By John S Tjia
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Extra info for Building financial models : the complete guide to designing, building, and applying projection models. Chapter 14. Ratios
7 e. v. f o r Hz @ a n d ff-P 26. 5 e. v. f o r Hz) a r e amazingly close, if we define the binding f energies a s the energy of putting the electron(s) into the framework of the nuclei a t the equilibrium distance. 06 iand 0 . 7 4 irespec- tively, so that t h e r e i s not the slightest justification f o r assuming a and p (or S n ) to be the s a m e f o r Hz @ and Hz. Second, the coulombic repulsion between the two e l e c t r o n s in Hz i s calculated to be 17. 8 e. v. , and no account was taken of such repulsion in assuming the binding energy of Hz i s twice a + p for Hz 0 E x e r c i s e 2-5 + Calculate a p f o r HzQand Hz f r o m the following data: The Coulomb internuclear repulsions of Hz @ and Hz a r e 13.
B UTADIENE, E, F o r butadiene we can m a k e a calculation of the T-electron energy by considering that the u-bond framework i s such a s to have TT overlap of four p a r a l l e l 2p - orbitals. Our starting wave function will then b e where the normalization condition m u s t hold. The possible values of E that correspond to this equation a r e the r o o t s of a determinant where S.. (i # j) has been s e t to z e r o a s shown 1J by the determinant on the next page. , we shall a s s u m e that a1 = a2 = a3 = a4 = a, since the 1 surroundings of each carbon a r e s i m i l a r although not identical.
MOLECULAR ORBITALS. ,might be calculated through consideration of e r t i e s of HZ, the two nuclei surrounded by a single molecular orbital r e presented by +molecule and containing one electron. J ('molecule where l2 d~ = 1, if +molecule Thus, i s normalized. These equations a r e not formidable; the trouble comes in the f o r m of H and $molecule and the u s e of them to calcul a t e E. The 0 linear combination of atomic orbital (LCAO) method f o r H ~ @ a s s u m e s that $molecule can be approximated :> A serious notational problem a r i s e s with r e g a r d to the atomic wave functions.