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We report theoretical quantum chemical design and investigation of supramolecular structures formed by cisplatin and a single-wall carbon nanotube (SWCNT). Through density functional theory calculations, plausible modes of interaction between cisplatin and a SWCNT zigzag (12,0) model were found (inclusion and adsorption complex forms). B3LYP/6-31G(d,p)/Lanl2DZ calculations of NMR chemical shifts for the free and interacting molecular structures were shown to be very promising for assisting the experimental identification of these structures. Our results strongly indicate that the cisplatin–nanotube system forms a stable molecular complex that can be used as a new drug delivery device.