By Thomas H. And Kathleen Schueller Richardson Lowry
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Hence, the best result possible with an approximate wave function of a particular type will be obtained when it is chosen so as to minimize E. The more rigorous approach to finding the orbital functions is the Hartree-Fock-Roothaan method. 3. 3, which must now be solved for t,h and E. 4), where y j are atomic orbital functions and cj are coefficients that give the contribution of each atomic orbital to the molecular orbital. 2. Valence atomic orbitals are ordinarily chosen for the basis. We always require that orbital functions be normalized.
15) by roughly 20 powers of ten,29a difference in reaction free energies of some 27 kcal mole-l. Three-meinbered ring systems have also provided examples of aromatic and antiaromatic behavior. 32 The contrasting reluctance of the three-membered ring T system to take on four electrons is illustrated by the very low acidity of triphenyl cyclopropene (54), estimated to be roughly 18 powers of ten less than that of t r i ~ h e n y l m e t h a n e . 34 PROBLEMS 1. (a) Write Lewis structures for each of the following molecules or ions.
A) Diamagnetic 4n + 2 ring. The induced field Hi opposes the applied field Ho for protons inside the ring and adds to it for protons outside. (b) Paramagnetic 4n ring. The induced field Hi adds to the applied field Ho inside but opposes it outside the ring. rings the induced field adds to the applied field for outside protons but is opposed to the applied field inside the ring. The situation is reversed in 4n rings. Theory of aromaticity is not restricted to the simple planar conjugated rings.