Using crystal-chemical knowledge it is possible to fully partition the chemical bonding properties of a given inorganic crystal structure since the interactions found in any inorganic solid-state compound can be reduced to a few different fundamental types. Their corresponding potentials can be expressed in analytical form.

The (typically strong) interactions between metals and nonmetals (or, somewhat simplified, cation-anion interactions) may exhibit different degrees of ionic or covalent character. The strength of these interactions can be mathematically analyzed using the bond valence concept (BVC) [1] by evaluating an atom's charge which totally depends on its individual coordination. The bond valence of a given bond between two atoms depends on the interatomic distance, and the summation over all bond valences results in the total charge for this atom, irrespective of whether or not the metal-nonmetal bonding is more ionic or more covalent in nature. This approach allows the calculation of the atomic charge at a given timestep. Since the charge can vary with time, it is now a dynamical variable. Upon simulation of materials showing metallic behavior, the effective shielding of atomic charges due to the surrounding gas of conduction electrons has to be taken into account.

For small interatomic distances, an additional interaction (Pauli repulsion) is needed only for atoms of opposite charge to both pretend structural collapse and ensure equilibrium geometry for an appropriate repulsion value.

The (typically weaker) interactions between chemically identical metal (or nonmetal) atoms may arise in case of excess electrons which are then used in (covalent or metallic) bonding states. Fortunately enough, there exists a universal bonding energy-distance relationship (UBER) [2] for such interactions, and it covers both metal-metal as well as nonmetal-nonmetal combinations. UBER links the total energy of a system and its interatomic distances. The bond energy may be evaluated upon knowledge of the experimental cohesive energy while UBER's bond distance is the distance at the minimum of the potential energy, or, from a more experimental point of view, the shortest nearest-neighbor distance; in addition, the screening length of the electron gas is a scaling factor which effectively determines the range of the UBER interaction.

In addition, (even weaker) attractive interactions between different kinds of metal (or nonmetal) atoms will be paralleled by an interatomic charge transfer. The latter takes place if there exists a difference in electronegativities. The concept of absolute electronegativity and absolute hardness (AEH) [3] is then utilized to determine the amount of charge transfered. 

The above chemical parameterization procedure forms the mathematical core of aixCCAD; the program scans all metal-nonmetal combinations by use of the BVC method and generates the atomic charges; shielding and repulsion corrections are applied. In addition, metal-metal (nonmetal-nonmetal) interactions (UBER type) are included in the force calculations; these may be augmented by minor charge corrections (AEH). The basic algorithms follow standard methods while the general propagation method is the Velocity Verlet algorithm. The summation of the Coulomb interactions is done using the Ewald summation technique. The calculation of the atomic charges is performed every timestep, preceding the calculation of interatomic forces; the charges therefore reflect the actual geometry. 

For further information, please study the original literature in our references section.

[1] I.D. Brown and D. Altermatt, Acta Cryst., 1985, 41, 244 
[2] J. Smith, J. Ferrante and J. H. Rose, Phys. Rev. B, 1982, 25, 1419 
[3] R. G. Pearson, Inorg. Chem. 1988, 27, 734 

Institute of Inorganic Chemistry
Chair of Solid-State and Quantum Chemistry
Prof. Dr. R. Dronskowski