You might consider GAMESS-US -- I'm assuming you're looking for molecular orbital eigenvalues (like for electronic transitions or possibly vibrational transitions).  I have never used the software, but it's one of the no-cost versions of electronic structure calculation software (apparently it is not technically open source).

http://www.msg.ameslab.gov/gamess/download.html

"A site license for GAMESS is available at no cost to both academic and industrial users"

A branch of that software  which we used is Firefly (look on their site on remarks wrt GAMESS-US).

http://classic.chem.msu.su/gran/gamess/index.html

You need quite some insight to use it; practically for ease I made batch files to run it.  With respect to the background I was helped my a colleague, as I'm not a specialist myself on this. Our licensing was done through Alex Granovsky. On a normal office PC calculations (under Win) can easily be run overnight; I simply put calculations on several ones of them, they could be used for other work in the mean time too.,

It worked;, we tried to predict catalyst activity on some reactions, internal unpublished results.

you can download mathematica for a month free of costs and diagonalize your Hamiltonian

Sanaz,

Actually, finding eigenvalues is a mathematical method that applies to solving many problems. From the question asked you do not state what is the problem you try to solve beside getting eigenvalues.

Then you can use all kind of mathematical solvers like Mathematica,Matlab,but they are not  free.

You may want to ask your math department to figure out what they have available for your need.

Kind regards

 Sanaz,

I am troubled by way of carrying this discussion and  so could be the previous contributors and readers could have a hard time making sense of the previous answers.

It would have been better to make some additional comments to clarify your question, or to start a new discussion altogether rather than change you question in the middle of the answering process.

@G Havet: for completeness, the original question statement was "is there any open source software for calculating eigenvalue of polymers?"  The updated question statement is a lot clearer, so it is quite welcome. 

Aou, indeed the question is a lot clearer but in my vue it should have been the initial one.

Language barriers seem to have stopped the diplomacy of my first message. Unfortunately, I understand that my second message troubled you and makes me  feel like I was not clear enough. 

Again, " Is there any open source software for calculating HOMO LUMO level of polymers like p3ht? "  was not the initial question, the question should have been clarified within the thread (ie answering to my first message or any other message for that matter) rather than changing it.

Alternatively, the later question could have been asked in another discussion altogether.