A new cluster-expansion approach to the calculation of the energy structure of crystals

We propose a new approach to the calculation of energy spectra for strongly compressed or imperfect crystals in the case where the localized orbitals (LO) of atoms with different space positions overlap considerably. This approach is based on the exact orthogonalization of the LO for all atoms according to Lovdin's method and on the cluster expansion (CE). In all nth orders of the CE, we take into account the overlapping integrals (OI) of the LO for atoms belonging to the same n-particle cluster. For every n, such clusters comprise the whole crystal. For n →; ∞, the CE converges exponentially to the OI. The two-particle cluster expansion is discussed in detail.