In order to give you an idea of some of the different types of bonds that form between elements we are going to consider several representative elements from different areas of the periodic table. For starters, let us take a look at carbon.  Carbon (C) belongs to the family of elements known as non-metals. The bonding between C atoms (and to other types of atoms) is typically described using the covalent bonding model. Each bond involves two electrons (one from each of the bonded atoms).

3.1 Elements & Bonding
3.2 Interactions
3.3 Carbon
3.4 Metals

While this is the most common model, we will see that it is not the only possible one; we will introduce other models as they are needed. Diamond is the name given to one of the naturally occurring forms (allotropes) of pure C; the other allotropes of carbon are graphite, graphene, and various fullerenes (FIGURE BELOW) – which we will return to later.

Diamonds form from carbon rich materials subjected to very high pressure (45,000-60,000 atmospheres) but relatively low temperatures (900-1300 ºC). Such conditions can be found about 100 miles under the Earth’s crust, the region known as the lithosphere. Diamonds have also been found in asteroids, which originate from outside of the earth. Diamonds are so valued because they are rare, sparkly, hard, and almost completely inert. That is: it is very hard to make diamonds do anything at all except sit there and sparkle – they don’t dissolve in water and they melt only at very high temperatures (mp 3330°C ). Diamond has the highest melting point of any known substance, so high that these measurements are actually done under high pressure and then calculated to estimate what the value would be at atmospheric pressure.

Let us step back and look at the properties of diamond and see if we can make sense of them. Since diamond is so stable (chemically inert), it must have very strong bonds that take a lot of energy to break. Since it doesn’t conduct electricity the electrons must not be free to move around within a diamond. A polished diamond is sparkly because some light is reflected from the surface and some light passes through it - making it transparent. If the diamond were not cut with so many facets it would allow most light to pass through it.

If we look at an X-ray diffraction-based structure of diamond, we find that each carbon atom is surrounded by four other carbon atoms situated at equal distances and equal angles from each other. In this context, the most useful model of bonding involves thinking of each carbon atom as forming four covalent (electron sharing) bonds, all arranged so that the electron pairs are as far apart as possible – this places the four bonded atoms at the corners of a tetrahedron, with a central carbon atom.

How do we explain this arrangement in terms of what we know about the electronic structure of carbon atoms? The answer is that the electronic structure of the carbon atoms is reorganized to form molecular orbitals. In the case of carbon, each atom can form four bonding molecular orbitals that are oriented as far apart as possible. There are several models to explain how this occurs, but it is important to remember that they are all models, designed to help us understand the properties of diamond.

The molecular orbital model

Another way to consider how these bonds form is similar to the way we approached molecular hydrogen. That is we consider that when carbon–carbon (C–C) bonds form, atomic orbitals are transformed into molecular orbitals. For each stabilizing bonding orbital, a destabilizing anti-bonding orbital is also formed. Using the molecular orbital approach we can model the bonding in diamond as carbon atoms forming a three-dimensional network held together by these molecular bonding orbitals. Carbon-carbon bonds are very stable - that is the bonding MOs are sitting in a low energy potential well and only the low energy, stabilizing, bonding orbitals are occupied. There is a large energy gap between the bonding and anti-bonding molecular orbitals and the high energy anti-bonding orbitals are empty. Because of this large gap between the filled and empty orbitals it is hard to remove an electron from a C-C bonding molecular orbital, the electrons are not free to move between energy levels. Since electrical conduction depends upon the relatively free movement of electrons, it is not surprising that diamonds do not conduct electricity. But why, you might ask, is a diamond transparent, rather than opaque, like a block of graphite (also composed of only carbon atoms).For an object to be transparent, most of the light that hits it must pass through it; the light can be neither reflected or absorbed. For a diamond to absorb light, a photon would need to move an electron from an low energy bonding molecular orbital to a high energy anti-bonding orbital. However, visible light does not have enough energy to bridge the “energy gap” between the bonding and anti-bonding orbitals. Based on this thinking, we immediately conclude that there is something different between bonds holding C atoms together in diamond from the bonds holding C atoms together in graphite, even though we do not know, at this point, what it could be.

An important point to consider here is that we have described the bonding in carbon using two different models (hybridization and molecular orbital). While this may be (a bit!) confusing, and may take some getting used to, it is quite common to describe chemical and physical phenomena using different models. Typically we use the simplest model that will allow us to explain and predict the phenomenon we are interested in. Usually the bonding in carbon is described using the hybrid orbital model, because it is highly predictive and easier to use in practice.

Graphite

Different allotropes (that is different forms of the same element) can have quite different properties. The carbon allotrope graphite is soft, slippery (it can be used as a lubricant), grey/black, opaque and conducts electricity. Diamond is hard, transparent, and does not conduct electricity. How can this be possible if both are pure carbon? The answer lies in how the carbon atoms are organized with respect to one another. While the carbon atoms in diamond form a three-dimensional network, in graphite, the atoms are organized in two-dimensional sheets that stack one on top of the other. Within each two dimensional sheet, the carbon atoms are linked via covalent bonds in an extended array of six-membered rings. This means that the carbon sheets are very strongly bonded, but the interactions between sheets are much weaker. While there are no covalent bonds between the sheets, the atoms of the sheets do interact via London dispersion forces, very much like the interactions that hold He atoms together. Because the sheets interact over very much larger surface areas, however, these interactions are much stronger than those in helium. Yet another allotrope of carbon, graphene, consists of a single sheet of carbon atoms, these sheets can be rolled into tubes to form nanotubes, which are the subject of a great deal of interest because of their inherently high tensile strength. Carbon atoms can also form spherical molecules, known as buckminsterfullerenes (or buckyballs).

The obvious question is why don’t covalent bonds form between graphite sheets? Why are the patterns of covalent bonding so different, three-dimensional (tetrahedral) in diamond, with each carbon bonded to four others, and two-dimensional (planar) in graphite and graphene, with each carbon atom bonded to only three others? As we discussed above, to form the four bonds attached to each carbon atom in diamond, we needed to hybridize four atomic orbitals to form four bonding orbitals. Since in graphite/graphene each carbon is only connected to three others we might think we only need three bonds. This is not exactly true. We do indeed use a model in which we consider that only three atomic orbitals are hybridized – an s and 2 p orbitals in order to form three sp2 bonding orbitals.

These orbitals are used where each carbon atom is attached to three other atoms, as in the case of graphite/graphene. Just like in diamond, the three bonds associated with each carbon atom in graphite/graphene move as far apart as possible to minimize electron pair repulsion; they lie at the points of a triangle (rather than a tetrahedron). This geometry is called trigonal planar and the C–C–C bond angle is 120°.

All well and good, but this does not really explain why the carbons in graphite/graphene are attached to three other carbon atoms, while in diamond each carbon is attached to four others. Perhaps surprisingly, there is no good answer for why carbon takes up different forms – except maybe because it can.

But in fact, carbon does form four bonds in graphite (carbon almost always forms four bonds - a central principle of organic chemistry.) The trick is that the four bonds are not always equivalent; in graphite, the fourth bond is not formed by the sp2 bonding orbitals, but rather involves an unhybridized 2p atomic orbital. These p orbitals stick out at right angles to the sheet and can overlap with p orbitals from adjacent carbons in the same sheet. (Remember that p orbitals have two regions of electron density).

Note that we use both the hybridization model,which explains the planar framework of C–C bonds in graphite, and molecular orbital theory which explains graphite’s electrical conductivity. So before we delve further into the properties associated with graphite, let us take a look at bonding in metals.

3.1 Elements & Bonding
3.2 Interactions
3.3 Carbon
3.4 Metals

Question to answer:

• Diamond and graphite appear to be quite different substances, yet both contain only contain carbon atoms. Why are the observable properties of diamond and graphite so different when they are made of the same substance?
• The electron configuration of C is 1s2 2s2 2p2. Using the idea that each atom provides one electron to a bond - If carbon used atomic orbitals to bond, how many bonds would it form?
  Would they all be the same?
• What would be the bond angles if this were to happen. (Draw a picture of what this might look like).
• We have seen that carbon can form materials in which it bonds to 4 other atoms (sp3 hybridization), and three other atoms (sp2 hybridization).What would be the hybridization for a carbon that was only bonded to two atoms?
• How would the other (unhybridized) p orbitals influence the behavior of such material (assuming that it could form)?
• Could carbon form a 3 dimensional structure like by linking to two other carbon atoms?
  

Questions for ponder:

• Do you think diamonds are transparent to all forms of light, such as x-rays?
  What does the color of graphite imply about the energies of the photons it absorbs?