Method approximate density functional theory

In the frozen MO approximation the last terms are zero and the Fukui functions are given directly by the contributions from the HOMO and LUMO. The preferred site of attack is therefore at the atom(s) with the largest MO coefficients in the HOMO/LUMO, in exact agreement with FMO theory. The Fukui function(s) may be considered as the equivalent (or generalization) of FMO methods within Density Functional Theory (Chapter 6). 

Approximate density functional theory calculations have been used to investigate the irons influence in [Os(N)(X)4] (X = Cl, Me, SMe) and [Os(N)(Cl)5] ". By using the transition state method the relative effects of steric and electronic stabilization on the trans influence in these complexes have been quantitatively assessed. It is found that the electronic stabilization is greater than the steric stabilization for these complexes. 

Methods of density functional theory (DFT) originate from the Xa method originally proposed by Slater [78] on the base of statistical description of atomic electron structure within the Thomas-Fermi theory [79]. From the point of view of Eq. (3), fundamental idea of the DFT based methods consist first of all in approximate treatment of the electron-electron interaction energy which is represented as ... 

For anything but the most trivial systems, it is not possible to solve the electronic Schrodinger equation exactly, and approximate techniques must instead be used. There exist a variety of approximate methods, including Hartree-Fock (HF) theory, single- and multireference correlated ab initio methods, semiempirical methods, and density functional theory. We discuss each of these in turn. In Hartree-Fock theory, the many-electron wavefunction vF(r1, r2,..., r ) is approximated as an antisymmetrized product of one-electron wavefunctions, ifijfi) x Pauli principle. This antisymmetrized product is known as a Slater determinant. 

Applying ab initio quantum-chemical methods and density functional theory in the local density approximation, different (BH) spherical clusters for n — 12,20,32,42 and 92 have been investigated. Most of the clusters show nearly icosahedral symmetry. The hydrogen atoms are bonded to the spherical surface as prickles. The relative stability of the spheres measured as the binding energy per molecule has been analyzed. All the clusters studied are very stable, and the spherical (BH)32 cluster Seems to be the most stable structure. The effect of the hydrogen atoms is to increase the stability of the bare boron clusters. 

DF theory has the simplicity of an independent-particle model, yet it can be applied successfully to those systems-such as transition metal complexes - where non-dynamical electron correlation is of primary importance. DF-based methods are, in general, very easy to use, no matter how sophisticated the functional employed to describe the electron correlation. Also, more sophisticated functionals do not increase the computational requirements significantly, as opposed to post Hartree-Fock ab initio calculations. The application of approximate density functional theory has been reviewed by Ziegler and others [5]. 

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