Class content > Energy: The Quantity of Motion  > Interatomic forces

Prerequisites

• Forces from potential energy
• Electric potential energy
• Interatomic forces 

Our simple model of interatomic forces has more implications than just the idea that neutral atoms attract due to mutual polarizations and repel when they get too close. It can actually provide a simple model of chemical bonding. Although most real chemical bonds are more complex than this (and rely heavily on the quantum character of electrons), this simple model gives a decent qualitative idea of how things work and interpreting the atom-atom PE graph provides a basis for understanding some of the more sophisticated (and subtle) representations of chemical reactions.

At large r, the potential energy graph looks flat.  The slope is just about zero.  Thus, atoms that are far apart feel just about no force.  At small r, the graph slopes very steeply down and to the right, indicating that there is a very strong repulsive force at close range.

Since the strong positive repulsion dominates at short distances, while the longer range negative attraction dominates at longer distances, in between the graph has to turn around.  As the atoms come towards each other from far away, the potential energy slopes downward going negative, and then becomes repulsive and goes positive.  Somewhere in between, it has to reach a minimum potential energy, before going back up again.  The slope of the graph at this point is zero, so two atoms located at this distance experience no force.  The attractive and repulsive forces balance exactly.  This is a stable equilibrium:  if you move the atom away from this point in either direction, it will experience a force pushing it back towards the equilibrium point.  Therefore, atoms that have this potential energy interaction can form stable molecules!  The value of r, where the potential energy is at a minimum, tells us the bond length for that particular bond.

Here's a simulation of two atoms coming together and forming a bond.  (In this simulation, the atoms don't stay together!  Why not?  What would need to happen for them to stay together?)

An example of a pair of atoms in a bound state is shown in the figure at the right by the heavy black line. This represents a particular case of a state of the total mechanical (kinetic plus potential) of the atoms' relative motion.   Note that we have chosen the zero of our potential so that the total energy of the bound atoms is NEGATIVE.  "Negative relative to what?", you might ask.  Relative to our "zero" potential energy, which we take to be when the atoms are far apart and at rest.  So there is LESS total mechanical energy when atoms are bonded together than when they are separated. This has two important consequences:

1. If atoms start out bonded together, you have to ADD energy just to get them back to "zero" potential energy, i.e. to pull them far apart. "Breaking" the bond requires an input of energy.
2. In reverse: If a bond is formed (between atoms which were previously separate), the result is less potential energy than they started with, but by the principle of conservation of energy, we know this energy had to go somewhere else (it doesn't just disappear).  Thus, when bonds are formed, energy is released. (Where does the energy go when a bond is formed?  We'll get into some answers to this question later on, but in the meantime, think about this question and try to come up with some possible answers yourself.)
   
   

You might also notice that we haven't put the energy line at the very bottom of well to indicate that the two atoms have zero KE and are therefore at rest. In quantum physics objects can never be perfectly at rest: there is always some motion, even at the lowest possible energy (ground state) of the system. The "bond length" measured for various bondings is an average. The atoms actually jiggle a bit about the bond length.   What is also important is that not every total energy is allowed. In the example shown at the right, only 5 particular energies are allowed (and all the E's are negative combined to the separated atoms showing that the system is bound).

The Lennard-Jones potential (and the more accurate Morse potential) is only a simplified model for atom-atom interactions. When one has strong bonds where the electron orbitals are shared and even modified, a model describing the interaction as occurring between atoms is not really sufficient. A better description explicitly needs to consider the structure of the atom, separating it into a nucleus and electrons. But these potential models allow us to talk about the energy balances involved when chemical reactions happen in a simpler way. It describes the transfer of energy accurately, even if the mechanism is not quite correct.

Ben Dreyfus 10/30/11 and Joe Redish 11/17/11

Joe Redish 11/27/12