Linear combination of atomic orbitals method

The present article is an attempt to review those studies of pyridinelike heterocycles (mono-azines) and, to a lesser extent, their analogues and derivatives that have interpreted the behavior and estimated various physico-chemical properties of the compounds by the use of data calculated by the simplest version of the MO LCAO (molecular orbital, linear combination of atomic orbitals) method (both molecular orbital energies and expansion coefficients). In this review, attention is focused upon the use of the simple method because it has been applied to quite extensive sets of compounds and to the calculation of the most diverse properties. On the other hand, many fewer compounds and physico-chemical properties have been investigated by the more sophisticated methods. Such studies are referred to without being discussed in detail. In a couple of years, we believe, the extent of the applications of such methods will also be wide enough to warrant a detailed review. 

The Feynman Model. The Feynman approach, or the LCAO (linear combination of atomic orbitals) method, assumes that a wavefunction of valence electrons i/> in a metal is a linear combination of atomic functions. 

Ditchfield, R. Self-consistent perturbation theory of diamagnetism. I. A gage-invariant LCAO(linear combination of atomic orbitals) method for NMR chemical shifts, Mol. Phys. 1974, 27, 789-807. 

Chelikowsky, J. R., and S. G. Louie (1984). First principles linear combination of atomic orbitals methods for the cohesive and structural properties of solids Application to diamond. Phys. Rev. B29, 3470-81. 

Summary Comments for the Linear Combination of Atomic Orbitals Method and Diatomic Molecules... 

This method is called the LCAO (Linear Combination of Atomic Orbitals) method. The electron density p(7) becomes ... 

This is called the linear combination of atomic orbitals method for creating molecular orbitals (the LC AO-MO method). As long as each AO is represented by a single mathematical function (corresponding to a minimal basis set see below), the calculations produce the same number of t/s as 0 s included. This corresponds to the statement that one gets as many molecular orbitals for a molecule as there are atomic orbitals on the individual atoms. Note that LCAO-MO is just one of many possible ways to computationally develop MOs. It is computationally expedient, and it is consistent with our notion that molecules are built up from combinations of atomic orbitals, a conceptual advantage over other possible ways of building up MOs. 

Reactivity indices for each of the ring carbons of phenylsulfide acetic acid and eleven chlorinated derivatives have been calculated by the linear combination of atomic orbitals method. Cocordano has shown that the auxinic activities of these compounds correlated well with the sum of the reactivity indices of the 3- and 6- carbon atoms.In addition, Mainster and Memory have proposed that alternative electronic indices, founded upon the Hu ckel molecular orbital theory, may be used to characterize chemical carcinogens.29 Based upon the use of superdelocalizability to estimate relative chemical reactivity, these indices have been Ugad to characterize molecular carcinogenicity accurately.29... 

The simplest MOs are constructed using the LCAO (linear combination of atomic orbitals) method introduced by Eq. 4.25, adding atomic orbital wave-functions centered on different nuclei in different proportions to obtain one MO wavefunction, often with the electron density delocalized across several nuclei. Extended to several nuclei, Eq. 4.25 becomes... 

Calculated by using the first-principles orthogonalized linear combination of atomic orbitals method in the local density approximation. The effective masses were found to be highly anisotropic and the values in the table are for F-A. Other values are 0.37 (F—K) and 0.32 (F—M) for the electron... 

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