Comparison of localization procedures for applications in crystal embedding

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

Strongly localised molecular orbitals for α\alpha-quartz

A previously proposed computational procedure for constructing a set of nonorthogonal strongly localised one-electron molecular orbitals (O. Danyliv, L. Kantorovich - physics/0401107) is applied to a perfect $\alpha$-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

Calculation of electron density of periodic systems using non-orthogonal localised orbitals

Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix into a power series can only be used when the orbitals are highly localised (e.g. ionic systems). In other cases including covalent crystals or those with an intermediate type of chemical bonding this method may be either numerically inefficient or fail altogether. Instead, we suggest an exact and numerically efficient method which can be used for orbitals of practically arbitrary localisation. Theory is illustrated by numerical calculations on a model system.Comment: 12 pages, 4 figure