By W. Kutzelnigg, G. Del Re, G. Berthier
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Extra info for σ and π Electrons in Organic Compounds
If one wants to avoid a CI treatment, one can note t h a t correlation does not Correlation Effects in ~ E l e c t r o n S y s t e m s much change the expectation values of typical one-particle operators, like the kinetic energy or the potential energy in the field of the core. It does however, change appreciably the electron repulsion energy. g. 41)) and agrees to treat an effect going beyond the a-r~ separation within the formalism of this separation, it is plausible that one should take smaller values for the two-electron integrals.
In order to assess the difference clearly, we have to discuss at some length what the terms 'localized' and ' d e l o calized' really mean. e. they extend over the whole molecule. For closed shell systems, the SCF functions can be written in determinant form (Slater determinant). An important theorem states t h a t certain linear transformations among the orbitals of the determinant can be carried out without changing the value of a n y physical observable. s) s) T h e Hi~ckel m e t h o d p r e d i c t s t h a t in t h e case of a long polyene chain t h e l o n g i t u d i n a l polarizability of ~z electrons varies as t h e c u b e of t h e m o l e c u l a r l e n g t h , while t h e a p o l a r i z a b i l i t y s h o u l d i n c r e a s e o n l y linearly ls).
8) can still be retained (with a somewhat different meaning for W1,) provided all the matrix elements in the brackets are proportional to the overlap integrals S~oa.