• When atoms were formed, whether in the big bang event, or during star evolution, or supernova, it was too hot for the electrons to be localized around a nucleus. Only when the surrounding temperature cooled down enough could the electrons remain around a nucleus.
• This tells us that the energy needed to keep electrons around a nucleus is much smaller than the energies associated with the nucleus or the formation of electrons to begin with.
• It is this low energy environment, where electrons are bound to a nucleus, that define the conditions in which humans may exist, because groups of atoms stay together as molecules or solids only by the bonding of their electrons. Electrons are the glue that holds groups of atoms together.

• Let's review the nature of the atom from the point of view of the electrons.
• The atom is mainly low-density space with a very dense, small nucleus that defines its center.
• Electrons are located around the nucleus.
• The distributions of electrons define the size of each atom.
1. In a given column of the periodic table, atoms from lower rows (i.e. greater principal quantum numbers) are larger than atoms from the higher rows. The reason is that atoms in lower rows have more electrons, these electrons repel each other and so are spread out around the nucleus. The volume of space occupied by electrons increases and so the size of the atom increases.
2. In a given row, the atoms are larger on the sides, but are smaller towards the middle. The reason is that as you go from left to right across a given row the charge of the nucleus increases. This charge pulls the electrons in closer to the nucleus, till there is a critical number of electrons that start to interfere with each other. Their mutual repulsion overcomes the attraction to the nucleus, resulting in a more diffuse electron density and thus a larger atom.
• These electrons can be classified in terms of shells that correspond to the rows in the periodic table. Each shell can fit a certain number of electrons, depending upon how far away from the nucleus it is. A shell that is close to the nucleus can only contain a small number of electrons, otherwise the electrons are too close together, and electrostatic repulsive forces push them apart.
• Shells of electrons are most stable when they contain the maximum number of electrons that they can hold. On the one hand, if there are too few electrons, then the electrons are constantly whizzing about, trying to fill all of the available space. Therefore, they have high kinetic energy. On the other hand, if there are too many electrons then electrostatic repulsion takes over and pushes them apart.
• Define the electrons in an unfilled outer shell as valence electrons.
• Since these are the outermost electrons, these are the ones that are perturbed by bringing another atom close by. These are the ones that are involved in bonding.
• Define: A chemical bond is the result of a redistribution of electrons that leads to a more stable configuration between two or more atoms.
• The electron density of the free atom in space is spherical. Only in the presence of an electric field do the electrons configure themselves into orbitals of other shapes. We model the shapes after H, the only atom for which we can do exact computations. The model is called the Linear Combinations of Atomic Orbitals (LCAO), where the electrons for a given atom are considered to be the combination of the many orbitals that were computed for H. This seems to work well in practise.
• When two or more atoms get close enough together the electrons may reorganize themselves to achieve a different energy configuration. The resulting shapes may be different than the s, p, d, or f shaped orbitals. It is a shape that is determined by e^--e^- and p⁺-p⁺ repulsion and e^--p⁺ attraction.
• If the energy configuration is lower when the electrons have reorganized themselves, then the atoms will stay together and we say that a bond has been formed.
• Some electrons can no longer be associated only with one of the atoms, but instead are associated with both atoms in a bond. In general, these electrons come from the set of valence electrons. The others are called core electrons. Core electrons have a closed shell configuration.
• Since the bond is formed by some sort of distribution of + and - charges, then there is a force (called the bonding force) that can be ascribed to the bond. The + charges repel each other, keeping the nuclei from getting too close to each other, while the nuclei and electrons attract. A proton cannot leave the nucleus, so we consider it to be a point charge. The electrons move about to try and stabilize the group. The more electrons between a pair of atoms then the less the nuclei can repel each other. We say that the electrons screen the nuclei. But there is a limit to the number of electrons that can be put between the nuclei because the electrons repel each other too. You can imagine that with all the many types of atoms there are many types of bonds, all of different strengths and properties. Each pair of unique elements has its own unique bond.
• Recent work has shown that a pair of atoms is bonded if and only if there is a critical point in the electron density between the pair. Here is an example of a Na atom moving closer to an O atom in a O-Si-O-Si-O linkage. An O atom is stationary in the center of the imiage. Notice the bond forming between Na (coming in from the top) and O. Notice also the way that the electrons redistribute themselves, especially along the central O and Si bonds. As the Na atom forms a bond to the central O atom, the electron density along the O-Si bonds decreases and moves into the region between Na and O. The Si-O distance increases as Na-O gets shorter because the Si-O bond is losing electrons.
• The more electron density at the critical point then the stronger the bond and the shorter the bond. Short bonds are strong, long bonds are weak.

• Experience has shown us that we can classify the bonds into 7 different types, the first 3 of which are of major importance.

1. Ionic
2. Metallic
3. Covalent
4. Polarized
5. Hydrogen
6. van der Waals
7. Clathrate

• Definition of an ion: an atom in which the number of electrons does not equal the number of protons.
• There are several ways to turn an atom into an ion.
1. Light, e.g. photoelectric effect
2. Heat, e.g. sun
3. Exchange electrons with another atom, via the ionic bond.
• Ionic bonding occurs between a pair of atoms when one of the atoms gives up its valence electrons to the other. The result is that both atoms have filled shells. Both atoms also end up with a charge, one negative, and the other positive. We call the positive charged atom a cation, and the negatively charged one, an anion.

• A classic example of ionic bonding is between Na and Cl. Na is a silvery metal. It has 1 valence electron. Cl is a yellow-green gas, and it needs 1 electron to fill its valence shell. If you put the gas and the metal together, then they will burn as electrons are exchanged. The metal dissolves and the gas disappears. The ions now have opposite charges and are attracted to each other by electrostatic forces. They form a crystal with the rock salt structure.

• Ionic bonds commonly form between atoms of the 1st column and the 7th, and between the 2nd column and the 6th. E.g. NaCl, MgO
• We assume that ions have a closed shell and so their shape can be assumed to be spherical.
• Cations have diffuse electron densities while the electron density in anions drops off sharply.

• Properties: Materials composed of ionic bonds have distinctive properties that depend upon bond length, R. This is because the forces are coulombic.
• Eg. Melting temperature versus R.

• Ionic solids are strong when pushed together, but weak if cleaved or sheared.Once the bond breaks it is not easy to put back together. For instance, suppose you cleaved NaCl.  Then Na is short 1 electron and Cl has one extra. They have no need to come close enough together to exchange electrons.
• Ionic crystals also dissolve easily in water and have high melting points.
• So if you break a crystal apart, you can put it back together by dissolving it, or by heating it enough to excite the valence electrons off of the atoms.
• Ionic bonding is often found between pairs of atoms. However, it can also occur within larger groups. E.g. CaCl₂.

Problem: Determine the spin diagrams for O^2-, Si⁴⁺, Mg²⁺, Fe²⁺, Fe³⁺