Derivation of atomistic models for lattices consisting of weakly overlapping structural elements
✍ Scribed by L. N. Kantorovich
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 530 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0020-7608
No coin nor oath required. For personal study only.
✦ Synopsis
A theoretical approach based on the arrow diagram technique within the group function theory is applied to an infinite crystal consisting of weakly overlapping structural elements (SE: ions, atoms, and molecules). A perturbation method is used to derive the lattice energy in terms of two-body, three-body, etc. types of interactions accompanied by electronic polarization of SEs for the system which is slightly away from some reference configuration. It is demonstrated how an atomistic model for the particular material can be derived from the general theory. A general approach to obtain a parametrization scheme is suggested which is based on a representation of transition and ground-state reduced density matrices (RDM) of various orders via a finite set of basis functions. Using group theory and necessary conditions for N-representability of the RDMs, the representation containing the least possible number of the fitting parameters is worked out. The method is illustrated on a special case of spherical SEs (e.g., atoms/ions in atomic/ionic solids) and it is discussed whether existing models are in accord with the ideas developed.