Orthogonalized LCAO method

Huang and Ching [129 131] followed the scheme elaborated by Sipe and coworkers while using the self-consistent orthogonalized-LCAO method in the local density approximation (LDA) to determine the band structures and... 

Population anaiysis methods of assigning charges rely on the LCAO approximation and express the numbers of electrons assigned to an atom as the sum of the populations of the AOs centered at its nucleus. The simplest of these methods is the Coulson analysis usually used in semi-empirical MO theory. This analysis assumes that the orbitals are orthogonal, which leads to the very simple expression for the electronic population of atom i that is given by Eq. (53), where Natomic orbitals centered... 

Lowdin s symmetric orthogonalization method is an often employed technique for the generation of orthonormal molecular basis sets. Since within most LCAO MO methods, density matrices are determined by AO basis set coefficients, and idempotency of density matrices is a property easily controlled on an orthonormal basis, Lowdin s transforma-... 

Within density-functional theory, a linear combination of overlapping non-orthogonal orbitals from first principles may be utilized to arrive at at full-potential local orbital (FPLO) method [213], and this k-dependent LCAO approach comes close to full-potential APW-based methods (see Sections 2.15.3 and 2.15.4) in terms of numerical accuracy, although FPLO is much faster simply because of the locality of the basis set. Even faster, due to a strongly simplified potential, is a parameter-free (density-functional) tight-binding method called TB-LMTO-ASA, derived through localization of a delocalized basis set (see Section 2.15.4). 

The most important feature of the SINDOl method is that an orthogonalization transformation of the basis functions is taken into account exphcitly in solving the HF LCAO equations. The one-electron integral matrix H is transformed to Lowdin symmetrically orthogonahzed [225] AOs = S / x... 

As a result of spin orthogonality, only (1 /2) of the exchange terms are nonzero but they are there This was first pointed out by Fock [6] and was added as a correction to the method then developed by Hartree [7]. The combined method is now called the Hartree-Fock method if tabulated numerical orbitals are used, but the Hartree-Fock-Roothaan method in an LCAO basis. Today this method is... 

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