CM3109 Practical 3

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```					CM3109 Practical 3.

CM4113 Years Work

Using Symmetry to simplify the calculation of the Huckel molecular orbitals of naphthalene.

Calculating the Huckel molecular orbitals of naphthalene does not involve solving a 10 x 10 secular
determinant. The molecule only has three symmetry distinct carbon atoms:

carbons 1, 5 and 9. If the LCAO coefficient of carbon 1 has been determined to be c1, then clearly the
coefficient of carbons 2, 3 and 4 are ±c1. Similarly carbons 5, 6, 7 an 8 are related and carbons 9 and 10.

All possible relationships can be generated by using the mirror planes perpendicular to the molecular
plane:

c1 = c2 = c3 = c 4
c5 = c6 = c7 = c 8
c9 = c10

a 3x3 problem

c1 = c2 = -c3 = -c4
c5 = c6 = -c7 = -c8
c9 = c10 = 0

a 2x2 problem
c1 = -c2 = -c3 = c4
c5 = -c6 = -c7 = c8
c9 = -c10

a 3x3 problem

c1 = -c2 = c3 = -c4
c5 = -c6 = c7 = -c8
c9 = c10 = 0

a 2x2 problem

Notice that in 2 cases it is only possible to satisfy the left/right mirror symmetry if the coefficients on
carbons 9 and 10 are zero. From these 4 diagrams 10 values of the orbital energy and the corresponding
molecular orbitals can be calculated.

The three secular equations needed are:

n = 1:   x c1 + c5 + c 9 = 0
n = 5:   c1 + x c 5 + c 6 = 0
n = 9:   c1 + c4 + xc9 +c10 = 0   (this one only needed in two cases).

For each set of symmetry conditions solve the secular equations for the values of x and hence the
molecular orbital energy ε. For each value of x < 0 (bonding orbitals) calculate the molecular orbital
coefficients. NOTE, the normalization requires that
c12 + c22 + … + c102 = 1
which reduces to
4c12 + 4c52 + 2c92 = 1
Show that the net charges on carbon atoms 1, 5 an 9 are zero. Calculate the bond order of the 4 distinct
C-C bonds in the molecule and estimate their bond lengths. Compare with experimental data.
Use the web site: http://www.chem.ucalgary.ca/SHMO/ to check your results.

The report should contain a good presentation of the 10 energy levels, the 5 bonding molecular orbitals
(chemdraw can help with this) and charge and bond order calculations. Comment on the molecular
orbital energies.

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