special relativity - How does matter turn to energy at the atomic level?

When matter is converted to energy by means of $E=mc^2$, it produces quite a lot of "energy". What I am having trouble understanding is exactly how the matter is transformed to energy at the atomic level. Do the atoms gain something or lose something in their internal structure? Do they just vibrate at different frequencies when the conversion occurs?
Edit: This is a duplicate of the question, pardon me. Sorry.

Answer

Let us get down to basics, to convert matter to energy the special relativity algebra has to be used. This describes elementary and complex particles by a four vector, whose "length" is the invariant mass of the system described, invariant to Lorenz transformations.

The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.

The $M$ in the famous $E=Mc^2$ coincides with the invariant mass only in the rest frame of the particle/system, because this $M$ is a function of velocity and is called the relativistic mass and has nothing to do with the energy budget of particles, except at the rest frame of the system.

The fact that energy can be extracted from particles and systems with an invariant mass depends on the quantum mechanical nature of atoms. Atoms are composed out of electrons trapped in the electric potential well of the nucleus, in stable orbitals, , but the energies stored are of order of keV, not really exploitable, also because the orbitals are stable.

A lot of energy can exist in a nucleus , order of MeV, where neutrons, protons, are bound by the strong force in potential wells, and also where there also exist instabilities that can be exploited, by forcing changes in nuclear structure, i.e. the type and number of nucleons.

This is the binding energy curve

for the nuclei. It gives for each known nucleus the average binding energy per nucleon, in the collective strong potential well. The fact that one can extract energy from transitions is based on this curve.

Mass defect is defined as the difference between the mass of a nucleus, and the sum of the masses of the nucleons of which it is composed. The mass defect is determined by calculating three quantities. These are: the actual mass of the nucleus, the composition of the nucleus (number of protons and of neutrons), and the masses of a proton and of a neutron. This is then followed by converting the mass defect into energy. This quantity is the nuclear binding energy, however it must be expressed as energy per mole of atoms or as energy per nucleon.

Nuclei where the nucleons, protons and neutrons, are less bound , if fused will give off energy order of MeV. Heavy nuclei, like uranium, broken into pieces with less binding energy will give off energy again order of MeV.

One more link for fusion.