Uso di calcoli quantochimici Density Functional Theory per lo studio di materiali di carbonio nanostrutturati Matteo Tommasini, E. Di Donato, C. Castiglioni, G. Zerbi Dipartimento di Chimica, Materiali e Ingegneria Chimica “G. Natta” Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 Milano email: matteo.tommasini@polimi.it

DFT: concetti essenziali L’energia di una molecola o di un solido è un funzionale universale della densità elettronica r: La densità elettronica è esprimibile attraverso funzioni d’onda di particella singola (orbitali molecolari) yi Ogni orbitale soddisfa l’equazione di Schroedinger efficace:

Il potenziale efficace è dato dalla somma di tre contributi: v(r) è il potenziale esterno, ovvero il potenziale elettrostatico attrattivo generato dai nuclei atomici j(r) rappresenta la repulsione coulombiana elettrone-elettrone vxc(r) è il potenziale di scambio e correlazione, ha natura quantistica e non ha interpretazione classica

Spettroscopia Raman CCl4 Schema concettuale dell’esperimento n0-nvib1 n0-nvib2 n0-nvib3 Spettro Raman CCl4 n0+nvib1 n0+nvib2 n0+nvib3 n0 detettore reticolo campione LASER

Simulazione di spettri Raman M: masse atomiche wk: frequenza modo k Lk: autovettore modo k (M-1 F) Lk = Lk wk2 Alla base: DFT  E[r] Matrice delle costanti di forza F Spettro  somma di lorenziane centrate su wk e di area Ik xi: coordinate cartesiane atomiche Intensità del modo k a: polarizzabilità e: campo elettrico

Polyynes are present in interstellar dust and particulates Polyynes are intermediates in the initial stages of the formation of nanostructured carbon materials Polyyne ring nucleus growth model for single-layer carbon nanotubes, C.H. Kiang, W. A. Goddard, Phys. Rev. Lett., 76, 2515 (1996) Polyynes are present in interstellar dust and particulates http://www.uic.edu/eng/ems/Combustion/Oran.Astro.Comb.talk.pdf Chem. Soc. Rev., 2001, 30, 177–185

Polyynes are “dimerized” linear chains (in Peierls terms) Equilibrium bond lengths of C16H2 (BPW91/6-311G** computations)

C8H2: CC stretching high intensity Raman modes 2107 cm-1

C16H2: CC stretching high intensity Raman mode allungamento di legame CC

Let us first try to explain the experimental Raman spectrum First principles DFT BPW91/6-311G** … summing up each computed spectrum weighted according to the experimental distribution data Softening of the intense Raman peak as conjugation length increases C16 C14 C12 C10 C8 C6 wavenumbers (cm-1)

Simulation of the Raman response Sample: methanol solution of polyynes produced by Prof. F. Cataldo C10 C8 C8 C12 C16 C14 Distribution of lengths C6 C8 C10 C12 C14 C16 wavenumbers (cm-1)

mechanical and tribological applications CARBON MATERIALS fullerenes fullerenes nanotubes amorphous carbons carbon nanotubes porous graphites carbon fibers, amorphous carbons and DLC hard coatings APPLICATIONS electronics energy storage, batteries, sensors mechanical and tribological applications nanotubes Carbon nanotubes, M.S. Dresselhaus, G. Dresselhaus, Ph. Avouris (Eds.) Springer (2001) micro and nano crystalline graphites carbon fibers glassy carbon porous graphites carbon black D. Donadio, L. Colombo, P. Milani, G. Benedek, Phys. Rev. Lett., 83, 776-779 (1999) “graphitic” mixed sp2, sp3, sp C atoms amorphous carbons diamond like carbons (DLC) disordered carbons

THE MOLECULAR APPROACH 2D p conjugated molecules Polycyclic Aromatic Hydrocarbons (PAHs)

Simulazione esperimenti STM (Scanning Tunneling Microscopy) attraverso la teoria di Tersoff-Hamann [1] segnale STM Densità di carica per l’orbitale all’energia di Fermi [1] J. Tersoff, D. R. Hamann, Phys. Rev. Lett., 50, 1998-2001 (1983). J. Tersoff, D. R. Hamann, Phys. Rev. B, 31, 805-813 (1985). J. Tersoff, Phys. Rev. Lett., 57, 440-443 (1986).

Scanning Tunneling Microscope Energy levels scheme tip Conductive substrate Molecular layer (+) electron flow (-) Depending on - relative position of the HOMO, LUMO, EF(tip), EF(substrate) - the sign and magnitude of V we can tunnel through the HOMO or the LUMO LUMO V HOMO Vsubstrate Vtip

C42 STM on molecular layers: seeing molecular orbitals STM Original Filtered Zoom C42 Alkyl-hexabenzocoronene THEORY (HOMO orbital)

HOMO Electron density map STM C60 C 1 2 H 5 THEORY HOMO Electron density map The densities coming from the two uppermost almost degenerate occupied levels have been summed up; E = 0.21 eV.

Maps of |yHOMO|2 and |yLUMO|2 according to DFT BPW91/3-21G** C42H18 C114H32 C222H42 C366H54

based on DFT and tight binding calculations STM image across graphite step edge 2 layers zoom Theory based on DFT and tight binding calculations

Cartoon explaining the observed STM image stripes Bright spots Dark spots Original STM image Scheme and theoretical prediction Analysis

Graphitic edges as nanostructures Maps of |yHOMO|2 and |yLUMO|2 according to DFT BPW91/3-21G** (PAH) and BPW91/6-311G** (rylene)

D D Dispersion of Raman with respect to the size HOMO LUMO D Dispersion experimentally observed on multiwalled carbon nanotubes Multi-walled carbon nanotube samples kindly provided by M. Corrias, and P. Serp, ENSIACET, Toulouse - France. D Vibrations involved in Raman

Wavelength dependence of the Raman response Microcrystalline graphite D peak frequency dispersion Pócsik et al., J. Non-Crystalline Solids, 227-230, 1083 (1998) Slope ~ 50 cm-1/eV

D G Chopped (4,4) nanotube first principles simulation BPW91/6-311G** Computation time: 12 days, 15 hours 2 avogadro processors total of 3.9 Gb disk space

Ringraziamenti Esperimenti STM, discussioni scientifiche Prof. J. Rabe Dr. N. Severin Dept. of Physics, Von Humboldt University - Berlin Esperimenti Raman, discussioni scientifiche Dr. A. Lucotti Dr. C. S. Casari, Dr. A. Li Bassi, Dr. V. Russo, Prof. C. E. Bottani Politecnico di Milano Campioni poliine Prof. F. Cataldo Soc. Lupi arl, Chemical Research Institute, Roma