I studied theoretically Karplus equation to calculate the dihydral angle, I need to apply that for a small compound that I synthesized and I have the 1H'NMR data. Can anybody help me how to do that?
The simplest way to use the Karplus equation is to make an approximation using the Graph of the Karplus relation. I usually use this method when the rough estimation of dihedral angle is needed, however, I don't see problems for a more accurate assessment.
Don't forget that solution NMR is a dynamic process and you will see an averaged coupling of all of the solution conformations. A very large coupling may indicate a major conformer with a 180 degree (or 0) dihedral. Likewise a very small coupling may indicate a 90 degree dihedral. An intermediate coupling may indicate a 45 degree angle but may also indicate a range of conformers (e.g. a 180 and a 90 dihedral from two conformers).
The electronegativity of attached groups will have a significant impact on the size of the couplings. In practice, from simple observation you can identify 0, 180 and 90 dihedrals. Unless your molecule is very rigid, anything more will require a more rigorous approach - probably using nOe instead (or full conformational analysis).