MACROLIDES ARE A BROAD SPECTRUM OF ANTIBIOTICS THAT ARE COMMONLY USED IN HUMAN PATHOLOGIES AS WELL AS IN VETERINARY MEDICINE. THE ELECTROCHEMICAL DETECTION OF MACROLIDE ANTIBIOTICS WERE STUDIED BEFORE AT VARIOUS METHODS USING AMPEROMETRIC AND COULOMETRIC DETECTORS. SINCE THE DISCOVERY OF FULLERENES, ONE OF THE MAIN CLASSES OF CARBON COMPOUNDS, THE UNUSUAL STRUCTURES AND PHYSIOCHEMICAL PROPERTIES OF THE MOLECULES HAVE BEEN DISCOVERED. MANY POTENTIAL APPLICATIONS AND PHYSICOCHEMICAL PROPERTIES HAVE BEEN INTRODUCED FOR FULLERENES. UP TO NOW, VARIOUS EMPTY CARBON FULLERENES SUCH AS C60, C70, C76, C82 AND C86 HAVE BEEN OBTAINED. TOPOLOGICAL INDICES HAVE SUCCESSFULLY USED TO CONSTRUCT EFFECTIVE AND USEFUL MATHEMATICAL METHODS TO ESTABLISH CLEAR RELATIONSHIPS BETWEEN STRUCTURAL DATA AND THE PHYSICAL PROPERTIES OF THESE MATERIALS. IN THIS STUDY, THE NUMBER OF CARBON ATOMS IN THE FULLERENES WAS USED AS AN INDEX TO ESTABLISH A RELATIONSHIP BETWEEN THE STRUCTURES OF Erythromycin-A (EA) AND FULLERENES CN, WHICH CREATE [EA].CN, A-1 TO A-5. THE RELATIONSHIP BETWEEN THE NUMBER OF CARBON ATOMS IN CN AND THE FREE ENERGIES OF ELECTRON TRANSFER IS ASSESSED USING THE ELECTRON TRANSFER (ET) EQUATION FOR A-1 TO A-5 [EA].CN COMPLEXES.CALCULATIONS ARE PRESENTED FOR RED.E1 TO RED.E4 OF THE FULLERENES. THE RESULTS WERE USED TO CALCULATE THE DGET (1) TO DGET (4) OF COMPLEXES A-1 TO A-9 TO FOR FULLERENES C60 TO C120. THE FIRST TO FORTH FREE ACTIVATION ENERGIES OF ELECTRON TRANSFER AND THE MAXIMUM WAVE LENGTH OF THE ELECTRON TRANSFERS, DG# ET (N) AND LET (N=1-4), RESPECTIVELY, WERE CALCULATED IN THIS STUDY AND IN ACCORDANCE WITH THE MARCUS THEORY. THE SIGN OF WAVE FUNCTION WILL CHANGE IN PHOTO-ET PROCESS, BUT IN THE THERMAL-ET THE SAME SIGN WOULD BE PERFORMED FOR THE FULLERENES.