Self-consistent embedded clusters: Building block equations for localized orthogonal orbitals

Abstract

In order to be able to study a large electronic system following a building block approach, in which smaller tractable subsystems are handled at a time rather than the system as a whole, equations are proposed in this paper whose solutions are variational orthogonal orbitals localized on the subsystems. The equations for a given subsystem correspond to a molecular cluster embedded in the field created by the rest of the system, and are coupled to the corresponding equations for all subsystems under consideration, so that they must be solved self-consistently. While the localized nature of the solutions makes the equations appropriate for use in conjunction with local basis sets in practical implementations without significant loss of precision due to truncation errors, their orthogonality properties allow for the use of the advantages of the theory of separability of McWeeny in order to calculate total energies and (generalized product) wave functions. Since the building block equations proposed involve inter-subsystem interactions very cumbersome to calculate, an approximation is proposed in order to make their application to actual problems feasible: the representation of the cumbersome interaction operators by ab initio model potentials which are obtained directly from them, without resorting to any parametrization procedure based on a reference. This ab initio model potential approximation has been found to provide considerable computational savings without significant loss of accuracy in frozen-core calculations on molecules and frozen-lattice calculations on imperfect crystals.