CHM216_PS1 - CHEM 216 Problem Set 1 For these problems you...

CHEM 216
Problem Set 1.
For these problems you will need software to determine eigenvalues of matrices - I recommend
‘freemat’ (http://freemat.sourceforge.net) since it is available for all platforms (Windows, Mac
OSX, Linux) and, as the name suggests, is free. Other possibilities (that cost money) are Matlab
and Mathematica.
The syntax for matrix diagonalization (for freemat and matlab) is:
>matrix=[0 1 0 0;1 0 1 0; 0 1 0 1; 0 1 1 0]
>[eigenvectors,eigenvalues]=eig(matrix)
matrices are enclosed in [square brackets], each row of the matrix ends with a semicolon;
For applying the Hückel model to any particular problem, the matrix is constructed as follows.
The diagonal matrix elements represent the energies of the component p orbitals. If they
are set to zero, then all atoms are the same and all energies are relative to an isolated or-
bital. More electronegative/electropositive orbitals can be indicated by changing the
value of the appropriate diagonal element.
The off diagonal matrix elements represent the interaction between atoms. Usually these