Intermolecular forces are electrostatic in nature.  That is, they are simply attractions/repulsions obeying Coulomb's Law.  For instance, the force between two ions is given by

where K is a proportionality constant (determined by whatever system of units you are using), q₁ and q₂ are the charges on the ions, and r is the distance between the centers of the ions.  Forces between other types of particles (e.g., dipoles) can also be calculate using Coulomb's law and a little calculus.  We won't delve into these ideas any more deeply that to note that many intermolecular forces have potential energies proportional to 1/r⁶ (and since volume is proportional to r³, this accounts for the 1/V ² term in the van der Waals equation).  The most common intermolecular forces (excluding hydrogen bonding--well, actually, "sort of" including it as we shall discuss below) are shown in the following figure from the text book.

This list is by no means all-inclusive (for instance, ion-induced-dipole interactions are neglected) but is a good start to understanding intermolecular forces.

Ion-dipole forces are those which are responsible for the dissolving of ionic compounds in polar solvents such as water.  In many cases, these forces are actually strong enough to break the ion-ion forces in crystals.  Thus, salts such as NaCl or Na₂SO₄ dissolve quite readily in water and in many other polar solvents as well.  When the lattice energy cannot be overcome, the ionic solids remain blissfully at the bottom of the beaker.  (For instance, AgCl and Ag₂SO₄ are quite insoluble--only a few ions "sneak" into solution.)

Dipole-dipole interactions are also quite potent intermolecular forces.  Any solvent with the molecules possessing permanent dipole moments is termed a "polar solvent."  This, of course, includes water as an obvious example of a very polar solvent.  However, some solvents such as formamide are even more polar than water.  Many organic solvents such as alcohols (methanol and ethanol being the two most obvious examples) or chloroform or acetone are excellent polar solvents.   One of the most famous organic polar solvents is DMSO (for "dimethylsulfoxide"--(CH₃)₂SO).  For nearly all of these, dipole-dipole (or m-m) are the dominant interactions.  However, with molecules possessing -NH or -OH moieties, the situation is a little more complex.  Here, we are confronted with

Hydrogen bonding. Hydrogen bonds occur between molecules containing N-H or O-H bonds (and also in HF).  N, O, and F are very highly electronegative atoms.  Hydrogens bonded to them will form weak chemical bonds with other N, O, or F atoms.  These bonds are very weak as chemical bonds go but are very strong as far as intermolecular forces are concerned.  In fact, they are intermediate between a "bond" and a simple electrostatic "force."  It is hydrogen bonding which is responsible for the extremely high boiling point of water.  (For instance, this is a few hundred degrees higher than that of methane, a molecule with a similar molecular weight.)  Also, molecules such as ammonia, HF, and HCN also have abnormally high boiling points.  Again, this is caused by hydrogen bonding.

Hydrogen bonding is also responsible for the beautiful shapes of snowflakes--not often seen in Florida, but common in other places!  Also, hydrogen bonds are in part responsible for holding together the paired strands in DNA and RNA.  These are very strong intermolecular forces and are very important in many areas of chemistry and biochemistry.  In fact, whole books have been written about hydrogen bonds and, or that matter, even water.

To show the dramatic effects of hydrogen bonding, look at the normal boiling points of the following substances.

Graphs such as this will tell you a great deal if you let them.  First, notice that the boiling points of all the compounds for group II elements are abnormally high (except for methane).  In periods 3, 4, and 5, boiling points increase in a roughly linear manner.  (Maybe, it could be argued, HCl's boiling point is a little high--but many have said that chlorine, with the same electronegativity as nitrogen, should also occasionally allow hydrogen bonding.)  In any event, it is definitely hydrogen bonding which is responsible for the trends in the above graph.

Dipole-induced dipole forces are the next we consider.  Actually, one could consider hydrogen bonding to occur when these particular forces go to the extreme.  In essence, these forces can be considered to arise as follows:

Atoms and molecules consist of dense (positive) nuclei surrounded by rather diffuse electron (negative) clouds.  Whenever a positive or negative charge (this could be a cation, anion or the positive or negative end of a permanent dipole) approaches the cloud, the electrons redistribute themselves so as to get closer to an external positive charge or further away from a negative charge.  At the same time, the nuclei either "flee" from positive charges or "edge toward" negative ones.  The result of all this "suffling" is the production of what is called an "induced dipole moment."  Such induced moments are notated usually as m*; if a permanent produces and induced dipole, the result is termed a m-m* interaction.  m-m* interactions are very important with many interactions between molecules.  For instance, these are the reasons polar molecules such as chloroform or acetone are quite soluble in nonpolar solvents such as hexane or carbon tetrachloride.

Note that we said above that hydrogen bonds are these forces to an extreme.  What was meant was simply this:  The dipole-induced dipole force distorts an electron cloud in such an extreme fashion as to have some electron density transferred from one molecule to another.  This is a weak chemical bond and, hence, the term "hydrogen bond."

Induced dipole-induced dipole (m*-m*) are the last type of force we consider.  Occasionally, a molecule will have an electron spontaneously hop into a higher orbit.  This causes the generation of a "spontaneous induced dipole."  This term is, of course, paradoxical.  What induces the moment?  One could say that it is the random effects of thermal energy or an indirect effect of the Heisenberg uncertainty principle.  In any event, such dipoles do arise.  Incidentally they are most likely to arise with heavy atoms with large numbers of electrons (iodine is a good example of this).  In any event, once a spontaneous dipole appears, it can produce another induced dipole.  Thus we have m*-m* interactions.  These are commonly called dispersion forces or London forces.  (The latter are not named after the city but after the German scientist, Fritz London, who first wrote a paper describing them.)

Dispersion forces are the weakest of all intermolecular forces.  However, there is strength in numbers.  Even those these are weak, there are many more ways in which they can arise.  Thus, dispersion forces are the forces holding many covalent solids and liquids together.  In particular, nonpolar substances such as Br₂, I₂, or paraffin--or bee's wax for that matter--are held together primarily by these forces.