By W. Kutzelnigg, G. Del Re, G. Berthier
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Extra info for σ and π Electrons in Organic Compounds
The ~ systems just furnish well-defined models, for which b y definition a full CI calculation gives the exact solution, to be compared with various simplified treatments. For this reason, we shall not discuss these approaches in detail here. Suffice it to mention the following result concerning the horizontal correlation of ~ electrons: in systems like the polyenes, where the alternation of bonds suggests a description in terms of localized z~ bonds (see Sect. 5), almost the entire horizontal correlation energy is due to the 'intrapair' correlation energy of the electron pairs localized on the double bonds ~1~.
Tetrahedron 5, 166 (1959). 56 Treatment of Unsaturated Molecules in Pure ~ Electron Theories 5. 1. e. , can be interpreted qualitatively and often quantitatively in terms of the electronic structure of the n system alone. As the number of n electrons is small with respect to the total number of electrons of the molecule, a considerable simplification of the quantum-mechanical problem is obtained. However, it m u s t be noted immediately t h a t the assumptions of a complete a - ~ separation and of a rigid a frame are not sufficient to eliminate the a electrons completely from the theory; because the ~ electrons of an unsaturated molecule are not attracted b y bare nuclei, but are subject to an effective potential containing Coulomb and exchange contributions from the a electrons.
B) Cade, P. , Sales, K. , Wahl, A.. : J. Chem. Phys. 44, 1973 (1966). e) Cade, P. , Huo, W. : J. Chem. Phys. 47, 614 (1967). E l e c t r o n correlation p r o b a b l y also plays a n i m p o r t a n t role i n the t h e o r y of u n s a t u r a t e d or conjugated organic molecules. U n f o r t u n a t e l y , accurate n u m e r i c a l d a t a are so far lacking, a n d we m u s t discuss simplified models i n order to u n d e r s t a n d the electron correlation i n ~ electron systems. A l t h o u g h different c o n t r i b u t i o n s to electron correlation should be considered, n a m e l y the h o r i z o n t a l a n d tlie vertical correlation of t h e a a n d ~ systems a n d the i n t e r g r o u p correlation, so far tile correlation of the ~ s y s t e m alone has b e e n m o s t studied.