Asymptotic properties of inverses of cyclic overlap matrices in the large separation limit

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Abstract
This paper contains a discussion of asymptotic properties of inverses of cyclic overlap matrices relevant to LCAO theory based on localized orbitals. For inverse metric elements, Δ, and for large distances, R, between centres of localized orbital α in cell l and localized orbital β in cell l′, it is shown that: one‐dimensional case: two‐dimentional case: three‐dimentional case: These results are quite general and do not presuppose any restrictions as to symmetry (apart from the cyclic one), number of orbitals per unit cell, or vanishing of overlap integrals associated with neighbours beyond a fixed order. By way of illustration, explicit applications to one‐, two‐, and three‐dimensional, simple, mono‐orbitalic lattices with first‐neighbour overlap only are included.

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