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For 1,2-cyclobutanedione and cyclobutanone, we have carried out a comparative study of different methods like B3LYP, LSDA, and B3PW91 of DFT using 6-31G (d, p) basis set and MP2 method. On comparing these methods we find that B3PW91 method is closer to the experimental one. So by using B3PW91 method, we have made a comparative study of their structures, normal mode analysis, and other properties of the two derivatives of cyclobutane. The molecular HOMO, LUMO composition, their respective energy gaps, and MESP contours/surfaces have also been drawn to explain the activity of 1,2-cyclobutanedione and cyclobutanone.