Part (a) The cyclopentadienyl anion (C5H5 - ) is commonly usedaromatic ligand. The secular equations for describing theinteractions of the five unhybridized p orbitals lead to a matrixof the form:
( ?11 − ??11 ?12 − ??12 ?13 − ??13 ?14 − ??14 ?15 − ??15
?21 − ??21 ?22 − ??22 ?23 − ??23 ?24 − ??24 ?25 − ??25
?31 − ??31 ?32 − ??32 ?33 − ??33 ?34 − ??34 ?35 − ??35
?41 − ??41 ?42 − ??42 ?43 − ??43 ?44 − ??44 ?45 − ??45
?51 − ??51 ?52 − ??42 ?53 − ??53 ?54 − ??54 ?55 − ??55)
where ??? is the Hamiltonian integral for orbitals ? and ? and??? is the overlap integral for orbitals ? and ?. This matrix canbe simplified using the approximations of Hückel molecular orbital(MO) theory, which involves two constants ? and ?.
(i) Explain the approximations of Hückel MO theory in terms of??? and ???, and define ? and ?.
(ii) Re-write the above matrix applying these assumptions. [Youmay write this matrix (and only the matrix) on paper and copy andpaste and image of it into your word document if you wish.] (iii)Briefly explain (without performing any calculations) how thismatrix is used to determine the energies and coefficients of theMOs.
