quartz crystal structure

The chemical bond between oxygen (red) and silicon (blue) in quartz is one of the strongest known. That is why rocks are so hard!




Molecular vibrations




















Probing the structure of molecules

Molecules and atoms are very small so that it is difficult to observe them directly. However , there are various techniques that can be used to characterize them. 

Some of these techniques are based on the electromagnetic radiation they emit and they are called spectroscopy. 

The technique that allows us to detect this radiation so that we can interpret the results is called spectroscopy. 

There are three main types of molecular spectroscopy: rotational, vibrational and electronic .

Molecules are not static, as we see them in textbooks, but they are constantly rotating and also vibrating in all possible manners (normal modes).

 The first two types of spectroscopy, rotational and vibrational, can be easily understood like being the radiation emitted by moving charges. We know from classical electrodynamics that an accelerated charge emits radiation. For instance, electrons inside a typical aerial move back in forth, performing an harmonic motion, and they  emit a radiation that will depend on the characteristics of this movement :speed and  path length (sized of the aerial). In the case of molecules, the rotating and vibrating nuclei are the moving charges which are responsible for emitting radiation.  The deformations that the electron cloud suffers when subjected to the nuclear movements also contribute to the phenomenon.

 You may say that a rotating molecule is not like a moving charge because the negative electrons counterbalance the positive charge of the nuclei, so that there isn't a net charge on the system and, consequently, no accelerated charges. Yes , that's correct. As a result, only molecules which have a permanent electric dipole moment will produce a rotational spectrum.

 A rotational spectrum can be used to identify a molecule. Furthermore it can be used to calculate the bond lengths and also the temperature of the medium in which the molecule  is in. An important example of such technique is the study of interstellar molecules (astrophysical chemistry). A rotational spectrum allows us to identify which molecules are present on the interstellar medium, their abundance, temperature and other data. The CO molecule, which fortunately has a permanent dipole moment, is the second most abundant cosmic molecule (after hydrogen), and its spectrum is routinely recorded by means of large radiotelescopes and sophisticated electronics to amplify these weak signals.

 A permanent electric dipole moment  is not a requirement for the existence of the vibrational spectrum, though. Even if the vibrating molecule doesn’t have a permanent electric dipole moment, it will produce electromagnetic radiation. That is because the vibrations deform the molecule. There are stretches , bends an many other vibrating modes, which can be symmetric or asymmetric.

 The vibrational spectrum is very useful in organic chemistry, for instance, where we can associate a frequency to each functional group present in the molecule in study.

 Each type of spectroscopy ,vibrational, rotational or electronic, relates to a particular region of the electromagnetic specrum.

 The vibrating motion produces infrared (IR) radiation ,the rotational motion produces microwaves and the electronic transitions produce light (visible or UV). Fortunately all these types of radiation can be detected and analysed accurately. IR photons ( it is known that light and other types of electromagnetic radiation are made of particles and each of these particles is called a photon) carry more energy than microwave photons. That’s because  the vibrational movement is faster than the rotations, so that more energy is involved.


Digression: the vibrations of the ammonia molecule can produce microwaves so that a device called MASER (the analogous of laser, but with microwaves instead of light) can be built. That's due to a quantum effect which arises as a consequence of  the  inversion symmetry of ammonia. It is an important effect and it will be discussed later in relation to the formation of the hydrogen molecule.


Now let's discuss electronic spectroscopy. It is well known that electrons move in well defined areas around the nuclei, i.e., they are not randomly distributed. In elementary chemistry, we learn that they move in shells, and there is an energy associated to each shell. Electrons cannot be in the space between those shells because of the quantization of energy.

Quanta are like atoms of energy and their size depends on the system  under study.

The difference in energy between neighbouring shells (1 quantum) is the minimum possible, and the electron cannot have a fraction of that energy, because the quantum ia indivisible. The same also applies to vibrations and also to rotations. They are all quantized.

The further away from the nucleus is a shell, the more energy is associated to it.

Now we are in a position to understand the electronic spectrum .Imagine that an electron move from one shell to another (you may be tempted to ask why would it want to do that, but let's postpone this discussion for a while). If it moves from an outer shell to an inner one (providing there is space for it ,i.e., the inner shell is not filled up), it will be moving from a higher energy shell to a lower energy one. Energy must be conserved (the principle of conservation of energy always holds) , so where is the excess energy going to go? You could rightly guess that that energy goes away in the form of a photon. This time, the photons quite energetic ( more energy than the IR ones). These photons are in the region of visible and UV light.

Although the mechanism of production of these photons seem to be very complicated and cannot be interpreted classically (i.e. using classical physics- physics before the 20 th century), they are the easiest to detect and they have been detected since the turn of last century. These photons are like a fingerprint of an atom or molecule.

For instance, the element helium was first detected in the Sun, by spectroscopic techniques, and that is why it is called helium (Helios-sun). The element sodium emits a typical yellow light, and this is exploited  in street lightning.

In this work we will describe this phenomenon in more depth. We will  point out that the electrons don't move in shells, but instead, they occupy wider areas called orbitals. Each orbital is determined by a mathematical function, called a wave function This way, electrons don’t have well defined trajectories; instead ,they follow waves of probability that may have complex spatial distributions (figure). Furthermore we will find out that the energy of excitation is not only the difference in energy between two levels. The situation is more complicated than that. However, that can be used as a first approximation to calculate the excitation energy.

The fact that we have theories that allow us to calculate  and predict the various spectra emitted by atoms and molecules, with high precision and accuracy, is absolutely sensational.