Cluster Expansion of an Inverse Overlap Matrix for Solids

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Abstract
In this paper, a method is developed to compute an inverse overlap matrix based on a linked cluster expansion of a determinant. The inverse is expanded in terms of cluster integrals represented by diagrams and a recurrence relation for generation of all diagrams required is found. Thus the computation of an exact inverse overlap matrix is reduced to solving the recurrence equations self‐consistently. An approach for solving the equations is suggested and bounds for errors accompanying this procedure are calculated. The method is applied to the hydrogen lattice.