OICC Press Journal of Nanostructure in Chemistry 2193-8865 5 2 (June 2015) 2015 01 10 Structural relationships and theoretical study of the free energies of electron transfer, electrochemical properties, and electron transfer kinetic of cephalosporin antibiotics derivatives with fullerenes in nanostructure of [R]·Cn (R = cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone) supramolecular complexes 10.1007/s40097-014-0146-6 EN Avat Arman Taherpour Department of Organic Chemistry, Faculty of Chemistry, Razi University, Kermanshah, IR Medical Biology Research Center, Kermanshah University of Medical Sciences, Kermanshah, IR Doreena Narian Chemistry Department, Faculty of Science, Islamic Azad University, Arak, IR Arezou Taherpour Department of Microbiology, Kurdistan University of Medical Sciences, Sanandaj, IR Journal Article 2015 01 10 Abstract Various empty carbon fullerenes (C n ) with different carbon atoms have been obtained and investigated. Cephalosporin antibiotics and its derivatives have important medicinal properties. The β-lactam class of antibiotics has a broad spectrum of antimicrobial properties. Their antibacterial and pharmacokinetic properties have wide therapeutic applications. Topological indices have been 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 fullerenes was used as an index to establish a relationship between the structures of cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone (β-lactam antibiotics) and fullerenes (C n , n  = 60, 70, 76, 82 and 86), which create [cefadroxil]·C n , [cefepime]·C n , [cephalexin]·C n , [cefotaxime]·C n , [cefoperazone]·C n and [ceftriaxone]·C n . The relationship between the number of fullerene carbon atoms and the free energies of electron transfer (Δ G et(1) –Δ G et(4) ) are assessed using the Rehm-Weller equation for A-1 to A-5 , B1 to B-5 , C-1 to C-5 , D-1 to D-5 , E-1 to E-5 and F-1 to F-5 of the supramolecular complexes [R]·C n (where R = cefadroxil, cefepime, cephalexin, cefotaxime, cefoperazone and ceftriaxone) complexes. The calculations are presented for the four reduction potentials ( Red. E 1 – Red. E 4 ) of fullerenes C n . The results were used to calculate the four free energies of electron transfer (Δ G et(1) –Δ G et(4) ) of the cephalosporin-fullerene supramolecular complexes A-1 to A-5 , B1 to B-5 , C-1 to C-5 , D-1 to D-5 , E-1 to E-5 and F-1 to F-5 for fullerenes C 60 –C 120 . The free energies of activation for electron transfer, Δ Getn#\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ G_{{_{{{\text{et}}\left( n \right)}} }}^{{^{\# } }} $$\end{document} ( n  = 1–4) were also calculated for these complexes in accordance with the Marcus theory. In this study, was presented the calculated wavelengths (λ ( n ) ; n  = 1–4; in nm) of the photoelectron transfer process as well in the nanostructure complexes.