Question

Part (a) The cyclopentadienyl anion (C5H5 - ) is commonly used aromatic ligand. The secular equations for describing the interactions of the five unhybridized p orbitals lead to a matrix of 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 can be 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. [You may write this matrix (and only the matrix) on paper and copy and paste and image of it into your word document if you wish.] (iii) Briefly explain (without performing any calculations) how this matrix is used to determine the energies and coefficients of the MOs.

Answer 1

i)Ans: Huckel gave following assumptions to solve the secular determinant :

1. Sij =0 ,if i is not equal to j , i.e , Overlapping integral between two 2 atoms is considered to be zero . If i =j then Sij = 1. ( where as S is overlap integral).

2. Hii is coloumb integral .

H11 =H22 =H33 =H44 ..... so on = “alpha”

3. Hij is called Resonance integral .

When a Carbon is not bonded to another Carbon . Then this resonance integral is Zero otherwise if bonded directly then it is “beta"