Abstract:

In spite of Quantum Chemistry is nowadays part of practically any Chemistry Degree curriculum, it is still true that, to a first approximation, many chemists think of molecular structure in terms of ball and stick model (BSM). This is certainly a useful approximation for solving many chemical problems. Nevertheless, the BSM and, particularly, the way it is many times applied, leads to diverse false conclusions. One of them is to ignore there is not a unique rigorous definition for the term “bond distance”. Probably, a large number of graduated chemists remember, from the basic Quantum Chemistry lectures they attended, that the bond length at the minimum energy is different from that obtained experimentally. But, being in contact with chemists every day, we realize that most of our colleagues ignore there is an impressive amount of different physical magnitudes, all of them named “bond distance”, which cannot be directly compared although when they are obtained from the same experiment. This reason led us to design an exercise for our students of Applied Computational Chemistry (5th year of undergraduate Chemistry). We think that working on the concepts and obtaining numerical values by themselves will help them to get insight into some of the different kinds of bond distances they can find during their life as chemists and learn to be careful about certain quick comparisons.

Two sessions before proposing the exercise, the students were asked to look at the internet for numerical values of bond length for a well known diatomic molecule. Carbon monoxide was chosen as our “2012 molecule of the year” for this exercise. In the next class-room session we collected all the values and pointed out how diverse they were. Therefore, we asked them which could be the reason for such scattering? As expected, the students pointed out it was due to experimental errors and also to the limitations of quantum chemical methods and levels. At this point, making use of the usual Morse potential curve for diatomic molecules and the vibrational levels, we reminded them that molecules are not at rest vibrationally. Therefore, they are not always in the minimum energy bond length, re. Anharmonicity makes that averaged bond lengths become longer and longer as molecules reach a more excited vibrational quantum level. Then, we introduce another question: how is this average made? The students are requested to think that physical observables are “turned” into expected values by Quantum Mechanics. Thus, spectroscopic methods –exemplified by microwave spectroscopy- and diffraction methods –exemplified by neutron scattering- make different mathematical averages. This leads us to arrive to rg and ro bond lengths. We add more questions: concerning about the different origin for electron, neutron, or X-ray diffractions, guessing how many different vibrations we should average in a polyatomic molecule, etc.

At this point, after just 15 minutes of discussion, we proposed our exercise: Obtain ro and rg numerical values for the ground vibrational state of carbon monoxide once its harmonic force constant and re bond length are known. The students were asked to bring their results in two weeks. During this time they were allowed to ask/comment us all the doubts and difficulties they found.

Keywords:

Physical Chemistry, Computational Chemistry, DFT.