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Unformatted text preview: the plane of the atoms (i.e., the p orbitals forming the π system). In terms of 0, 1, α, and β, what are the specific values of all matrix elements that will appear in the secular determinant for ethylene? To what experimental quantities do α and β refer, specifically? S11 = S22 = 1, S12 = 0, H11 = H22 = α , H12 = β α is the negative of the ionization potential of the methyl radical (the energy of an electron in a free 2pz orbital) and β is one half the rotational barrier in ethylene. Write the Hückel theory secular equation for ethylene. What values of E permit solution of the secular equation? You may find the equation a2 – b2 = ( a + b ) (a – b ) to be helpful. "#E $ $ =0 "#E The solution to this secular equation is ! 0 = (" # E ) # $ 2 = (" # E + $)(" # E # $)
which is satisfied by E = α + β and E = α – β . The first root is lower in energy since α and β are negative quantities. 2 ! NAME: ________________________________________________________________ 6 What does Hückel theory predict for the singlet-triplet splitting in ethylene? Explain your answer. The energy of the singlet is computed from placing the two ethylene π electrons in the lowest en...
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This note was uploaded on 12/18/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.
- Fall '08