LCAO method, definition

Simple estimates for the cellular potentials can be extracted from the MO LCAO method in the two-level model eq. (2.96). If one considers the interaction of the type A (A = a, 7r, J) between the (/-orbital of the metal 4>d and the orbital o, representing a mixture of the orbitals of the ligand and corresponding by local symmetry s- and p-orbitals of the metal and taking into account that according to the definition of the... 

That said above does not mean that a semiempirical parameterization based on the HFR MO LCAO scheme and valid for a certain narrow class of compounds or even for a specific purpose cannot be built. It is done for example in [69] for iron(H) porphyrins. But in a more general case there is no way to arrive to any definite conclusion [76] about the validity of a semiempirical parameterization in the HFR context. On the other hand we have to mention that the semiempirical method ZINDO/1 [77] which allows for... 

The two methods have a definite relation which comes from the fact that the structure of the molecule, and particularly its dimensions, is regulated by the value of the exchange energy. We thought it possible to specify this relation by using the essential peculiarity of the free-electron model, that is,. the elimination of all dynamic constants by the LCAO MO method. 

The LCAO MO method. The method of molecular orbitals (MO) dominates in modern quantum chemistry. The main idea of the method is that the electrons in a molecule are accommodated in definite MOs just as in an atoni they... 

Formally, these equations are similar to the SCF LCAO MO equations. Thus, a good definition of //effective may yield satisfactory solutions, without the tedious iteration procedure of the SCF method. In practice, two calculation procedures have evolved from these equations, the Hiickel approximation and the Wheland-Mulliken approximation. Neither of them specifies the analytical form of H, but instead treats some of the matrix elements H,. as adjustable parameters. Their main difference resides in the neglect (Hiickel) or non-neglect (Wheland-Mulliken) of overlap. Their common feature is the tight-binding approximation, namely the neglect of all matrix elements which involve non-bonded atoms. 

Fig. 2.1 The electron density p is a three-dimensional function that can be obtained from three different routes X-ray diffraction (i.e. crystallography), SCF-LCAO-MO (or orbitals ) and a method without orbitals where the electron density is known only in given grid points. A method that defines an atom at the level of p has the advantage that its definition is independent on how the electron density was obtained...

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