The Huckel molecular Orbitals of Pyrrole.
The practical involves solving the Huckel secular equations for the molecular orbital energies and
orbitals of the molecule pyrrole and calculating the bond orders of the bonds and the charges on the
atoms to estimate the dipole moment of the molecule.
Method:
a) Write down the 5 Huckel secular equations.
e.g.
n = 1:
(αN – ε) c1 + βNc2 + βc5 = 0
b) Make the hetero atom approximations:
hN = 1.5 , kn =1.0 and the substitution x = (α – ε)/ β
e.g.
n = 1: (x +1.5) c1 + c2 + c5 = 0
or:
(x +1.5) c1 + c2 + 0c3 + 0c4 + c5 = 0
the latter version is useful to make sure nothing is forgotten when setting up the
determinant.
c) One option would be to set up the 5x5 secular determinant and multiple out and solve the
quintic equation for 5 values of x. Easier is to note that the molecule has a symmetry plane
and that the orbitals are either symmetric or antisymmetric with respect to this plane and
that this forces a relationship between the coefficients of the orbitals:
symmetric
c1 ≠ 0, c2 = c5, c3 = c4
antisymmetric
c1 = 0, c2 = -c5, c3 = -c4
Introducing the symmetry relationships between the coefficients in the symmetric diagram
(on the left) results in3 unique secular equations and a 3x3 determinant which yields a cubic
equation to solve. Use a cubic equation solver from the web to get the values of x (and
hence ε) and determine the coefficients for each orbital. The antisymmetric conditions will
yield two secular equations and a quadratic equation and the other 2 values of ε. Determine
the coefficients of these orbitals.
d) Using ChemDraw (or otherwise) present your results as a molecular orbital diagram for the π
molecular orbitals of the molecule. (You can easily go to town doing this – projection views
of the ring and properly sized atomic p-orbitals on the atoms allowing for perspective! This is
not recommended – overhead views are perfectly ok. Don’t spend too much time making
the diagram look good.)
e) Calculate the bond orders, pnm, of the 3 unique bonds in the molecule and charges, qn, on
the atoms. Convert the bond orders to bond lengths ( Rnm = 1.54 – 0.16 pnm) and estimate
the dipole moment of the molecule .
You can check all you results by using the Simple Huckel Molecular Orbital calculator at:
http://www.chem.ucalgary.ca/SHMO/
This programme is largely self explanatory and can be used to review the whole Huckel section of
CM3109.