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2. Calculations for the electronic transport in molecular nanostructures Gotthard Seifert Institut für Physikalische Chemie und Elektrochemie Technische Universität Dresden

3. Greens-Function Method Calculation of Transport Properties in molecular Systems Green‘s Function G(E) S,H – Overlap- and Hamilton Matrices Model: Molecule (M) and two contacts (α, β) Calculation of H and S matrices Aldo di Carlo!

4. LCAO Ansatz Atomic Orbitals - AO Slater Type Orbitals - STO

5. Hamilton matrix Overlap matrix Density-Functional based „tight binding“ DF-TB

6. - electron density - magnetization density Density fluctuations: Total Energy in DFT - E DFT

7. Expansion of E DFT around n=n 0, μ=0

8. Approximations: Minimal (valence) basis in LCAO ansatz Neglect of pseudopotential terms in h 0 μν  2-center approximation -Mulliken gross population at j 2nd order approximation in energy

9. Cancellation of „double counting terms“ E B /eV R/a B U(R jk ) E B - U(R jk ) Li 2 - dimer Short range repulsive energy U(R jk )

10. Approximation for magnetization density

11. Energy :

12. Hamiltonian: : Self Consistent Charge method SCC-DFTB

13. with Γ α - Spectral functions of the Selfenergy-operators Transmission coefficient T(E)

14. Electronic Current – I Keldysh formalism Contact scattering functions Scattering function Inelastic processes (e-e, e-p intereaction) Non-equilibrium Green‘s functions

15. External bias – V Modification of the Hamiltonian matrix elements Calculation of I-V curves

16. Application ∞ Examples

17. Nanotubes of Carbon S. Iijima Nature 354 (1991) 56 ~1nm~ μm Single-wall Nanotubes – SWNT‘s

18. (10,0) zig-zag tube10-10 arm chair tube

19. Electronic Structure of Nanotubes Band-structure graphene monolayer k  Rolling „Zone folding“

20. zig-zag tube (n,0) mod(n,3)=0mod(n,3)≠0

21. arm chair tube (n,n)

22. Functionalization of Carbon Nanotubes ? Graphite > Lamellar intercalation: > Lamellar covalent: O, F, S Fluorination Li, Na, K, Rb; Cl, Br, I

23. 2C graphite + F 2  2CF sp 2 -C graphite  sp 3 -C Fluorination F F

24. Carbon Nanotubes fluorination 2C + F 2  2CF 2C+1/2F 2  C 2 F

26. Decoration pattern – no „frustration“!

27. C 2 F – fluorine decoration pattern n,0 F Ethylen - like

28. C 2 F – fluorine decoration pattern Ethylen - like

29. EFEF Density-of-States 10,0 C 2 F NT 10,0 CNT Large gap

30. C 2 F – fluorine decoration pattern n,0 F trans-polyacetylen – like helical C C ∞

31. C 2 F – fluorine decoration pattern Trans-polyacetylen – like helical C C ∞

32. 10,0 C 2 F NT Density-of-States energy/eV Density-of-States small gap

33. projected Density-of-States

34. C 2 F – fluorine decoration pattern cis-polyacetylen – like chain CC ∞

35. Density-of-States 10,0 C 2 F NT no gap

37. Transmission 10,0 C 2 F NanoTubes cis-polyacetylen – like chain ethylen - like

38. Transmission as function of coverage C 2 F (10,0) Nanotube cis-polyacetylen – like chain

39. trans-Polyacetylene

40. C 2 F (10,10) Nanotube chain (10,10) Nanotube

42. (9,0) Nanotube

43. 9,0 C 2 F NT ring HOMO –LUMO „aromatic“ π-states

45. Fluorine Carbon

47. Outlook/Problems ->Contacts – Molecule interaction -> electron-phonon interaction -> electron-electron interaction? -> non-adiabatic description -> Applications.

48. Thanks Aldo di Carlo (Rome) Thomas Niehaus (Paderborn) Nitesh Ranjan (Dresden)