# Catenation

Discussion Questions

Catenation of chemical bonds leads to the formation of inorganic polymers. However, inorganic polymers are mostly solids in the form of crystals. Typical inorganic polymers are diamond, graphite, silicates, and other solids in which all atoms are connected by covalent bonds.

### Atoms and Their Nuclei

During the 20th century, the investigation of the material world turned to the very heart of material world - the structure of atoms. The discovery of electrons in 1897 by J.J. Thomson showed that there were more fundamental particles present in the atoms. Fourteen years later, Rutherford discovered that most of the mass of an atom resides in a tiny nucleus whose radius is 100,000 times smaller than that of an atom. In the mean time, light beams were discovered to be made of photons which are equivalent to particles of wave motion. These discoveries created new concepts. When these concepts and discoveries are integrated, new ideas emerge. The result is quantum theory. This theory gives good interpretations of the phenomena of the atomic and subatomic world. In this microscopic world, distances are measured in nanometers (10-9 or 1e-9 meter) and fantometers (1e-15 meter, also called fermi, in honour of Fermi who built the first nuclear reactor).

The electrons in an atom are confined by the electromagnetic force of the atomic nuclei. At this level, we need a quantum mechanical approach to understand the energy states of the electrons in the atom. However, we do not have the time to discuss this in details.

#### Quantum Number and Atomic Orbitals

Quantum mechanics on atomic structures is a mathematical approach to describe the behavior of electrons in atoms. The electrons are represented by wavefunctions, and each of them are characterized by a set of numbers. Each set of numbers represent a state, which is often called an orbital. Quantum Numbers and Atomic Orbitals are pages that give a bit more details on this subject, but a summary of the atomic orbitals is given below:

1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f 5g
6s 6p 6d 6f 6g 7h
7s 7p 7d 7f 7g 7h 8i

A film has shown how these are related to the Period Tables of Elements, and it also shows the shape and concepts of atomic orbitals. These concepts are vital for the understanding of bonding, such as the bonds formed between carbon atoms of diamond, silicon, graphite etc.

In the assignment, you have been asked to apply these concept to describe the bonding for carbon. The same argument also applies to the bonding of silicon.

### Electronic Configurations

The electronic configuration of an element or atom shows the energy states of electrons in it. Pauli exclusion principle and Hund's rules are some of the theories involved in assigning electronic configurations. For the discussion of bondings in some light elements, please note the following:

H: 1s1
He: 1s2
Li: 1s2*2s1     after * are valence electrons
Be: 1s2*2s2
B: 1s2*2s22p1
C: 1s2*2s22p2
N: 1s2*2s22p3
O: 1s2*2s22p4
F: 1s2*2s22p5
Ne: 1s2*2s22p6
...
Si: 1s22s22p6*3s23p2
P: 1s22s22p6*3s23p3
S: 1s22s22p6*3s23p4
Cl: 1s22s22p6*3s23p5
Ar: 1s22s22p63s23p6
Na: {Ar}*4s1 ...

### Hybrid Orbitals

Electrons in an atom may have properties of several orbitals, and they share each other's characters. In other words, atomic orbitals may be combined to form hybrid orbitals. These hybrid orbitals are particularly useful in the discussion of chemical bonding. For carbon, the hybrid orbitals are made up of

2s, 2po, 2p+ and 2p-

orbitals. Since 1 s and 3 p orbitals are used, the 4 orbitals sharing s and p characters are called sp3 hybrid orbitals. The shapes and directions of these orbitals should have been demonstrated in lectures, and diagrams are needed here. The bonding of diamond is beautifully described using the sp3 hybrid orbitals.

#### Bonding in Benzene and Graphite

The bonding of benzene should have been fully discussed in the organic chemistry course you have taken. Simply, the orbitals used to form the sigma bond are sp2 hybrid orbitals resulting from combining

2s, 2p+ and 2p-

orbitals. Furthermore, the overlap of the 2po orbitals leads to the formation of the pi bond.

#### Resonance, Benzene and Graphite

Again, the structure of benzene serves an excellent example for the concept called resonance. If one insisted on the fact that the 3 double bonds and 3 single bonds in benzene alternate along the ring, one can start with a single or a double bond. Nether structure represent the structure of benzene, beccause all 6 bond lengths are about the same. Thus a combination of the two structures is used to represent the structure of benzene, and such an approach is called resonance. In other words, electrons in the double bonds delocalize over the entire ring.

The bonding description for benzene can be applied to that of a sheet of graphite. The electrons are delocalized on two planes in graphite. Thus, it no surprize that graphite is a good conductor along the sheet.

#### Buckminsterfullerenes

The graphite structure is the result of expanding the pi electrons into planes. Since all rings in graphite consist of 6 carbon atoms, the sheets are flat. If the hybrid orbitals are somewhat flexible, it is easy to understand that the 5-member rings are also possibilities. However, formation of 5-member rings reults in buckling of a flat structure, and we usually do not think this will happen.

The discoverer of the buckminsterfullerenes spent a long time figuring out the structure of a cluster of carbon consisting of 60 carbon atoms, which is represented by C60. However, once they have deducted the structure, its shape is very common. The carbon atoms are at the junction of lines on a soccer ball (other parts of the world call it foot ball). A geometric description is a truncated icosahedron. The fullerenes, or buckyballs have become the talk of the news media since the award of Nobel Prize to its discoverers. The fullerenes actually are common, and their discovery adds a nice touch to theories of bonding and electronic structures. The electrons on the surface of the ball perhaps think they are on a very large atom. The discoverers are still very active in the study of fullerenes.

#### Boron Nitride, BN

A compound with equal number of boron and nitrogen atoms, BN, has on average 4 valence electrons per atom, same as that of diamond or graphite in carbon. Thus, we anticipate BN to form solids with simlar bonding and structures as diamond and graphite.

In fact, the bonding of boron and boron compounds is also very interesting.  The following items are mentioned here for future development.

• Geometry of significant cages. Comparison of organic and inorganic polymers. Survey of catenation in the Periodic Table. Bonding by bridging groups.
• Boron: borides (mainly but not exclusively MB2, MB6, MB12), borates, B-N systems.
• Silane
Structural chemistry of silicates, including clays, and zeolites.
• Phosphorus, phosphates, P-N systems. Sulphur, polycations, S-N compounds, (SN)x and other inorganic conductors.

### Questions

1. How many valence electrons do carbon, silicon, and germanium have?

Skill -
Give the electronic configuration of an element.

### Solutions

1. They all have 4.