Calculations for optical excitations in confined systems require knowledge of the inverse screening dielectric function [Formula presented], which plays a crucial role in determining exciton binding energies. We present a new efficient real-space method of inverting and storing large ab initio dielectric matrices of confined systems, which relies on the separability of [Formula presented] matrix in [Formula presented] and [Formula presented]. The method has allowed, for the first time, full ab initio calculation of [Formula presented] of dimension [Formula presented], and for quantum dots as large as [Formula presented]. The effective screening in Si quantum dots up to 1.1 nm in diameter is found to be very ineffective with average dielectric constants ranging from 1.1 to 1.4.
Bibliographical noteFunding Information:
This work was supported by the Computational Materials Science Network of the Department of En?>ergy, the National Science Foundation, and the Minne?>sota Supercomputing Institute.