The Hueckel MO theory predicts for an acetylene molecule two degenerated pi-bonding orbitals (occupied by four electrons) and two empty degenerated pi-antibonding orbitals.  This can be readily obtained if you represent the molecular orbital of acetylene as a linear combination of four 2p- atomic orbitals (from two different centers) and solve the stationary Schroedinger equation using the well-known Hueckel approximations.

1) Draw acetylene in Avogadro, optimize geometry. 2)Save the file in Gaussian format as acetylene.gau. 3) Modify the input file:

%chk=acetylene

# T Huckel

Acetylene Huc. Energy

0 1

C -2.85904 3.94652 -0.43438

C -1.68220 3.78362 -0.60536

H -3.90410 4.09117 -0.28255

H -0.63731 3.63899 -0.75717

4) You must leave the blank lines as I wrote. From the terminal run: g09 < acetylene.gau > acetylene.out & 5) You received the results after 1 sec. I used the program Gaussian 09 for Linux. (Opensuse 13.1). The energy appears in the output as follows (followed by the x, y, and z components of the dipole moment):Huckel eigenvalues -- -1.001 -0.736 -0.570 -0.498 -0.498 -0.259 -0.259 0.392 0.664 3.442

Energy= -6.60658111 NIter= 0.

Dipole moment= 0.000000 0.000000 0.000000   

The energy is in Hartrees. 1 Hartree=627.5095 kcal/mol.

Thanks for reply to both Renat and Charis. I have a small doubt. If i take linear combination of 4 atomic orbital i may end up with either a butadiene or two ethylene configurations. Is their any notes or any article where people might have used huckel theory for 4 e- in acetylene or atleast annulenic systems with acetylene group.

Thanks in advance.

Huckel MOs for acetylene are just twice the MO diagram for ethene.

Thank you for reply. But still my problem is not sorted out. How i can apply huckle molecular orbital theory to 1-butene-3-yne and compare it with 1,3 butadiene. 

The non-conjugated MO has the same coefficients and energies as ethene.

Thank you sir. But i just want to know what will be the beta value (off-diagonal element) for C-C double bond and C-C triple bond. Should I consider same value for both the bonds. C-C (Beta value ~ 2.3 eV or 70 kcal/mol)

Yes, simple Huckel theory does not distinguish between C=C in a double bond and C=C in a triple bond.

Simple Huckel theory has only one beta parameter for any kind of C-C pi-bond, that's right, but this is the Huckel theory in scholar textbooks. In many applications of the theory the beta parameter was considered to be free, and was chosen to particular problem, i.e. thermochemistry or UV/Vis spectra calculation. See book of T.E. Peacock, Electronic properties of aromatic and heterocyclic molecules, 1965 or A. Streitwieser, Molecular Orbital Theory for Organic Chemists, 1961.