With the aim of future applications in quantum mechanical embedding in extended systems such as crystals, we suggest a simple and computationally efficient method which enables construction of a set of nonorthogonal highly localized one-electron orbitals for periodic nonmetallic crystals which reflect their chemical nature. The orbitals are also used to build up the Hartree-Fock (HF) electron density of the entire crystals. The simplicity of the method stems from the fact that it does not require usage and/or modification of periodic electronic structure codes, and is instead based on the HF calculation of a sequence of finite clusters with subsequent application of a localization procedure to transform the HF canonical molecular orbitals. Two extreme cases of chemical bonding, ionic (MgO crystal) and covalent (Si crystal), are considered for which a number of known localization schemes are applied and compared. With some modifications our method can also be applied to nonperiodic nonmetallic systems as well.

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A direct-space electronic structure method for electronic structure calculations of periodic systems, based on highly localized ͑noncanonical͒ molecular orbitals ͑MOs͒ and the quantum cluster embedding, is suggested. The method utilizes a modified Adams-Gilbert approach that allows one to find self-consistently ͑for the given geometry͒ the system energy and the corresponding localized MOs which give the correct total electron density. The approach suggested here can also be considered as an exact derivation of embedded quantum cluster models. We illustrate this method on a Hartree-Fock calculation of a model periodic He system and the MgO crystal, and the results are compared with a conventional approach based on canonical Bloch-like orbitals as implemented in the CRYSTAL code. Our method, which scales linearly with the system size, can also be used to solve the Kohn-Sham equations of density-functional theory.

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Abstract. A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich -Phys. Rev. B, 2004, to be published) is applied to a perfect α-quartz crystal characterised by an intermediate type of chemical bonding. The orbitals are constructed by applying various localisation methods to canonical Hartree-Fock orbitals calculated for a succession of finite molecular clusters of increased size with appropriate boundary conditions. The calculated orbitals span the same occupied Fock space as the canonical HF solutions, but have an advantage of reflecting the true chemical nature of the bonding in the system. The applicability of several localisation techniques as well as of a number of possible choices of localisation regions (structure elements) are discussed for this system in detail.