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

We propose a new approach to the energy structure calculation for strongly compressed or imperfect crystals in the case where the overlapping between localized orbitals (LO) of atoms with different space positions is large. This approach is based on the exact (in the sense of Lövdin) ortogonalization of LO for all atoms in crystal and on the cluster expansion (CE). In all $n$-th orders of CE we take into account overlapping integrals (OI) of LO for atoms, which belong to the same $n$-particle cluster. For every $n$ such clusters comprise a whole crystal. The CE converges rapidly as a power law in OI for $n\to \infty$. The two-particle cluster expansion is discussed in details.