Valence-electron approximation

These results also follow from the cross sections through the potential energy surfaces calculated in the semiempirical all-valence electron approximation by the MNDOC-CI method for acetaldehyde, acrolein, and benzal-dehyde, which are displayed in Figure 7.13. Stabilization of the state... 

In the TT-electron approximation, the n tt electrons are treated separately by incorporating the effects of the cr electrons and the nuclei into some sort of effective TT-electron Hamiltonian (recall the similar valence-electron approximation Sections 13.20 and 15.5) ... 

Both groups of methods use the valence-electron approximation, i.e. all core electrons are ignored. It is assumed that core electrons are sufficiently invariant to differing chemical environments so that changes in their orbitals as a function of environment are of no chemical consequence, energetic or otherwise. The valence atomic orbitals are represented by a so-called Slater-type orbital (STO). The mathematical form of a normalized STO (in atom-centered polar coordinates) is... 

As the valence-electron approximation is supposed to be introduced, the term Zm/Rm in (6.16) means the electron interaction with the core of atom M in the point-charge approximation. As AO Xmm( ) can be considered as an eigenfunction of opera tor (—4+ m) and introducing the point-charge approximation for Zm/Rn N / M), we obtain the matrix elements of operator (6.15) in the form [222]... 

The main features of the CNDO and INDO approaches to periodic qrstems are similar to those used for molecules. A valence-electron approximation is adopted, which impUes that only the valence electrons are in the bonding region and are polarized by the presence of neighboring atoms [277]. For periodic systems the LCAO approximation is based on use of the Bloch sums (4.53) of AOs x>jn( ) = - )... 

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