The LCAO approach to the embedding problem

The embedding method invented by Inglesfield (1981) is a method for solving the Schrodinger equation for a small but interesting part of the larger system. It is based on minimising the energy by varying the wavefunction within a closed surface surrounding the region of interest. The correct non-local energy-dependent boundary conditions on this surface then appear as a surface potential term in the functional to be varied. The authors show that in the usual LCAO Green function method there exists a way to accomplish this same embedding using a matrix operator, with structure similar to the boundary condition kernel of Inglesfield's method.