**BASIC THEORETICAL ASSUMPTIONS**Fine Electronic Structute based methods make it possible to reconstruct with extraordinary effectiveness the permanent properties of real materials and predict the properties of new unstudied experimental materials. No other theoretical model can achieve this type of result. The main assumptions of the theoretical approach applied in ATOMIC MATTERS can be summarized in several key points:

- Ions/atoms with an unclosed 2
*p*, 3*p*, 3*d*, 4*d*, 5*d*, 4*f*, or 5*f*electronic shell have the structure of discrete electron states that affect the properties of the whole compound. - Multi-electron systems 2
*p*^{n}, 3*p*^{ n}, 3*d*^{ n}, 4*d*^{ n}, 5*d*^{ n}, 4*f*^{ n}, and 5*f*^{n}are strongly correlated systems. - In a solid, an atom/ion interacts with the charge environment (Stark effect). This interaction leads to the removal of the degeneracy of states and is referred to as the Crystal Electric Field (CEF). The symmetry of the local surrounding is reflected in the symmetry of the crystal-field (CEF) Hamiltonian.
- Through modifications of the fine structure of electron states of the atom, the CEF determines the properties of an atom in a solid and corresponds to the properties of the whole crystal.
- Magnetic interactions, both internal-intra ionic and with an external field, lead to further reduction in the degeneracy of states (Zeeman effect).
- A correct description of such multi-electron systems is based on atomic physics, with atomic numbers S, L, of the entire shell. This results in a space of n=(2S+1)(2L+1) states.
- In some cases (4
*f*and 5*f*electron systems) description of multi-electron systems based on atomic numbers S, L and J is passible. - Spin-orbit coupling makes an important contribution to the structure of states and must be taken into account in calculations.

Collecting the most fundamental interactions in one Hamiltonian matrix (without perturbation methodology) allows unification of calculation methods for ions/atoms from all groups of the Periodic Table in one scientific workspace. Now, applying special treatment for Strong Field, Intermediate Field and Weak Crystal Field ions can be achieved according to traditional classification. The value of the spin-orbit coupling parameter in relation to CEF parameters defines the types of interactions fully and correctly.