# How is the potential energy between two atoms measured?

In class, we learned about the interatomic potential graph.

How does one actually measure the potential energy between two atoms experimentally to ensure the graph is correct? What device is used?

• We don't. (At least directly, that is.) May 8 '19 at 18:38
• Basic vibrational and microwave spectroscopy experiments give you the necessary parameters.
– Karl
May 8 '19 at 20:28
• Please consider writing an answer, if you're able and willing to, of course; @Karl... May 8 '19 at 22:44
• ...and @IvanNeretin. May 8 '19 at 22:44
• @orthocresol That'd be a replication of textbook knowledge, a lot of work if done properly. ;-)
– Karl
May 8 '19 at 23:04

## 2 Answers

The morse potential (equation see e.g. wikipedia) basically contains the bond dissociation energy, a "force constant" and the bond length at ground state. It does not give any measurable reality, but is just a mathematical model describing (approximating) the same.

The lower part of the curve (usually the ground state and perhaps the first two vibrationally excited states) are approximated by the harmonic oscillator, the energies of which you can get from IR or Raman spectroscopy. The harmonic oscillator (= an ideal spring) has only one parameter, the force constant.

The bond lengths you can get either directly from microwave rotational spectroscopy, or from the rotational fine structure of you IR spectrum. They give you the reduced mass of the structure, which gives you the bond length if you know the absolute mass of the two atoms.

For the math and actual application, I refer you to any standard physical chemistry textbook.

• @CharlieCrown tnx for fixing up my late-night goof-ups
– Karl
May 9 '19 at 17:34
• no worries. It is a good answer and was probably the easiest 2 points I have ever gotten :) May 9 '19 at 17:53
• @CharlieCrown My pleasure! ;-)
– Karl
May 9 '19 at 18:01

The most common and 'classical' method is to use Infra-red, Raman and Microwave spectroscopy to give the frequencies, and equivalently, the gaps between the vibrational and rotational energy levels. Microwaave spectroscopy also give the average bond length as but only as $$\langle 1/r^2\rangle$$.

Normally in a text book a model of the potential energy is assumed such as the harmonic oscillator or Morse potential. This is used because the potential exactly solves the Schroedinger equation. This is a good approximation, but never exact, and is poor at high vibrational energies and close to the molecules dissociation energy. This approach only really works for diatomic molecules.

If you are not satisfied with this approach the next step is through a complicated algorithm (RKR method for example) using the energy levels to define the experimental potential energy which exists as a set on numbers rather than a formula (as in the Morse case), i.e. it is empirical but correct. This 'data' can then be used to test a quantum model of the molecules bonding to try to reproduce the potential and so try to understand why it has the form it does, such as the fraction contribution from 'normal' bonding plus a fraction from ionic forms etc.

Molecules also have electronic excited states and using femtosecond duration laser pulses it is possible to watch the molecule as the vibrational and rotational wavepackets move on the potential energy. (A wavepacket is a collective motion of oscillators, such as vibrations). Analysing this motion produces the potential, but much more exciting is to see how a molecule dissociates, and in the case of NaI in the gas phase it does so in steps. Each time the bond extends a little dissociation occurs. Look up work by Ahmed Zewail.

Finally it is possible to react, say, a diatomic molecule with an atom, say OH+Cl, in the gas phase and by colliding two molecular beams, and look at the energy and angle at which the products are produced. As the reaction must occur on a potential energy surface the products' properties are defined by this and so can be used to determine the potential.