Ab initio calculations for large dielectric matrices of confined systems

Calculations for optical excitations in confined systems require knowledge of the inverse screening dielectric function epsilon(-1)(r,r(')), 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 epsilon matrix in r and r('). The method has allowed, for the first time, full ab initio calculation of epsilon(-1)(r,r(')) of dimension N approximately 270 000, and for quantum dots as large as Si35H36. 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.