecules.
• Eg: Surface of NaCl, Na exposed, H₂O bonds to it with the O-side of the molecule facing the Na atom. Where the Cl is exposed, then the water molecule bonds to Cl with an orientation such that the H-side of the molecule is towards the Cl.
• If the bonding in a molecule leaves one part of the molecule with more charge than another, then we have polar bonds. This is why the neutral molecule H₂O can dissolve rocksalt.
• Another example is the CO₂ quadrupole, forming dry ice.

Hydrogen Bond
• We assume that H, with only 1 electron, should be able to bond to only one other atom. But experimental evidence suggests that this is not so. There is often a second weak polar bond on the proton side of H. We should consider that the hydrogen bond is a special case of a polar bond. For example, brucite, Mg(OH)₂. The hydrogen bonds hold the layers together.

van der Waals
• Bonding between dynamic dipoles.
• Eg graphite: C = sp² hybrid.

• Eg. He is solid at low T, here is a cartoon of the He₂ system in its crystal structure.

• "The assumption of van der Waals forces is usually made in the absence of better information and is an admission of ignorance about the detailed nature of the intermolecular interaction." Zallen, Slade and Ward (1971)

Clathrates
• Molecules in cages.
• Eg. CH₄ in H₂O clathrate at pressure in deep ocean floors is estimated by the US federal government to have enough methane to satisfy the energy needs for the entire Earth for the next 300 years. link