What causes molecules to vibrate when exposed to electromagnetic radiation TL;DR: why atoms gain kinetic energy when hit by a photon?
I'm trying to understand the process that converts light into heat. I found poor explanation that do not include the whole process.


*

*A photon hits an atom of a molecule 

*The electron is excited and moved to a higher energy state

*Assuming the energy is not remitted

*The overall charge of the atom did not change (?)

*(?) causes the molecules to vibrate


Are the vibration caused by the change in charge between the molecules?
I assume that the atoms are not ionized, since it would cause the matter to conduct electricity, wouldn't it?
Am I missing something?
 A: Even though photons have zero rest mass, they carry a finite amount of energy and momentum.
A photon's energy & momentum is given by,
$$E = h\nu\space,\space \space p = \frac{hc}{\lambda}$$
where $\nu$ and $\lambda$ are frequency and wavelength of the photon respectively.
If the photon is absorbed by an atom and not re-emitted, the energy of the photon is completely transferred to the atom. These kind of collisions are inelastic. The atom takes up the energy as kinetic or vibrational energy. 
If a new photon is emitted immediately after photon absorption with the same energy as that of the incident photon, the overall collision is said to be elastic. There won't be a change in energy, however, changing momentum is allowed.
However, sometimes, the emitted photon doesn't necessarily have the same energy as that of the incident photon and this kind of collusion (overall process)is also called inelastic collision.(Raman Scattering & Compton Scattering)
This missing energy is taken up by the atom as kinetic energy or vibrational energy.
The answer is highly simplified. The energy gained from the photon could be used for other purposes such as pair production of particles, knocking electrons off, etc. Also, the mechanism of absorption and emission are a bit complicated.
References: Photon-Atom Interactions - MIT OCW
A: 
I'm trying to understand the process that converts light into heat. I found poor explanation that do not include the whole process.

How any atom, or most likely any molecule, reacts when a photon interacts with it, depends on the structure of the molecule. The incoming photon has a certain energy and, depending on this energy, it may cause the molecule to vibrate, producing heat.


If you look at the diagrams above of a two atom molecule, the springs represent the bonds and, if the incoming photon has the right amount of energy, it may cause vibration or rotation of the molecule, producing heat.
It's all down to conservation of energy and momentum.  The relatively high energy incoming photon, say an infrared frequency  photon, interacts with the molecule. The energy available from the incoming photon is split between moving the atoms apart (which takes energy). The moving atoms may then produce a photon in a lower frequency infra red part of the electromagnetic spectrum, which you feel as heat.

Are the vibration caused by the change in charge between the molecules?
I assume that the atoms are not ionized, since it would cause the matter to conduct electricity, wouldn't it?

The system is based on simple harmonic motion, the atoms use kinetic energy to move closer together, and then mutual repulsion pushes them apart, like a mass on a spring.
The atoms can be ionized,  but that takes higher energy  photons to remove electrons, rather than this case, where infrared radiation is enough to cause vibrations, but not ionization.
I write the following few lines because I feel you want to understand this problem in as much detail as you can. The links are to articles on Wikipedia.
There are three different levels at which we can understand most physical problems, in order of accuracy of prediction and intuitive understanding, these are:
Classical mechanics, which you have obviously gone beyond in this case.
The second is Quantum Mechanics, which is what your question is based on,  although you are still using classical concepts, so when you say "a photon hits an atom of a molecule", that is not how Q.M. describes things.
The third, which models interactions such as the above to give us the best picture of "what really happens", is Quantum Field Theory.
A: I don't believe any of the explanations posted so far are correct. I have never seen a convincing explanation for the absorption of light by opaque materials. People often say that the optical frequency molecular modes are excited, and then the vibrations somehow work its way down to the thermal spectrum. But the never explain quite how.
I don't believe the incident light interacts with single atoms or molecules. I believe it interacts directly with the mechanical modes. Any mechanical oscillation is bound to be associated with some electronic oscillation. The problem is that the frequencies of the mechanical oscillations are much lower than the optical frequencies. But there is another mechanism associated with wavelength. When the wavelength of the mechanical oscillation is equal to the wavelength of the incident light, there can be a strong interaction. It's a bit like the Compton effect, where the light and the electron (in a COM frame) have the same wavelength/momentum. And like the Compton effect, this interaction can indeed remove energy from the incident light. 
I explained this mechanism in another thread a week or two ago.
